IGBT (Insulated Gate Bipolar Translator) service life prediction method for optimizing particle filter based on particle swarm optimization

By constructing the state equation and observation equation and using the particle swarm algorithm to optimize the particle filter adjustment weight, the complexity and data dependence problems of IGBT life prediction are solved, and high-precision online prediction is achieved.

CN120610137APending Publication Date: 2025-09-09GUILIN UNIV OF ELECTRONIC TECH +1
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Patent Information

Application Number
CN202510578657.4
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-05-07
Publication Date
2025-09-09

AI Technical Summary

Technical Problem

Existing IGBT life prediction technology has problems such as complex models, difficulty in obtaining parameters, and reliance on large-scale sample data, which makes it difficult to improve prediction accuracy and difficult to adapt to different product types and operating scenarios.

Method used

By fitting the degradation model of failure characteristic parameter data, constructing the state equation and observation equation, optimizing the particle filter using the particle swarm algorithm, and adjusting the particle weight, the IGBT life prediction is realized.

Benefits of technology

The accuracy and applicability of IGBT life prediction have been improved, making it applicable to a variety of modules and realizing online life prediction with a stable prediction accuracy exceeding 96%.

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Abstract

The invention discloses an IGBT (Insulated Gate Bipolar Translator) life prediction method based on particle swarm optimization and particle filtering, which comprises the following steps of: fitting a degradation model of failure characteristic parameter aging data, determining model parameters, constructing a state equation and an observation equation according to the degradation model, and replacing prediction data with real-time measurement data to finish parameter adjustment of the observation equation. Particle filtering is optimized by using a particle swarm algorithm, particle weights in a prediction stage and a resampling stage of the particle filtering are respectively adjusted through optimal parameter searching of the particle swarm algorithm, and the purposes of inhibiting particle degradation, reducing data samples, accelerating convergence speed and improving prediction precision are achieved. The method can be suitable for prediction of various different modules in the system, the prediction precision is high, and a reference scheme is provided for IGBT online life prediction.
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Description

Technical Field

[0001] The present invention mainly relates to the technical field of semiconductor device prediction, and in particular to an IGBT life prediction method based on particle swarm algorithm optimized particle filtering. Background Art

[0002] In recent years, power electronic equipment has experienced rapid development, and its application areas continue to expand. However, complex operating environments pose a severe challenge to the reliability of the core component, the insulated-gate bipolar transistor (IGBT), significantly increasing the risk of failure. Against this backdrop, research into IGBT operational reliability assessment technology is of great engineering significance. By establishing efficient condition monitoring and early warning mechanisms, the risk of major accidents can be significantly reduced. Focusing on IGBT life prediction technology to avoid catastrophic failures has become a key area of ​​current reliability research.

[0003] Existing IGBT life prediction technologies mainly include analytical models, physical models, and data-driven models. Among them, although analytical models and physical models have the ability to clearly explain physical mechanisms, they face problems such as complex modeling processes and difficulty in obtaining parameters. The relevant parameters are strongly correlated with material properties, device geometry, full-cycle load conditions, and failure modes. In addition, the internal failure mechanism of the IGBT module under complex working conditions is difficult to directly observe, resulting in limited model universality. Data-driven models are further divided into machine learning models and statistical sequence models. Among them, although machine learning models can achieve high prediction accuracy, they are highly dependent on large-scale sample data and cannot quickly adapt to different product types and working scenarios. Research on statistical sequence models is currently in its initial stages. The above technical bottlenecks not only restrict the engineering application of online prediction methods in industrial sites, but also face challenges in improving their prediction accuracy at both theoretical and practical levels. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to address the deficiencies of the existing technology and provide an IGBT life prediction method based on particle swarm algorithm optimized particle filtering.

[0005] To achieve the aforementioned objectives, the present invention employs a technical solution: A degradation model is fitted to failure characteristic parameter data to determine model parameters, and a state equation and observation equation are constructed based on the degradation model. The observation equation parameters are adjusted by replacing the prediction data with real-time measurement data. A particle swarm algorithm is then used to optimize the particle filter. The particle weights in the prediction and resampling phases of the particle filter are adjusted using the particle swarm algorithm to achieve optimal parameter search, thus enabling IGBT life prediction.

[0006] The present invention is also characterized in that:

[0007] Please follow the steps below to implement it:

[0008] Step 1: Under actual working conditions, connect the saturated on-state collector-emitter voltage measurement module to the collector and emitter terminals of the IGBT. Under constant collector current working conditions, monitor the IGBT case temperature. When the case temperature reaches the minimum preset value T c_min When the IGBT is turned on, the saturated collector-emitter voltage is accurately measured. V ce_on );

[0009] Step 2: Collect the aging priori data of the IGBT module, record the saturated on-state collector-emitter voltage data obtained from each measurement and the corresponding number of IGBT turn-on times, and then obtain a complete degradation data sequence;

[0010] Step 3: Preprocessing degradation data;

[0011] Step 4: Fitting the degradation prior function based on the saturated on-state collector-emitter voltage data set of the IGBT module;

[0012] Step 5: Establish the state equation and observation equation of the particle filter based on the IGBT degradation model;

[0013] Step 6: Initialization;

[0014] According to the prior probability Initialize particle state distribution and generate particle set , each particle has a corresponding weight ;

[0015] Step 7: Define the state vector of the particle filter as X k =[a k ,b k ,c k ,d k ], when k=0, X0 is obtained by fitting the data obtained in step 4;

[0016] Step 8: Particle sampling;

[0017] According to the importance density function, importance sampling N particles are performed and expressed as, and each particle corresponds to a weight , where the importance density function is the importance density function of particle filter theory;

[0018] Step 9: Particle swarm algorithm optimizes particles;

[0019] Update the speed and position of each particle according to the particle swarm algorithm, so that the particles are closer to the posterior probability distribution of the system;

[0020] Step 10: Weight update and normalization;

[0021] Update the current particle weight according to the most recent measurement value and perform normalization;

[0022] Step 11: Resampling;

[0023] Step 12: State estimation;

[0024] Step 13: Determine the new observation;

[0025] By repeatedly calculating the particle state estimate at the next moment, we can get V ce_on Estimated value, judgment V ce_on Whether the estimate reaches the failure threshold;

[0026] Step 14: Life expectancy prediction;

[0027] V ce_on The moment k when the estimated value reaches the failure threshold is the IGBT failure moment, completing the IGBT life prediction;

[0028] Step 15: Replace the last power-on prediction data with the actual measured data, repeat steps 6 to 15, and update the data after the prediction in real time to complete the real-time life prediction of the IGBT module.

[0029] Step 1 is as follows: Set V ce_on The failure threshold is 20% of the initial value. According to the range in the IGBT module product manual, the T c_min Get the value.

[0030] Step three specifically includes: removing outliers from the complete data collected in step two, and performing Gaussian filtering and smoothing on the remaining data.

[0031] Specifically in step 5: the degradation model of IGBT is , where a, b, c, d are model parameters, k is the time, that is, the number of aging cycles, and the state equation and observation equation are as follows:

[0032]

[0033]

[0034] In formula (1), a, b, c, and d represent the model parameters obtained from the degradation model, 𝜔(𝑘) represents the process noise, and in formula (2), 𝑣(𝑘) represents the observation noise. Both the process noise and the observation noise have a mean of 0 and a variance of Gaussian white noise.

[0035] Step 7 is as follows: state vector X k =[ak ,b k ,c k ,d k ] a, b, c, and d are the same as the coefficients in step 5 and are the model parameters of the degradation model.

[0036] In step nine: the equations for updating the velocity and position of each particle using the particle swarm algorithm are as follows:

[0037]

[0038] In formula (3), is the velocity of the i-th particle at time k, is the position of the i-th particle at time k, c 1 and c 2 represents a non-negative constant learning factor, r 1 and r 2 is a random number in [0,1], P best Best for individuals, G best is the global best;

[0039] In step 10: the specific calculation of weight update is as follows:

[0040]

[0041] In formula (4), is the weight value of the i-th particle at time k, is the estimated value at time k, is the measurement value at time k, and R is the measurement noise variance.

[0042] In step 10: the specific calculation of weight normalization is as follows:

[0043]

[0044] In formula (5), for The weight value after normalization, is the weight value of the i-th particle at time k, N is the number of sampled particles.

[0045] Step 11 is as follows: In the resampling phase, if N eff ≥ N thres (set up N thres =2 / 3) then , , otherwise resample according to the importance weight and apply the velocity perturbation of the particle swarm algorithm to the copied particles.N eff And the resampled particles are calculated as follows:

[0046]

[0047]

[0048] In formula (6) N eff is the effective sample of particles, is the weight value of the i-th particle at time k, N is the number of sampled particles, and in formula (7) is the resampled particle, are the particles in the sample set, β is the disturbance intensity coefficient, is the speed of PSO.

[0049] Step 12 is as follows: Calculate ,Will As output, let =X k Substitute the state vector X k =[a k ,b k ,c k ,d k ], thereby updating the state of the system, that is, updating the model parameters a, b, c, d in the degradation model, determining the observation equation (2), and calculating the particle's V ce_on Estimated value, The calculation is as follows:

[0050]

[0051] In formula (8), is the estimated value of the system state at time k, N is the number of sampled particles, for The weight value after normalization, is the system state value of the i-th particle at time k.

[0052] Beneficial effects of the present invention:

[0053] The present invention discloses an IGBT life prediction method based on particle swarm algorithm optimization particle filter, which selects degradation characteristic parameters that are obvious in characterizing aging and easy to collect, determines model parameters by fitting the degradation model of failure characteristic parameter data, constructs state equations and observation equations according to the degradation model, replaces the predicted time data with the measured time data to complete the parameter adjustment of the observation equation, and uses the particle swarm algorithm to find the optimal parameters to adjust the particle weights in the prediction stage and resampling stage of the particle filter, thereby achieving the purpose of suppressing particle degradation, reducing data samples, accelerating convergence speed, and improving prediction accuracy. The method of the present invention has a wide range of applicability and can carry out life prediction for multiple modules under the same type of product. It is significantly different from the existing life prediction methods that rely on analytical models, physical models, and machine learning in data-driven models. Traditional analytical models and physical models are complex to construct, and parameter setting and acquisition are difficult. In addition, the parameters are closely related to material properties, product structure, load conditions, and failure modes, which increases the difficulty of application. The machine learning method of the data-driven model relies on large-scale sample data, while the method of the present invention only requires a small amount of data samples to realize online life prediction of IGBT modules, which is more flexible and feasible. Compared with the traditional particle filtering method, the prediction accuracy is significantly improved. Under normal working conditions, the average prediction accuracy is stably over 96%, providing reliable support for IGBT life prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 This is a schematic diagram of the IGBT life prediction principle of the present invention;

[0055] Figure 2 This is a flow chart of an IGBT life prediction method based on particle swarm optimization particle filtering of the present invention. Specific implementation plan

[0056] The principles and features of the present invention are described in detail below with reference to the accompanying drawings and specific embodiments.

[0057] As IGBTs age and fail, their electrical characteristic parameters will show a trend change. Existing studies have shown that the collector-emitter saturation voltage drop in the electrical characteristic parameters shows an upward trend with the number of aging cycles, and a sharp increase occurs when it reaches 20% of the initial value. Based on this, the IGBT module failure can be determined. By fitting a degradation model to the historical data of the collector-emitter saturation voltage drop, a degradation function is fitted. The state equation and observation equation are constructed according to the degradation model, the state vector of the particle filter is initialized, and N particles are sampled according to the importance density function. The present invention provides an IGBT life prediction method based on particle swarm optimization to optimize the particle filter. In order to make the particles converge to the high likelihood region faster, the proposed particle swarm algorithm is used to optimize the parameters, and the sampled initial particle filter is weighted and optimized. The weights are redistributed to increase the optimal particle weights and reduce the impact of particle degradation. The optimized particle weights are calculated and normalized. The particles are resampled according to the particle weight threshold, and the particles with larger weights are copied and the particles with smaller weights are eliminated. At the same time, the speed perturbation of the particle swarm algorithm is applied to the copied particles to increase the diversity of the particles and make them closer to the posterior probability distribution of the system. After resampling, the particles have the same weights, such as Figure 1 As shown, after the particle state is estimated, the next moment is calculated V ce_on Repeat the algorithm until V ce_on When the predicted value reaches the failure threshold, the moment when it reaches the failure threshold is the IGBT failure moment. Then, based on the data collected by the monitoring module, the observation value of the previous moment is replaced, the prediction is updated, and online prediction of IGBT life is achieved.

[0058] The present invention provides an IGBT life prediction method based on particle swarm optimization and particle filtering. The method performs degradation model fitting on historical data of collector-emitter saturation voltage drop to obtain a degradation function. The state equation and observation equation are constructed according to the degradation model. The coefficient of the observation equation is adjusted by replacing the data at the prediction time with real-time measurement data. The particle swarm optimization algorithm is used to find the optimal parameters to adjust the particle weights in the prediction stage and resampling stage of the particle filter, thereby completing the online prediction of the IGBT life. Figure 2 As shown, please follow the steps below:

[0059] Step 1: Under actual working conditions, connect the saturated on-state collector-emitter voltage measurement module to the collector and emitter terminals of the IGBT. Under constant collector current working conditions, monitor the IGBT case temperature. When the case temperature reaches the minimum preset value T c_min When the IGBT is turned on, the saturated collector-emitter voltage is accurately measured. V ce_on );

[0060] Because under the same stress conditions,V ce_on As the IGBT module ages, the value increases. When it reaches 20% of the initial value, a surge occurs. Based on this, it can be determined that the IGBT module has failed. Therefore, the V ce_on The failure threshold is 1.2 times the initial value, and the minimum case temperature setting value T is reached at the same collector current. c_min The saturated on-state collector-emitter voltage of the IGBT at the moment of first turn-on is to control the variable. V ce_on Value and T c_min The value can be selected according to the range in the product manual of the IGBT module.

[0061] Step 2: Collect the aging priori data of the IGBT module, record the saturated on-state collector-emitter voltage data obtained from each measurement and the corresponding number of IGBT turn-on times, and then obtain a complete degradation data sequence;

[0062] Step 3: Preprocessing degradation data;

[0063] Step three specifically includes: removing outliers from the complete data collected in step two, and performing Gaussian filtering and smoothing on the remaining data.

[0064] Step 4: Fitting the degradation prior function based on the saturated on-state collector-emitter voltage data set of the IGBT module;

[0065] Step 5: Establish the state equation and observation equation of the particle filter based on the IGBT degradation model;

[0066] The specific steps in step 5 are: IGBT degradation model is , where a, b, c, d are model parameters, k is the time, that is, the number of aging cycles, and the state equation and observation equation are as follows:

[0067]

[0068]

[0069] In formula (1), a, b, c, and d represent the model parameters obtained from the degradation model, 𝜔(𝑘) represents the process noise, and in formula (2), 𝑣(𝑘) represents the observation noise. Both the process noise and the observation noise have a mean of 0 and a variance of Gaussian white noise.

[0070] Steps 1 to 5 are intended to obtain a data set for lifetime prediction as input for the method of the present invention. The method of the present invention is illustrated using the saturated on-state collector-emitter voltage as an example. In fact, this data set covers sensitive parameters that have been clearly studied and show significant threshold changes with the aging process, such as: junction temperature-case temperature transient thermal resistance, collector-emitter turn-off spike voltage, turn-off time, etc. As long as the control variable method is used for measurement under the same stress conditions, the data composed of these parameters can be used as input data for this method.

[0071] Step 6: Initialization;

[0072] According to the prior probability Initialize particle state distribution and generate particle set , each particle has a corresponding weight ;

[0073] Step 7: Define the state vector of the particle filter as X k =[a k ,b k ,c k ,d k ], at the moment k=0, X0 is obtained by fitting the data obtained in step 4;

[0074] In step seven, the state vector is X k =[a k ,b k ,c k ,d k ] a, b, c, and d are the same as the coefficients in step 5 and represent the model parameters of the degradation model.

[0075] Step 8: Particle sampling;

[0076] Importance sampling is performed on N particles according to the importance density function, and the Indicates that each particle corresponds to a weight , where the importance density function is the importance density function of particle filter theory;

[0077] Step 9: Particle swarm algorithm optimizes particles;

[0078] In step nine: the equations for updating the velocity and position of each particle using the particle swarm algorithm are as follows:

[0079]

[0080] In formula (3), is the velocity of the i-th particle at time k, is the position of the i-th particle at time k, c 1 and c 2 represents a non-negative constant learning factor,r 1 and r 2 is a random number in [0,1], P best Best for individuals, G best is the global best;

[0081] Update the speed and position of each particle according to the particle swarm algorithm, so that the particles are closer to the posterior probability distribution of the system;

[0082] Step 10: Weight update and normalization;

[0083] In step 10: the specific calculation of weight update is as follows:

[0084]

[0085] In formula (4), is the weight value of the i-th particle at time k, is the estimated value at time k, is the measurement value at time k, and R is the measurement noise variance.

[0086] In step 10: the specific calculation of normalization is as follows:

[0087]

[0088] In formula (5), for The weight value after normalization, is the weight value of the i-th particle at time k, N is the number of sampled particles.

[0089] Update the current particle weight according to the most recent measurement value and perform normalization.

[0090] Step 11: Resampling;

[0091] Step 11 is as follows: In the resampling phase, if N eff ≥ N thres (set up N thres =2 / 3) then , , otherwise resample according to the importance weight and apply the velocity perturbation of the particle swarm algorithm to the copied particles. N eff And the resampled particles are calculated as follows:

[0092]

[0093]

[0094] In formula (6) N eff is the effective sample of particles, is the weight value of the i-th particle at time k, N is the number of sampled particles, and in formula (7) is the resampled particle, are the particles in the sample set, β is the disturbance intensity coefficient, is the speed of PSO.

[0095] Step 12: State estimation;

[0096] Step 12 is as follows: Calculate ,Will As output, let =X k Substitute the state vector X k =[a k ,b k ,c k ,d k ], thereby updating the state of the system, that is, updating the model parameters a, b, c, d in the degradation model, determining the observation equation (2), and calculating the particle's V ce_on Estimated value, The calculation is as follows:

[0097]

[0098] In formula (8), is the estimated value of the system state at time k, N is the number of sampled particles, for The weight value after normalization, is the system state value of the i-th particle at time k.

[0099] Step 13: Determine the new observation;

[0100] By repeatedly calculating the particle state estimate at the next moment, we can get V ce_on Estimated value, judgment V ce_on Whether the estimate reaches the failure threshold;

[0101] Step 14: Life expectancy prediction;

[0102] according to V ce_on The moment k when the estimated value reaches the failure threshold is the IGBT failure moment, completing the IGBT life prediction;

[0103] Step 15: Replace the last power-on prediction data with the actual measured data, repeat steps 6 to 15, and update the data after the prediction in real time to complete the real-time life prediction of the IGBT module.

[0104] From the above content, it can be seen that the IGBT life prediction method based on particle swarm algorithm optimized particle filtering in the present invention avoids complex model analysis and internal aging failure mechanism research, and selects easily monitored degradation characteristic parameters as input and prediction variables. The method of the present invention can be used in a system containing multiple different IGBT modules, and life prediction can be performed using a small amount of data samples, and is suitable for real-time life prediction scenarios of IGBT modules.

Claims

1. A method for predicting IGBT lifespan based on particle swarm optimization and particle filtering, characterized in that: By fitting the degradation model of failure characteristic parameter data, the model parameters are determined, the state equation and observation equation are constructed according to the degradation model, and the parameters of the observation equation are adjusted by replacing the prediction data with real-time measurement data. The particle swarm algorithm is used to optimize the particle filter, and the particle weights in the prediction stage and resampling stage of the particle filter are adjusted through the optimal parameter search of the particle swarm algorithm to realize IGBT life prediction.

2. The IGBT life prediction method based on particle swarm optimization and particle filtering according to claim 1, characterized in that: Please follow the steps below to implement it: Step 1: Under actual working conditions, connect the saturated on-state collector-emitter voltage measurement module to the collector and emitter terminals of the IGBT. Under constant collector current working conditions, monitor the IGBT case temperature. When the case temperature reaches the minimum preset value T c_min When the IGBT is turned on, the saturated collector-emitter voltage ( V ce_on ); Step 2: Collect the aging priori data of the IGBT module, record the saturated on-state collector-emitter voltage data obtained from each measurement and the corresponding number of IGBT turn-on times, and then obtain a complete degradation data sequence; Step 3: Preprocessing degradation data; Step 4: Fitting the degradation prior function based on the saturated on-state collector-emitter voltage data set of the IGBT module; Step 5: Construct the state equation and observation equation based on the IGBT degradation model; Step 6: Initialization; According to the prior probability Initialize particle state distribution and generate particle set , each particle has a corresponding weight ; Step 7: Define the state vector of the particle filter as X k =[a k ,b k ,c k ,d k ], when k=0, X0 is obtained by fitting the data obtained in step 4; Step 8: Particle sampling; Importance sampling is performed on N particles according to the importance density function, and the Indicates that each particle corresponds to a weight , where the importance density function is the importance density function of particle filter theory; Step 9: Particle swarm algorithm optimizes particles; Update the speed and position of each particle according to the particle swarm algorithm, so that the particles are closer to the posterior probability distribution of the system; Step 10: Weight update and normalization; Update the current particle weight according to the real-time measurement value and perform normalization; Step 11: Resampling; Step 12: State estimation; Step 13: Determine the new observation; By repeatedly calculating the particle state estimate at the next moment, we can get V ce_on Estimated value, judgment V ce_on Whether the estimate reaches the failure threshold; Step 14: Life expectancy prediction; V ce_on The moment k when the estimated value reaches the failure threshold is the IGBT failure moment, completing the IGBT life prediction; Step 15: Replace the last power-on prediction data with the actual measured data, repeat steps 6 to 15, and update the data after the prediction in real time to complete the real-time life prediction of the IGBT module.

3. The IGBT life prediction method based on particle swarm optimization and particle filtering according to claim 2, characterized in that: The specific step 1 is: setting V ce_on The failure threshold is 20% of the initial value. According to the range in the IGBT module product manual, the T c_min Get the value.

4. The IGBT life prediction method based on particle swarm optimization and particle filtering according to claim 2, characterized in that: The step three specifically includes: removing outliers from the complete data collected in the step two, and performing Gaussian filtering and smoothing on the remaining data.

5. The IGBT life prediction method based on particle swarm optimization and particle filtering according to claim 2, characterized in that: The specific step 5 is: IGBT degradation model is , where a, b, c, d are model parameters, k is the time, that is, the number of aging cycles, and the state equation and observation equation are as follows: ; ; In formula (1), a, b, c, and d represent the model parameters obtained from the degradation model, 𝜔(𝑘) represents the process noise, and in formula (2), 𝑣(𝑘) represents the observation noise. Both the process noise and the observation noise have a mean of 0 and a variance of is Gaussian white noise.

6. The IGBT life prediction method based on particle swarm optimization and particle filtering according to claim 2, characterized in that: The specific step seven is: the state vector X k =[a k ,b k ,c k ,d k ] a, b, c, and d are the same as the coefficients in step 5 and are the model parameters of the degradation model.

7. The IGBT life prediction method based on particle swarm optimization and particle filtering according to claim 2, characterized in that: In step nine, the equations for updating the velocity and position of each particle using the particle swarm optimization algorithm are as follows: ; In formula (3), is the velocity of the i-th particle at time k, is the position of the i-th particle at time k, c 1 and c 2 represents a non-negative constant learning factor, r 1 and r 2 is a random number in [0,1], P best Best for individuals, G best is the global best; In step 10, the specific calculation of weight update is as follows: ; In formula (4), is the weight value of the i-th particle at time k, is the estimated value at time k, is the measurement value at time k, R is the measurement noise variance; In the step 10, the specific calculation of weight normalization is as follows: ; In formula (5), for The normalized weight value, is the weight value of the i-th particle at time k, N is the number of sampled particles.

8. The IGBT life prediction method based on particle swarm optimization and particle filtering according to claim 2, characterized in that: The specific step 11 is: in the resampling stage, if N eff ≥ N thres (set up N thres =2 / 3) then , , otherwise resample according to the importance weight and apply the velocity perturbation of the particle swarm algorithm to the copied particles. N eff and the resampled particles are calculated as follows: ; ; In formula (6) N eff is the effective sample of particles, is the weight value of the i-th particle at time k, N is the number of sampled particles, and in formula (7) is the resampled particle, are the particles in the sample set, β is the disturbance intensity coefficient, is the speed of PSO.

9. The IGBT life prediction method based on particle swarm optimization and particle filtering according to claim 2, characterized in that: The specific steps of step 12 are: calculating ,Will As output, let =X k Substitute the state vector X k =[a k ,b k ,c k ,d k ], thereby updating the state of the system, that is, updating the model parameters a, b, c, d in the degradation model, determining the observation equation (2), and calculating the particle's V ce_on Estimated value, The calculation is as follows: ; In formula (8), is the estimated value of the system state at time k, N is the number of sampled particles, for The normalized weight value, is the system state value of the i-th particle at time k.