Report

A Sensor Fault Diagnosis Scheme for a DC/DC Converter used in Hybrid Electric Vehicles Hiba Al-SHEIKH Ghaleb HOBLOS Nazih MOUBAYED 2 Overview Examined power converter system Hardware prototype Converter Modelling Proposed residual-based fault diagnosis scheme Bank of extended Kalman filters Generalized likelihood ratio test Tuning using receiver operating characteristic curve Conclusion and future perspectives 3 Recent advances in power electronics encouraged the Power converters are intensively used in HEVs development of new initiatives for Hybrid Electric Vehicles • convert power at different levels (HEVs) with advanced multi-level power electronic systems. • drive various load • electric drives 4 Intensive use of power converters in modern hybrid vehicles Need for efficient methods of condition monitoring and fault diagnosis Reliability of the automotive electrical power system 5 Common Electrical Faults in Electric Drive Systems Machine AC Side • high power • relatively low voltage Sensors Power Converters Controller Connectors/ DC Bus high current increase thermal and electric stresses on the converter components and monitoring sensors 6 Common Electrical Faults in Electric Drive Systems Machine AC Side Sensors • AC current sensor • DC bus voltage sensor Power Converters Controller Connectors/ DC Bus Sensor faults in a DC/DC power converter system used in HEV 7 Fault Diagnosis Techniques for Power Converters Knowledge-based methods Fault diagnosis methods Analytical model-based methods Observer-based Signal-based methods For HEV applications where converters operate under variable load conditions, model-based diagnosis is of particular interest. 7 8 Examined Power Converter System 9 DC Main System DC Distribution AC Distribution Automotive Electrical System 10 Power Converters DC/DC Choppers DC/AC Inverters AC/DC Rectifiers Automotive Electrical System 11 12 13 Examined Power Converter System Battery UC Energy Storage System Multi-port DC bus Inverter DC/DC Converter AC Drive Parallel DC-linked Multi-input DC/DC Converter consisting of two bidirectional half-bridge cells PM 14 Bidirectional DC/DC Converter Topologies Isolated topologies boost-half bridge half-bridge full-bridge Non-isolated topologies SEPIC cuk buck-boost 15 Examined Power Converter System Converter Parameters Parameter Symbol Value Design Requirements Input Capacitance Input Capacitor ESR Inductance Inductor ESR Output Capacitance Output Capacitor ESR Transistor ON resistance Cin RCin L RL Co RCo RON 80µF 100mΩ 146µH 5mΩ 5mF 80mΩ 1mΩ Source voltage DC-link voltage Rated Power Switching frequency Source voltage ripple DC-link voltage ripple Inductor current ripple 200V 300V 30kW 15kHz 2% p/p 4.5% p/p ±10% 16 Examined Power Converter System s (duty cycle) State variables , , 17 0.02 0.04 0.06 0.08 0.1 in 0 1 194 600 y =i Cin 196 x =v 198 1 200 200 0 0.02 0.04 0.06 0.08 0.1 0 0.02 0.04 0.06 0.08 0.1 o 350 0 0.02 0.04 0.06 0.08 0.1 300 250 2 0 200 0 400 y =v 2 x =i L 600 400 400 Co 3 150 300 200 x =v 200 100 time (sec) Observed variables during healthy boost operation 0 0.02 0.04 0.06 0.08 time (sec) State variables during healthy boost operation 0.1 18 Hardware Prototype of Converter System 19 Hardware Prototype Experimental test bench Hardware prototype of bidirectional DC/DC converter 20 Hardware Prototype Measurement of sensor 1 (measuring load voltage ) Measurement of sensor 2 (measuring source current ) 21 Hardware Prototype Sensor 2 Sensor 1 22 Modelling of Power Converter 23 Converter State-Space Model The examined converter is a nonlinear and time-varying system Battery UC Multi-input DC bus Inverter DC/DC Converter Boost operation PM 24 Converter State-Space Model The examined converter is a nonlinear and time-varying system Battery UC Multi-input DC bus Inverter DC/DC Converter Buck operation PM 25 Converter State-Space Model The examined converter is a nonlinear and time-varying system The converter state-space model is obtained in three steps: 1. 2. 3. Piece-wise linear state-space model Continuous-time nonlinear state-space model Discrete-time nonlinear state-space model 26 Converter State-Space Model 1. During each switching configuration, the converter is linear and possesses a piece-wise switched linear state-space model Boost mode Buck mode Switching configuration 1 (T1 ON; D2 OFF) Switching configuration 1 (T2 ON; D1 OFF) Switching configuration 2 (T1 OFF; D2 ON) Switching configuration 2 (T2 OFF; D1 ON) 27 Converter State-Space Model 1. During each switching configuration, the converter is linear and possesses a piece-wise switched linear state-space model = + = + Operation Mode j=1 (Boost) j=2 (Buck) Switching State i=1 T1 D1 T2 D2 ON OFF OFF OFF i=2 i=1 i=2 OFF OFF OFF OFF OFF ON OFF ON OFF ON OFF OFF 28 Converter State-Space Model 2. Averaged continuous-time model Operation Mode j=1 (Boost) Switching State i=1 T1 D1 T2 D2 ON OFF OFF OFF i=2 i=1 i=2 OFF OFF OFF OFF OFF ON OFF ON OFF ON OFF OFF = + where = + j=2 (Buck) = + 1 − = + 1 − = + 1 − = + 1 − averaged using as control variable 29 Converter State-Space Model 2. Averaged continuous-time model = + = + where = + 1 − = + 1 − = + 1 − = + 1 − The continuous-time model is nonlinear The duty cycle is a function of the state variables, = () is obtained from the converter dynamics during steady state 30 Converter State-Space Model . 1 Cin RiCin Rin A av x LRiCin 0 1 C R in iCin RCin B av x LR iCin 0 Rin 0 Cin RiCin RL RiCin f x RON RiCin 1 f x RCo RiCin 1 f x LRiCin L 1 f x 0 Co Rin RCin 0 1 f x RCo L 1 Co 1 Cav x RiCin 0 1 RCin 0 D av RiCin RiCin 1 f xRCo 1 0 RCo 0 31 Converter State-Space Model 3. The continuous-time model is discretized using first order hold with sampling period = 1 seconds. Including process noise and measurement noise, the discrete-time statespace model becomes + 1 = + + = + + and are white Gaussian, zero-mean, independent random processes with constant auto-covariance matrices Q and R. 32 Proposed Fault Diagnosis Algorithm 33 Fault Diagnosis of Converter Sensor Faults Sensor 2 Sensor 1 Model-Based Residual Approach 34 Fault Diagnosis of Converter Sensor Faults Input variables Power Converter System Residual Generation Residuals Residual Evaluation Fault/No fault Output variables 35 Residual Generation using Bank of Extended Kalman Filters 36 The Extended Kalman Filter (EKF) Converter input signals Converter statespace model + + Sensor measured signals + Estimates of the measured signals - Residual signals “Innovations” 37 The Extended Kalman Filter (EKF) Recursive application of prediction and correction cycles At the end of sampling period, the nonlinearity of the converter system is approximated by a linear model around the last predicted and corrected estimate 38 The EKF Algorithm Initialization = 0, 0|0 = () and P 0|0 = P(0) Prediction Cycle ( + 1|) = x(|) x(|) + x(|) () ( + 1|k) = ()(|) (k) + + 1| = x + 1 ( + 1|) + () where () is the jacobian matrix of x(|) x(|) Correction Cycle A new measurement is obtained + 1 ( + 1| + 1) = (k + 1|) + + 1 ( + 1) + 1| + 1 = I − + 1 + 1 + 1| where ( + 1) = ( + 1|) ( + 1) + 1 k + 1 (k + 1) + + 1 = + 1 − + 1| () is the jacobian matrix of x(|) x(|) −1 increments Prediction and correction repeat with corrected estimates used to predict new estimates 39 Residuals Generated by the Bank of EKF Observer 1 Observer 2 300 Residual r2 ey1 Residual r1 ey1 400 300 200 Instant of fault 100 200 100 0 0 0 0.01 0.02 0.03 time (s) 0.04 0.05 -100 100 50 0 -50 0 0.01 0.02 0.03 time (s) 0.04 0.05 0 0.01 0.02 0.03 time (s) 0.04 0.05 4 Residual r2 ey2 Residual r1 ey2 150 0 0.01 0.02 0.03 time (s) 0.04 0.05 2 0 -2 -4 Standardized residuals with fault on sensor 1 occurring at 0.03s 40 Residuals Generated by the Bank of EKF Observer 1 Observer 2 2 0 -2 -4 2000 1500 1000 500 0 0 0.01 0.02 0.03 time (s) 0.04 0.05 0 2500 2500 2000 2000 Residual r2 ey2 Residual r1 ey2 2500 Residual r2 ey1 Residual r1 ey1 4 1500 1000 500 0 0.01 0.02 0.03 time (s) 0.04 0.05 0.04 0.05 1500 1000 Instant of fault 500 0 0 0.01 0.02 0.03 time (s) 0.04 0.05 0 0.01 0.02 0.03 time (s) Standardized residuals with fault on sensor 2 occurring at 0.03s 41 Residuals Generated by the Bank of EKF Advantage of Kalman Filtering independent residuals with white Gaussian, zero-mean and unit-covariance characteristics in case of faultless operation with altered statistical characteristics in case of sensor faults Statistical change detection approaches 42 Residual Evaluation using Generalized Likelihood Ratio Test 43 Residuals Evaluation Approaches Statistical data processing Correlation Pattern recognition Fuzzy logic Fixed threshold Adaptive threshold Likelihood ratio tests Generalized Likelihood Ratio (GLR) Test Stochastic envirmonent 44 Residuals Evaluation using GLR Test Statistical Hypothesis Testing Problem Ho and H1 sensor is faultless residuals are Gaussain with 0 = 0 and 02 = 1 sensor is faulty 0 is altered into 1 and 02 into 12 45 Residuals Evaluation using GLR Test Statistical Hypothesis Testing Problem Ho and H1 Maximizing the likelihhod ratio L e yi p e yi ; ˆ 1 , H 1 ln p e yi ; ˆ o , H o 1 is the Maximum Likelihood Estimate (MLE) of 1 0 is the MLE of 0 46 GLR Algorithm At every time step t Apply the GLR statistic on the recent W residual values Evaluate () for all 1 ≤ ≤ using k x (k ) GLRt k t 2 2 Yes Is residual variance known? No Evaluate () for all 1 ≤ ≤ using 2 k xt (k ) GLRt k ln 1 2 t (k ) Generate a detection function = () for each residual Decide H1 (fault) Yes Is () > ? No Decide H0 (No fault) 47 Detection Function Generated by GLR Test Residual r1 ey1 Residual r2 ey2 5 300 200 instant of fault 0 100 0 0 0.01 0.02 0.03 0.04 0.05 -5 0 0.01 GLRt for r1 ey1 0.02 0.03 0.04 0.05 GLRt for r2 ey2 30 20 unknown 20 10 10 0 unknown 0 0.01 0.02 0.03 0.04 0.05 0 0 0.01 GLRt for r1 ey1 0.02 0.03 0.04 0.05 GLRt for r2 ey2 30 20 known 20 10 10 0 known 0 0.01 0.02 0.03 time (s) 0.04 0.05 0 0 0.01 0.02 0.03 time (s) Detection function with fault on sensor 1 0.04 0.05 48 Detection Function Generated by GLR Test Residual r1 ey1 Residual r2 ey2 5 2000 0 1000 instant of fault 0 -5 0 0.01 0.02 0.03 0.04 0.05 0 0.01 GLRt for r1 ey1 0.03 0.04 0.05 0.02 0.03 0.04 GLRt for r2 ey2 0.05 GLRt for r2 ey2 4 40 unknown unknown 2 0 0.02 20 0 0.01 0.02 0.03 0.04 GLRt for r1 ey1 0.05 3 0 0 0.01 40 known 2 known 20 1 0 0 0.01 0.02 0.03 time (s) 0.04 0.05 0 0 0.01 0.02 0.03 time (s) Detection function with fault on sensor 2 0.04 0.05 49 Tuning using Receiver Operating Characteristic Curve 50 ROC Analysis 1) residualAn evaluation tool to measure the performance of(1,the 1 based GLR test. true positives rate (fpr) + optimal as increase (0, 0) 0 false positives rate (tpr) 1 51 ROC Analysis Three ROC Plots: W = 30 W = 50 W = 70 For each W, is varied from 0 to For each , a test set of 1000 simulations is used Healthy and faulty trials During faulty trials, different fault amplitudes were injected At the end of every trial, the detection function is generated using and compared the corresponding At the end of the 1000 trials, the tpr and fpr are calculated and the corresponding point is located on the ROC curve. 52 ROCCurve curve (Observer 1) r1ey1 r e ROC for1/ Residual Residual 1 y1 ROCCurve curve (Observer 2) r2ey2 r2ey2 ROC for2/ Residual Residual 1 X: 0 Y: 1 X: 0.002894 Y: 1 X: 0.0152 Y: 0.9942 0.98 X: 0 Y: 1 truepositive positiverate rate true truepositive positiverate rate true 1 X: 0.01333 Y: 1 X: 0.0304 Y: 1 0.9 0.8 0.96 W=30 W=50 W=70 0.94 0 5 10 false positive rate 15 28.05 28.08 1 28.1 0.99 21.24 21.56 W=50 0.7 W=70 0.6 -0.005 20 false positive rate W=30 0 0.005 0.01 -3 x 10 20.31 19.8 1 17.88 35.31 35.32 optimal point for =28.05 and =70 optimal point (0,1) 17.63 34.83 0.015 0.02 0.025 false positive false positive rate rate 17.39 31.43 16.35 30.66 0.03 14.9 0.035 29.71 0.04 14.8 14.49 optimal point for =35.31 and =70 optimal point (0,1) 0.8 35.33 0.6 28.11 0.4 0.98 28.13 0.2 28.14 0.97 -1 0 1 2 3 4 5 6 7 -3 x 10 28.16 28.17 0 35.34 35.35 -1 0 1 2 3 4 5 6 7 -3 x 10 53 Conclusion and Future Perspectives 54 Proposed Fault Diagnosis Algorithm Input variables Power Converter System Bank of Kalman Filters Output variables Residual Generation Residuals , Tuning of W ROC curve Tuning of GLR Test Detection function () Decision () ≷ Fault/No fault Residual Evaluation 55 Conclusion “Combining several disciplines to achieve an efficient comprehensive fault diagnosis scheme” sensor faults Battery UC DC/DC DC bus Inverter Converter PM 56 Conclusion + Model-based Residual generation GLR Test + ROC Curves Power Converter Process 57 « Study on power converters used in hybrid vehicles with monitoring and diagnostics techniques » 17th IEEE MELECON’14 Mediterranean Electrotechnical Conference « Power electronics interface configurations for hybrid energy storage in hybrid electric vehicles » 17th IEEE MELECON’14 Mediterranean Electrotechnical Conference « Modeling, design and fault analysis of bidirectional DC-DC converter for hybrid electric vehicles » 23rd IEEE ISIE’14 International Symposium on Industrial Electronics « Condition Monitoring of Bidirectional DC-DC Converter for Hybrid Electric Vehicles » 22nd MED’14 Mediterranean Conference on Control & Automation 58 « A Sensor fault diagnosis scheme for a DC/DC converter used in hybrid electric vehicles » 9th IFAC Symposium on Fault Detection, Supervision and Safety for Technical Processes SAFEPROCESS'15 59 Future Perspectives Future work will utilize the proposed model-based approach to detect/diagnose component faults in the converter such as open-circuited transistor short-circuited diode degraded capacitor 60 Thank you