$30 off During Our Annual Pro Sale. View Details »

210311_samcon

yuki
March 11, 2021
40

 210311_samcon

yuki

March 11, 2021
Tweet

Transcript

  1. Reducing Design Time of Permanent
    Magnet Volume Minimization
    for IPMSM for Automotive Applications
    Using Machine Learning
    Osaka Prefecture University
    ◎Yuki Shimizu, Shigeo Morimoto,
    Masayuki Sanada, and Yukinori Inoue
    2021/3/11 SAMCON2021

    View Slide

  2. 2
    Agenda
    ⚫ Research background and purpose
    ⚫ Generation of training data
    ⚫ Prediction results
    ⚫ PM volume minimization design
    ⚫ Conclusion

    View Slide

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

    View Slide

  4. 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

    View Slide

  5. 5
    Presentation Contents
    ✓ Propose a surrogate model construction method
    that can accurately predict the speed-torque
    characteristics of an IPMSM for automotive applications
    ✓ Use the trained surrogate models and real-coded
    genetic algorithm to minimize the permanent magnet
    (PM) volumes
    ✓ Show that our surrogate models can reduce the
    design time significantly
    Structure
    Predict by
    a surrogate model
    Speed
    Torque
    Driving characteristics
    with machine learning

    View Slide

  6. 6
    Agenda
    ⚫ Research background and purpose
    ⚫ Generation of training data
    ⚫ Prediction results
    ⚫ PM volume minimization design
    ⚫ Conclusion

    View Slide

  7. 7
    Example
    Fig. Settings for geometrical parameters
    d
    9
    d
    8
    (r
    1

    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[1]
    ✓ Generate random numbers within the range of the upper and
    lower limit values of the geometry, and generate the shapes
    [1] Y. Shimizu et al., IEEJ Trans. Ind.
    Appl., Vol. 6, No. 6, pp. 401-408 (2017)

    View Slide

  8. 8
    Target of Surrogate Model
    The maximum output control is
    performed with following equations
    𝑇𝑎𝑣𝑔
    = 𝑃
    𝑛
    𝛹𝑎
    𝐼𝑎
    cos 𝛽
    +
    1
    2
    𝐿𝑞
    − 𝐿𝑑
    𝐼𝑎
    2 sin 2𝛽
    𝑁𝑙𝑖𝑚
    =
    𝑉𝑜𝑚
    𝛹𝑎
    − 𝐿𝑑
    𝐼𝑎
    sin 𝛽 2 + 𝐿𝑞
    𝐼𝑎
    cos 𝛽 2
    ✓ Predict the motor parameters under each current vector
    condition with surrogate models
    N-T characteristics
    Rotor geometry
    Predicting
    N
    T
    Motor parameters
    L
    d,
    L
    q
    β
    I
    a
    Ψ
    a
    I
    a
    PM flux linkage
    d-, q-axis inductance
    𝛹𝑎
    = 𝑓 𝐼𝑎
    , 𝐱𝑔𝑒𝑜𝑚
    𝐿𝑑
    = 𝑔 𝐼𝑎
    , 𝛽, 𝐱𝑔𝑒𝑜𝑚
    𝐿𝑞
    = ℎ 𝐼𝑎
    , 𝛽, 𝐱𝑔𝑒𝑜𝑚
    Learn the relationship
    between rotor geometry,
    current conditions, and
    motor parameters
    𝐼𝑎
    : Armature current
    𝛽: Current phase angle
    𝐱𝑔𝑒𝑜𝑚
    : Geometrical
    parameter vector
    𝑃𝑛
    : Number of pole pairs,
    𝑅𝑎
    : Winding resistance,
    𝑉𝑜𝑚
    : Induced voltage limit
    Independent
    of current
    phase angle
    Computing

    View Slide

  9. 9
    Training Data Generation and Analysis
    ✓ Generate training dataset for the PM flux linkage and
    train the surrogate model
    1. Generate FEA conditions for Ψ
    a
    2. Train the surrogate model for Ψ
    a
    3. Generate FEA conditions for L
    d
    , L
    q
    4. Predict Ψ
    a
    and
    Compute L
    d
    4. Remove the
    outliers of L
    d
    4. Compute L
    q
    5. Train the surrogate models for L
    d
    ,L
    q
    Fig. 3. Generation and analysis flowchart
    for the training data.
    1. Generate FEA conditions (Ψ
    a
    )
    2. Train a model for Ψ
    a
    ( ) ( ) ( )
    ~ (0,140) (Arms)
    ~ ( , ) ( 1,...,11)
    e
    j j j
    geom lwr upr
    I U
    x U x x j



    =


    Surrogate
    model
    a
    geom
    I

     
    =  
     
    x
    x
    Features Targets
    Randomly generate 2,000 cases,
    where β = 0°
    ( , )
    U a b :uniform
    distribution on
    interval (a,b)
    cos
    a
    o

     
    =
    a b
    Prob.
    Phase current

    View Slide

  10. 10
    Training Data Generation and Analysis
    ✓ Generate training dataset for inductances
    ✓ Compute q-axis inductances
    3. Generate FEA conditions (L
    d
    , L
    q
    )
    4. Compute L
    q
    Randomly generate 6,000 cases
    ( ) ( ) ( )
    ~140 (0,1) (Arms)
    ~ (0,90) (°)
    ~ ( , ) ( 1,...,11)
    e
    j j j
    geom lwr upr
    I U
    U
    x U x x j




     =

    i
    d
    i
    q
    sin
    cos
    o
    q
    a
    L
    I
     

    =
    Compute L
    q
    from FEA results
    i
    d
    i
    q
    ~140 (0,1)
    e
    I U ~ (0,140)
    e
    I U
    NOT
    uniform
    Uniform
    Inverse transform
    method
    1. Generate FEA conditions for Ψ
    a
    2. Train the surrogate model for Ψ
    a
    3. Generate FEA conditions for L
    d
    , L
    q
    4. Predict Ψ
    a
    and
    Compute L
    d
    4. Remove the
    outliers of L
    d
    4. Compute L
    q
    5. Train the surrogate models for L
    d
    ,L
    q
    Fig. 3. Generation and analysis flowchart
    for the training data.

    View Slide

  11. 11
    Training Data Generation and Analysis
    4. Predict Ψ
    a
    and compute L
    d
    Predict Ψ
    a
    using the surrogate
    model in Step 2 and compute L
    d
    Computed L
    d
    has the prediction
    error in Ψ
    a
    Computation error of L
    d
    becomes
    large in the case of small i
    d
    ( )
    ˆ
    cos
    cos
    a a
    o a
    d
    d
    o a
    d
    d d
    L
    i
    L
    i i
     
      
        

    =
    − +
    = = −
      
    Ψ
    a
    prediction
    True Ψ
    a
    Prediction
    error
    Error of L
    d
    ✓ Predict PM flux linkages of each case and compute d-
    axis inductances using prediction and FEA results
    1. Generate FEA conditions for Ψ
    a
    2. Train the surrogate model for Ψ
    a
    3. Generate FEA conditions for L
    d
    , L
    q
    4. Predict Ψ
    a
    and
    Compute L
    d
    4. Remove the
    outliers of L
    d
    4. Compute L
    q
    5. Train the surrogate models for L
    d
    ,L
    q
    Fig. 3. Generation and analysis flowchart
    for the training data.

    View Slide

  12. 12
    Training Data Generation and Analysis
    ✓ Remove the outliers of the computed d-axis inductances
    and train the surrogate models for inductances
    4. Remove the outliers of L
    d
    5. Train models for L
    d
    ,L
    q
    Remove the outliers of L
    d
    using
    the Hampel identifier method
    d
    L q
    geom
    i
    i
     
     
    =  
     
     
    x
    x
    d
    L
    q
    L
    ( ) ( )
    ( )
    ( ) ( ) ( )
    med 3 1.4826 med med
    i i i
    d d d
    i i i
    L L L
       −
    Data No. (1~6000)
    L
    d
    Thre-
    sholds
    Remove
    1. Generate FEA conditions for Ψ
    a
    2. Train the surrogate model for Ψ
    a
    3. Generate FEA conditions for L
    d
    , L
    q
    4. Predict Ψ
    a
    and
    Compute L
    d
    4. Remove the
    outliers of L
    d
    4. Compute L
    q
    5. Train the surrogate models for L
    d
    ,L
    q
    Fig. 3. Generation and analysis flowchart
    for the training data.
    Features Targets
    Surrogate
    model
    Surrogate
    model
    Remove

    View Slide

  13. 13
    Agenda
    ⚫ Research background and purpose
    ⚫ Generation of training data
    ⚫ Prediction results
    ⚫ PM volume minimization design
    ⚫ Conclusion

    View Slide

  14. 14
    Prediction Accuracies of Surrogate Models
    ✓ Use Ridge regression, Support vector regression, and XGBoost
    Ridge SVR XGBoost
    Predicted (mH)
    d-axis inductance
    Analyzed (mH)
    Ridge SVR XGBoost
    q-axis inductance
    Predicted (Wb)
    Ridge SVR XGBoost
    Analyzed (Wb)
    Predicted (Wb)
    Analyzed (Wb)
    Predicted (Wb)
    Analyzed (Wb)
    Predicted (mH)
    Analyzed (mH)
    Predicted (mH)
    Analyzed (mH)
    Predicted (mH)
    Analyzed (mH)
    Predicted (mH)
    Analyzed (mH)
    Predicted (mH)
    Analyzed (mH)
    PM flux linkage

    View Slide

  15. 15
    ✓ SVR was most accurate
    Ridge SVR XGBoost
    Predicted (mH)
    d-axis inductance
    Analyzed (mH)
    Ridge SVR XGBoost
    q-axis inductance
    Predicted (Wb)
    Ridge SVR XGBoost
    PM flux linkage
    Analyzed (Wb)
    Predicted (Wb)
    Analyzed (Wb)
    Predicted (Wb)
    Analyzed (Wb)
    Predicted (mH)
    Analyzed (mH)
    Predicted (mH)
    Analyzed (mH)
    Predicted (mH)
    Analyzed (mH)
    Predicted (mH)
    Analyzed (mH)
    Predicted (mH)
    Analyzed (mH)
    Ridge; the lowest accuracy because of linear regression
    SVR; the highest accuracy
    XGBoost; tendency to overfit the training data
    r2 (higher is better)
    train: 0.961
    test: 0.963
    r2 (higher is better)
    train: 0.999
    test: 0.997
    r2 (higher is better)
    train: 1.000
    test: 0.983
    SVR: Support Vector Regression
    r2: the coefficient of determination
    Prediction Accuracies of Surrogate Models

    View Slide

  16. 16
    ✓ SVR was most accurate
    Ridge SVR XGBoost
    Predicted (mH)
    d-axis inductance
    Analyzed (mH)
    Ridge SVR XGBoost
    q-axis inductance
    Predicted (Wb)
    Ridge SVR XGBoost
    Analyzed (Wb)
    Predicted (Wb)
    Analyzed (Wb)
    Predicted (Wb)
    Analyzed (Wb)
    Predicted (mH)
    Analyzed (mH)
    Predicted (mH)
    Analyzed (mH)
    Predicted (mH)
    Analyzed (mH)
    Predicted (mH)
    Analyzed (mH)
    Predicted (mH)
    Analyzed (mH)
    PM flux linkage
    SVR: Support Vector Regression
    r2: the coefficient of determination
    r2 (higher is better)
    train: 0.864
    test: 0.890
    r2 (higher is better)
    train: 0.961
    test: 0.973
    r2 (higher is better)
    train: 0.996
    test: 0.963
    There are some plots where the predicted values deviate
    significantly because of the prediction error in Ψ
    a
    Ridge; the lowest accuracy because of linear regression
    SVR; high accuracy even for unknown test data
    XGBoost; learned perfectly even the prediction errors
    Prediction Accuracies of Surrogate Models

    View Slide

  17. 17
    ✓ XGBoost was the most accurate
    Ridge SVR XGBoost
    Predicted (mH)
    d-axis inductance
    Analyzed (mH)
    Ridge SVR XGBoost
    q-axis inductance
    Predicted (Wb)
    Ridge SVR XGBoost
    Analyzed (Wb)
    Predicted (Wb)
    Analyzed (Wb)
    Predicted (Wb)
    Analyzed (Wb)
    Predicted (mH)
    Analyzed (mH)
    Predicted (mH)
    Analyzed (mH)
    Predicted (mH)
    Analyzed (mH)
    Predicted (mH)
    Analyzed (mH)
    Predicted (mH)
    PM flux linkage
    Analyzed (mH)
    SVR: Support Vector Regression
    r2: the coefficient of determination
    r2 (higher is better)
    train: 0.918
    test: 0.918
    r2 (higher is better)
    train: 0.998
    test: 0.994
    r2 (higher is better)
    train: 1.000
    test: 0.998
    Ridge; the lowest accuracy because of linear regression
    SVR; not able to accurately predict the inductance variation
    XGBoost; the highest accuracy for both the training and test data
    Prediction Accuracies of Surrogate Models

    View Slide

  18. 18
    ✓ SVR and XGBoost that can represent nonlinearity are accurate
    Ridge SVR XGBoost
    Predicted (mH)
    d-axis inductance
    Analyzed (mH)
    Ridge SVR XGBoost
    q-axis inductance
    Predicted (Wb)
    Ridge SVR XGBoost
    Analyzed (Wb)
    Predicted (Wb)
    Analyzed (Wb)
    Predicted (Wb)
    Analyzed (Wb)
    Predicted (mH)
    Analyzed (mH)
    Predicted (mH)
    Analyzed (mH)
    Predicted (mH)
    Analyzed (mH)
    Predicted (mH)
    Analyzed (mH)
    Predicted (mH)
    Analyzed (mH)
    Prediction Accuracies of Surrogate Models
    PM flux linkage

    View Slide

  19. 19
    ✓ Proposed method reduced the RMSEs
    by 68.1% and 67.7%
    Results of Speed-Torque Characteristics
    Fig. 5. Prediction results for speed-torque characteristics
    (a) Motor parameter prediction
    I
    em
    = 134A
    I
    em
    = 30A
    Torque (Nm)
    Speed (min-1)
    Proposed method
    I
    em
    = 134A
    I
    em
    = 30A
    Torque (Nm)
    Speed (min-1)
    Conventional method
    (b) Direct torque-and-speed prediction
    *RMSE: Root Mean Square Error
    Initial shape
    RMSE (lower is better)
    134A: 3.88 Nm
    30A: 1.82 Nm
    RMSE (lower is better)
    134A: 12.14 Nm
    30A: 5.65 Nm

    View Slide

  20. 20
    Agenda
    ⚫ Research background and purpose
    ⚫ Generation of training data
    ⚫ Prediction results
    ⚫ PM volume minimization design
    ⚫ Conclusion

    View Slide

  21. 21
    Minimizing PM Volume by Real Number GA
    ✓ Minimize the permanent magnet volumes with a combination of
    the surrogate models and real number genetic algorithm
    Start
    Create initial population
    Unsatisfied
    End
    Satisfied
    Select parents
    Generate children by UNDX-m
    Modify children to satisfy
    geometric constraint
    Calculate fitness function
    Select top children
    Termination conditions
    Fitness function
    𝑓𝑖𝑡𝑛𝑒𝑠𝑠 =
    𝑉(𝐱
    𝑔𝑒𝑜𝑚
    )
    𝑉
    𝑖𝑛𝑖𝑡
    + 𝑃𝑇(𝐱𝑔𝑒𝑜𝑚
    ) + 𝑃𝐴𝐷(𝐱𝑔𝑒𝑜𝑚
    )
    𝑉(𝐱𝑔𝑒𝑜𝑚
    ): PM volume
    𝑉𝑖𝑛𝑖𝑡
    : PM volume of initial shape (100cm3)
    𝑃𝑇
    𝐱𝑔𝑒𝑜𝑚
    , 𝑃𝐴𝐷
    (𝐱𝑔𝑒𝑜𝑚
    ): Penalty functions
    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

    View Slide

  22. 22
    Applicability Domain Constraints
    ✓ Set the applicability domain constraints with OCSVM
    Applicability domain constraints
    ・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)
    *OCSVM: One-Class Support Vector Machine
    *Applicability domain: Area where the accuracy of a model is guaranteed
    Start
    Create initial population
    Unsatisfied
    End
    Satisfied
    Select parents
    Generate children by UNDX-m
    Modify children to satisfy
    geometric constraint
    Calculate fitness function
    Select top children
    Termination conditions

    View Slide

  23. 23
    Prediction Accuracy for Best Individuals
    ✓ Ran the optimization design five times
    ✓ Prediction error rates of all models are less than 5%
    ✓ All the best individuals satisfied the constraints
    Fig. Torque prediction results of the best individuals at required drive points.
    0
    50
    100
    150
    200
    250
    1st 2nd 3rd 4th 5th 1st 2nd 3rd 4th 5th
    PA PB
    Torque (Nm)
    予測 FEA
    @3000 min-1 (P
    A
    ) @11000 min-1 (P
    B
    )
    Reqd: 197Nm
    Reqd:
    40Nm
    N
    T
    P
    B
    11000
    min-1
    P
    A
    40Nm
    197Nm
    3000
    min-1
    Pred.

    View Slide

  24. 24
    0
    500
    1000
    1500
    2000
    2500
    3000
    FEAのみ
    提案法
    FEAのみ
    提案法
    FEAのみ
    提案法
    FEAのみ
    提案法
    FEAのみ
    提案法
    1st 2nd 3rd 4th 5th
    Computation time (hour)
    1762
    2744
    1789 1898
    1121
    78.5 79.1 78.6
    78.5 78.0
    Comparison of Optimization Design Time
    ✓ The total computation time of the proposed method
    can be reduced to less than 1/14th to 1/35th
    Fig. Computation time for optimization design
    Convergent
    generation 128 gen. 200 gen. 130 gen. 138 gen. 81 gen.
    ×
    1
    22
    ×
    1
    35
    ×
    1
    23
    ×
    1
    24 ×
    1
    14
    1st 2nd 3rd 4th 5th
    Only FEA
    Proposed
    method
    Only FEA
    Proposed
    method
    Only FEA
    Proposed
    method
    Only FEA
    Proposed
    method
    Only FEA
    Proposed
    method

    View Slide

  25. 25
    Agenda
    ⚫ Research background and purpose
    ⚫ Generation of training data
    ⚫ Prediction results
    ⚫ PM volume minimization design
    ⚫ Conclusion

    View Slide

  26. 26
    Conclusion
    ✓ Proposed a surrogate model construction method that can
    accurately predict the speed-torque characteristics
    ✓ Following methods were the most accurate for each parameter
    ⚫ Permanent magnet flux density; SVR
    ⚫ d-axis inductance; SVR
    ⚫ q-axis inductance; XGBoost
    ✓ Proposed shapes that reduced the PM volumes while
    satisfying the required torques using surrogate models and
    real-coded genetic algorithm
    ✓ The proposed method took less than 1/14th to 1/35th of
    the optimization design time compared to FEA-only design

    View Slide