Failure Prognosis for Permanent Magnet AC Drives Based on Wavelet Analysis Wesley G Zanardelli Elias G Strangas and Selin Aviyente zanardel egr msu edu strangas egr msu edu aviyente egr msu edu

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							                                                                                                                                                                        Failure Prognosis for Permanent
                                                                                                                                                                         Magnet AC Drives Based on
                                                                                                                                                                                Wavelet Analysis
                                                                                                                                                                        Wesley G. Zanardelli, Elias G. Strangas, and Selin Aviyente
                                                                                                                                                                              zanardel@egr.msu.edu                         strangas@egr.msu.edu                               aviyente@egr.msu.edu



•Objectives                                                                                                                                                                         •Linear Discriminant Analysis                                                                               •Linear discriminant analysis applied to the 64
 •Detection of non-catastrophic faults in Permanent                                                                                                                                    Dk (x ) = x1 1k + x2 2k + , , + x N Nk + N +1,k                           k = 1,2 ,...,K                 samples beginning 8 samples prior to where detection
 Magnet AC machines which lead to reduced life and                                                                                                                                    •Categorization of xi into j                                                                              occurred
 eventually failure                                                                                                                                                                     D j (x ) > Dk (x )         for every k ≠ j
 •Stator Faults                                                                                                                                                                       •Iterative training procedure for the weighting                                                     •Experimental Setup
   •Insulation failures                                                                                                                                                               coefficients makes adjustments to j and l following an
   •Resistance changes                                                                                                                                                                initial guess, where
                                                                                                                                                                                        Dl (x ) = max l ≠ j [D1 (x ),           , DK (x )]
                                                                                                                                                                                          j   (i + 1) =   j   (i ) + axi               l   (i + 1) = l (i ) − axi
•Discrete Wavelet Transform (DWT)                                                                                                                                                     •and a is a gain constant
 •Wavelets have finite energy concentrated around a
 point which helps to localize irregularities in a signal
 •Can give a sparse representation of a fault                                                                                                                                       •Faults Explored
 •Can choose different basis functions (mother wavelets)                                                                                                                              •Series Resistance (5 and 10ms)                                                                     •Typical Results
                                                                                                                                                                                                                                                                                                                                 Iq for Series Resistance Fault (10ms)                        Iq for Turn-Phase Short (10ms)
 to achieve the best results for a specific application                                                                                                                                 •Intermittent increased series contact resistance                                                                                   28                                                         29




                                                                                                                                                                                                                                                                                                              Current (A)




                                                                                                                                                                                                                                                                                                                                                                         Current (A)
 •Coefficients can be realized using a filter bank                                                                                                                                      •A normally closed switch and a resistance in parallel                                                                              26
                                                                                                                                                                                                                                                                                                                            24                                                         28
                                                                                                                                                                                                                                                                                                                            22

 •FIR filter coefficients h1 and h0 based on the scaling                                                                                                                                are added in series with one of the motor phases                                                                                    20
                                                                                                                                                                                                                                                                                                                            18
                                                                                                                                                                                                                                                                                                                                                                                       27



 and wavelet functions                                                                                                                                                                                                     Inverter         Electronic
                                                                                                                                                                                                                                             Switch
                                                                                                                                                                                                                                                         PMAC
                                                                                                                                                                                                                                                         Motor
                                                                                                                                                                                                                                                                                                                            6
                                                                                                                                                                                                                                                                                                                                 UDWT for Series Resistance (10ms)
                                                                                                                                                                                                                                                                                                                                                                                        6
                                                                                                                                                                                                                                                                                                                                                                                            UDW T for Turn-Phase Short (10ms)

                                                                                                                                                                                                                                                                                                                            5                                                           5




                                                                                                                                                                                                                                                                                                                    Scale




                                                                                                                                                                                                                                                                                                                                                                                Scale
                                                     h1 ( −n )                      2             dj                                                                                                                                            R                                                                           4
                                                                                                                                                                                                                                                                                                                            3
                                                                                                                                                                                                                                                                                                                                                                                        4
                                                                                                                                                                                                                                                                                                                                                                                        3

                            c j +1                                                                            h1 ( −n )                  2            d j −1
                                                                                                                                                                                          •Turn-to-Phase Short (5 and 10ms)                                                                                                 2
                                                                                                                                                                                                                                                                                                                            1
                                                                                                                                                                                                                                                                                                                                                                                        2
                                                                                                                                                                                                                                                                                                                                                                                        1

                                                     h0 ( − n )                     2             cj                                                                                        •Insulation failure in the stator windings of the motor                                                                         4
                                                                                                                                                                                                                                                                                                                                             Classification
                                                                                                                                                                                                                                                                                                                                                                                        4
                                                                                                                                                                                                                                                                                                                                                                                                       Classification


                                                                                                              h0 ( − n )                 2            c j −1                                •A normally open switch is added between a                                                                                      3                                                           3
                                                                                                                                                                                                                                                                                                                            2                                                           2
                                                                                                                                                                                            winding and its corresponding phase                                                                                             1                                                           1
                                                                                                                                                                                                                                                                                                                            0                                                           0
                                                                                                                                                                                                                                                                                                                                       2.1      2.2       2.3     2.4                            2.1      2.2     2.3      2.4
                                                                                                                                                                                                                                                                                                                                               Time (s)                                                  Time (s)

•Undecimated Discrete Wavelet Transform                                                                                                                                                                                                                                                   •Algorithm Performance
(UDWT)                                                                                                                                                                              •Analysis Methods
 •Shift-invariant representation of the DWT                                                                                                                                           •Field oriented currents are used since the fundamental                                                                                                        Number of False
                                                                                                                                                                                                                                                                                                                                                                     Fault Inception      Fault Clearing
                                                                                                                                                                                                                                                                                           Test Description                                                          Total / Detected /   Total / Detected /
 •Realized using the “Algorithme à Trous”, which omits                                                                                                                                electrical frequency is not present                                                                                                                            Detections
                                                                                                                                                                                                                                                                                                                                                                     Classified Correctly Classified Correctly

 downsampling and inserts zeros between filter                                                                                                                                        •UDWT applied to measured q-axis current                                                             Healthy                                                           0              0/0/0                0/0/0
                                                                                                                                                                                                                                                                                           Series Resistance (5ms)                                           0              2/2/2                2/2/2
 coefficients at each successive scale                                                                                                                                                •Daubechies D4 wavelet used                                                                          Series Resistance (10ms)                                          0              2/2/2                2/2/2
                                                                                                                                                                                      •Decomposition performed for 6 scales                                                                Turn-to-Phase Short (5ms)                                         0              2/1/1                2/2/2
                               Original Signal                                      DWT of Original Signal                                   UDW T of Original Signal
                                                                                                                                                                                                                                                                                           Turn-to-Phase Short (10ms)                                        0              2/2/2                2/2/2
                28
                26
                                                                          4                                                        4                                                  •Inception and clearing of faults are identified separately
    Amplitude




                24                                                        3                                                        3
                                                                  Scale




                                                                                                                           Scale




                22                                                        2                                                        2                                                  •Detection Algorithm
                20
                18
                                 Original Signal
                                                                          1
                                                                                    DWT of Original Signal
                                                                                                                                   1
                                                                                                                                             UDW T of Original Signal
                                                                                                                                                                                         •A threshold is applied to the weighted energy of the                                            •Conclusions
                           (S hifted by 6 Samples)                                  (Shifted by 6 Samples )                                  (Shifted by 6 S amples)
                28
                26
                                                                          4                                                        4                                                     UDWT at each time instant                                                                          •Detection and classification of machine faults which
    Amplitude




                24                                                        3                                                        3
                                                                                                                                                                                         •Threshold is set to 40% greater than the largest
                                                                  Scale




                                                                                                                           Scale




                22
                20
                                                                          2                                                        2                                                                                                                                                        manifest themselves in the stator current is achieved
                18
                     100     120      140             160
                                                                          1
                                                                              100        120      140               160
                                                                                                                                   1
                                                                                                                                       100      120      140            160
                                                                                                                                                                                         observed on healthy motors                                                                         •Data from an exhaustive set of operating conditions is
                            Sample Number                                               Sample Number                                          Sample Number
                                                                                                                                                                                      •Classification Algorithm                                                                             necessary to develop a robust algorithm

						
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