An Improved Prediction Model of IGBT Junction Temperature Based on Backpropagation Neural Network and Kalman Filter

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Introduction
e insulated gate bipolar transistor (IGBT) is the main power electronic energy conversion device and transmission device.It combines the merits of MOSFET and BJT with low drive power and low saturation voltage.e IGBT has become the pivotal supporting technology to alleviate energy shortages and reduce carbon emissions since it is highly efficient, energy-saving, and environmentally friendly.Nowadays, it is widely utilized in communication, rail transit, smart grid, aerospace, electric vehicles, and new energy power generation [1].Given the significance of the IGBT, it is essential to maintain safety and reliability during the IGBT device's operation.
One of the most important factors affecting the technical progress and development of the IGBT is operating temperature.e high junction temperature resulted from large heat fluxes will significantly deteriorate the performance and reliability of the IGBT device [2].e electronics prognostics supplied by the NASA AMES Laboratory also pointed out that overheating of the IGBT die is one of the main causes of the failure [3].In a related survey on the power device's reliability, the failure rate due to junction temperature is as high as 55% and doubles for every 10 °C increase [4].us, ensuring the IGBT junction is maintained at a controllable temperature is the cornerstone of keeping the IGBT device's stability.Monitoring IGBT junction temperature during the operation has become the major challenge and top priority at present.
ere have already been many approaches to monitor junction temperature, including optical, physical, and electrical methods [5,6].e optical method measures the energy change of lattice photons to infer the junction temperature using infrared (IR) cameras [7], IR sensors [8], IR microscope [9], and optical fiber [10].is method can directly and accurately obtain the junction surface temperature map, but the implementation usually requires expensive instruments and extra modification on the standard module package.e typical physical method is the electrothermal model, which uses thermistors or thermocouples to physically contact the IGBT chip and infer the junction temperature [11,12].However, this method's response time is usually long because of the thermal capacitance of thermistors and thermocouples [5].Besides, the physical method relies too much on complex physical models.e accuracy of prediction will be greatly reduced once the physical models change for some reason.e electrical method uses temperature-sensitive electrical parameters (TSEPs) such as gate threshold voltage (V th ) [13], on-state voltage (V CEon ) [14], short circuit current (I sc ) [15], and peak gate current (I Gpeak ) [16] to calculate or infer the junction temperature.It can be found either in the scientific literature or the device datasheet published by the manufacturer that there is good linearity between TSEPs and junction temperature.A major benefit of using the electrical method is that the junction temperature can be obtained without modifying the standard module package, which is also the main reason it is used more now.is article will focus on the approach of using on-state voltage (V CEon ) at a high current.
e conventional V CEon (high-current) TSEP method attempts to build a temperature model using linear equations.However, the relationship between on-state voltage and junction temperature does not perform absolute linearity.ere is always an error between the real value and the calculated value [17].Dong and coworkers recently proposed a new junction temperature prediction model using an artificial neural network (ANN) [18].ey applied the backpropagation (BP) neural network to predict the junction temperature using on-state voltage and collector current.e results are compared with the conventional TSEP method, and the feasibility of the BP neural network is proved.However, because of the inherent data, randomness during the training process, and intrinsic nonidentifiability of the model, the prediction results are prone to strong instability [19]. is article proposes a new method using the Kalman filter based on BP neural network and interpolation to stabilize the prediction.e flowchart of this approach is shown in Figure 1.
is article is organized as follows: Section 2 describes the object of study and simulation environment.Section 3 introduces three methods used to predict junction temperature and their parameter settings.e results are given in Section 4. e validities of the BP neural network and Kalman filter are verified.ere is also a comparison between the errors of the three predicting methods in this section.Section 5 discusses the superiority of the Kalman filter prediction and the possibility of improvement.Finally, the conclusion is drawn.e on-state voltage test circuit is built to measure the on-state voltage V CEon of the IGBT discrete.e test circuit includes current source, power load, IGBT discrete, control system, and voltmeter, as shown in Figure 2. e junction temperature extraction can be carried out without modifying the standard package even under the real experimental environment.

Simulation Settings
In LTspice, set the global temperature to a certain value, which is also assumed to be the junction temperature.Next, set the output of the current source I S and drive IGBT discrete with a single pulse.
en measure the on-state voltage under this condition.Afterward, tune the collector current I C and junction temperature T j (global temperature) to obtain the on-state voltages V CEon under different conditions.In the simulation, this task can be completed quickly by using the sweep function.e value range of collector current I C is from 5 A to 75 A, and junction temperature T j is from 25 °C to 175 °C.e sample intervals are one ampere (1 A) and one-degree centigrade (1 °C), respectively.Hence, 10721 groups of data in total can be obtained.One thousand groups for the training set and 20 groups for the test set are randomly assigned, respectively.Random sampling intends to check the neural network's robustness, but it is recommended to sample evenly in the real experiment.

Methods
is section introduces three methods, including backpropagation (BP) neural network, interpolation, and the Kalman Filter.e BP estimation and interpolated value are used as the Kalman filter measurement and prediction model, respectively.
e setup and application of each method are also drawn.

Backpropagation Neural
Network.Backpropagation (BP) neural network is a multilayer feedforward neural network trained according to the error backpropagation algorithm.It is capable of classifying arbitrary complex patterns and mapping multidimensional functions.e BP neural network base is the gradient descent method, which uses gradient search to minimize the mean square error between the actual and the expected output.e inputs are transmitted from the input layer to the output layer after being processed by the hidden layers during forward propagation.If the actual output is inconsistent with the expected output, then move to backpropagation.During backpropagation, the output is back transmitted to the input layer somehow, and the error is distributed to all units of each layer.en, each layer's error can be obtained, which is used to correct the weight of each unit.With the continuous correction of the error, the network's accuracy will be improved step by step [20].
e junction temperature prediction model can be regarded as a complex nonlinear system, which is difficult to be accurately modelled with a single mathematical method.In this case, BP neural network can be constructed to express it.On-state voltage V CEon and collector current I C of IGBT discrete are chosen as the inputs.e junction temperature T j is chosen to be the output.When the signal is transmitted, the inputs V CEon and I C act on the output node through the hidden layer.After the nonlinear transformation, the prediction of junction temperature T e is generated from the output layer.If the actual output T e is equal to the expected 2 Complexity output T j , then propagation is terminated.Otherwise, the error will be allocated to all nodes in each layer through backpropagation.e neural network's weight and deviation are updated in the fastest increasing direction to minimize the error.e structure of the BP neural network in this article is shown in Figure 3.As the figure shows, the neural network consists of two inputs, one output, and one hidden layer including ten neurons.For a complex task, choose 0.01 for learning rate and 0.9 for the momentum parameter to achieve high performance [20].e other parameter settings for training the neural network are listed in Table 1, and the implementation is based on the MATLAB "neural network training toolbox."It is worth mentioning that, before starting the training, the dataset should be normalized to avoid possible numerical problems [21].e BP estimation will be used in Section 3.3 as the measurement model of the Kalman filter.

Interpolation Method.
e interpolation method interpolates the continuous function based on the discrete data.e continuous curve passes through all data points, which is a vital approach to approximate discrete functions.It can estimate the approximation of other points by analyzing the function value of finite points.
Use the interpolation function in MATLAB to generate an interpolation graph composed of on-state voltage V CEon , collector current I C , and junction temperature T j , as shown in Figure 4.Because of the resolution limitation, the extracted temperature will be slightly different from the real junction temperature.On top of that, the personal error also probably exists during the extraction.e interpolated value will be used in Section 3.3 as the prediction model of the Kalman filter.

Kalman
Filter.Kalman filter (KF) is an algorithm using the linear system's state equation to predict the system state through measurement.Since the measurement includes some noise and disturbance, the optimal estimation can also be regarded as a filtering process [22].e first step is to predict the current state based on the previous state and control vector.e state equation from time k − 1 to k is defined as where A and B are the state transition matrix and controlinput matrix, respectively, A is set as identity matrix I, and control vector u k−1 is set as zero since the temperature does not change in a short time.e w k−1 is the noise during the prediction process.It is assumed to be white Gaussian noise with mean zero and covariance Q, denoted as w k−1 ∼N(0, Q).Because of the limited resolution and personal error, the interpolated value will have some fluctuations.Hence, it can be considered to satisfy the Gaussian distribution with covariance Q. e measurement equation defines the relationship between the state and the measurement at the time k as follows: where v k is the noise from the measurement.It is assumed to be white Gaussian noise with mean zero and covariance R, denoted as v k ∼N(0, R). e measurement will be directly loaded from the BP estimations.e neural network's estimations can also be considered to satisfy the Gaussian distribution with covariance R since it has the oscillation around a fixed point.When both the prediction and measurement model satisfy Gaussian distribution, their product will also be Gaussian distribution.e fused Gaussian distribution has a higher probability density and smaller variance, as shown in Figure 5. Kalman algorithm is a recursive prediction-update method and can be divided into prediction stage and correction stage.e prediction stage calculates the state variable's prior estimate based on the posterior estimate of the Complexity 3 previous moment.It can be described in the next two equations: where P is the state error covariance; it represents the credibility of the prediction stage.e correction stage combines the prior estimate with the new measurement variables to construct the optimal estimate.It can be described in the following three equations: where R is the covariance of the measurement noise; it represents the measurement stage's credibility.e implementation of the Kalman filter is based on the MATLAB code.Use the interpolated value as the prediction and 100 different BP estimations to measure the Kalman filter, respectively.R and Q's values need to be tuned to obtain the most appropriate result, that is, make the optimal estimation closer to the expected value.

Results and Discussion
is section provides the validities of the BP neural network and the Kalman filter.Also, the detailed results of the three methods introduced in Section 3 are given.In the end, the experimental conclusions are also drawn.

Inflection Point of IGBT.
Based on the simulation's collected data, the relationship between on-state voltage V CEon , collector current I C , and junction temperature T j is drawn.Figure 6 shows that these coordinate points can make up a smooth surface.It is apparent that the value of V CEon is affected by both I C and T j , which verifies the correctness of selecting V CEon and I C as the inputs of the temperature prediction model.
Figure 7 indicates that on-state voltage increases with the increment of junction temperature in the above three conditions but decreases below three conditions.is normal phenomenon is caused by the manufacturing process, which is known as the inflection point.e curves with positive and negative temperature coefficients intersect at this point.
By checking the data table obtained from simulation, the inflection point is found around 42 A. On-state voltage and junction temperature have a positive correlation when the collector current is larger than 42 A and a negative correlation when the collector current is smaller than 42 A. Consequently, the next sections' analysis will be divided into two parts (I C < 42 A and I C > 42 A).Limited to the article's length, this article's analysis will focus on the condition when the collector current is larger than 42 A. Still, the result of both conditions will be given in Section 4.5.

Validity of BP Neural
Network.Sometimes, the BP neural network can only accurately predict specific but not all test sets because of contingency.To avoid that, it is necessary to pick different training and test sets to check the validity [23].In this case, three completely different training and test sets are used to construct and evaluate the neural network.Each training set contains 1000 groups of data, and each test set includes 20 data groups.Besides, the parameter settings of the three control groups are the same.
e three control groups' error and percentage error are shown in Figures 8(a) and 8(b).It is observed that the absolute errors are mostly below 10 °C and the percentage errors are mostly below 15%.e neural network performs well with each dataset, which also confirms its strong generalization ability.

Oscillation of BP Neural Network Estimations.
Because the BP neural network model is initialized when built, the estimated value will differ each time.Pick three test data and put them in 100 different neural networks.e results are shown in Figure 9, and three test data are coloured differently.It is observed that the BP estimations are unstable but oscillate around their mean values.e oscillation appears because the initial weights and thresholds are   Complexity generated randomly.Most of the points are close, but a few are far from the mean value.In other words, the closer to the mean, the higher probability of a point occurs.It indicates that the BP estimations used as the Kalman filter measurement model conform to the Gaussian distribution approximately.It is also found that the mean value of estimations becomes stable after around 15 repetitions.us, using the mean value is a feasible way to stabilize the oscillation.However, the estimation given by BP neural network can be further treated to increase the accuracy.

Validity of Kalman Filter.
e BP estimations obtained from Section 4.3 are used as the measurement of the Kalman filter.e interpolated value obtained from Section 3.2 is used as the initial estimate of the Kalman filter.Pick one test data randomly to check the performance of the Kalman filter based on BP and interpolation.e results are shown in Figure 10.
e figure shows the performance comparison between interpolation, BP neural network, and Kalman filter.It is observed that the curve of Kalman filter prediction moves 6 Complexity towards where the BP estimations occur more frequently.Also, it converges after about 85 iterations and will be finally stabilized around the expected value.In this case, Kalman filter prediction has a big advantage over the other two methods in both stability and accuracy.

Performance Comparison between ree Predicting
Methods.Check the Kalman filter's performance on all test data and compare the result with the mean value of BP estimations and the interpolated value.As shown in Figures 11(a e detailed predicted values in the two conditions are given in Tables 2 and 3.In most cases, the Kalman filter prediction is between the BP mean and interpolated value because the nature of the Kalman filter is the weighted average.e comparison of errors is shown in Table 4.In condition I C < 42 A, RMSE and MAPE of Kalman prediction are 2.6415 and 0.0166, respectively, which are smaller than the other two predicting methods.In condition I C > 42 A, RMSE and MAPE of Kalman filter prediction are 4.8282 and 0.0284, respectively, which are also smaller than the other two predicting methods.e results indicate that the Kalman filter has a significant advantage in predicting junction temperature.e feasibility of using the Kalman filter based on BP neural network and interpolation has been further confirmed.

Discussion
In Section 4.2, the validity of the BP neural network has been confirmed.e absolute errors of estimation are mostly less than 10 °C, but the oscillation still impedes the accurate prediction of junction temperature.Calculating their mean can reduce the error and stabilize the oscillation to some extent.As Table 4 shows, the RMSE and MAPE of BP estimation are 3.6528 and 0.0221 (I C < 42 A), respectively.e RMSE and MAPE of the interpolated value are 5.9161 and 0.0349 (I C < 42 A), respectively.However, the BP neural network estimation and interpolation accuracy will be reduced in the real experiment because it is hard to obtain over 1000 samples.Using the Kalman filter based on BP neural network and interpolation can further stabilize the oscillation and reduce the error below 5 °C.e RMSE and MAPE of Kalman filter prediction are 2.6415 and 0.0166 (I C < 42 A), respectively.As one can see, Kalman filter prediction performs better than interpolation or BP estimation.In another condition (I C > 42 A), the three predicting methods perform similarly.e prediction of junction temperature is important for condition monitoring and degradation of the IGBT devices.Section 4.2 indicates it is feasible to estimate the junction temperature using BP neural network without modifying the standard package.Section 4.5 shows that the Kalman filter prediction accuracy in both conditions (I C < 42 A and I C > 42 A) is higher than the BP estimation or interpolation.In addition to increasing accuracy, it also enhances robustness.Even when outliers appear, the prediction filtered by the Kalman filter can still maintain stability.
Furthermore, there are several possibilities for improvement in this scheme.First, the updated version of the BP neural network such as PSO-BP [24], GA-BP [25], and MEA-BP [26] can be applied to increase the speed and accuracy of the convergence.Second, the use of the combined TSEPs can increase the reliability of the prediction [27,28].ird, other prediction models can be used instead  e Kalman filter method further enhances accuracy and robustness.Nevertheless, compared with BP neural network, the Kalman filter based on it requires more complex processes.With the rapid development of deep learning or neural network, the accuracy of junction temperature prediction is expected to be further improved.eoretically, the neural network can approach any complex function perfectly.What is more, the application scope of deep learning can be expanded to evaluate the aging degree or failure rate of the power device.

Conclusions
e Kalman filter based on BP neural network and interpolation proposed in this article has the following advantages: (1) ere is no need to modify the standard module package.
(2) It is simpler than the conventional TSEP method.
e voltage drop between the junction and the measurement point can be neglected.
(3) It is more accurate and stable than the BP neural network estimation.(4) It can be migrated to online monitoring after the entire prediction model has been built.(5) ere is a large room for improvement.
Deep learning in power electronics devices can help monitor the operating condition and evaluate the degradation from a new perspective.It is expected to promote the development of power electronics further.
is article's research object is Infineon IKW75N65ET7 IGBT discrete (650 V, 75 A) and the simulation is based on LTspice.e SPICE model downloaded from Infineon has already included the temperature module.

Figure 1 :Figure 2 :
Figure 1: Block diagram of the methods for predicting junction temperature.

Figure 3 :
Figure 3: e flowchart of the BP neural network for estimating junction temperature.

Figure 4 :Figure 5 :Figure 6 :
Figure 4: e interpolation graph which is composed of the training set.
) and 11(b), the Kalman filter greatly stabilizes the BP estimations and interpolated values.In both conditions (I C < 42 A and I C > 42 A), the errors are mostly below 5 °C.

Figure 9 :
Figure 9: e temperature estimations of three samples with 100 times repetition.

Figure 10 :
Figure 10: Performance comparison with 100 times of repetition.

Figure 11 :
Figure 11: (a) e comparison of errors when I C < 42 A. (b) e comparison of errors when I C > 42 A.

Table 1 :
BP neural network training parameters.

Table 3 :
e numerical comparison of three methods when I C > 42 A.

Table 2 :
e numerical comparison of three methods when I C < 42 A.

Table 4 :
8MSE and MAPE comparisons of three predicting methods.Root mean square error.2Meanabsolutepercentageerror.8Complexity of interpolation, because the accuracy of interpolation could be greatly affected by the sample size.In sum, both BP neural network and Kalman filter can work well in predicting IGBT junction temperature.