This paper applies inverse transform sampling to sample training points for surrogate models. Inverse transform sampling uniformly generates a sequence of real numbers ranging from 0 to 1 as the probabilities at sample points. The coordinates of the sample points are evaluated using the inverse functions of Cumulative Distribution Functions (CDF). The inputs to surrogate models are assumed to be independent random variables. The sample points obtained by inverse transform sampling can effectively represent the frequency of occurrence of the inputs. The distributions of inputs to the surrogate models are fitted to their observed data. These distributions are used for inverse transform sampling. The sample points have larger densities in the regions where the Probability Density Functions (PDF) are higher. This sampling approach ensures that the regions with higher densities of sample points are more prevalent in the observations of the random variables. Inverse transform sampling is applied to the development of surrogate models for window performance evaluation. The distributions of the following three climatic conditions are fitted: (i) the outside temperature, (ii) the wind speed, and (iii) the solar radiation. The sample climatic conditions obtained by the inverse transform sampling are used as training points to evaluate the heat transfer through a generic triple pane window. Using the simulation results at the sample points, surrogate models are developed to represent the heat transfer through the window as a function of the climatic conditions. It is observed that surrogate models developed using the inverse transform sampling can provide higher accuracy than that developed using the Sobol sequence directly for the window performance evaluation.
- Project Title: Seoul City Weather Data Analysis
- Course name: Principles and Practice in Data Mining
- Semester: Autumn 2016
- Professor: Yuran SEO
- Sungkyunkwan University
- Department: Consumer & Family Science
- Name: Lee dong hee
- Contact: molou@naver.com
Quality control of rain gauge measurements using telecommunication microwave ...JoergRieckermann
Accurate rain rate measurements are essential for many hydrological applications. Although rain gauge remains the reference instrument for the measurement of rain rate, the strong spatial and temporal variability of rainfall makes it difficult to spot faulty rain gauges. Due to the poor spatial representativeness of the point rainfall measurements, this is particularly difficult where their density is low. Taking advantage of the high density of telecommunication microwave links in urban areas, a consistency check is proposed to identify faulty rain gauges using nearby microwave links. The methodology is tested on a data set from operational rain gauges and microwave links, in Zürich (Switzerland). The malfunctioning of rain gauges leading to errors in the occurrence of dry/rainy periods are well identified. In addition, the gross errors affecting quantitative rain gauge measurements during rainy periods, such as blocking at a constant value, random noise and systematic bias, can be detected. The proposed approach can be implemented in real time.
Use of Probabilistic Statistical Techniques in AERMOD Modeling EvaluationsSergio A. Guerra
The advent of the short term National Ambient Air Quality Standards (NAAQS) prompted modelers to reassess the common practices in dispersion modeling analyses. The probabilistic nature of the new short term standards also opens the door to alternative modeling techniques that are based on probability. One of these is the Monte Carlo technique that can be used to account for emission variability in permit modeling.
Currently, it is assumed that a given emission unit is in operation at its maximum capacity every hour of the year. This assumption may be appropriate for facilities that operate at full capacity most of the time. However, in most cases, emission units operate at variable loads that produce variable emissions. Thus, assuming constant maximum emissions is overly conservative for facilities such as power plants that are not in operation all the time and which exhibit high concentrations during very short periods of time.
Another element of conservatism in NAAQS demonstrations relates to combining predicted concentrations from the AMS/EPA Regulatory Model (AERMOD) with observed (monitored) background concentrations. Normally, some of the highest monitored observations are added to the AERMOD results yielding a very conservative combined concentration.
A case study is presented to evaluate the use of alternative probabilistic methods to complement the shortcomings of current dispersion modeling practices. This case study includes the use of the Monte Carlo technique and the use of a reasonable background concentration to combine with the AERMOD predicted concentrations. The use of these methods is in harmony with the probabilistic nature of the NAAQS and can help demonstrate compliance through dispersion modeling analyses, while still being protective of the NAAQS.
Estimating Ammonia Emissions from Livestock Operations Using Low-Cost, Time-A...LPE Learning Center
For more: http://www.extension.org/67697 Recent regulations on ammonia (NH3) and other gaseous emissions by the EPA requires managers of animal feeding operations (AFOs) to report their annual emissions of greenhouse gases (GHGs), with the possibility of federal funding in the near future to be allocated for enforcement of GHG reporting as well as to levy large fines against AFOs that exceed the regulation limitations for GHG emissions. The current method of estimating NH3 emissions for AFOs is a “back of the envelope” type calculation based upon population and type of animal within an individual AFO.
Amy Stidworthy - Optimising local air quality models with sensor data - DMUG17IES / IAQM
An unapologetically technical conference, DMUG remains the key annual event for experts in this field. Unmissable speakers will be examining topical issues in emissions, exposure and dispersion modelling.
INNOVATIVE DISPERSION MODELING PRACTICES TO ACHIEVE A REASONABLE LEVEL OF CON...Sergio A. Guerra
Presentation delivered at the Annual Air and Waste Management Association conference in Long beach, California on June 26, 2014.
Innovative dispersion modeling techniques are presented including ARM2, EMVAP and the 50th percentile background concentration. Case study involves peaking engines that are used 250 hour per year. These intermittent sources are required to undergo a modeling evaluation in many states. Current modeling techniques grossly overestimate the emissions from these sporadic sources.
- Project Title: Seoul City Weather Data Analysis
- Course name: Principles and Practice in Data Mining
- Semester: Autumn 2016
- Professor: Yuran SEO
- Sungkyunkwan University
- Department: Consumer & Family Science
- Name: Lee dong hee
- Contact: molou@naver.com
Quality control of rain gauge measurements using telecommunication microwave ...JoergRieckermann
Accurate rain rate measurements are essential for many hydrological applications. Although rain gauge remains the reference instrument for the measurement of rain rate, the strong spatial and temporal variability of rainfall makes it difficult to spot faulty rain gauges. Due to the poor spatial representativeness of the point rainfall measurements, this is particularly difficult where their density is low. Taking advantage of the high density of telecommunication microwave links in urban areas, a consistency check is proposed to identify faulty rain gauges using nearby microwave links. The methodology is tested on a data set from operational rain gauges and microwave links, in Zürich (Switzerland). The malfunctioning of rain gauges leading to errors in the occurrence of dry/rainy periods are well identified. In addition, the gross errors affecting quantitative rain gauge measurements during rainy periods, such as blocking at a constant value, random noise and systematic bias, can be detected. The proposed approach can be implemented in real time.
Use of Probabilistic Statistical Techniques in AERMOD Modeling EvaluationsSergio A. Guerra
The advent of the short term National Ambient Air Quality Standards (NAAQS) prompted modelers to reassess the common practices in dispersion modeling analyses. The probabilistic nature of the new short term standards also opens the door to alternative modeling techniques that are based on probability. One of these is the Monte Carlo technique that can be used to account for emission variability in permit modeling.
Currently, it is assumed that a given emission unit is in operation at its maximum capacity every hour of the year. This assumption may be appropriate for facilities that operate at full capacity most of the time. However, in most cases, emission units operate at variable loads that produce variable emissions. Thus, assuming constant maximum emissions is overly conservative for facilities such as power plants that are not in operation all the time and which exhibit high concentrations during very short periods of time.
Another element of conservatism in NAAQS demonstrations relates to combining predicted concentrations from the AMS/EPA Regulatory Model (AERMOD) with observed (monitored) background concentrations. Normally, some of the highest monitored observations are added to the AERMOD results yielding a very conservative combined concentration.
A case study is presented to evaluate the use of alternative probabilistic methods to complement the shortcomings of current dispersion modeling practices. This case study includes the use of the Monte Carlo technique and the use of a reasonable background concentration to combine with the AERMOD predicted concentrations. The use of these methods is in harmony with the probabilistic nature of the NAAQS and can help demonstrate compliance through dispersion modeling analyses, while still being protective of the NAAQS.
Estimating Ammonia Emissions from Livestock Operations Using Low-Cost, Time-A...LPE Learning Center
For more: http://www.extension.org/67697 Recent regulations on ammonia (NH3) and other gaseous emissions by the EPA requires managers of animal feeding operations (AFOs) to report their annual emissions of greenhouse gases (GHGs), with the possibility of federal funding in the near future to be allocated for enforcement of GHG reporting as well as to levy large fines against AFOs that exceed the regulation limitations for GHG emissions. The current method of estimating NH3 emissions for AFOs is a “back of the envelope” type calculation based upon population and type of animal within an individual AFO.
Amy Stidworthy - Optimising local air quality models with sensor data - DMUG17IES / IAQM
An unapologetically technical conference, DMUG remains the key annual event for experts in this field. Unmissable speakers will be examining topical issues in emissions, exposure and dispersion modelling.
INNOVATIVE DISPERSION MODELING PRACTICES TO ACHIEVE A REASONABLE LEVEL OF CON...Sergio A. Guerra
Presentation delivered at the Annual Air and Waste Management Association conference in Long beach, California on June 26, 2014.
Innovative dispersion modeling techniques are presented including ARM2, EMVAP and the 50th percentile background concentration. Case study involves peaking engines that are used 250 hour per year. These intermittent sources are required to undergo a modeling evaluation in many states. Current modeling techniques grossly overestimate the emissions from these sporadic sources.
INNOVATIVE DISPERSION MODELING PRACTICES TO ACHIEVE A REASONABLE LEVEL OF CON...Sergio A. Guerra
Presentation delivered at the Board meeting for the Upper Midwest section of the Air and Waste Management Association meeting on September 16, 2014.
Innovative dispersion modeling techniques are presented including ARM2, EMVAP and the 50th percentile background concentration. Case study involves peaking engines that are used 250 hour per year. These intermittent sources are required to undergo a modeling evaluation in many states. Current modeling techniques grossly overestimate the emissions from these sporadic sources.
New generation of high sensitivity airborne potassium magnetometersGem Systems
Overview
Airborne Trends in Mineral Exploration
Why Potassium?
Benefits of Potassium Vapour Magnetometers
How we did it!
Bird’s family
Gradiometers – Rationale
Tri-Directional Gradiometer – Bird
GEM DAS
Sample Customer Maps
Conclusion
Source : http://www.gemsys.ca/technology/tech-notes-papers/
Advanced Modeling Techniques for Permit Modeling - Turning challenges into o...Sergio A. Guerra
Advance modeling techniques can be used in AERMOD to refine the inputs that are entered in the model to get more accurate results. This presentation covers:
-AERMOD’s Temporal Mismatch Limitation
-Building Downwash Limitations in BPIP/PRIME
-Advanced Modeling Techniques to Overcome these Limitations
Solutions include:
Equivalent Building Dimensions (EBD)
Emission Variability Processor (EMVAP)
Updated ambient ratio method (ARM2)
Pairing AERMOD values with the 50th % background concentrations in cumulative analyses.
AIR DISPERSION MODELING HIGHLIGHTS FROM 2012 ACESergio A. Guerra
Presentation includes some highlights from the dispersion modeling papers presented at the Annual AWMA conference in San Antonio, TX. Topics covered include: EMVAP, distance limitations of AERMOD, and two case studies comparing predicted and monitoring data,
Presented at the A&WMA UMS Board Meeting on August 21, 2012.
dispersion modeling requirements are more common in air permitting projects and in many cases become the bottleneck in permitting. Unlike any other consulting firm, CPP promotes cutting edge techniques which can alleviate excessive conservatism in permit modeling to a reasonable level that still protects public health. At CPP we start with the standard modeling techniques and apply the following advanced analysis tools, as needed, to optimize your permitting strategy:
• Analysis of BPIP output to verify if AERMOD is overpredicting,
• Screening tool to assess the benefit of refining the BPIP building dimensions inputs,
• Use of Equivalent Building Dimension (EBD) studies to correct building wake effects in AERMOD,
• Evaluation of background concentrations to determine a reasonable value to combine with predicted concentrations,
• Use of the Monte Carlo approach (i.e., EMVAP) to address sources with variable emissions,
• Use of the adjusted friction velocity (u-star) option in AERMET to address AERMOD’s overestimation during low wind stable hours,
• Site analysis to determine whether stacks taller than formula GEP stack heights are justified,
• Site specific wind tunnel modeling to determine GEP stack heights and Equivalent Building Dimensions,
• Site-specific wind erosion inputs, and
• Area and volume source enhancements.
The PuffR R Package for Conducting Air Quality Dispersion AnalysesRichard Iannone
PuffR is all about helping you conduct dispersion modelling using the CALPUFF modelling system. It is a software package currently being developed using the R statistical programming language. Dispersion modelling is a great tool for understanding how pollutants disperse from sources to receptors, and, how these dispersed pollutants affect populations’ exposure. The presentation goes over basic concepts in air dispersion modelling using CALPUFF, the goals of the project are outlined, the PuffR workflow is described, and a project roadmap is provided.
EFFECTS OF MET DATA PROCESSING IN AERMOD CONCENTRATIONSSergio A. Guerra
The current study evaluates the effect that different parameters used to process meteorological data have on AERMOD concentrations. Specifically, this study evaluates the effect from the use of AERMET processed with; 1-minute wind data collected by the Automated Surface Observing System (ASOS) and pre-processed using AERMINUTE, refined National Climatic Data Center (NCDC) station location and anemometer height, surface moisture, and urban/rural options. In this evaluation, one year of meteorological data was processed with nine different sets of input parameters and then used in AERMOD to run a short, medium and tall stack scenario for 1-hour, 24-hour and annual averaging periods. Downwash and terrain effects were not considered in this study. The results indicate that the three stack scenarios are sensitive to the location used for the meteorological station. Anemometer height changes had a small effect on concentrations for all scenarios except for the tall stack scenario which produced a modest increase in concentrations for the annual averaging period. Surface moisture was not found to have a strong effect on the scenarios evaluated. The use of AERMINUTE data resulted in significantly higher concentrations for the 1-hour (85%), 24-hour (81%), and annual (88%) averaging periods. The ice free group station option in AERMINUTE was also evaluated. When using AERMINUTE without specifying that the station is part of the ice free wind group stations, the concentrations obtained for tall stack scenario were lower for the 1-hour (64%), 24-hour (68%), and annual (78%) averaging periods. Finally, when it comes to the urban/rural evaluation, the greatest effect is observed in the medium stack scenario where concentrations double for the 1-hour scenario when using the rural option. However, in the tall stack scenario, significantly lower concentrations were obtained by using the urban parameter for the three averaging periods evaluated.
Presented at the 10th Conference of Air Quality Modeling
EPA‐Research Triangle Park, NC Campus on March 15, 2012; at the AWMA UMS Dispersion Modeling Workshop on May 15, 2012 and at the Annual AWMA Conference on June 20, 2012.
Presentation includes information related to gently sloping terrain, AERMINUTE, and EPA formula height.
Presented at the 27th Annual Conference on the Environment on November 13, 2012.
Pairing aermod concentrations with the 50th percentile monitored valueSergio A. Guerra
Presentation delivered to the Background Concentrations Workgroup for Air Dispersion Modeling organized by the Minnesota Pollution Control Agency. delivered on May 29, 2014. Three topics covered include 1) Screening monitoring data, 2) AERMOD’s time-space mismatch, and
3) Proposed 50th % Bkg Method
NOVEL DATA ANALYSIS TECHNIQUE USED TO EVALUATE NOX AND CO2 CONTINUOUS EMISSIO...Sergio A. Guerra
The current study presents a new data analysis technique developed while evaluating continuous emission data collected from a trash compactor. The evaluation involved tailpipe sampling with a portable emission monitoring system (PEMS) from a diesel fueled 525-horsepower trash
compactor. The sampling campaign took place by running the compactor with regular no. 2 diesel, B20 and ULSD fuels. The purpose was to determine the possible emission reductions in nitrous oxides (NOx) and carbon dioxide (CO2) from the use of B20 and ULSD in an off-road
vehicle. The results from the NOx analysis are discussed.
The initial data analysis identified two important issues. The first concern related to a bias in the calculated F values due to the very large number of samples (N). The large N influenced the probability values and indicated a false statistical significance for all factors tested. Additionally,
the data observations were found to be highly autocorrelated. Thus, a time interval data reduction
technique was used to address these two statistical limitations to the robustness of the statistical
analyses. The result in each case was a subset of quasi-independent observations sampled at an interval of 800 seconds. The autocorrelation and false statistical significance issues were promptly resolved by using this technique. Since the issues of false statistical significance and autocorrelation are inherent in continuous data, the positive results obtained from the use of this technique can be far-reaching. This technique allowed for a valid use of the general linear model (GLM) with engine speed as the covariate factor to test day, fuel type and compactor factors. This technique is most relevant given the advancements in data collection capabilities that
require data handling techniques to satisfy the statistical assumptions necessary for valid analyses to ensue.
Background Concentrations and the Need for a New System to Update AERMODSergio A. Guerra
Presentation delivered at the EPA 11th Conference on Air Quality Modeling at RTP, NC.
Topics covered include background concentrations and the need for a new system to update AERMOD. An evaluation of what is being proposed in the draft guidance related to background concentrations and an alternative approach to determine background concentrations for dispersion modeling evaluations is presented. A review of the lessons learned from Appendix W and a proposed new method to incorporate science into the model.
Using Physical Modeling to Evaluate Re-entrainment of Stack EmissionsSergio A. Guerra
Fume re-entry is an important concern for many types of facilities such as hospitals and laboratories that emit pathogens and toxic chemicals that may impact public health by being re-entrained into the building though nearby air intakes. Numerical methods can be used to evaluate dispersion of pollutants from stacks at sensitive receptors. However, numerical methods have limitations and simplifications that can significantly affect its predictions. An alternate way of analyzing stack re-entrainment is with physical modeling in a wind tunnel. In such a study, a scale model that accounts for buildings, topography, and vegetation is used with planned and alternate stack designs to determine the toxic emission impacts on air intakes and other sensitive locations. In a wind tunnel study different stack designs and possible mitigation options can be evaluated. This method is superior to numerical methods (e.g., dispersion models) because it accounts for the immediate structures, topography, and vegetation that is often ignored or oversimplified in numerical methods.
This presentation will show a hypothetical case study evaluating a site with toxic air emissions using AERMOD and physical modeling.
Highlights from the 2016 Guideline on Air Quality Models ConferenceSergio A. Guerra
The revision of the Guideline on AQ Models (Appendix W) will prompt many changes in the way dispersion modeling is conducted for regulatory purposes. Some of the changes to the Guideline include enhancements and bug fixes to the AERMOD modeling system, new screening techniques to address ozone and secondary PM2.5, delisting CALPUFF as the preferred long-range transport model, and updates on the use of meteorological input data. These changes will have a significant impact on the regulated community. In anticipation of these updates, the Air & Waste Management Association will hold its 6th Specialty Conference: “Guideline on Air Quality Models: The New Path” to provide a technical forum to discuss the Guideline. This talk covered the main highlights from this conference including the presentations from EPA on the status and future direction of the Guideline. Learn how these changes may impact dispersion modeling evaluations for short and long range transport.
Presentatie door Pooyan Ghasemi en Mario Martinelli, Deltares, op de Geo Klantendag 2018, tijdens de Deltares Software Dagen - Editie 2018. Donderdag, 7 juni 2018, Delft.
INNOVATIVE DISPERSION MODELING PRACTICES TO ACHIEVE A REASONABLE LEVEL OF CON...Sergio A. Guerra
Presentation delivered at the Board meeting for the Upper Midwest section of the Air and Waste Management Association meeting on September 16, 2014.
Innovative dispersion modeling techniques are presented including ARM2, EMVAP and the 50th percentile background concentration. Case study involves peaking engines that are used 250 hour per year. These intermittent sources are required to undergo a modeling evaluation in many states. Current modeling techniques grossly overestimate the emissions from these sporadic sources.
New generation of high sensitivity airborne potassium magnetometersGem Systems
Overview
Airborne Trends in Mineral Exploration
Why Potassium?
Benefits of Potassium Vapour Magnetometers
How we did it!
Bird’s family
Gradiometers – Rationale
Tri-Directional Gradiometer – Bird
GEM DAS
Sample Customer Maps
Conclusion
Source : http://www.gemsys.ca/technology/tech-notes-papers/
Advanced Modeling Techniques for Permit Modeling - Turning challenges into o...Sergio A. Guerra
Advance modeling techniques can be used in AERMOD to refine the inputs that are entered in the model to get more accurate results. This presentation covers:
-AERMOD’s Temporal Mismatch Limitation
-Building Downwash Limitations in BPIP/PRIME
-Advanced Modeling Techniques to Overcome these Limitations
Solutions include:
Equivalent Building Dimensions (EBD)
Emission Variability Processor (EMVAP)
Updated ambient ratio method (ARM2)
Pairing AERMOD values with the 50th % background concentrations in cumulative analyses.
AIR DISPERSION MODELING HIGHLIGHTS FROM 2012 ACESergio A. Guerra
Presentation includes some highlights from the dispersion modeling papers presented at the Annual AWMA conference in San Antonio, TX. Topics covered include: EMVAP, distance limitations of AERMOD, and two case studies comparing predicted and monitoring data,
Presented at the A&WMA UMS Board Meeting on August 21, 2012.
dispersion modeling requirements are more common in air permitting projects and in many cases become the bottleneck in permitting. Unlike any other consulting firm, CPP promotes cutting edge techniques which can alleviate excessive conservatism in permit modeling to a reasonable level that still protects public health. At CPP we start with the standard modeling techniques and apply the following advanced analysis tools, as needed, to optimize your permitting strategy:
• Analysis of BPIP output to verify if AERMOD is overpredicting,
• Screening tool to assess the benefit of refining the BPIP building dimensions inputs,
• Use of Equivalent Building Dimension (EBD) studies to correct building wake effects in AERMOD,
• Evaluation of background concentrations to determine a reasonable value to combine with predicted concentrations,
• Use of the Monte Carlo approach (i.e., EMVAP) to address sources with variable emissions,
• Use of the adjusted friction velocity (u-star) option in AERMET to address AERMOD’s overestimation during low wind stable hours,
• Site analysis to determine whether stacks taller than formula GEP stack heights are justified,
• Site specific wind tunnel modeling to determine GEP stack heights and Equivalent Building Dimensions,
• Site-specific wind erosion inputs, and
• Area and volume source enhancements.
The PuffR R Package for Conducting Air Quality Dispersion AnalysesRichard Iannone
PuffR is all about helping you conduct dispersion modelling using the CALPUFF modelling system. It is a software package currently being developed using the R statistical programming language. Dispersion modelling is a great tool for understanding how pollutants disperse from sources to receptors, and, how these dispersed pollutants affect populations’ exposure. The presentation goes over basic concepts in air dispersion modelling using CALPUFF, the goals of the project are outlined, the PuffR workflow is described, and a project roadmap is provided.
EFFECTS OF MET DATA PROCESSING IN AERMOD CONCENTRATIONSSergio A. Guerra
The current study evaluates the effect that different parameters used to process meteorological data have on AERMOD concentrations. Specifically, this study evaluates the effect from the use of AERMET processed with; 1-minute wind data collected by the Automated Surface Observing System (ASOS) and pre-processed using AERMINUTE, refined National Climatic Data Center (NCDC) station location and anemometer height, surface moisture, and urban/rural options. In this evaluation, one year of meteorological data was processed with nine different sets of input parameters and then used in AERMOD to run a short, medium and tall stack scenario for 1-hour, 24-hour and annual averaging periods. Downwash and terrain effects were not considered in this study. The results indicate that the three stack scenarios are sensitive to the location used for the meteorological station. Anemometer height changes had a small effect on concentrations for all scenarios except for the tall stack scenario which produced a modest increase in concentrations for the annual averaging period. Surface moisture was not found to have a strong effect on the scenarios evaluated. The use of AERMINUTE data resulted in significantly higher concentrations for the 1-hour (85%), 24-hour (81%), and annual (88%) averaging periods. The ice free group station option in AERMINUTE was also evaluated. When using AERMINUTE without specifying that the station is part of the ice free wind group stations, the concentrations obtained for tall stack scenario were lower for the 1-hour (64%), 24-hour (68%), and annual (78%) averaging periods. Finally, when it comes to the urban/rural evaluation, the greatest effect is observed in the medium stack scenario where concentrations double for the 1-hour scenario when using the rural option. However, in the tall stack scenario, significantly lower concentrations were obtained by using the urban parameter for the three averaging periods evaluated.
Presented at the 10th Conference of Air Quality Modeling
EPA‐Research Triangle Park, NC Campus on March 15, 2012; at the AWMA UMS Dispersion Modeling Workshop on May 15, 2012 and at the Annual AWMA Conference on June 20, 2012.
Presentation includes information related to gently sloping terrain, AERMINUTE, and EPA formula height.
Presented at the 27th Annual Conference on the Environment on November 13, 2012.
Pairing aermod concentrations with the 50th percentile monitored valueSergio A. Guerra
Presentation delivered to the Background Concentrations Workgroup for Air Dispersion Modeling organized by the Minnesota Pollution Control Agency. delivered on May 29, 2014. Three topics covered include 1) Screening monitoring data, 2) AERMOD’s time-space mismatch, and
3) Proposed 50th % Bkg Method
NOVEL DATA ANALYSIS TECHNIQUE USED TO EVALUATE NOX AND CO2 CONTINUOUS EMISSIO...Sergio A. Guerra
The current study presents a new data analysis technique developed while evaluating continuous emission data collected from a trash compactor. The evaluation involved tailpipe sampling with a portable emission monitoring system (PEMS) from a diesel fueled 525-horsepower trash
compactor. The sampling campaign took place by running the compactor with regular no. 2 diesel, B20 and ULSD fuels. The purpose was to determine the possible emission reductions in nitrous oxides (NOx) and carbon dioxide (CO2) from the use of B20 and ULSD in an off-road
vehicle. The results from the NOx analysis are discussed.
The initial data analysis identified two important issues. The first concern related to a bias in the calculated F values due to the very large number of samples (N). The large N influenced the probability values and indicated a false statistical significance for all factors tested. Additionally,
the data observations were found to be highly autocorrelated. Thus, a time interval data reduction
technique was used to address these two statistical limitations to the robustness of the statistical
analyses. The result in each case was a subset of quasi-independent observations sampled at an interval of 800 seconds. The autocorrelation and false statistical significance issues were promptly resolved by using this technique. Since the issues of false statistical significance and autocorrelation are inherent in continuous data, the positive results obtained from the use of this technique can be far-reaching. This technique allowed for a valid use of the general linear model (GLM) with engine speed as the covariate factor to test day, fuel type and compactor factors. This technique is most relevant given the advancements in data collection capabilities that
require data handling techniques to satisfy the statistical assumptions necessary for valid analyses to ensue.
Background Concentrations and the Need for a New System to Update AERMODSergio A. Guerra
Presentation delivered at the EPA 11th Conference on Air Quality Modeling at RTP, NC.
Topics covered include background concentrations and the need for a new system to update AERMOD. An evaluation of what is being proposed in the draft guidance related to background concentrations and an alternative approach to determine background concentrations for dispersion modeling evaluations is presented. A review of the lessons learned from Appendix W and a proposed new method to incorporate science into the model.
Using Physical Modeling to Evaluate Re-entrainment of Stack EmissionsSergio A. Guerra
Fume re-entry is an important concern for many types of facilities such as hospitals and laboratories that emit pathogens and toxic chemicals that may impact public health by being re-entrained into the building though nearby air intakes. Numerical methods can be used to evaluate dispersion of pollutants from stacks at sensitive receptors. However, numerical methods have limitations and simplifications that can significantly affect its predictions. An alternate way of analyzing stack re-entrainment is with physical modeling in a wind tunnel. In such a study, a scale model that accounts for buildings, topography, and vegetation is used with planned and alternate stack designs to determine the toxic emission impacts on air intakes and other sensitive locations. In a wind tunnel study different stack designs and possible mitigation options can be evaluated. This method is superior to numerical methods (e.g., dispersion models) because it accounts for the immediate structures, topography, and vegetation that is often ignored or oversimplified in numerical methods.
This presentation will show a hypothetical case study evaluating a site with toxic air emissions using AERMOD and physical modeling.
Highlights from the 2016 Guideline on Air Quality Models ConferenceSergio A. Guerra
The revision of the Guideline on AQ Models (Appendix W) will prompt many changes in the way dispersion modeling is conducted for regulatory purposes. Some of the changes to the Guideline include enhancements and bug fixes to the AERMOD modeling system, new screening techniques to address ozone and secondary PM2.5, delisting CALPUFF as the preferred long-range transport model, and updates on the use of meteorological input data. These changes will have a significant impact on the regulated community. In anticipation of these updates, the Air & Waste Management Association will hold its 6th Specialty Conference: “Guideline on Air Quality Models: The New Path” to provide a technical forum to discuss the Guideline. This talk covered the main highlights from this conference including the presentations from EPA on the status and future direction of the Guideline. Learn how these changes may impact dispersion modeling evaluations for short and long range transport.
Presentatie door Pooyan Ghasemi en Mario Martinelli, Deltares, op de Geo Klantendag 2018, tijdens de Deltares Software Dagen - Editie 2018. Donderdag, 7 juni 2018, Delft.
In spite of the recent developments in surrogate modeling techniques, the low fidelity of these models often limits their use in practical engineering design optimization. When surrogate models are used to represent the behavior of a complex system, it is challenging to simultaneously obtain high accuracy over the entire design space. When such surrogates are used for optimization, it becomes challening to find the optimum/optima with certainty. Sequential sampling methods offer a powerful solution to this challenge by providing the surrogate with reasonable accuracy where and when needed. When surrogate-based design optimization (SBDO) is performed using sequential sampling, the typical SBDO process is repeated multiple times, where each time the surrogate is improved by addition of new sam- ple points. This paper presents a new adaptive approach to add infill points during SBDO, called Adaptive Sequential Sampling (ASS). In this approach, both local exploitation and global exploration aspects are considered for updating the surrogate during optimization, where multiple iterations of the SBDO process is performed to increase the quality of the optimal solution. This approach adaptively improves the accuracy of the surrogate in the region of the current global optimum as well as in the regions of higher relative errors. Based on the initial sample points and the fitted surrogate, the ASS method adds infill points at each iteration in the locations of: (i) the current optimum found based on the fitted surrogate; and (ii) the points generated using cross-over between sample points that have relatively higher cross-validation errors. The Nelder and Mead Simplex method is adopted as the optimization algorithm. The effectiveness of the proposed method is illus- trated using a series of standard numerical test problems.
In spite of the recent developments in surrogate modeling techniques, the low fidelity of these models often limits their use in practical engineering design optimization. When surrogate models are used to represent the behavior of a complex system, it is challenging to simultaneously obtain high accuracy over the entire design space. When such surrogates are used for optimization, it becomes challenging to find the optimum/optima with certainty. Sequential sampling methods offer a powerful solution to this challenge by providing the surrogate with reasonable accuracy where and when needed. When surrogate-based design optimization (SBDO) is performed using sequential sampling, the typical SBDO process is repeated multiple times, where each time the surrogate is improved by addition of new sample points. This paper presents a new adaptive approach to add infill points during SBDO, called Adaptive Sequential Sampling (ASS). In this approach, both local exploitation and global exploration aspects are considered for updating the surrogate during optimization, where multiple iterations of the SBDO process is performed to increase the quality of the optimal solution. This approach adaptively improves the accuracy of the surrogate in the region of the current global optimum as well as in the regions of higher relative errors. Based on the initial sample points and the fitted surrogate, the ASS method adds infill points at each iteration in the locations of: (i) the current optimum found based on the
fitted surrogate; and (ii) the points generated using cross-over between sample points that
have relatively higher cross-validation errors. The Nelder and Mead Simplex method is adopted as the optimization algorithm. The effectiveness of the proposed method is illustrated using a series of standard numerical test problems.
This paper advances the Domain Segmentation based on Uncertainty in the Surrogate (DSUS) framework which is a novel approach to characterize the uncertainty in surrogates. The leave-one-out cross-validation technique is adopted in the DSUS framework to measure local errors of a surrogate. A method is proposed in this paper to evaluate the performance of the leave-out-out cross-validation errors as local error measures. This method evaluates local errors by comparing: (i) the leave-one-out cross-validation error with (ii) the actual local error estimated within a local hypercube for each training point. The comparison results show that the leave-one-out cross-validation strategy can capture the local errors of a surrogate. The DSUS framework is then applied to key aspects of wind resource as- sessment and wind farm cost modeling. The uncertainties in the wind farm cost and the wind power potential are successfully characterized, which provides designers/users more confidence when using these models
Surrogate-based design is an effective approach for modeling computationally expensive system behavior. In such application, it is often challenging to characterize the expected accuracy of the surrogate. In addition to global and local error measures, regional error measures can be used to understand and interpret the surrogate accuracy in the regions of interest. This paper develops the Regional Error Estimation of Surrogate (REES) method to quantify the level of the error in any given subspace (or region) of the entire domain, when all the available training points have been invested to build the surrogate. In this approach, the accuracy of the surrogate in each subspace is estimated by modeling the variations of the mean and the maximum error in that subspace with increasing number of training points (in an iterative process). A regression model is used for this purpose. At each iteration, the intermediate surrogate is constructed using a subset of the entire train- ing data, and tested over the remaining points. The evaluated errors at the intermediate test points at each iteration are used for training the regression model that represents the error variation with sample points. The effectiveness of the proposed method is illustrated using standard test problems. To this end, the predicted regional errors of the surrogate constructed using all the training points are compared with the regional errors estimated over a large set of test points.
Owing to the multitude of surrogate modeling techniques, developed in the recent years and the diverse characteristics offered by them, automated adaptive model selection ap- proaches could be helpful in selecting the most suitable surrogate for a given problem. Surrogate selection could be performed at three different levels: (i) model type selection, (ii) basis (or kernel) function selection, and (iii) hyper-parameter selection where hyper- parameters are those kernel parameters that are generally given by the users. Unlike the majority of existing model selection techniques, this paper explores the development of a method that performs selection coherently at all the three levels. In this context, the REES method is used to provide measures of the median and maximum errors of a candi- date surrogate model. Two approaches are used for the 3-level selection; (i) A Cascaded approach performs each level in a nested loop in the order going from model-kernel-hyper- parameters; (ii) A more advanced One-Step approach solves a MINLP to simultaneously optimize the model, kernel, and hyper-parameters. In both approaches, multiobjective optimization is performed to yield the best trade-offs between the estimated median and maximum errors. Candidate surrogates that are considered include (i) Kriging, (ii) Radial Basis Function (RBF), and (iii) Support Vector Regression (SVR), and multiple candidate kernels are allowed within these surrogate models. The 3-level REES-based model selec- tion is compared with model selection based on error estimated on a large set of additional test points, for validation purposes. Numerical experiments on a 2-variable, 6-variable, and 18-variable test problems, and wind farm power generation problem, show that the proposed approach provides unique flexibility in model selection and is also reasonably ac- curate when compared with selection based on errors estimated on additional test points.
Aplication of on line data analytics to a continuous process polybetene unitEmerson Exchange
This Emerson Exchange, 2013 presentation summarizes the 2013 field trail results achieved by applying on-line continuous data analytics to Lubrizol’s continuous polybutene process. Continuous data analytics may be used to provide an on-line prediction of quality parameters, and enable on-line detection of fault conditions. Information is provided on improvements made in the model used for quality parameter prediction, and how the field trail platform was integrated into the process unit. Presenters Qiwei Li, production engineer, Efren Hernandez and Robert Wojewodka, Lubrizol Corp., and Terry Blevins, principal technologist at Emerson, won best in conference in the process optimization track for this presentation.
Automating Speed: A Proven Approach to Preventing Performance Regressions in ...HostedbyConfluent
"Regular performance testing is one of the pillars of Kafka Streams’ reliability and efficiency. Beyond ensuring dependable releases, regular performance testing supports engineers in new feature development with the ability to easily test the performance impact of their features, compare different approaches, etc.
In this session, Alex and John share their experience from developing, using, and maintaining a performance testing framework for Kafka Streams that has prevented multiple performance regressions over the last 5 years. They cover guiding principles and architecture, how to ensure statistical significance and stability of results, and how to automate regression detection for actionable notifications.
This talk sheds light on how Apache Kafka is able to foster a vibrant open-source community while maintaining a high performance bar across many years and releases. It also empowers performance-minded engineers to avoid common pitfalls and bring high-quality performance testing to their own systems."
The analysis of complex system behavior often demands expensive experiments or computational simulations. Surrogates modeling techniques are often used to provide a tractable and inexpensive approximation of such complex system behavior. Owing to the lack of knowledge regarding the suitability of particular surrogate modeling techniques, model selection approach can be helpful to choose the best surrogate technique. Popular model selection approaches include: (i) split sample, (ii) cross-validation, (iii) bootstrapping, and (iv) Akaike's information criterion (AIC) (Queipo et al. 2005; Bozdogan et al. 2000). However, the effectiveness of these model selection methods is limited by the lack of accurate measures of local and global errors in surrogates.
This paper develops a novel and model-independent concept to quantify the local/global reliability of surrogates, to assist in model selection (in surrogate applications). This method is called the Generalized-Regional Error Estimation of Surrogate (G-REES). In this method, intermediate surrogates are iteratively constructed over heuristic subsets of the available sample points (i.e., intermediate training points), and tested over the remaining available sample points (i.e., intermediate test points). The fraction of sample points used as intermediate training points is fixed at each iteration, with the total number of iterations being pre-specified. The estimated median and maximum relative errors for the heuristic subsets at each iteration are used to fit a distribution of the median and maximum error, respectively. The statistical mode of the median and the maximum error distributions are then determined. These mode values are then represented as functions of the density of training points (at the corresponding iteration). Regression methods, called Variation of Error with Sample Density (VESD), are used for this purpose. The VESD models are then used to predict the expected median and maximum errors, when all the sample points are used as training points.
The effectiveness of the proposed model selection criterion is explored to find the best surrogate between candidates including: (i) Kriging, (ii) Radial Basis Functions (RBF), (iii) Extended Radial Basis Functions (ERBF), and (iv) Quadratic Response Surface (QRS), for standard test functions and a wind farm capacity factor function. The results will be compared with the relative accuracy of the surrogates evaluated on additional test points, and also with the prediction sum of square (PRESS) error given by leave-one-out cross-validation.
The application of G-REES to a standard test problem with two design variables (Branin-hoo function) show that the proposed method predicts the median and the maximum value of the global error with a higher level of confidence compared to PRESS. It also shows that model selection based on G-REES method is significantly more reliable than that currently performed using error measures such as PRESS. The
Wind farm development is an extremely complex process, most often driven by three im- portant performance criteria: (i) annual energy production, (ii) lifetime costs, and (iii) net impact on surroundings. Generally, planning a commercial scale wind farm takes several years. Undesirable concept-to-installation delays are primarily attributed to the lack of an upfront understanding of how different factors collectively affect the overall performance of a wind farm. More specifically, it is necessary to understand the balance between the socio-economic, engineering, and environmental objectives at an early stage in the design process. This paper proposes a Wind Farm Tradeoff Visualization (WiFToV) framework that aims to develop first-of-its-kind generalized guidelines for the conceptual design of wind farms, especially at early stages of wind farm development. Two major performance objectives are considered in this work: (i) cost of energy (COE) and (ii) land area per MW installed (LAMI). The COE is estimated using the Wind Turbine Design Cost and Scaling Model (WTDCS) and the Annual Energy Production (AEP) model incorporated by the Unrestricted Wind Farm Layout Optimization (UWFLO) framework. The LAMI is esti- mated using an optimal-layout based land usage model, which is treated as a post-process of the wind farm layout optimization. A Multi-Objective Mixed-Discrete Particle Swarm Optimization (MO-MDPSO) algorithm is used to perform the bi-objective optimization, which simultaneously optimizes the location and types of turbines. Together with a novel Pareto translation technique, the proposed WiFToV framework allows the exploration of the trade-off between COE and LAMI, and their variations with respect to multiple values of nameplate capacity.
Effective and time-efficient decision-making in the early stages of wind farm planning can lay the foundation of a successful wind energy project. Undesirable concept-to-installation delays in wind farm development is often caused by conflicting decisions from the major parties involved (e.g., developer, investors, landowners, and local communities), which in turn can be (in a major part) attributed to the lack of an upfront understanding of the trade-offs between the technical, socio-economic, and environmental-impact aspects of the wind farm for the given site. This paper proposes a consolidated visualization platform for wind farm planning, which could facilitate informed and co-operative decision-making by the parties involved. This visualization platform offers a GUI-based land shape chart, which provides the following information: the variation of the energy production capacity and of the corresponding required optimal land shape with different land area and nameplate capacity decisions. In order to develop this chart, a bi-objective optimization problem is formulated (using the Unrestricted Wind Farm Layout Optimization framework) to max- imize the capacity factor and minimize the land usage, subject to different nameplate capacity decisions. The application of an Optimal Layout-based land usage estimate allows the wind farm layout optimization to run without pre-specifying any farm boundaries; the optimal land shape is instead determined as a post process, using convex hull and minimum bounding rectangle concept, based on the optimal arrangement of turbines. Three land shape charts are generated under three characteristic wind patterns - (i) single dominant wind direction, (ii) two opposite dominant wind directions, and (ii) two orthogonal domi- nant wind directions, all three patterns comprising the same wind speed distribution. The results indicate that the optimal land shape is highly sensitive to the variation in LAMI for small-capacity wind farms (few turbines) and to the variation in nameplate capacity for small allowed land area. For the same decided nameplate capacity and LAMI values, we observe reasonable similarity in the optimal land shapes and the maximum energy pro- duction potentials given the “single dominant direction” and the “two opposite dominant directions” wind patterns; the optimal land shapes and the maximum energy production potentials yielded by the “two orthogonal dominant directions” wind pattern is however observed to be relatively different from the other two cases.
Complex system design problems tend to be high dimen- sional and nonlinear, and also often involve multiple objectives and mixed-integer variables. Heuristic optimization algorithms have the potential to address the typical (if not most) charac- teristics of such complex problems. Among them, the Particle Swarm Optimization (PSO) algorithm has gained significant popularity due to its maturity and fast convergence abilities. This paper seeks to translate the unique benefits of PSO from solving typical continuous single-objective optimization problems to solving multi-objective mixed-discrete problems, which is a relatively new ground for PSO application. The previously de- veloped Mixed-Discrete Particle Swarm Optimization (MDPSO) algorithm, which includes an exclusive diversity preservation technique to prevent premature particle clustering, has been shown to be a powerful single-objective solver for highly con- strained MINLP problems. In this paper, we make fundamental advancements to the MDPSO algorithm, enabling it to solve challenging multi-objective problems with mixed-discrete design variables. In the velocity update equation, the explorative term is modified to point towards the non-dominated solution that is the closest to the corresponding particle (at any iteration). The fractional domain in the diversity preservation technique, which was previously defined in terms of a single global leader, is now applied to multiple global leaders in the intermediate Pareto front. The multi-objective MDPSO (MO-MDPSO) algorithm is tested using a suite of diverse benchmark problems and a disc-brake design problem. To illustrate the advantages of the new MO-MDPSO algorithm, the results are compared with those given by the popular Elitist Non-dominated Sorting Genetic Algorithm-II (NSGA-II).
The performance of a wind farm is affected by several key factors that can be classified into two cate- gories: the natural factors and the design factors. Hence, the planning of a wind farm requires a clear quantitative understanding of how the balance between the concerned objectives (e.g., socia-economic, engineering, and environmental objectives) is affected by these key factors. This understanding is lacking in the state of the art in wind farm design. The wind farm capacity factor is one of the primary perfor- mance criteria of a wind energy project. For a given land (or sea area) and wind resource, the maximum capacity factor of a particular number of wind turbines can be reached by optimally adjusting the layout of turbines. However, this layout adjustment is constrained owing to the limited land resource. This paper proposes a Bi-level Multi-objective Wind Farm Optimization (BMWFO) framework for planning effective wind energy projects. Two important performance objectives considered in this paper are: (i) wind farm Capacity Factor (CF) and (ii) Land Area per MW Installed (LAMI). Turbine locations, land area, and nameplate capacity are treated as design variables in this work. In the proposed framework, the Capacity Factor - Land Area per MW Installed (CF - LAMI) trade-off is parametrically represented as a function of the nameplate capacity. Such a helpful parameterization of trade-offs is unique in the wind energy literature. The farm output is computed using the wind farm power generation model adopted from the Unrestricted Wind Farm Layout Optimization (UWFLO) framework. The Smallest Bounding Rectangle (SBR) enclosing all turbines is used to calculate the actual land area occupied by the farm site. The wind farm layout optimization is performed in the lower level using the Mixed-Discrete Particle Swarm Optimization (MDPSO), while the CF - LAMI trade-off is parameterized in the upper level. In this work, the CF - LAMI trade-off is successfully quantified by nameplate capacity in the 20 MW to 100 MW range. The Pareto curves obtained from the proposed framework provide important in- sights into the trade-offs between the two performance objectives, which can significantly streamline the decision-making process in wind farm development.
The creation of wakes, with unique turbulence charac- teristics, downstream of turbines significantly increases the complexity of the boundary layer flow within a wind farm. In conventional wind farm design, analytical wake models are generally used to compute the wake-induced power losses, with different wake models yielding significantly different estimates. In this context, the wake behavior, and subsequently the farm power generation, can be expressed as functions of a series of key factors. A quantitative understanding of the relative impact of each of these factors is paramount to the development of more reliable power generation models; such an understanding is however missing in the current state of the art in wind farm design. In this paper, we quantitatively explore how the farm power generation, estimated using four different analytical wake models, is influenced by the following key factors: (i) incoming wind speed, (ii) land configuration, and (iii) ambient turbulence. The sensitivity of the maximum farm output potential to the input factors, when using different wake models, is also analyzed. The extended Fourier Amplitude Sensitivity Test (eFAST) method is used to perform the sensitivity analysis. The power generation model and the optimization strategy is adopted from the Unrestricted Wind Farm Layout Optimization (UWFLO) framework. In the case of an array-like turbine arrangement, both the first-order and the total-order sensitivity analysis indices of the power output with respect to the incoming wind speed were found to reach a value of 99%, irrespective of the choice of wake models. However, in the case of maximum power output, significant variation (around 30%) in the indices was observed across different wake models, especially when the incoming wind speed is close to the rated speed of the turbines.
The power generation of a wind farm is significantly less than the summation of the power generated by each turbine when operating as a standalone entity. This power reduction can be attributed to the energy loss due to the wake effects − the resulting velocity deficit in the wind downstream of a turbine. In the case of wind farm design, the wake losses are generally quantified using wake models. The effectiveness of wind farm design (seeking to maximize the farm output) therefore depends on the accuracy and the reliability of the wake models. This paper compares the impact of the following four analytical wake
models on the wind farm power generation: (i) the Jensen model, (ii) the Larsen model, (iii) the Frandsen model, and (iv) the Ishihara model. The sensitivity of this impact to the Land Area per Turbine (LAT) and the incoming wind speed is also investigated. The wind farm power generation model used in this paper is adopted from the Unrestricted Wind Farm Layout Optimization (UWFLO) methodology. Single wake case studies show that the velocity deficit and the wake diameter estimated by the different analytical wake models can be significantly different. A maximum difference of 70% was also observed for the wind farm capacity factor values estimated using different wake models.
Development of a family of products that satisfies different sectors of the market introduces significant challenges to today’s manufacturing industries – from development time to aftermarket services. A product family with a common platform paradigm offers a powerful solution to these daunting challenges. The Comprehensive Product Platform Planning (CP3) framework formulates a flexible product family model that (i) seeks to eliminate traditional boundaries between modular and scalable families, (ii) allows the formation of sub-families of products, and (iii) yield the optimal depth and number of platforms. In this paper, the CP3 framework introduces a solution strategy that obviates common assumptions; namely (i) the identification of platform/non-platform design variables and the determination of variable values are separate processes, and (ii) the cost reduction of creating product platforms is independent of the total number of each product manufactured. A new Cost Decay Function (CDF) is developed to approximate the reduction in cost with increasing commonalities among products, for a specified capacity of production. The Mixed Integer Non-Liner Programming (MINLP) problem, presented by the CP3 model, is solved using a novel Platform Segregating Mapping Function (PSMF). The proposed CP3 framework is implemented on a family of universal electric motors.
This paper explores the adaptive optimal design of Active Thermally Insulated (ATI) windows to significantly improve energy efficiency. The ATI window design uses ther- mostats to actively control thermoelectric (TE) units and fans to regulate the overall ther- modynamic properties of the windows. The windows are used to maintain a comfortable indoor temperature. Since weather conditions vary with different geographical locations and with time, the thermodynamic properties of the windows should adapt accordingly. The electric power supplied to the TE units and the fans are dynamically controlled so as to provide an optimal operation under varying weather conditions. Optimization of the ATI window design is a multiobjective problem. The problem minimizes both the heat trans- ferred through the window and electric power consumption. The heat transfer through the ATI windows is analyzed using FLUENT; and the optimization is performed using MAT- LAB. Since the computational expense of optimization for numerous weather conditions is excessive, the power supplies are optimized under a reasonably small number of weather conditions. Based on the optimal results obtained for these conditions, a surrogate model is developed to represent the optimal results in a wide range of weather conditions. The surrogate model is used to evaluate optimal power supplies with respect to different val- ues of outside temperature, wind speed, and intensity of solar radiation. Thermometers, anemometers, and solar radiation sensors are used to sense these weather conditions. With the inputs from the sensors, the thermostats determine the operating conditions and cal- culate the corresponding optimal power supplies using the surrogate model. Since the ATI windows are operated with optimal power supplies, high energy efficiency is achieved.
The Comprehensive Product Platform Planning (CP3) framework presents a flexible mathematical model of the platform planning process, which allows (i) the formation of sub-families of products, and (ii) the simultaneous identification and quantification of plat- form/scaling design variables. The CP3 model is founded on a generalized commonality matrix that represents the product platform plan, and yields a mixed binary-integer non- linear programming problem. In this paper, we develop a methodology to reduce the high dimensional binary integer problem to a more tractable integer problem, where the com- monality matrix is represented by a set of integer variables. Subsequently, we determine the feasible set of values for the integer variables in the case of families with 3 − 7 kinds of products. The cardinality of the feasible set is found to be orders of magnitude smaller than the total number of unique combinations of the commonality variables. In addition, we also present the development of a generalized approach to Mixed-Discrete Non-Linear Optimization (MDNLO) that can be implemented through standard non-gradient based op- timization algorithms. This MDNLO technique is expected to provide a robust and compu- tationally inexpensive optimization framework for the reduced CP3 model. The generalized approach to MDNLO uses continuous optimization as the primary search strategy, how- ever, evaluates the system model only at the feasible locations in the discrete variable space.
The planning of a wind farm, which minimizes the project costs and maximizes the power generation capacity, presents significant challenges to today’s wind energy industry. An optimal wind farm planning strategy that accounts for the key factors (that can be designed) influencing the net power generation offers a powerful solution to these daunting challenges. This paper explores the influences of (i) the number of turbines, (ii) the farm size, and (iii) the use of a combination of turbines with differing rotor diameters, on the optimal power generated by a wind farm. We use a recently developed method of arranging turbines in a wind farm (the Unrestricted Wind Farm Layout Optimization (UWFLO)) to maximize the farm efficiency. Response surface based cost models are used to estimate the cost of the wind farm as a function of the the turbine rotor diameters and number of tur- bines. Optimization is performed using a Particle Swarm Optimization (PSO) algorithm. A robust mixed-discrete version of the PSO algorithm is implemented to appropriately account for the discrete choice of feasible rotor diameters. The use of an optimal combi- nation of turbines with differing rotor diameters was observed to significantly improve the net power generation. Exploration of the influences of (i) the number of turbines, and (ii) the farm size, on the cost per KW of power produced, provided interesting observations.
This paper compares the performances of standard surrogate models in the development of an optimal control framework. The optimal control strategy is implemented on an Active Thermoelectric (ATE) window design. The ATE window design uses thermoelectric units to actively regulate the overall thermodynamic properties of the windows. The optimization of the design is a multiobjective problem, where both the heat transferred through the window and electric power consumption are minimized. The power supplies and the heat transfer are optimized under a reasonable number of randomly sampled environmental conditions. The subsequent optimal designs obtained are represented as functions of the corresponding environmental conditions using surrogate models. To this end, four types of surrogate models are used, namely, (i) Quadratic Response Surface Methodology (QRSM), (ii) Radial Basis Functions (RBF), (iii) Extended Radial Basis Functions (E-RBF), and (iv) Kriging. Their performances are compared using two accuracy measurement metrics: Root Mean Squared Error (RMSE) and Maximum Absolute Error (MAE). We found that any one of the surrogate modeling methods is not superior to the others over the whole domain for the optimal control of the ATE window.
A Response Surface Based Wind Farm Cost (RS-WFC) model, is developed to evaluate the economics of wind farms. The RS-WFC model is developed using Extended Radial Basis Functions (E-RBF) for onshore wind farms in the U.S.. This model is then used to explore the in uence of di erent design and economic parameters, including number of turbines, rotor diameter and labor cost, on the cost of a wind farm. The RS-WFC model is composed of three parts that estimate (i) the installation cost, (ii) the annual Operation and Maintenance (O&M) cost, and (iii) the total annual cost of a wind farm. The accuracy of the cost model is favorably established through comparison with pertinent commercial data. Moreover, the RS-WFC model is integrated with an analytical power generation model of a wind farm. A recently developed Unrestricted Wind Farm Layout Optimization (UWFLO) model is used to determine the power generated by a farm. The ratio of the total annual cost and the energy generated by the wind farm in one year (commonly known as the Cost of Energy, COE) is minimized in this paper. The results show that the COE could decreasesigni cantlythroughlayoutoptimization,toobtainmillionsofannualcostsavings.
This paper presents a new method (the Unrestricted Wind Farm Layout Optimization (UWFLO)) of arranging turbines in a wind farm to achieve maximum farm efficiency. The powers generated by individual turbines in a wind farm are dependent on each other, due to velocity deficits created by the wake effect. A standard analytical wake model has been used to account for the mutual influences of the turbines in a wind farm. A variable induction factor, dependent on the approaching wind velocity, estimates the velocity deficit across each turbine. Optimization is performed using a constrained Particle Swarm Optimization (PSO) algorithm. The model is validated against experimental data from a wind tunnel experiment on a scaled down wind farm. Reasonable agreement between the model and experimental results is obtained. A preliminary wind farm cost analysis is also performed to explore the effect of using turbines with different rotor diameters on the total power generation. The use of differing rotor diameters is observed to play an important role in improving the overall efficiency of a wind farm.
This paper develops a cost model for onshore wind farms in the U.S.. This model is then used to analyze the influence of different designs and economic parameters on the cost of a wind farm. A response surface based cost model is developed using Extended Radial Basis Functions (E-RBF). The E-RBF ap- proach, a combination of radial and non-radial basis functions, can provide the designer with significant flexibility and freedom in the metamodeling process. The E-RBF based cost model is composed of three parts that can estimate (i) the installation cost, (ii) the annual Operation and Maintenance (O&M) cost, and (iii) the total annual cost of a wind farm. The input param- eters for the E-RBF based cost model include the rotor diameter of a wind turbine,the number of wind turbines in a wind farm, the construction labor cost, the management labor cost and the technician labor cost. The accuracy of the model is favorably explored through comparison with pertinent real world data. It is found that the cost of a wind farm is appreciably sensitive to
the rotor diameter and the number of wind turbines for a given desirable total power output.
In the past decade or so, there has been appreciable progress in developing renewable energy resources; among them, wind energy has taken a lead, and is currently contributing towards 2.5% of the global electricity consumption (WWEA, 2011). On the downside, the variability of this resource itself has been one of the major factors restricting its potential growth – wind speed and direction show strong temporal variations. In addition, the distribution of wind conditions varies significantly from year to year. The resulting ill-predictability of the annual distribution of wind conditions introduces significant uncertainties in the estimated resource potential and the predicted performance of the wind farm.
The planning of a wind farm, which minimizes the lifecycle project costs and maximizes the reliability of the expected power generation, presents significant challenges to today’s wind energy industry. An optimal wind farm planning strategy that simultaneously (i) accounts for the key engineering design factors, and (ii) addresses the major sources of un- certainty in a wind farm, can offer a powerful solution to these daunting challenges. In this paper, we develop a new methodology to characterize the long term uncertainties, partic- ularly those introduced by the ill-predictability of the annual variation in wind conditions (wind speed and direction, and air density). The annual variation in wind conditions is rep- resented using a non-parametric wind distribution model. The uncertainty in the predicted annual wind distribution is then characterized using a set of lognormal distributions. The uncertainties in the estimated (i) farm power generation and (ii) Cost of energy (COE) are represented as functions of the variances of these lognormal distributions. Subsequently, we minimize the uncertainty in the COE through wind farm optimization. To this end, we apply the Unrestricted Wind Farm Layout Optimization (UWFLO) framework, which provides a comprehensive platform for wind farm design. This methodology for robust wind farm optimization is applied to design a 25MW wind farm in N. Dakota. We found that layout optimization is appreciably sensitive to the uncertainties in wind conditions.
The determination of complex underlying relationships between system parameters from simulated and/or recorded data requires advanced interpolating functions, also known as surrogates. The development of surrogates for such complex relationships often requires the modeling of high dimensional and non-smooth functions using limited information. To this end, the hybrid surrogate modeling paradigm, where different surrogate models are aggregated, offers a robust solution. In this paper, we develop a new high fidelity surro- gate modeling technique that we call the Reliability Based Hybrid Functions (RBHF). The RBHF formulates a reliable Crowding Distance-Based Trust Region (CD-TR), and adap- tively combines the favorable characteristics of different surrogate models. The weight of each contributing surrogate model is determined based on the local reliability measure for that surrogate model in the pertinent trust region. Such an approach is intended to ex- ploit the advantages of each component surrogate. This approach seeks to simultaneously capture the global trend of the function and the local deviations. In this paper, the RBHF integrates four component surrogate models: (i) the Quadratic Response Surface Model (QRSM), (ii) the Radial Basis Functions (RBF), (iii) the Extended Radial Basis Functions (E-RBF), and (iv) the Kriging model. The RBHF is applied to standard test problems. Subsequent evaluations of the Root Mean Squared Error (RMSE) and the Maximum Ab- solute Error (MAE), illustrate the promising potential of this hybrid surrogate modeling approach.
The development of large scale wind farms that can produce energy at a cost comparable to that of other conventional energy resources presents significant challenges to today’s wind energy industry. The consideration of the key design and environmental factors that influence the performance of a wind farm is a crucial part of the solution to this challenge. In this paper, we develop a methodology to account for the configuration of the farm land (length-to-breadth ratio and North-South-East-West orientation) within the scope of wind farm optimization. This approach appropriately captures the correlation between the (i) land configuration, (ii) the farm layout, and (iii) the selection of turbines-types. Simultaneous optimization of the farm layout and turbine selection is performed to minimize the Cost of Energy (COE), for a set of sample land configurations. The optimized COE and farm efficiency are then represented as functions of the land aspect ratio and the land orientation. To this end, we apply a recently developed response surface method known as the Reliability-Based Hybrid Functions. The overall wind farm design methodology is applied to design a 25MW farm in North Dakota. This case study provides helpful insights into the influence of the land configuration on the optimum farm performance that can be obtained for a particular site.
This paper explores the effectiveness of the recently devel- oped surrogate modeling method, the Adaptive Hybrid Functions (AHF), through its application to complex engineered systems design. The AHF is a hybrid surrogate modeling method that seeks to exploit the advantages of each component surrogate. In this paper, the AHF integrates three component surrogate mod- els: (i) the Radial Basis Functions (RBF), (ii) the Extended Ra- dial Basis Functions (E-RBF), and (iii) the Kriging model, by characterizing and evaluating the local measure of accuracy of each model. The AHF is applied to model complex engineer- ing systems and an economic system, namely: (i) wind farm de- sign; (ii) product family design (for universal electric motors); (iii) three-pane window design; and (iv) onshore wind farm cost estimation. We use three differing sampling techniques to inves- tigate their influence on the quality of the resulting surrogates. These sampling techniques are (i) Latin Hypercube Sampling
∗Doctoral Student, Multidisciplinary Design and Optimization Laboratory, Department of Mechanical, Aerospace and Nuclear Engineering, ASME student member.
†Distinguished Professor and Department Chair. Department of Mechanical and Aerospace Engineering, ASME Lifetime Fellow. Corresponding author.
‡Associate Professor, Department of Mechanical Aerospace and Nuclear En- gineering, ASME member (LHS), (ii) Sobol’s quasirandom sequence, and (iii) Hammers- ley Sequence Sampling (HSS). Cross-validation is used to evalu- ate the accuracy of the resulting surrogate models. As expected, the accuracy of the surrogate model was found to improve with increase in the sample size. We also observed that, the Sobol’s and the LHS sampling techniques performed better in the case of high-dimensional problems, whereas the HSS sampling tech- nique performed better in the case of low-dimensional problems. Overall, the AHF method was observed to provide acceptable- to-high accuracy in representing complex design systems.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
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Sampling-SDM2012_Jun
1. Improving the Accuracy of Surrogate Models
Using Inverse Transform Sampling
Junqiang Zhang*, Achille Messac#, Jie Zhang*, and Souma Chowdhury*
* Rensselaer Polytechnic Institute, Department of Mechanical, Aerospace, and Nuclear Engineering
# Syracuse University, Department of Mechanical and Aerospace Engineering
53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics
and Materials Conference
8th AIAA Multidisciplinary Design Optimization Specialist Conference
April 23 - 26, 2012
Honolulu, Hawaii
2. Introduction
• Sampling is an important component of optimization, numerical
simulations, design of experiments and uncertainty analysis.
• Surrogate modeling is concerned with the construction of
approximation models to estimate the system performance, and to
develop relationships between specific system inputs and outputs.
• It is expected that an intelligent selection of sample points can
increase the accuracy of surrogate models.
2
Surrogate
3. 3
Sampling Based on Probability Distribution
• Observations of inputs often follow a distribution.
• A set of sample points representative of the naturally
occurring distribution of inputs is often desirable.
Distribution of a population Sample points
-20
0
20
-20
0
6
4
2
0
20
x 10-3
x2 x1
PDF
x1
x2
20
10
0
-10
-20
-20 -10 0 10 20
4. Presentation Outline
4
Research Objectives and Motivation
Probability-based sampling methods overview
Inverse transform sampling
Surrogate model development
• Surrogate model performance comparison
• Performance in increasing sample space
Concluding remarks
5. Certain inputs occur more frequently, comprising regions of
high interests in the condition space.
It is desirable to have higher accuracy in the system response
(surrogate) in the regions of higher interest.
5
Motivation and Research Objectives
Motivation:
Objectives:
Develop a sampling strategy for surrogate model
development, which promotes higher accuracy in regions of
high interest (of the observed input).
7. 7
Inverse Transform Sampling: Key Features
Inverse transform can
• Sample more points in the regions where random variables
have higher probability densities; and
• Sample fewer points in the regions where random variables
have low probability densities.
The probability of random variables is used as the metric of
distance instead of the Euclidean distance.
Sample points are uniform in terms of the probability
differences.
8. 8
Procedure: Step 1
Random Variable Observations
Distribution Function Fitting
Generating the Sequence of CDFs
Coordinates Evaluation
Step 1
Step 2
Step 3
Step 4
The occurrence of sampling
variables should be sufficiently
observed.
10
5
0
-5
-10
-15
-20
-5 0 5 10 15
x1
x2
9. 9
Procedure : Step 2
Approaches
• The least squares method
• The least absolute deviations method
• The generalized method of moments
• The Maximum Likelihood Estimation
Random Variable Observations
Distribution Function Fitting
Generating the Sequence of CDFs
Coordinates Evaluation
Step 1
Step 2
Step 3
Step 4
-20
0
20
-20
0
0.015
0.01
0.005
0
20
x2 x1
PDF
10. 10
Procedure : Step 3
• CDF increases from 0 to 1.
• Low-discrepancy sampling methods
generate uniformly distributed
sequences between 0 and 1 in all
dimensions of a sample space.
• Van der Corput sequence
• Halton/Hammersley sequence
• Sobol sequence
• Faure sequence
Random Variable Observations
Distribution Function Fitting
Generate the Sequence of CDFs
Coordinates Evaluation
Step 1
Step 2
Step 3
Step 4
1
0.8
0.6
0.4
0.2
0
0 0.2 0.4 0.6 0.8 1
CDF(x1)
CDF(x2)
11. 11
Procedure : Step 4
• Coordinates are evaluated using the
inverse function of CDF.
• Analytical expressions
• Numerical approaches
• The Newton’s method
• The Levenberg-Marquardt algorithm
• The trust region methods
Random Variable Observations
Distribution Function Fitting
Generating the Sequence of CDFs
Coordinates Evaluation
Step 1
Step 2
Step 3
Step 4
x1
x2
20
10
0
-10
-20
-20 -10 0 10 20
13. 13
Window Performance Evaluation
• The heat transfer rate through a triple pane window is
evaluated under varying climatic conditions.
• A CFD model of the triple pane window is created.
• Sample climatic conditions are boundary conditions of the
window CFD model.
Cross Section
14. 14
Window Performance Evaluation
Step 1 Random Variable Observations
Three climatic conditions:
• Air temperature
• Wind speed
• Solar radiation
.
Michigan, ND.
3720 hourly observations for either
January or August from 2006 to 2010
15. 15
Window Performance Evaluation
Step 2 Distribution Function Fitting
Three climatic conditions:
• Air temperature: Gaussian
• Wind speed: Weibull
• Solar radiation: Gamma
Parameters are fitted using the Maximum Likelihood Estimation.
Michigan, ND.
3720 hourly observations for either
January or August from 2006 to 2010
16. Three climatic conditions:
• Air temperature: Gaussian
• Wind speed: Weibull
• Solar radiation: Gamma
Parameters are fitted using the Maximum Likelihood Estimation.
Michigan, ND.
3720 hourly observations for either
January or August from 2006 to 2010
16
Window Performance Evaluation
Step 3 Generate the Sequence of CDFs
1
0.8
0.6
0.4
0.2
0
270 280 290 300 310
Temperature
CDF
1
0.8
0.6
0.4
0.2
0
0 5 10 15
Wind Speed
CDF
1
0.8
0.6
0.4
0.2
0
0 500 1000 1500
Solar radiation
CDF
Sobol sequence
17. Three climatic conditions:
• Air temperature: Gaussian
• Wind speed: Weibull
• Solar radiation: Gamma
Parameters are fitted using the Maximum Likelihood Estimation.
Michigan, ND.
3720 hourly observations for either
January or August from 2006 to 2010
17
Window Performance Evaluation
Step 4 Coordinates Evaluation
1
0.8
0.6
0.4
0.2
0
270 280 290 300 310
Temperature
CDF
1
0.8
0.6
0.4
0.2
0
0 5 10 15
Wind Speed
CDF
1
0.8
0.6
0.4
0.2
0
0 500 1000 1500
Solar radiation
CDF
18. 18
Distribution of Sample Points
• Sample climatic conditions for January
• Sample climatic conditions for August
Sample points crowd in the region where PDF is high.
19. 19
Surrogate Model Development
• The heat transfer rate through the window is evaluated using
31 sample climatic conditions for either January or August,
respectively.
• Two surrogate models are developed for January and August
using Kriging, respectively.
Outdoor temperature
Wind speed
Solar radiation
Heat flux
Kriging
Inputs
Output
In this paper, we use a Matlab Kriging
toolbox DACE (Design and Analysis
of Computer Experiments), developed
by Dr. Nielsen.
20. 20
Surrogate Model Performance Criteria
For January and August, 3720 climatic conditions are used to
evaluate errors of each surrogate.
The performance of the surrogate can be evaluated using:
• Root Mean Squared Error (RMSE)
• Root Mean Squared Percentage Error (RMSPE)
• Maximum Absolute Error (MAE)
• Maximum Percentage Error (MPE)
21. 21
Surrogate Model Performance Comparison
Month Method RMSE MAE RMSPE MPE
January Inverse 0.047 0.49 0.64% 7.2%
Sobol 0.054 0.30 0.68% 9.3%
August Inverse 0.079 0.54 11% 318%
Sobol 0.094 0.32 85% 4373%
• RMSE, RMSPE, and MPE: Inverse transform sampling
performs better than the Sobol sequence.
• MAE: Inverse transform sampling has a larger MAE values.
22. 22
Performance in Increasing Sample Space
• All the hourly climatic conditions are classified into regions
with increasing PDF values in the sample space.
• The performance of the surrogate models is evaluated in
increasing sample space.
280
285
290
295
300
305
2
4
6
8
800
600
400
200
0
10
Wind speed (m/s) Temperature (K)
Solar radiation (W/m2)
100%
…
…
0.8%
0.1%
3720 climatic conditions
23. Root Mean Squared Percentage Error
23
Performance in Increasing Sample Space
The surrogate model for January
Root Mean Squared Error
Increasing percentage of sample space
Increasing percentage of sample space
24. The surrogate model for January
Maximum Percentage Error
24
Performance in Increasing Sample Space
Maximum Absolute Error
Increasing percentage of sample space
Increasing percentage of sample space
25. Root Mean Squared Percentage Error
25
Performance in Increasing Sample Space
The surrogate model for August
Root Mean Squared Error
Increasing percentage of sample space
Increasing percentage of sample space
26. The surrogate model for August
Maximum Percentage Error
26
Performance in Increasing Sample Space
Maximum Absolute Error
Increasing percentage of sample space
Increasing percentage of sample space
27. 27
Conclusions
• Inverse transform sampling is uniquely helpful for surrogate
development where the system inputs follow a certain distribution.
• The CDF of the inputs are made to follow a pseudorandom
sequence (such as Sobol).
• For window performance evaluation, the surrogate models
developed using inverse transform sampling have lower root mean
squared error than those developed using the Sobol sequence.
• For window performance evaluation, the surrogate models
developed using inverse transform sampling have higher maximum
absolute error than those developed using the Sobol sequence.
28. 28
Future Work
• Extend the applicability of inverse transform sampling to
correlated multi-variate/multi-input systems.
29. Acknowledgement
• I would like to acknowledge my research adviser
Prof. Achille Messac, for his immense help and
support in this research.
• Support from the NSF Awards is also
acknowledged.
29
30. 30
Selected References
• Husslage, B. G., Rennen, G., van Dam, E. R., and den Hertog, D., “Space-filling Latin Hypercube Designs for Computer
Experiments,” Optimization and Engineering, Vol. 12, 2011, pp. 611–632.
• Clarkson, K. L. and Shor, P. W., “Applications of Random Sampling in Computational Geometry, II,” Discrete and Computational
Geometry, Vol. 4, 1989, pp. 387–421.
• Goldreich, O., Computational Complexity: A Conceptual Perspective, Cambridge University Press, 1st ed., 2008.
• LaValle, S. M., Planning Algorithms, Cambridge University Press, 2006.
• Niederreiter, H., “Point Sets and Sequences with Small Discrepancy,” Monatshefte fr Mathematik, Vol. 104, December 1987, pp.
273–337.
• van der Corput, J. G., “Verteilungsfunktionen,” Nederl. Akad. Wetensch. Proc., Vol. 38, 1935, pp. 813–821.
• Diaconis, P., “The Distribution of Leading Digits and Uniform Distribution Mod 1,” The Annals of Probability, Vol. 5, No. 1, Feb
1977, pp. 72–81.
• Sobol, I. M., “Uniformly Distributed Sequences with an Additional Uniform Property,” USSR Computational Mathematics and
Mathematical Physics, Vol. 16, 1976, pp. 236–242.
• Faure, H., “Discrpances de suites associes un systme de numration en dimension s,” Acta Arithmetica, Vol. 41, 1982, pp. 337–351.
• Miller, F., Vandome, A., and John, M., Inverse Transform Sampling, VDM Verlag Dr. Mueller e.K., 2010.
• von Neumann, J., “Various Techniques Used in Connection with Random Digits,” Nat. Bureau Stand. Appl. Math. Ser., Vol. 12,
1951, pp. 3638.
• Marshall, A. W., “The Use of Multi-stage Sampling Schemes in Monte Carlo Computations,” H. A. Meyer (ed.), Symposium on
Monte Carlo Methods, edited by N. Y. John Wiley & Sons, Inc., 1956, p. 123140.
• Gilks, W., Gilks, W., Richardson, S., and Spiegelhalter, D., Markov Chain Monte Carlo in Practice, Interdisciplinary Statistics,
Chapman & Hall, 1996.
31. 31
Performance in Increasing Sample Space
• All the hourly climatic conditions are classified into regions
with increasing PDF values in the sample space.
• For each variable, the probability is the integral of the fitted
PDF in the shortest interval.
• The performance of the surrogate models is evaluated in
increasing sample space.
32. 32
Review
• Sampling sequences
• Latin hypercube
• Random
• Pseudorandom
• Low-dispersion
• Low-discrepancy
• Generating sample points from a probability distribution
• Inverse transform sampling
• rejection sampling
• importance sampling
• Markov Chain Monte Carlo
• Metropolis-Hastings Sampling
• Gibbs Sampling
33. Comparisons and Analyses
33
Sobol sequence Inverse transform
• A Voronoi diagram is a special kind of decomposition of a metric space
determined by distances to a specified discrete set of points in the space.
• Each point has a cell that includes the region closer to the point than to
any others.
• The lines are equidistant to the two nearest points.
Editor's Notes
Inverse transform sampling was applied to a unimodal distribution to sample 31 points in previous slides to show how the sampling approach works.
It can also be used to sample more points. The figure on the left shows that, when the number of sample points is increased from 31 to 127, the sample points obtained from this approach still crowd in the region where the probability density is high. Although the number of points in the regions with low probability density also increase, it is increasing at a lower rate than that of points in the regions with high probability density.
Inverse transform sampling can also be used to sample multi-modal distributions. The two figures show the sample points for a bimodal distribution and a quad-modal distribution. The sample points crowd in the regions where the probability density is high.
Higher MAE: It is because in the region with very low distribution density, the sample points are far from each other. The absolute errors at some points in this region are higher for the inverse than the sobol.
August high MPE at 4373%: At some points, their values are very close to zero. These values are used as denominators.
For the sobol sequence, Root Mean Squared Error and Root Mean Squared Percentage Error are similar in different percentages of sample space.
For the inverse transform sampling, Root Mean Squared Error and Root Mean Squared Percentage Error are increasing as the percentage increases. Their overall performance is still better than the sobol sequence.
As the percentage of sample space increases, maximum absolute error and maximum percentage error are both increasing.
When the whole space is reached, the density of sample points obtained by inverse transform sampling in some space becomes lower than those for sobol. The maximum absolute error for inverse becomes higher than that of sobol. However, the maximum percentage error for inverse is still lower than that for sobol
The spike for the root mean squared percentage error is because in the 12.5% region but not in the 10.0% region, the actual heat flux through the window is very close to zero. It is used as the denominator for percentage error evaluation.
The spike for the maximum percentage error is because in the 12.5% region but not in the 10.0% region, the actual heat flux through the window is very close to zero. It is used as the denominator for percentage error evaluation.