Traction Inverter Open Switch Fault Diagnosis Based on Choi – Williams Distribution Spectral Kurtosis and Wavelet-Packet Energy Shannon Entropy

In this paper, a new approach for fault detection and location of open switch faults in the closed-loop inverter fed vector controlled drives of Electric Multiple Units is proposed. Spectral kurtosis (SK) based on Choi–Williams distribution (CWD) as a statistical tool can effectively indicate the presence of transients and locations in the frequency domain. Wavelet-packet energy Shannon entropy (WPESE) is appropriate for the transient changes detection of complex non-linear and non-stationary signals. Based on the analyses of currents in normal and fault conditions, SK based on CWD and WPESE are combined with the DC component method. SK based on CWD and WPESE are used for the fault detection, and the DC component method is used for the fault localization. This approach can diagnose the specific locations of faulty Insulated Gate Bipolar Transistors (IGBTs) with high accuracy, and it requires no additional devices. Experiments on the RT-LAB platform are carried out and the experimental results verify the feasibility and effectiveness of the diagnosis method.


Introduction
In recent years, the rapid development of high-speed railways has drawn attention to the security and stability requirements of operation.In the operation process of Electric Multiple Units, sensor failures, open-circuit and short-circuit faults of converter power devices could easily occur due to the complex and changeable environment, which could threat the operational safety of trains [1].
Presently, closed-loop inverters are applied widely in engineering projects, and they realize their function by semiconductor power devices (SPDs).An earlier survey has pointed out that SPDs are ranked among the most fragile components in power electronic converters [2].SPD failures include open switch faults and short switch faults.For the short switch fault condition, the time between fault initiation and failure is short, thus, it is generally protected by hardware.For the open switch fault condition, they are not only difficult to find, but also cause additional failures and damage to the system [3].Hence, it is of great importance to diagnose the open switch faults in a timely way.
Numerous methods have been proposed for the diagnosis of open switch faults, which can be classified into current-based and voltage-based methods.Generally, voltage-based methods realized the detection by comparisons of the faulty motor phase voltage or line voltage of the inverter with a normal reference voltage [4,5].In addition, the diagnosis was performed by integrating the voltage with intelligent algorithms, such as artificial neural network [6].However, voltage-based methods Considering the good performance of SK and entropy in diagnosis of faults, a new approach for vector controlled induction motor drives is presented in this paper.This method consists of two parts: the fault detection and fault location.For the fault detection part, SK based on CWD is utilized to detect the faults and combined with wavelet-packet energy Shannon entropy (WPESE) method to determine the fault phase.Then for the fault location part, DC components of the fault phase are calculated and compared to identify the upper switch fault (USF) and the lower switch fault (LSF).This approach could solve the false alarm problem which would be caused by the system noise and has good robustness.Compared with some previous methods, it can realize the diagnosis of all single and two IGBTs fault cases, which is easily-operated and requires no additional devices.Finally, experiments on the RT-LAB platform are carried out, and the results verify the effectiveness of the proposed approach.

Spectral Kurtosis Based on Choi-Williams Distribution
As a statistical tool, SK can detect the non-Gaussian components in a signal, which can indicate the presence of transients and their locations in the frequency domain.Once the open switch fault of an IGBT occurs, the harmonic components in fault currents that are different from the main frequency components would increase, thus, the amplitude of SK in the frequency domain would get increased correspondingly.Therefore, SK is adopted in this paper to detect faults.There are many algorithms combined with SK, such as STFT, WT, WVD [22].SK based on STFT shows a low time-frequency resolution, and it is limited to the choice of window functions.Besides, the results are poor when the system is influenced by much noise.SK based on WT has a strong ability to acquire the characteristics in the time and frequency domain, however, the wavelet bases and decomposition scales are difficult to determine, which cannot get the most excellent diagnosis results.SK based on WVD has many good properties, but the cross-term in the signals cannot be completely eliminated, and it affects the analyses of results.In order to solve the cross-term problem, SK based on CWD is developed.It inherits the excellent time-frequency performance of WVD, and suppresses the interference of the cross-term effectively.Therefore, this paper adopts SK based on CWD method to recognize the fault conditions.
For a nonstationary signal x(t), based on CWD algorithm, C x (t, f ) can be presented below [29]: where, τ is the time shift parameter, σ is the scale factor and µ represents the partial time.
g(0, τ) = g(θ, 0) = 1, g(0, 0) = 1, and when θ = 0, τ = 0, g(θ, τ) < 1, where, θ represents the frequency offset parameter, and σ is a constant.If σ gets large, the resolution would become higher.If σ gets small, the inhibitory effect of cross-term would become stronger.Thus, σ should be determined by considering the two aspects.Therefore, the exponential kernel function can suppress the interference of the cross-term and show high time-frequency performance.
The second order and fourth order spectral moments also can be shown as follows: where, E{•} k represents the average of k-th order.Finally, based on the definition of SK [21], SK based on CWD is defined below:

Wavelet-Packet Energy Shannon Entropy
The Shannon entropy was proposed to solve the problem of quantitative measurement of information by Shannon.Once a fault occurs in the inverter, more frequency components would appear in three-phase currents.Thus, the value of entropy in a fault case is more than that in a healthy condition, which is appropriate for diagnosis of open switch faults.
Compared with the wavelet transform, the wavelet-packet transform has a high resolution to decompose the detail part in each level, which is more fit for the detection of fault [28].The recursive decomposition of discrete wavelet-packet can be expressed as follows: where, k is the index of sampling point, f (x) represents the original signal, g(k) and h(k) are the low pass filter and high pass filter respectively, and d i,j (k) is the reconstructed signal of wavelet packet decomposition for the j-th node at the i-th level.Supposing a random variable X (X = X 1 , X 2 , . . ., X N , N is the number of probable states) as the state of an uncertain system, the definition of Shannon entropy is shown below: where, p j is the probability of x i , and Based on the wavelet-packet transform, the wavelet-packet energy can be obtained by the Equation (6), and the total energy E j is the sum of wavelet-packet energy of every node.Hence, its probability can be acquired in Equation (7), and WPESE is defined as Equation ( 8):

Analyses of Faults and Diagnosis Plan
The schematic diagram of a traction system is shown in Figure 1.The vector controlled traction inverter mainly consists of six SPDs, namely S1, S2, S3, S4, S5, S6.IGBT with antiparallel diode is a kind of commonly adopted SPD [30].In this paper, compared with the open-loop system, the closed-loop system is adopted, and it has a feedback loop, which can be utilized to detect the control output and then revise control errors.As a consequence, the closed-loop system has an ability of restraining interference and improving the response of the system.However, if an IGBT fails, the output currents of other phases would be influenced, which would add much difficulty to the fault diagnosis. There

Feature Extraction
In this paper, there are three significant features to be extracted.The diagnosis plan contains three analysis methods.Hence, these features are divided into three classes.

 SK Based on CWD Feature
This method contains a feature named K, which represents the value of SK.The results of SK in fault-free, Fault A and C cases are shown in Figure 3a-c

Feature Extraction
In this paper, there are three significant features to be extracted.The diagnosis plan contains three analysis methods.Hence, these features are divided into three classes.

 SK Based on CWD Feature
This method contains a feature named K, which represents the value of SK.The results of SK in fault-free, Fault A and C cases are shown in Figure 3a-c

Feature Extraction
In this paper, there are three significant features to be extracted.The diagnosis plan contains three analysis methods.Hence, these features are divided into three classes.3d shows that the increase of K b is small and K a gets greater.It is found that if a fault occurs in one phase, SK results of the phase would become much greater than under the normal condition.Thus, it is appropriate for the detection of Fault A and C cases, but it is not suitable for Fault B and D cases.It might be that if the faults occur in two IGBTs located in the different phases, the fault-free phase would be influenced simultaneously.Thus, it might cause a false alarm and affect the diagnosis results.In order to reduce the interruptions of sudden increase or decrease for SK curves, the mean value of SK is selected as the characteristic, as shown in Table 1.It is found that in fault-free case, the average values are not more than 3.If a failure of Fault A case occurs, the value of SK in fault phase increases and the average value is about 5 while the values of normal phases basically remain the same.Meanwhile, if a failure of Fault C case occurs, the value of fault phase is more than 10.Therefore, the thresholds are set to be 5 and 10 for Fault A and C cases, respectively.In order to reduce the interruptions of sudden increase or decrease for SK curves, the mean value of SK is selected as the characteristic, as shown in Table 1.It is found that in fault-free case, the average values are not more than 3.If a failure of Fault A case occurs, the value of SK in fault phase increases and the average value is about 5 while the values of normal phases basically remain the same.Meanwhile, if a failure of Fault C case occurs, the value of fault phase is more than 10.Therefore, the thresholds are set to be 5 and 10 for Fault A and C cases, respectively.• WPESE Feature In the above discussion, SK cannot realize the diagnosis of Fault B and D cases, WPESE is proposed to solve the problem.There is a feature named S WPESE , which represents the amplitude of WPESE.Considering that the fault can be detected accurately with less time, the sliding window L, sliding factor a and decomposition level are set to be 50 sampling points, 1 sampling point and 3.The conditions about normal and the failure of two IGBTs (S1, S6) with different mother wavelets are shown in Figure 4.If the condition is healthy, the entropy amplitudes of three-phase currents are small and less than 1.Once the faults appear in the S1 and S6 simultaneously, WPESE results of A and B-phases become larger and much more than C-phase.It draws a conclusion that once the values of S WPESE in two phases get much larger, the failure would occur in them.Therefore, WPESE method can detect the fault time and fault phase by setting threshold properly.In addition, it is found that the results of three mother wavelets ("db2", "db3", "db4") are similar and they could realize the detection of open switch faults with high accuracy.In order to ensure the correctness and reduce the computational time, "db2" is selected as the mother wavelet in this paper.The simulations also indicate that, when the threshold is set to be 1, WPESE performs very well.
In the above discussion, SK cannot realize the diagnosis of Fault B and D cases, WPESE is proposed to solve the problem.There is a feature named SWPESE, which represents the amplitude of WPESE.Considering that the fault can be detected accurately with less time, the sliding window L, sliding factor a and decomposition level are set to be 50 sampling points, 1 sampling point and 3.The conditions about normal and the failure of two IGBTs (S1, S6) with different mother wavelets are shown in Figure 4.If the condition is healthy, the entropy amplitudes of three-phase currents are small and less than 1.Once the faults appear in the S1 and S6 simultaneously, WPESE results of A and B-phases become larger and much more than C-phase.It draws a conclusion that once the values of SWPESE in two phases get much larger, the failure would occur in them.Therefore, WPESE method can detect the fault time and fault phase by setting threshold properly.In addition, it is found that the results of three mother wavelets ("db2", "db3", "db4") are similar and they could realize the detection of open switch faults with high accuracy.In order to ensure the correctness and reduce the computational time, "db2" is selected as the mother wavelet in this paper.The simulations also indicate that, when the threshold is set to be 1, WPESE performs very well.• DC Component method This method also contains a feature named I dc , which means the value of DC component.DC component I dc can be calculated with the following formula: where, M is the number of sampling points in one cycle, and i represents the phase index.Current flows and current waves of USF and LSF in A-phase are shown in Figure 5 [28].Obviously, I dc is zero in fault-free case.Supposing there is a USF, the current wave can be seen in Figure 5b,c.It is apparent that the current cannot go through S1, which means that the positive current of A-phase must be zero.Meanwhile, the negative current can go through S4 as before.Thus, the sampling points' value of the current will be non-positive once the fault appears.In the same way, if there is a LSF, the current waves are shown in Figure 5e,f, and the sampling points' value of the current will be non-negative after fault is triggered.Therefore, the locations of fault IGBT can be diagnosed by the calculation of DC components during the next cycle.
where, M is the number of sampling points in one cycle, and i represents the phase index.Current flows and current waves of USF and LSF in A-phase are shown in Figure 5 [28].Obviously, Idc is zero in fault-free case.Supposing there is a USF, the current wave can be seen in Figure 5b,c.It is apparent that the current cannot go through S1, which means that the positive current of A-phase must be zero.Meanwhile, the negative current can go through S4 as before.Thus, the sampling points' value of the current will be non-positive once the fault appears.In the same way, if there is a LSF, the current waves are shown in Figure 5e,f, and the sampling points' value of the current will be non-negative after fault is triggered.Therefore, the locations of fault IGBT can be diagnosed by the calculation of DC components during the next cycle.

Diagnosis Flow
The diagnosis flow of the proposed approach is shown in Figure 6.The three-phase currents show different characteristics in fault conditions, and a novel approach combining SK based on CWD and WPESE with the DC component method is adopted to realize the diagnosis.Firstly, SK based on CWD method is utilized to acquire the average value of K.It is discussed that mean(K) in normal condition is not more than 3, thus, the fault would be detected if the results do not satisfy Rule 1.
If a fault is detected, Fault A and C cases can be diagnosed based on comparison of the value of SK with the set threshold.If the results of SK do not meet Rules 2 and 3, the condition belongs to a failure of two IGBTs located in different bridge arms, and WPESE is adopted.Once the results satisfy Rule 4, the condition is judged to be Fault B case.If not, it belongs to Fault D case.In Fault D case, DC components of three-phase currents are calculated.Once the polarity of two DC components is the same, IGBTs in the two bridge arms have faults.In the location part, for Fault C case, it is easily to confirm two fault IGBTs located in fault phase.For Fault A, B and D cases, DC components of fault phases are calculated to confirm the USF or LSF.If the value of DC component is positive, it is the LSF; If is negative, it is the USF.The rules in the diagnosis flow are as follows: The ceil(x) function represents to take the smallest integer which is more than x.

Diagnosis Flow
The diagnosis flow of the proposed approach is shown in Figure 6.The three-phase currents show different characteristics in fault conditions, and a novel approach combining SK based on CWD and WPESE with the DC component method is adopted to realize the diagnosis.Firstly, SK based on CWD method is utilized to acquire the average value of K.It is discussed that mean(K) in normal condition is not more than 3, thus, the fault would be detected if the results do not satisfy Rule 1.
If a fault is detected, Fault A and C cases can be diagnosed based on comparison of the value of SK with the set threshold.If the results of SK do not meet Rules 2 and 3, the condition belongs to a failure of two IGBTs located in different bridge arms, and WPESE is adopted.Once the results satisfy Rule 4, the condition is judged to be Fault B case.If not, it belongs to Fault D case.In Fault D case, DC components of three-phase currents are calculated.Once the polarity of two DC components is the same, IGBTs in the two bridge arms have faults.In the location part, for Fault C case, it is easily to

 SK Based on CWD and Window Function
SK is a time-frequency analysis algorithm.Once the window function is determined, the timefrequency resolution is fixed [22].Thus, SK based on CWD is related with the window function.There are some typical window functions, such as rectangular, Hanning, Hamming, Blackman and Kaiser

• SK Based on CWD and Window Function
SK is a time-frequency analysis algorithm.Once the window function is determined, the time-frequency resolution is fixed [22].Thus, SK based on CWD is related with the window function.There are some typical window functions, such as rectangular, Hanning, Hamming, Blackman and Kaiser windows, etc. SK curves with Hanning and rectangular windows are shown in Figure 7a (1 ( )) f x + where, ( ) f x ′ is the first derivation of x, and ( ) The deviation of curvature is calculated and adopted to evaluate the complexity of curve shape.The smoothness of curve can be defined below [31]: where, n is the index of sampling point, m represents the length of data, kn and kmean are the estimated curvature of the n-th discrete point and the average of the estimated curvature respectively.Based on the formula, if the value is large, the smoothness effect of curve is bad.If not, the smoothness effect of curve is good.The curvatures of C-phase current with Hanning and rectangular window are shown in Figure 7c.It is found that the change of curvature result with rectangular window is much than that with Hanning window, which is consistent with the results in Figure 7a,b.In addition, the average smoothness results of three-phase currents with five windows are calculated and shown in Table 2.The result with rectangular window is much larger than other windows, and results of four windows are quite similar.Actually, SK based on CWD with rectangular window is equivalent to SK without window, and the smoothing effect is not good.Hence, it is necessary to choose the efficient window function.And the results with above four windows are similar, which indicate that SK based on CWD is not sensitive with window functions.In order to compare the smoothness of SK based on CWD curves with different window functions intuitively, the curvature is adopted.Supposing that there is a curve y = f (x), the curvature k can be obtained from the mathematical computation as follows: 3/2 (10) where, f (x) is the first derivation of x, and f (x) is the second derivation of x.
The deviation of curvature is calculated and adopted to evaluate the complexity of curve shape.The smoothness of curve can be defined below [31]: where, n is the index of sampling point, m represents the length of data, k n and k mean are the estimated curvature of the n-th discrete point and the average of the estimated curvature respectively.Based on the formula, if the value is large, the smoothness effect of curve is bad.If not, the smoothness effect of curve is good.The curvatures of C-phase current with Hanning and rectangular window are shown in Figure 7c.It is found that the change of curvature result with rectangular window is much than that with Hanning window, which is consistent with the results in Figure 7a,b.In addition, the average smoothness results of three-phase currents with five windows are calculated and shown in Table 2.The result with rectangular window is much larger than other windows, and results of four windows are quite similar.Actually, SK based on CWD with rectangular window is equivalent to SK without window, and the smoothing effect is not good.Hence, it is necessary to choose the efficient window function.And the results with above four windows are similar, which indicate that SK based on CWD is not sensitive with window functions.• SK Based on CWD and Noise In an actual system, signals would easily be affected by the noise, which would cause false alarms.SK is a high order cumulant with an anti-noise ability [29].In order to reflect the performance of detection and diagnosis under fault conditions with different signal-to-noise ratio (SNR), the Gaussian white noise with SNR of 20, 30 and 40 dB is added to the original signals.In the discussion in Section 3.2, SK based on CWD is appropriate for diagnosis of Fault A and B cases.Hence, the normal case, Fault A and B cases are detected and diagnosed by SK based on CWD, and the results are shown in Figure 8.It is found that the results of SK based on CWD are nearly same in the normal case with different white noise, which indicate that SK could solve the false alarm problem in the fault detection.In addition, diagnosis results of Fault A and B cases could not be influenced by the noise in the system.As a consequence, the comparisons of results fully verify that SK based on CWD method has a good anti-noise performance and not easily interfered by the system noise.In an actual system, signals would easily be affected by the noise, which would cause false alarms.SK is a high order cumulant with an anti-noise ability [29].In order to reflect the performance of detection and diagnosis under fault conditions with different signal-to-noise ratio (SNR), the Gaussian white noise with SNR of 20, 30 and 40 dB is added to the original signals.In the discussion in Section 3.2, SK based on CWD is appropriate for diagnosis of Fault A and B cases.Hence, the normal case, Fault A and B cases are detected and diagnosed by SK based on CWD, and the results are shown in Figure 8.It is found that the results of SK based on CWD are nearly same in the normal case with different white noise, which indicate that SK could solve the false alarm problem in the fault detection.In addition, diagnosis results of Fault A and B cases could not be influenced by the noise in the system.As a consequence, the comparisons of results fully verify that SK based on CWD method has a good anti-noise performance and not easily interfered by the system noise.

 Comparison of WPESE with Empirical Mode Decomposition energy Shannon Entropy
There are many traditional forms of entropy, such Shannon entropy, wavelet entropy, time entropy, energy entropy, etc.Recently, a new algorithm combined empirical mode decomposition (EMD) with energy Shannon entropy was proposed to detect the open switch fault of IGBT [28].
EMD method is an effective way to acquire the inherent characteristics of signals, which can separate the different scale signals to generate several series.Each series is called intrinsic mode function (IMF), and the IMFs must satisfy the following constraints [28]: (1) In the whole data set, the number of extrema and the number of zero-crossings must either be equal or differ at most by one; (2) At any point, the mean value of the envelope defined by local maxima and the envelope defined by the local minima is zero.
Essentially speaking, IMFs are the extractions of signal decomposition which is achieved by the

• Comparison of WPESE with Empirical Mode Decomposition energy Shannon Entropy
There are many traditional forms of entropy, such Shannon entropy, wavelet entropy, time entropy, energy entropy, etc.Recently, a new algorithm combined empirical mode decomposition (EMD) with energy Shannon entropy was proposed to detect the open switch fault of IGBT [28].
EMD method is an effective way to acquire the inherent characteristics of signals, which can separate the different scale signals to generate several series.Each series is called intrinsic mode function (IMF), and the IMFs must satisfy the following constraints [28]: (1) In the whole data set, the number of extrema and the number of zero-crossings must either be equal or differ at most by one; (2) At any point, the mean value of the envelope defined by local maxima and the envelope defined by the local minima is zero.
Essentially speaking, IMFs are the extractions of signal decomposition which is achieved by the screening process.Hence, EMD method can be implemented by the following steps [32]: (1) For a given signal x(t), it is first to determine its local maxima and minima.Then cubic spline line is adopted to connect all the local maxima and minima, respectively.Thus, the upper envelope and lower envelop can be obtained and the average value is calculated as m 1 (t).Denote: (2) If h 1 (t) satisfies the constraints of IMF, it can be the first IMF of the original signal.
Else let x(t) = h 1 (t), and repeat the Steps (1) until h 1k (t) satisfies the IMF constraints is the first IMF of the original signal.(3) Separate c 1 (t) from x(t), and the residual can be obtained as below: Let r 1 (t) be the original signal instead of x(t), and repeat the Steps ( 1) and ( 2), the second IMF c 2 (t) can be acquired.Based on that, repeat the steps above until the residual is monotonous.The original signal can be expressed as: where, r n represents the average trend of the signal, and IMF components c i , i = 1, 2, . . ., n represent the different frequency components from high to low.The probability and empirical mode decomposition Shannon entropy (EMDESE) can be obtained as Equations ( 15) and ( 16): The results of EMD and EMDESE are shown in Figure 9.The sliding window L = 150 sampling points, sliding factor a = 1 sampling points and decomposed layer y = 7.It is found that EMDESE result of A-phase is more than the threshold before fault trigging, which would cause false alarms and affect the accuracy of the diagnosis.Thus, compared with EMDESE, WPESE is more appropriate for the diagnosis of faults.
Based on the above discussion, SK based on CWD is not sensitive with window functions and has a strong anti-noise ability.Besides, through the comparison of WPESE with EMDESE, the diagnosis result of WPESE is more reliable.Therefore, the approach could solve the false alarm problem which could be caused by the system noise and has good robustness.
The results of EMD and EMDESE are shown in Figure 9.The sliding window L = 150 sampling points, sliding factor a = 1 sampling points and decomposed layer y = 7.It is found that EMDESE result of A-phase is more than the threshold before fault trigging, which would cause false alarms and affect the accuracy of the diagnosis.Thus, compared with EMDESE, WPESE is more appropriate for the diagnosis of faults.Based on the above discussion, SK based on CWD is not sensitive with window functions and has a strong anti-noise ability.Besides, through the comparison of WPESE with EMDESE, the diagnosis result of WPESE is more reliable.Therefore, the approach could solve the false alarm problem which could be caused by the system noise and has good robustness.

Experiment Results
To further validate the performance of the proposed method, some real-time online experiments about the open switch faults of IGBTs in the inverter are implemented by the RT-LAB (v11.0.8.13) platform.Through the combination of an OP5600 real-time digital simulator (OPAL-RT technologies, Canada) and its upper computer interface, the validation can be carried out.The structure diagram and the real products of real-time online simulation system are shown in Figure 10a,b, respectively.

Experiment Results
To further validate the performance of the proposed method, some real-time online experiments about the open switch faults of IGBTs in the inverter are implemented by the RT-LAB (v11.0.8.13) platform.Through the combination of an OP5600 real-time digital simulator (OPAL-RT technologies, Canada) and its upper computer interface, the validation can be carried out.The structure diagram and the real products of real-time online simulation system are shown in Figure 10a,b, respectively.First of all, the model of closed-loop controlled traction drive system is established in SIMULINK (MATLAB 2011b).There are three main parts of this model, namely, the traction motor (a squirrel cage induction motor), the DC voltage fed inverter, and the controller.The overall sketch can be seen in Figure 1.The parameters of the traction motor are shown in Table 3.The operating switch frequency of the inverter is 500 Hz, and the fall time and tail of time for each IGBT are 1 μs and 2 μs, respectively.The control strategy is vector control which is a popular strategy in traction drive system, and the modulation method is space vector pulse width modulation.
Then, the model is transformed into the real-time OP5600 digital simulator, where the validation is performed.To create the condition where the IGBT is open, the drive pulse of the corresponding IGBT will be removed.For example, to make S1 open at 3.5 s, the pulse of S1 will be removed at 3.5 s, then S1 keeps off.An upper computer is utilized as the data monitor, and the sampling frequency is 50 kHz.It keeps receiving the data from RT-LAB, which makes it possible to perform our method to diagnose the open switch faults of IGBT.Finally, aiming at the four open-switch faults and the First of all, the model of closed-loop controlled traction drive system is established in SIMULINK (MATLAB 2011b).There are three main parts of this model, namely, the traction motor (a squirrel cage induction motor), the DC voltage fed inverter, and the controller.The overall sketch can be seen in Figure 1.The parameters of the traction motor are shown in Table 3.The operating switch frequency of the inverter is 500 Hz, and the fall time and tail of time for each IGBT are 1 µs and 2 µs, respectively.The control strategy is vector control which is a popular strategy in traction drive system, and the modulation method is space vector pulse width modulation.Then, the model is transformed into the real-time OP5600 digital simulator, where the validation is performed.To create the condition where the IGBT is open, the drive pulse of the corresponding IGBT will be removed.For example, to make S1 open at 3.5 s, the pulse of S1 will be removed at 3.5 s, then S1 keeps off.An upper computer is utilized as the data monitor, and the sampling frequency is 50 kHz.It keeps receiving the data from RT-LAB, which makes it possible to perform our method to diagnose the open switch faults of IGBT.Finally, aiming at the four open-switch faults and the fault-free case, in total five conditions have been considered for further discussion.

Fault-Free Case
In a normal condition, three-phase currents and SK based on CWD curves of currents are depicted in Figure 11.The amplitudes of currents are the same.The average values of SK based on CWD are all less than 3 and satisfy Rule 1, thus, the results do not meet the fault condition, which verifies that the system is in the fault-free case.

Fault A Case
The open switch fault of an IGBT (S1) is carried out, and three-phase fault currents can be seen in Figure 12a.It is found the positive half cycle of A-phase current becomes zero at the fault time.SK based on CWD is utilized to detect the fault firstly, and curves of results are shown in Figure 12b.The average values of SK results are calculated and satisfy Rule 3, which indicates that the fault occurs in A-phase.Then, DC component of fault phase is calculated, as shown in Figure 12c.Since the DC component is negative after fault triggering, the fault can be diagnosed in the USF of A-phase, i.e., S1.

Fault A Case
The open switch fault of an IGBT (S1) is carried out, and three-phase fault currents can be seen in Figure 12a.It is found the positive half cycle of A-phase current becomes zero at the fault time.SK based on CWD is utilized to detect the fault firstly, and curves of results are shown in Figure 12b.The average values of SK results are calculated and satisfy Rule 3, which indicates that the fault occurs in A-phase.Then, DC component of fault phase is calculated, as shown in Figure 12c.Since the DC component is negative after fault triggering, the fault can be diagnosed in the USF of A-phase, i.e., S1.
The open switch fault of an IGBT (S1) is carried out, and three-phase fault currents can be seen in Figure 12a.It is found the positive half cycle of A-phase current becomes zero at the fault time.SK based on CWD is utilized to detect the fault firstly, and curves of results are shown in Figure 12b.The average values of SK results are calculated and satisfy Rule 3, which indicates that the fault occurs in A-phase.Then, DC component of fault phase is calculated, as shown in Figure 12c.Since the DC component is negative after fault triggering, the fault can be diagnosed in the USF of A-phase, i.e., S1.

Fault B Case
In this condition, open switch fault of IGBTs (S1, S6) is carried out, and fault currents can be seen in Figure 13a.The current of A-phase is non-positive while B-phase is non-negative.Also, SK based on CWD is applied to detect the fault firstly, and result is shown in Figure 13b.It indicates that a fault occurs in IGBT, and the result does not satisfy Rules 2 and 3. Hence, the WPESE method is adopted to acquire SWPESE of three-phase currents and the consequences are shown in Figure 13c.According to the results, SWPESE of A and B-phases are both more than the threshold while SWPESE of C-phase is less than the threshold.Since the results satisfy Rule 4, it is judged to be the Fault B case, and the faults appear in the A and B-phases.In addition, the DC component of the A-phase is negative and that of B-phase is positive in Figure 13d.Therefore, it turns out that the fault is diagnosed in the USF of Aphase and the LSF of B-phase, i.e., S1 and S6.

Fault B Case
In this condition, open switch fault of IGBTs (S1, S6) is carried out, and fault currents can be seen in Figure 13a.The current of A-phase is non-positive while B-phase is non-negative.Also, SK based on CWD is applied to detect the fault firstly, and result is shown in Figure 13b.It indicates that a fault occurs in IGBT, and the result does not satisfy Rules 2 and 3. Hence, the WPESE method is adopted to acquire S WPESE of three-phase currents and the consequences are shown in Figure 13c.According to the results, S WPESE of A and B-phases are both more than the threshold while S WPESE of C-phase is less than the threshold.Since the results satisfy Rule 4, it is judged to be the Fault B case, and the faults appear in the A and B-phases.In addition, the DC component of the A-phase is negative and that of B-phase is positive in Figure 13d.Therefore, it turns out that the fault is diagnosed in the USF of A-phase and the LSF of B-phase, i.e., S1 and S6.   ) is carried out.The fault currents can be seen in Figure 15a.The currents of A and B-phases are non-positive and current of C-phase is non-negative.This fault case is special and it is easily to cause the false alarm.Firstly, SK based on CWD is adopted and the results cannot satisfy Rule 2 and Rule 3 in Figure 15b.Thus, the WPESE method is applied to diagnose the fault condition in Figure 15c.It is found that S WPESE of three-phase currents are all more than the set threshold.Based on the proposed algorithm, the condition is judged to be the Fault D case.Then, diagnosis of IGBTs is realized by calculating DC components of three-phase currents, and the results are shown in Figure 15d.The results of DC components show that the DC components of A and B-phases are negative while C-phase is positive, thus, the faults can be diagnosed in A and B-phases, and the locations are the USF of fault legs, i.e., S1, S3.
In conclusion, the experimental results verify the effectiveness of the proposed fault diagnosis method.Compared to the existing fault diagnosis methods, the proposed approach can realize the diagnosis of the faults more effectively and it requires no additional devices.currents, and the results are shown in Figure 15d.The results of DC components show that the DC components of A and B-phases are negative while C-phase is positive, thus, the faults can be diagnosed in A and B-phases, and the locations are the USF of fault legs, i.e., S1, S3.
In conclusion, the experimental results verify the effectiveness of the proposed fault diagnosis method.Compared to the existing fault diagnosis methods, the proposed approach can realize the diagnosis of the faults more effectively and it requires no additional devices.

Conclusions
In this paper, aiming at detecting open switch faults in an IGBT or IGBTs, a novel diagnosis approach is proposed based on the analyses of three-phase currents.The approach mainly contains two parts, namely the fault detection part with SK based on the CWD and WPESE methods, and the fault location part with DC component method.In the fault detection part, SK based on CWD is utilized to detect the fault firstly and combined with WPESE to detect the fault phase.In the fault

Conclusions
In this paper, aiming at detecting open switch faults in an IGBT or IGBTs, a novel diagnosis approach is proposed based on the analyses of three-phase currents.The approach mainly contains two parts, namely the fault detection part with SK based on the CWD and WPESE methods, and the fault location part with DC component method.In the fault detection part, SK based on CWD is utilized to detect the fault firstly and combined with WPESE to detect the fault phase.In the fault location part, the DC components of the fault phase are calculated for determining the specific locations of faulty IGBT or IGBTs.In addition, the experiments on the RT-LAB platform of fault-free and four typical fault cases are implemented, and the results show that the proposed approach can diagnose the faults feasibly and effectively.The properties of the method can be summarized as follows: (1) SK based on CWD is not sensitive to the window functions and has an anti-noise ability, WPESE could diagnose the fault with accuracy compared with EMDESE.Therefore, the approach could solve the false alarm problem which would be caused by the system noise and has good robustness.(2) Compared with some previous methods, the method can realize the diagnosis of all single and two IGBTs fault cases and it can detect a fault and locate the open switch fault IGBTs with high accuracy.(3) The method is easily operated and requires no additional devices.

Figure 1 .Figure 2 .
Figure 1.Schematic diagram of vector controlled traction system.The diagnosis plan of open switch faults is shown in Figure 2. The fault detection part mainly contains two methods: SK based on CWD and WPESE.SK based on CWD is applied to detect the occurrence of fault firstly, then it is utilized to detect the fault phase with WPESE.Since the two methods could only detect the fault phase, the fault location part needs to calculate DC component of fault phase, which determines the specific locations of fault IGBT or IGBTs.Combined SK based on CWD, WPESE with DC component methods in the proposed approach, and the faulty IGBT or IGBTs can be diagnosed accurately.

Figure 2 .
Figure 2. Diagnosis plan of open switch faults in the inverter.

19 •
SK Based on CWD Feature This method contains a feature named K, which represents the value of SK.The results of SK in fault-free, Fault A and C cases are shown in Figure 3a-c.In normal conditions, K a , K b , K c are almost equal and keep stable at about 3 in the high-frequency domain.In Fault A case with S1 open or S4 open, K b , K c are similar with that in normal conditions.Meanwhile, K a becomes greater and the value approaches 5.The result of Fault C case with S1, S4 open shows that K a gets much greater than K b , K c , which approaches about 12. Besides, Fault B and D cases belong to the fault condition of two IGBTs in different bridge arms.The result of Fault B case with S1, S6 open in Figure

Figure 4 .
Figure 4. (a) Wavelet-packet energy Shannon entropy (WPESE) results in fault-free case; (b) WPESE results with S1, S6 open with "db2"; (c) WPESE results with S1, S6 open with "db3"; (d) WPESE results with S1, S6 open with "db4".DC Component methodThis method also contains a feature named Idc, which means the value of DC component.DC component Idc can be calculated with the following formula:

Figure 5 .
Figure 5. (a) Current flow of upper switch fault (USF); Current wave when USF occurs in(b) negative current flow; (c) Positive current flow; (d) Current flow of lower switch fault (LSF); Current wave when LSF occurs in (e) positive current flow; (f) Negative current flow.

Figure 5 .
Figure 5. (a) Current flow of upper switch fault (USF); Current wave when USF occurs in(b) negative current flow; (c) Positive current flow; (d) Current flow of lower switch fault (LSF); Current wave when LSF occurs in (e) positive current flow; (f) Negative current flow.
,b.It is found that the result of SK based on CWD with rectangular window has many oscillations and fluctuations.The result of SK based on CWD with Hanning window is steadier in the high-frequency domain.If the fluctuation values are too large, they might reach the set threshold and influence the diagnosis results.Hence, it is necessary to compare the smoothness of the curves.

Figure 7 .
Figure 7. (a) SK result with Hanning window (sampling frequency is 50 kHz); (b) SK result with rectangular window (sampling frequency is 50 kHz); (c) The result of curvature with Hanning window; (d) The result of curvature with rectangular window.

Figure 7 .
Figure 7. (a) SK result with Hanning window (sampling frequency is 50 kHz); (b) SK result with rectangular window (sampling frequency is 50 kHz); (c) The result of curvature with Hanning window; (d) The result of curvature with rectangular window.

Figure 8 .
Figure 8.(a) SK results with different noise in normal case (sampling frequency is 50 kHz); (b) SK results with different noise in Fault A case (sampling frequency is 50 kHz); (c) SK results with different noise in Fault B case (sampling frequency is 50 kHz).

Figure 8 .
Figure 8.(a) SK results with different noise in normal case (sampling frequency is 50 kHz); (b) SK results with different noise in Fault A case (sampling frequency is 50 kHz); (c) SK results with different noise in Fault B case (sampling frequency is 50 kHz).

Figure 9 .
Figure 9. (a) Empirical mode decomposition (EMD) results of A-phase fault current with S1 open; (b) empirical mode decomposition Shannon entropy (EMDESE) results of A-phase fault current with S1 open.

Figure 9 .
Figure 9. (a) Empirical mode decomposition (EMD) results of A-phase fault current with S1 open; (b) empirical mode decomposition Shannon entropy (EMDESE) results of A-phase fault current with S1 open.

Figure 10 .
Figure 10.Real-time online simulation system.(a) Real products of the system; (b) Structure diagram of the system.

Figure 10 .
Figure 10.Real-time online simulation system.(a) Real products of the system; (b) Structure diagram of the system.

Figure 11 .
Figure 11.(a) Three-phase currents in fault-free case; (b) SK results in fault-free condition.

Figure 11 .
Figure 11.(a) Three-phase currents in fault-free case; (b) SK results in fault-free condition.

Figure 12 .
Figure 12.(a) Three-phase currents with S1 open; (b) Results of SK with S1 open; (c) DC component of A-phase with S1 open.

Figure 12 .
Figure 12.(a) Three-phase currents with S1 open; (b) Results of SK with S1 open; (c) DC component of A-phase with S1 open.

Figure 13 .Figure 13 .
Figure 13.(a) Three-phase currents with S1, S6 open; (b) SK results with S1, S6 open; (c) DC components of three-phase currents with S1, S6 open; (d) WPESE results of three-phase currents.4.2.4.Fault C Case Compared with Fault A and B cases, Fault C case is easier to be diagnosed.The open switch fault of A-phase (S1, S4) is carried out and fault currents are shown in Figure 14a.Obviously, the currents of A-phase become zero when the fault occurs.The results of three-phase currents are acquired by SK based on CWD in Figure14b.Once the fault is triggered, the value of SK in A-phase is much more than B and C-phases, which approaches about 12 and meets Rule 2. Therefore, the fault can be diagnosed and judged to be Fault C case and the locations are the USF and LSF of A-phase, i.e., S1
. In normal conditions, Ka, Kb, Kc are almost equal and keep stable at about 3 in the high-frequency domain.In Fault A case with S1 open or S4 open, Kb, Kc are similar with that in normal conditions.Meanwhile, Ka becomes greater and the value approaches 5.The result of Fault C case with S1, S4 open shows that Ka gets much greater than Kb, Kc, . In normal conditions, Ka, Kb, Kc are almost equal and keep stable at about 3 in the high-frequency domain.In Fault A case with S1 open or S4 open, Kb, Kc are similar with that in normal conditions.Meanwhile, Ka becomes greater and the value

Table 1 .
The mean value of SK in different conditions.

Table 1 .
The mean value of SK in different conditions.

Table 2 .
Average smoothness of SK with different window functions.

Table 2 .
Average smoothness of SK with different window functions.

Table 3 .
Parameters of the traction motor.