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Jet engine remaining useful life prediction
- 1. Saudi Aramco: Company General Use Jet Engine Remaining Useful Life (RUL) Prediction Ali S. Alhamaly IT Engineering Dept. 10/31/2019
- 2. Saudi Aramco: Company General Use 2 The talk focuses on a data driven model to estimate the remaining time for an engine in operation Problem definition, objective, and dataset From raw data to health index (Training) Using the model to estimate RUL
- 3. 33 Problem definition objective and dataset 1
- 4. Saudi Aramco: Company General Use 4 The problem is to predict RUL based on measurements available from jet engines TemperaturePressureSpeedFlowRate Measurements from engine components
- 5. Saudi Aramco: Company General Use 5 The objective to characterize the engine health based on raw measurements TemperaturePressureSpeedFlowRate Measurements from engine components Characterized progression of engine health Final results : “You have 35 cycles before your engine is out of service”
- 6. Saudi Aramco: Company General Use 6 Dataset is composed of a simulated run-to- failure from a fleet of similar engines Fleet of similar engine Run-to-failure simulated data Using C-MAPSS – 21 sensors Saxena, Abhinav & Goebel, Kai & Simon, Don & Eklund, Neil. (2008). Damage propagation modeling for aircraft engine run-to-failure simulation. International Conference on Prognostics and Health Management. 10.1109/PHM.2008.4711414. Trajectories of damage propagation from a healthy state to failure
- 7. 77 From raw data to health index 2
- 8. Saudi Aramco: Company General Use 8 The approach is to explore the data, select sensors, and then fuse them to make a health index (HI) Explore sensors Select sensors Fuse sensors and health index
- 9. Saudi Aramco: Company General Use 9 the distribution of almost all sensors is e skewed Gaussian
- 10. Saudi Aramco: Company General Use 10 Raw sensor data for all engines End of lifeStart operation Each color represents different engine data There is a general trend toward end of life Some sensors lacks consistent trend toward end of life
- 11. Saudi Aramco: Company General Use 11 Sensors are selected based on magnitude of linear trend Number of sensors used in modeling are reduced to 6 PCA is done to further reduce the dimensionality to 3 only Sensors that do not change with time were removed
- 12. Saudi Aramco: Company General Use 12 Sensors need to be fused into one-dimensional health index (HI) 𝑯𝑰 𝒕 = 𝒊=𝟏 𝑵 𝜽𝒊 𝒙𝒊 𝒕 + 𝜽 𝟎 Healthy =1 End-life=0 Simple linear regression is used to find 𝜽𝒊
- 13. Saudi Aramco: Company General Use 13 Distribution of RUL is used to determine total life of a “100% healthy engine” Not so many engines have total life longer than 300 cycles Cycles above which an engine is 100% healthy
- 14. Saudi Aramco: Company General Use 14 Fused sensor (HI) as function of time after obtaining regression coefficients Sensors are transformed to HI (raw) and then exponential fitting is applied for HI (raw) for each engine.
- 15. Saudi Aramco: Company General Use 15 Raw HI for all engines The plot signifies the similarities and variations between engines
- 16. 1616 Using HI curves to estimate RUL: A similarity approach 3
- 17. Saudi Aramco: Company General Use 17 Predict RUL by comparing the total life of most similar “training” engine to the new engine New engine sensor data Transform and fuse to get new HI Compare new HI to the model HI Similarity score Estimate RUL
- 18. Saudi Aramco: Company General Use 18 RUL of a new engine is based on HI model that has the most similar degradation pattern T. Wang, Jianbo Yu, D. Siegel and J. Lee, "A similarity-based prognostics approach for Remaining Useful Life estimation of engineered systems," 2008 International Conference on Prognostics and Health Management, Denver, CO, 2008, pp. 1-6.
- 19. Saudi Aramco: Company General Use 19 Finding similarity score by comparing new data to each training engine HI curve 𝑺𝑺𝑫 = 𝒋=𝟏 𝑵 𝒏𝒆𝒘 𝑯𝑰 𝒋 𝒏𝒆𝒘 − 𝑯𝑰 𝒋 + 𝒕 𝟎 𝒎𝒐𝒅𝒆𝒍 𝟐 𝒕 𝟎 ∈ 𝟎, 𝑵 𝒅𝒊𝒇𝒇 , 𝑵 𝒅𝒊𝒇𝒇 = 𝑵 𝒎𝒐𝒅𝒆𝒍 − 𝑵 𝒏𝒆𝒘 Find 𝒕 𝟎 which minimizes 𝑺𝑺𝑫 for each engine in the model 𝒕 𝟎 ∗ Repeat process for each engine in training data 𝑹𝑼𝑳 𝒎 = 𝑵 𝒅𝒊𝒇𝒇 𝒎 − 𝒕 𝟎 ∗ 𝒎 # data points in new engine # data points in training engine 𝒎 ∈ 𝟏, 𝑴 , 𝑴 𝒕𝒐𝒕𝒂𝒍 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒕𝒓𝒂𝒊𝒏𝒊𝒏𝒈 𝒆𝒏𝒈𝒊𝒏𝒆𝒔
- 20. Saudi Aramco: Company General Use 20 Final RUL from several RUL candidate 𝑹𝑼𝑳 = 𝟏 𝑾 𝒎=𝟏 𝑴 𝒘 𝒎 𝑹𝑼𝑳 𝒎 𝑾 = 𝒎=𝟏 𝑴 𝒘 𝒎 • Median of all 𝑹𝑼𝑳 𝒎 • weighted mean based on SSD • mean of max and min 𝑹𝑼𝑳 𝒎 • Mean of all 𝑹𝑼𝑳 𝒎
- 21. Saudi Aramco: Company General Use 21 Accuracy of the model is measured using asymmetric exponential penalty score 𝒆𝒓𝒓𝒐𝒓 = 𝑹𝑼𝑳 − 𝑹𝑼𝑳
- 22. Saudi Aramco: Company General Use 22 Accuracy of the model is measured using asymmetric exponential penalty score • M1: Median • M2: SSD weighted mean • M3: mean of max and min • M4: Mean
- 23. Saudi Aramco: Company General Use 23 TemperaturePressureSpeedFlowRate 𝑯𝑰 𝒕 = 𝒊=𝟏 𝑵 𝜽𝒊 𝒙𝒊 𝒕 + 𝜽 𝟎 In conclusion, similarity based method is a simple and effective in estimate RUL
Editor's Notes
- Data simulated using C-MAPSS (Commercial Modular Aero-Propulsion System Simulation) The simulated data generated were used as challenge data for the 1st Prognostics and Health Management (PHM) data competition at PHM’08.
- from the above distribution plot, we can see that some sensors do not change and hence they can be removed from the analysis also the main takeaways: 1. the distribution of almost all variables is single skewed gaussian 2. op_cond_2 and sn_17 seem to be discrete variables and not continuous ( maybe these need to be deleted to keep only continuously varying variables for modeling) 3. the observations above holds when plotting all engines and when the plot is made for a specific engine. (means all engine are very similar in their output response)
- From the time series plot of all engine, we can find the below takeaways columns [op_cond_1, op_cond_2] do not have an apparent trend toward the end life of the engine. they are just random noise. so with great confidence, I can say that these two columns cannot help a predictive model that is based on the trend of the series to discover relevant information regarding estimating the RUL columns [s n_9, sn_14] indicates that the trend depends on the specific engine. some engines at the end of life tend to increase in these two columns while others tend to decrease. what is common about these two sensors is that the magnitude at the end life gets amplified. it is good to see that all other columns show an apparent trend as the fault propagate throughout the engine cycles and cause them to fail. [ this helps the model that will try to use the data to predict RUL :)
- based on the analysis of linear trend, the top 6 sensors are chosen based on the magnitude of their linear trend, i.e. the magnitude of their linear regression slope. it looks that based on these 6 sensors, taking 3 first principle components s captures about 90% of the data variability. hence the further reduction in dimensionality comes at a low loss of information. the sensors that do not change with time ( do not have variation with engine operational cycles) are dropped since they do not offer any information toward prediction the end of life the sensors that do not have apparent trend (looks like noise only, or do not have a trend toward the end of life) are dropped as well. this contains the sensors that behave differently for different engines ( since these will confuse the learning algorithm and can cause large testing errors since their behavior are not universal concerning all engines) based on linear regression of the remain sensor data with RUL, the highest 6 sensors in terms of the absolute values of the slopes are kept only. these sensors change predictably at the end of life for the engines. further, reduce the dimensionality by taking the first 3 principal components for the data the remaining 3 components of the data will be fused to make a Health Index (HI) function with RUL for each engine
- Based on the predictive health degradation curve (hp) from an offline system unit, an optimum fitting is conducted to determine a time-scale initial health condition (T0) that minimizes the sum of squared differences SSD between the online and offline health index