210518_iemdc

Transcript

1. 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
   

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

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3. 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
   

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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
   

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5. 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
   

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6. 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
   

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7. 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)
   

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

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9. 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)
   

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10. 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°
    

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11. 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
    

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12. 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
    

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13. 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)
    

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

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15. 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
    

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16. 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
    

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17. 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
    

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18. 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
    

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19. 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
    

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

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21. 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
    

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