Investigation of Irreversible Demagnetization Constraints in Magnet Volume Minimization Design of IPMSM for Automotive Applications Using Machine Learning Osaka Prefecture University, Japan ◎Yuki Shimizu, Shigeo Morimoto, Masayuki Sanada, and Yukinori Inoue 2021/5/18 IEMDC 2021

2 Agenda ⚫ Research background and purpose ⚫ Construction of surrogate models - Generation of training data - Feature engineering ⚫ Permanent magnet volume minimization design ⚫ Conclusion

3 ✓ Motors are used in a variety of products that run on electricity ⚫ Electric Vehicles ⚫ Drones ⚫ Industrial Robots ✓ IPMSMs have been widely adopted for such applications *IPMSM: Interior Permanent Magnet Synchronous Motor Stator core Rotor core Permanent magnet (high cost) About IPMSM

4 Issue with IPMSMs for Automotive Applications ✓ IPMSMs for automotive applications face the problem of a long development period Finite Element Analysis (FEA) Because characteristics computations are performed for each element, characteristics analysis is highly time-intensive Characteristics in a Wide Speed Range To obtain driving characteristics within a speed-torque region, FEA must be performed repeatedly under various current conditions Torque Speed The speed-torque characteristics under various current conditions

5 Surrogate Model Construction ✓ Surrogate models trained by machine learning reduce design time Structure Surrogate Model Surrogate model Structure Speed Torque Driving characteristics Finite Element Analysis (FEA) FEA A few hours to a few days A few seconds Speed Torque Driving characteristics

6 Previous Research ✓ Proposed surrogate models that can accurately predict the speed-torque characteristics and minimized permanent magnet volume in a shorter time ✓ Irreversible demagnetization was not considered 0 500 1000 1500 2000 FEAのみ 提案法 Computation time (hour) 1762 hour 78.5 hour × 𝟏 𝟐𝟐 Reduced permanent magnet volume Proposed Y. Shimizu et al., SAMCON2021, TT2-1 (2021) Design time to minimize magnet volume under torque constraint Conventional Only FEA (estimated) Surrogate Model Demagnetization properties were not considered, and permanent magnets are too thin

7 Speed Torque IPMSM shape Speed-torque characteristics Predicted by machine learning ✓ Propose a surrogate model construction method that can accurately predict the irreversible demagnetization of the permanent magnets of IPMSMs for automotive applications ✓ Minimize the permanent magnet volumes with the trained surrogate models and show that our surrogate models can reduce the design time significantly Presentation Contents Irreversible demagnetization characteristics (This research)

8 Agenda ⚫ Research background and purpose ⚫ Construction of surrogate models - Generate training data - Select input/output variables ⚫ Permanent magnet volume minimization design ⚫ Conclusion

9 Example Fig. Settings for geometrical parameters d 9 d 8 (r 1 ,θ 1 ) d 2 *Polar coordinate with the axis center as the origin Settings for Geometrical Parameters ✓ Set geometrical parameters based on the rotor geometry of the double-layered IPMSM [2] ✓ Generate random numbers within the range of the upper and lower limit values of the geometry, and generate 12,000 shapes [2] Y. Shimizu et al., IEEJ Trans. Ind. Appl., Vol. 6, No. 6, pp. 401-408 (2017)

10 Analysis Conditions for Irreversible Demagnetization ✓ The analysis conditions and evaluation method for irreversible demagnetization are as follows How to Evaluate Irreversible Demagnetization Evaluate demagnetization by comparing the minimum flux density of each magnet with the knee point The mesh width of the magnet edge is fixed to 0.5 mm regardless of the shape Phase currents are randomly generated 12,000 conditions between 50~250% of the maximum value Current Vector Conditions ~134× (0.5,2.5) (Arms) e I U ( , ) U a b : Uniform distribution on interval (a,b) a b Probability Maximum value : Magnetization direction Current phase is fixed under β=90°

11 d 9 d 8 (r 1 ,θ 1 ) d 2 d 1w a 1 (r 2 ,θ 2 ) (r 3 ,θ 3 ) a 2 Selecting Input Variables ✓ Important dimensions are selected with the library Boruta and used for learning ✓ To improve the prediction accuracy, dimensions other than the geometrical parameters are included as options Boruta: Feature selection methods using random forest and hypothesis testing Red: Geometrical parameter Black: Dimension automatically determined from geometrical parameter

12 Selecting Output Variables ✓ Since flux density of each magnet is nonlinear around the knee point, apparent permeance coefficient is set as the prediction target Number of cases Apparent permeance coefficient P c 0 min c min B P H  = Minimum value of flux density (T) Number of cases Histogram of FEA results for 12,000 cases Nonlinear behavior below the knee point B-H Curve of NMX-S49CH (at 60°C) -0.5 0.0 0.5 1.0 1.5 -1000 -750 -500 -250 0 H [kA/m] B [T] B min H min Remove nonlinearities 2nd layer/ side 2nd layer/ side Working point

13 Prediction Results ✓ Learning apparent permeance coefficients by Gaussian process regression ✓ Prediction accuracies are high and no overfitting occurs Gaussian Process Regression e selected I   =     x x Feature Target 0 min c min B P H  = Predicted P c r2=0.970 r2=0.968 train test 2nd layer/Center Predicted P c Analyzed P c train test r2=0.992 r2=0.988 1st layer Predicted P c r2=0.977 r2=0.976 train test 2nd layer/Side 2nd layer/Side 2nd layer/Center 1st layer 𝒙𝑠𝑒𝑙𝑒𝑐𝑡𝑒𝑑 : Dimension vector selected by Boruta Analyzed P c Analyzed P c Analyzed P c Analyzed P c Analyzed P c Predicted P c Predicted P c Predicted P c r2: the coefficient of determination (higher is better)

14 Agenda ⚫ Research background and purpose ⚫ Construction of surrogate models - Generation of training data - Feature engineering ⚫ Permanent magnet volume minimization design ⚫ Conclusion

15 Minimizing PM Volume by Real-Coded GA ✓ Minimize the permanent magnet volumes with a combination of the surrogate models and real-coded genetic algorithm Fitness function (minimization) 𝑉(𝐱𝑔𝑒𝑜𝑚 ): PM volume 𝑉𝑖𝑛𝑖𝑡 : PM volume of initial shape (100cm3) 𝑓𝑖𝑡𝑛𝑒𝑠𝑠 = 𝑉(𝐱 𝑔𝑒𝑜𝑚 ) 𝑉 𝑖𝑛𝑖𝑡 + 𝑃𝐴𝐷 + 𝑃𝑇 + 𝑃𝑑𝑒𝑚𝑎𝑔 AD constraint Demag. constraint Torque constraint Initialized PM volume AD (Applicability domain) constraints *OCSVM: One-Class Support Vector Machine ・Set the applicability domain using OCSVM ・Use geometrical parameters of training dataset x geom (1) x geom (2) ：training data Decision boundary Applicability domain Penalty function ( ) ( ) ( ) max 0, AD geom OCSVM geom P f = − x x 𝑓𝑂𝐶𝑆𝑉𝑀 : output of OCSVM （negative when outside AD） *Applicability domain: Area where the accuracy of a model is guaranteed

16 Other Constraints ✓ Minimize the permanent magnet volumes with a combination of the surrogate models and real number genetic algorithm Demag. constraints; assumes 100% and 150% of the maximum current -0.5 0.0 0.5 1.0 1.5 -1000 -750 -500 -250 0 H [kA/m] B [T] 150%: 𝐵𝑗𝑢𝑑𝑔𝑒 = 0.122T (by 3% demag. line) 100%: 𝐵𝑗𝑢𝑑𝑔𝑒 = 0.245T Knee point Penalty function 𝐵 𝑝𝑟𝑒𝑑 (𝑖) : Prediction results of the minimum flux density of each PM ( ) max 0, i judge pred demag i judge B B P B   − =        Penalty when lower than B judge Torque constraints 𝑃 𝐱geom = max 0,197 × 1.03 − 𝑇𝑝𝑟𝑒𝑑1 + max 0,40 × 1.03 − 𝑇𝑝𝑟𝑒𝑑2 𝑇𝑝𝑟𝑒𝑑1,2 : Torque prediction N T P B 11000min-1 P A 40Nm 197Nm 3000min-1 Penalty when not satisfied Prediction T pred1 T pred2 Penalty function

17 Results of Shape Optimization ✓ Reduced PM volume while satisfying the required drive points Conventional shape Best shape Reduced PM volume by 26.2% Torque (Nm) Speed (min-1) I em = 134 A P A P B Fig. Speed-torque characteristics of the best shape. Satisfy required points PM volume (p.u.) Generation Fig. Speed-torque characteristics of the best shape. Terminated in the 166th generation

18 Demagnetization Characteristics of Best Shape ✓ The first layer magnet at 150% current is closest to the constraint ✓ Best shape satisfies demagnetization constraint Fig. Minimum flux density of the best shape 0 0.2 0.4 0.6 1層目 2層目 中央 2層目 サイド 1層目 2層目 中央 2層目 サイド 定格100%通電時 定格150%通電時 Minimum flux density (T) 予測 FEA Reqd: 0.245T Reqd: 0.122T 100% of the maximum current 0.8 0.1 Flux density in the magnetization direction [T] A margin against required value ⇒Torque constraint is active 150% of the maximum current Pred. 1st layer 2nd layer/ Center 2nd layer/ Side 1st layer 2nd layer/ Center 2nd layer/ Side OK NG

19 Comparison of Optimization Design Time ✓ The total computation time of the proposed method can be reduced to less than 1/32nd Fig. Computation time for optimization design (lower is better) 0 500 1000 1500 2000 2500 FEAのみ 提案法 Computation time (hour) 2280 hour 70.5 hour × 𝟏 𝟑𝟐 Only FEA (estimated) Proposed method

20 Agenda ⚫ Research background and purpose ⚫ Construction of surrogate models - Generation of training data - Feature engineering ⚫ Permanent magnet volume minimization design ⚫ Conclusion

21 Conclusion ✓ Proposed a surrogate model construction method that can accurately predict the irreversible demagnetization characteristics by using Gaussian process regression ⚫ Select geometrical parameters for features using Boruta ⚫ Set the prediction target to the apparent permeance coefficient ✓ Proposed shapes that 26.2% reduced the PM volumes while satisfying the required torques and demagnetization characteristics using the surrogate models and real-coded genetic algorithm ✓ The proposed method took less than 1/32nd of the optimization design time compared to FEA-only design