The document summarizes the Monte Carlo method for simulating complex physical systems. It describes how Monte Carlo simulations can provide approximate solutions to problems that are difficult to solve analytically. Such simulations are important for understanding systems with many interacting particles, like spin glasses, and for problems in fields like condensed matter physics, particle physics, and quantum gravity. Markov chain Monte Carlo methods are surveyed as a way to realize the importance sampling idea in computer simulations of complex systems.
SEQUENTIAL CLUSTERING-BASED EVENT DETECTION FOR NONINTRUSIVE LOAD MONITORINGcsandit
The problem of change-point detection has been well studied and adopted in many signal processing applications. In such applications, the informative segments of the signal are the
stationary ones before and after the change-point. However, for some novel signal processing and machine learning applications such as Non-Intrusive Load Monitoring (NILM), the information contained in the non-stationary transient intervals is of equal or even more importance to the recognition process. In this paper, we introduce a novel clustering-based sequential detection of abrupt changes in an aggregate electricity consumption profile with
accurate decomposition of the input signal into stationary and non-stationary segments. We also introduce various event models in the context of clustering analysis. The proposed algorithm is applied to building-level energy profiles with promising results for the residential BLUED power dataset.
In this paper, block-oriented systems with linear parts based on Laguerre functions is used to
approximation of a cone crusher dynamics. Adaptive recursive least squares algorithm is used to
identification of Laguerre model. Various structures of Hammerstein, Wiener, Hammerstein-Wiener models
are tested and the MATLAB simulation results are compared. The mean square error is used for models
validation.It has been found that Hammerstein-Wiener with orthonormal basis functions improves the
quality of approximation plant dynamics. The mean square error for this model is 11% on average
throughout the considered range of the external disturbances amplitude. The analysis also showed that
Wiener model cannot provide sufficient approximation accuracy of the cone crusher dynamics. During the
process it is unstable due to the high sensitivity to disturbances on the output.The Hammerstein-Wiener
model will be used to the design nonlinear model predictive control application.
SEQUENTIAL CLUSTERING-BASED EVENT DETECTION FOR NONINTRUSIVE LOAD MONITORINGcsandit
The problem of change-point detection has been well studied and adopted in many signal processing applications. In such applications, the informative segments of the signal are the
stationary ones before and after the change-point. However, for some novel signal processing and machine learning applications such as Non-Intrusive Load Monitoring (NILM), the information contained in the non-stationary transient intervals is of equal or even more importance to the recognition process. In this paper, we introduce a novel clustering-based sequential detection of abrupt changes in an aggregate electricity consumption profile with
accurate decomposition of the input signal into stationary and non-stationary segments. We also introduce various event models in the context of clustering analysis. The proposed algorithm is applied to building-level energy profiles with promising results for the residential BLUED power dataset.
In this paper, block-oriented systems with linear parts based on Laguerre functions is used to
approximation of a cone crusher dynamics. Adaptive recursive least squares algorithm is used to
identification of Laguerre model. Various structures of Hammerstein, Wiener, Hammerstein-Wiener models
are tested and the MATLAB simulation results are compared. The mean square error is used for models
validation.It has been found that Hammerstein-Wiener with orthonormal basis functions improves the
quality of approximation plant dynamics. The mean square error for this model is 11% on average
throughout the considered range of the external disturbances amplitude. The analysis also showed that
Wiener model cannot provide sufficient approximation accuracy of the cone crusher dynamics. During the
process it is unstable due to the high sensitivity to disturbances on the output.The Hammerstein-Wiener
model will be used to the design nonlinear model predictive control application.
Em computação quântica, um algoritmo quântico é um algoritmo que funciona em um modelo realístico de computação quântica. O modelo mais utilizado é o modelo do circuito de computação quântica.
A COMPREHENSIVE ANALYSIS OF QUANTUM CLUSTERING : FINDING ALL THE POTENTIAL MI...IJDKP
Quantum clustering (QC), is a data clustering algorithm based on quantum mechanics which is
accomplished by substituting each point in a given dataset with a Gaussian. The width of the Gaussian is a
σ value, a hyper-parameter which can be manually defined and manipulated to suit the application.
Numerical methods are used to find all the minima of the quantum potential as they correspond to cluster
centers. Herein, we investigate the mathematical task of expressing and finding all the roots of the
exponential polynomial corresponding to the minima of a two-dimensional quantum potential. This is an
outstanding task because normally such expressions are impossible to solve analytically. However, we
prove that if the points are all included in a square region of size σ, there is only one minimum. This bound
is not only useful in the number of solutions to look for, by numerical means, it allows to to propose a new
numerical approach “per block”. This technique decreases the number of particles by approximating some
groups of particles to weighted particles. These findings are not only useful to the quantum clustering
problem but also for the exponential polynomials encountered in quantum chemistry, Solid-state Physics
and other applications.
FellowBuddy.com is an innovative platform that brings students together to share notes, exam papers, study guides, project reports and presentation for upcoming exams.
We connect Students who have an understanding of course material with Students who need help.
Benefits:-
# Students can catch up on notes they missed because of an absence.
# Underachievers can find peer developed notes that break down lecture and study material in a way that they can understand
# Students can earn better grades, save time and study effectively
Our Vision & Mission – Simplifying Students Life
Our Belief – “The great breakthrough in your life comes when you realize it, that you can learn anything you need to learn; to accomplish any goal that you have set for yourself. This means there are no limits on what you can be, have or do.”
Like Us - https://www.facebook.com/FellowBuddycom
A New Approach to Linear Estimation Problem in Multiuser Massive MIMO SystemsRadita Apriana
A novel approach for solving linear estimation problem in multi-user massive MIMO systems is
proposed. In this approach, the difficulty of matrix inversion is attributed to the incomplete definition of the
dot product. The general definition of dot product implies that the columns of channel matrix are always
orthogonal whereas, in practice, they may be not. If the latter information can be incorporated into dot
product, then the unknowns can be directly computed from projections without inverting the channel
matrix. By doing so, the proposed method is able to achieve an exact solution with a 25% reduction in
computational complexity as compared to the QR method. Proposed method is stable, offers an extra
flexibility of computing any single unknown, and can be implemented in just twelve lines of code.
Extended pso algorithm for improvement problems k means clustering algorithmIJMIT JOURNAL
The clustering is a without monitoring process and one of the most common data mining techniques. The
purpose of clustering is grouping similar data together in a group, so were most similar to each other in a
cluster and the difference with most other instances in the cluster are. In this paper we focus on clustering
partition k-means, due to ease of implementation and high-speed performance of large data sets, After 30
year it is still very popular among the developed clustering algorithm and then for improvement problem of
placing of k-means algorithm in local optimal, we pose extended PSO algorithm, that its name is ECPSO.
Our new algorithm is able to be cause of exit from local optimal and with high percent produce the
problem’s optimal answer. The probe of results show that mooted algorithm have better performance
regards as other clustering algorithms specially in two index, the carefulness of clustering and the quality
of clustering.
Power system static state estimation using Kalman filter algorithmPower System Operation
State estimation of power system is an important tool for operation, analysis and forecasting of electric
power system. In this paper, a Kalman filter algorithm is presented for static estimation of power system state
variables. IEEE 14 bus system is employed to check the accuracy of this method. Newton Raphson load flow study
is first carried out on our test system and a set of data from the output of load flow program is taken as measurement
input. Measurement inputs are simulated by adding Gaussian noise of zero mean. The results of Kalman estimation
are compared with traditional Weight Least Square (WLS) method and it is observed that Kalman filter algorithm is
numerically more efficient than traditional WLS method. Estimation accuracy is also tested for presence of parametric
error in the system. In addition, numerical stability of Kalman filter algorithm is tested by considering inclusion of
zero mean errors in the initial estimates.
Em computação quântica, um algoritmo quântico é um algoritmo que funciona em um modelo realístico de computação quântica. O modelo mais utilizado é o modelo do circuito de computação quântica.
A COMPREHENSIVE ANALYSIS OF QUANTUM CLUSTERING : FINDING ALL THE POTENTIAL MI...IJDKP
Quantum clustering (QC), is a data clustering algorithm based on quantum mechanics which is
accomplished by substituting each point in a given dataset with a Gaussian. The width of the Gaussian is a
σ value, a hyper-parameter which can be manually defined and manipulated to suit the application.
Numerical methods are used to find all the minima of the quantum potential as they correspond to cluster
centers. Herein, we investigate the mathematical task of expressing and finding all the roots of the
exponential polynomial corresponding to the minima of a two-dimensional quantum potential. This is an
outstanding task because normally such expressions are impossible to solve analytically. However, we
prove that if the points are all included in a square region of size σ, there is only one minimum. This bound
is not only useful in the number of solutions to look for, by numerical means, it allows to to propose a new
numerical approach “per block”. This technique decreases the number of particles by approximating some
groups of particles to weighted particles. These findings are not only useful to the quantum clustering
problem but also for the exponential polynomials encountered in quantum chemistry, Solid-state Physics
and other applications.
FellowBuddy.com is an innovative platform that brings students together to share notes, exam papers, study guides, project reports and presentation for upcoming exams.
We connect Students who have an understanding of course material with Students who need help.
Benefits:-
# Students can catch up on notes they missed because of an absence.
# Underachievers can find peer developed notes that break down lecture and study material in a way that they can understand
# Students can earn better grades, save time and study effectively
Our Vision & Mission – Simplifying Students Life
Our Belief – “The great breakthrough in your life comes when you realize it, that you can learn anything you need to learn; to accomplish any goal that you have set for yourself. This means there are no limits on what you can be, have or do.”
Like Us - https://www.facebook.com/FellowBuddycom
A New Approach to Linear Estimation Problem in Multiuser Massive MIMO SystemsRadita Apriana
A novel approach for solving linear estimation problem in multi-user massive MIMO systems is
proposed. In this approach, the difficulty of matrix inversion is attributed to the incomplete definition of the
dot product. The general definition of dot product implies that the columns of channel matrix are always
orthogonal whereas, in practice, they may be not. If the latter information can be incorporated into dot
product, then the unknowns can be directly computed from projections without inverting the channel
matrix. By doing so, the proposed method is able to achieve an exact solution with a 25% reduction in
computational complexity as compared to the QR method. Proposed method is stable, offers an extra
flexibility of computing any single unknown, and can be implemented in just twelve lines of code.
Extended pso algorithm for improvement problems k means clustering algorithmIJMIT JOURNAL
The clustering is a without monitoring process and one of the most common data mining techniques. The
purpose of clustering is grouping similar data together in a group, so were most similar to each other in a
cluster and the difference with most other instances in the cluster are. In this paper we focus on clustering
partition k-means, due to ease of implementation and high-speed performance of large data sets, After 30
year it is still very popular among the developed clustering algorithm and then for improvement problem of
placing of k-means algorithm in local optimal, we pose extended PSO algorithm, that its name is ECPSO.
Our new algorithm is able to be cause of exit from local optimal and with high percent produce the
problem’s optimal answer. The probe of results show that mooted algorithm have better performance
regards as other clustering algorithms specially in two index, the carefulness of clustering and the quality
of clustering.
Power system static state estimation using Kalman filter algorithmPower System Operation
State estimation of power system is an important tool for operation, analysis and forecasting of electric
power system. In this paper, a Kalman filter algorithm is presented for static estimation of power system state
variables. IEEE 14 bus system is employed to check the accuracy of this method. Newton Raphson load flow study
is first carried out on our test system and a set of data from the output of load flow program is taken as measurement
input. Measurement inputs are simulated by adding Gaussian noise of zero mean. The results of Kalman estimation
are compared with traditional Weight Least Square (WLS) method and it is observed that Kalman filter algorithm is
numerically more efficient than traditional WLS method. Estimation accuracy is also tested for presence of parametric
error in the system. In addition, numerical stability of Kalman filter algorithm is tested by considering inclusion of
zero mean errors in the initial estimates.
Power system static state estimation using Kalman filter algorithm
JOURNALnew
1. ST325
JOURNAL OF THE AMERICAN STATISTICAL
ASSOCIATION
NUMBER 247 SEPTEMBER 1949 VOLUME 44
THE MONTE CARLO METHOD
NICHOLAS METROPOLIS AND S. ULAM
LOS ALAMOS LABORATORY
The Monte Carlo Method..
3. Introduction
Classical statistical physics is a well understood
subject which poses, however, many difficult problems
when a concrete solution for interacting systems is
sought. In almost all non-trivial applications, analytical
methods can only provide approximate answers.
Numerical computer simulations are, therefore, an
important complementary method on our way to a deeper
understanding of complex physical systems such as
(spin) glasses and disordered magnets or of
biologically motivated problems such as protein
folding
4. Cont…
Quantum statistical problems in condensed matter or
the broad field of elementary particle physics and
quantum gravity are other major applications which,
after suitable mappings, also rely on classical simulation
techniques. we shall confine ourselves to a survey of
computer simulations based on Markov chain Monte
Carlo methods which realize the importance sampling
idea.
5. Method and Approach
We shall present here the motivation and a
general description of a method dealing with a
class of problems in mathematical physics.
The method is, Essentially, a statistical approach to
the study of differential equations ,or more
generally, of integro-differential equations that occur
in various branches of the natural sciences.
6. ALREADY in the nineteenth century a sharp
distinction began to appear between two different
mathematical methods of treating physical phenomena.
Problems involving only a few particles were studied in
classical mechanics, through the study of systems of
ordinary differential equations.
For the description of systems with very many particles,
an entirely different technique was used, namely, the
method of statistical mechanics. In this latter approach,
one does not concent rate on the individual particles but
studies the properties of sets of particles
7. PHYSICAL SCALES FOR DILUTE GASES
Collision
Collision
Molecular
Diameter
System Size
Gradient Scale
Quantum scale Kinetic scale Hydrodynamic scale
T/T
DSMC is the dominant
numerical algorithm at the
kinetic scale
DSMC applications are expanding to multi-scale problems
8. Divide the system into cells and generate particles in each cell
according to desired density, fluid velocity, and temperature.
From density, determine number of particles in cell volume, N,
either rounding to nearest integer or from Poisson distribution.
Assign each particle a position in the cell, either uniformly or
from the linear distribution using the density gradient.
From fluid velocity and temperature, assign each particle a
velocity from Maxwell-Boltzmann distribution P(v; {u,T}) or
from the Chapman-Enskog distribution .}),,,{;( TTP uuv
9. The Hamiltonian Function that is commonly used
representing the energy of the model when using Monte
Carlo Methods
we would see the great importance of Monte Carlo
methods applied in Physics. Furthermore,
Monte Carlo methods also play significant role in
quantum dynamics, physical chemistry, and related
applied fields.
In quantum dynamics, Quantum Monte Carlo methods
solve the multi-body problems for quantum system. In
experimental particle physics.
Monte Carlo Methods are use for designing detectors,
understanding their behavior and comparing experimental
data to theory.
11. Particle Markov chain Monte Carlo
methods
Markov chain Monte Carlo and sequential Monte Carlo
methods have emerged as the two main tools to sample from
high dimensional probability distributions. Although
asymptotic convergence of Markov chain Monte Carlo
algorithms is ensured under weak assumptions, the
performance of these algorithms is unreliable when the
proposal distributions that are used to explore the space are
poorly chosen and/or if highly correlated variables are
updated independently.
12. CHARACTERISTICS OF MARKOV CHAIN
Irreducible Chain
Aperiodic Chain
Stationary Distribution
Markov Chain can gradually forget its initial state
eventually converge to a unique stationary distribution
invariant distribution
Ergodic average
n
mt
tXf
mn
f
1
)(
1
13. TARGET DISTRIBUTION
Target Distribution Function
(x)=ce-h(x)
h(x)
in physics, the potential function
other system, the score function
c
normalization constant
make sure the integral of (x) is 1
Presumably, all pdfs can be written in this form
14. Each technique has it advantages and disadvantages ,Broadly, for
complex systems that may be subject to change later, the Monte-
Carlo method is preferred because of its flexibility. For simpler
systems, or studies to get a ‘feel’ for a problem, analytical methods
may suffice
The decision as to whether the modeller should use analytical (e.g.
deterministic equations) or simulation (i.e. Monte-Carlo) methods
may be influenced by the following factors:
Complexity
Scope
Accuracy.
Future development
Application
15. 15
SOME ADVANTAGES OF MC
Often the only type of model possible for complex systems
Analytical models frequently infeasible
Process of building simulation can clarify understanding of
real system
Sometimes more useful than actual application of final
simulation
Allows for sensitivity analysis and optimization of real system
without need to operate real system
Can maintain better control over experimental conditions than
real system
Time compression/expansion: Can evaluate system on slower
or faster time scale than real system
16. 16
SOME DISADVANTAGES OF MC
May be very expensive and time consuming to build
simulation
Easy to misuse simulation by “stretching” it beyond the
limits of credibility
Problem especially apparent when using commercial
simulation packages due to ease of use and lack of familiarity
with underlying assumptions and restrictions
Slick graphics, animation, tables, etc. may tempt user to
assign unwarranted credibility to output
Monte Carlo simulation usually requires several (perhaps
many) runs at given input values
Contrast: analytical solution provides exact values
17. Accuracy of Result..
The Monte-Carlo simulation method is a type of
sampling procedure, thus any output is not exact but a
statistical estimate whose accuracy depends on the
number of missions or failures generated. For example if
mission parameters are of prime important (e.g.
probability of mission survival failure free) then the
number of missions to be simulated is the important
parameter. The number of system failures generated is
not necessarily important, e.g. if in 1000 mission
simulated only 5 system failures are generated, mission
reliability is none the less reasonably well established.
However, if MTBF(mean time between failures)
estimates are the prime consideration then a sufficient
number of system failures must be simulated to yield the
desired accuracy.