Method for hybrid prediction of residual life of aero-engine based on two particle filters

Abstract

The invention discloses a method for hybrid prediction of the residual life of an aero-engine based on a two-particle filter, and belongs to the technical field of data prediction. Comprising the following steps: preprocessing data, establishing models, performing MO-RVM modeling on each piece of existing measurement data, and establishing initial ny MO-RVM prediction models; determining whether to dynamically update the model or not according to a prediction result of the prediction model; predicting health parameters: predicting a system state and hidden health parameters by using a state / health parameter two-particle filter to realize k-step forward prediction of the state and the health parameters; and residual life prediction: drawing a probability density function of health parameter prediction particles in the DPF to obtain a moment with the maximum probability. According to the method, long-term measurement data prediction is realized by using a data driving method based on dynamic updating, and then a predicted value of a health parameter is estimated by using a double-particle filter, so that the residual life from the current moment to the system failure moment is predicted, and the accuracy and reliability of life prediction are improved.

Description

Technical Field

[0001] The invention relates to the technical field of data prediction, in particular to a method for predicting the remaining life of an aeroengine based on a dual particle filter hybrid. Background Art

[0002] As the heart of an aircraft, the performance stability and reliability of an aircraft engine are directly related to the safety of the aircraft. With the rapid development of the aviation industry, the demand for real-time monitoring of aircraft engine performance and life prediction is growing. Traditional life prediction methods mainly rely on empirical formulas or simple statistical analysis, which often ignore the complexity and variability of engine operation.

[0003] Existing technical solutions: mainly include analytical methods based on physical models and statistical methods based on data-driven. The physical model-based method predicts the performance change trend by constructing the physical equation of engine performance. However, these methods require detailed physical parameters and accurate initial conditions, and in practical applications, the accuracy and practicality of their predictions are limited because the internal state of the engine is difficult to measure directly.

[0004] Data-driven methods, such as artificial neural networks and support vector machines, establish prediction models by analyzing historical data. Although these methods can reflect the statistical laws of engine performance to a certain extent, they usually lack a deep understanding of the physical processes inside the engine and have high requirements for data quality and quantity. In the case of insufficient data or low data quality, the prediction effect is limited.

[0005] Considering both safety and economy, with the rapid development of the aviation industry, the demand for fault diagnosis, prediction and health management in the aviation field is becoming more and more urgent. However, my country's research in this field is still in its infancy, showing a phenomenon of mismatch between demand and reality. Therefore, the present invention is oriented to the aviation field, and for aircraft engines, the application of a hybrid prediction method based on a dual particle filter in aircraft engines is used to study the remaining life prediction method. Summary of the invention

[0006] In order to solve the respective shortcomings of the two prediction methods of data-driven and physical model-based in the prior art and the problem that traditional observers only estimate the system state and usually cannot directly obtain health parameters, the present invention provides a method for hybrid prediction of the remaining life of an aircraft engine based on a dual-particle filter. The method combines the advantages of data-driven and physical model-based, estimates the state and health parameters of the aircraft engine through a dual-particle filter, and performs long-term prediction of the measured data through a dynamically updated multi-output correlation vector machine, effectively improving the accuracy and reliability of life prediction.

[0007] The purpose of the present invention is achieved through the following technical solutions: The method for predicting the remaining life of an aircraft engine based on a dual particle filter hybrid includes the following steps: Step 1: Data preprocessing and model building: Select states for calculation and estimation x , observe sensor measurements y and health parameters θ , conduct MO-RVM modeling for each existing measurement data and establish the initial n y MO-RVM prediction model; Step 2: According to the prediction results of the prediction model, decide whether to dynamically update the model: determine whether the MO-RVM model needs to be updated according to the state update rule. If the judgment result shows that it needs to be updated, then the DMO-RVM model will be further established, and then the sensor observation value will be predicted. If no dynamic update is required, the prediction will be made directly. Step 3: Predict health parameters: Use the state / health parameter dual particle filter to predict the system state and hidden health parameters based on the sensor observations predicted in step 2, and achieve k-step forward prediction of the state and health parameters; Step 4: Remaining life prediction: Based on the predicted health parameter values ​​obtained in step 3, the probability density distribution of the predicted health parameters is plotted. By plotting the probability density function of the health parameter prediction particles in the DPF, the moment with the highest probability is obtained, which is the estimated remaining life.

[0008] Furthermore, in step 1, MO-RVM modeling is performed on each existing initial measurement data to obtain n y The initial prediction models are: , according to the formula:

[0009] The initial k-step forward prediction results are obtained through iteration: .

[0010] Furthermore, the state update rule in step 2 is determined by the difference between the predicted measurement value and the actual measurement value, and the difference between the predicted measurement value and the actual measurement value is quantified using the Mahalanobis distance. The Mahalanobis distance of single-point comparison is defined as:

[0011] Where Σ is the covariance matrix of the multidimensional random variable, μ is the mean of the reference sample, is the matrix transpose, and x is the measured value.

[0012] Furthermore, the judgment criteria in step 2 are as follows: Measurements in the monitoring window m The average value of the lower Mahalanobis distance is ,when n Any of the average distances is greater than the threshold And it is greater than the average Mahalanobis distance of the previous window times, it is determined that an update is needed, and the judgment rules are as follows:

[0013] Where: is the threshold 1, used to determine the size of the distance, is threshold 2; used to determine the speed of the distance change rate; Since there is no need to n The prediction model of each measurement value is updated. Therefore, sub-rules are established under the above judgment rules for secondary judgment. The sub-rules are as follows:

[0014] Where: σ 3 is the secondary decision threshold, and , when the above sub-rules are met, it is determined that there is no need to Road update.

[0015] Furthermore, in step 3, the prediction process is as follows: For the time step : (1) Perform r-step forward prior state prediction: according to Predict a priori state particles, where is t+r The particle noise added to the state particles at all times has a distribution that conforms to , and They are t+ r- Status at moment 1 x and health parameters θ An estimated value of according to Estimate the prior state covariance matrix; (2) Perform r-step forward posterior state prediction: By resampling, we calculate ,get t+r Status at all times x Estimate filter weights ,in, for The probability density function of Compute the approximate posterior state distribution: ,in, Nreg is the regularization quantity, Depend on Calculated; According to the filter weight Resample the state estimation particles, which is done with The obtained posterior state estimate distribution after approximate resampling is , is the Dirac function; according to Approximate a posteriori state estimates; (3) Perform the first r-step forward posterior parameter prediction: Calculate the corrected output prediction error , is a nonlinear equation between the state, health parameters and measurements; Calculate correction parameters ,in, is the adaptive coefficient in the calibration process, For the j Jacobian determinant of the particle; The kernel shrinkage algorithm is used to calculate the first step posterior parameter prediction: , A is the contraction matrix, , is the noise distribution added to each particle; (4) Perform the second r-step forward posterior parameter prediction: Compute parameter estimates filter weights To resample, The first posterior parameter distribution is approximated as follows , Predicting particles based on resampling parameters After resampling, the approximate posterior parameter prediction distribution is , Get the posterior parameter prediction , Calculate the posterior parameter prediction covariance as ; According to the above prediction process, the predicted measurement data is used and resampling is maintained for future moments to generate a health parameter particle probability density function predicted k steps forward.

[0016] Furthermore, in step 4, for the D-dimensional data x, the health parameter particle probability density function The calculation formula is:

[0017] in, μ is the mean of x, Σ is the covariance of x, and x is the health parameter of the engine.

[0018] Furthermore, in step 4, the remaining life RUL (t) at time t is calculated as follows: ,

[0019] , Where: is the time when any relevant parameter reaches the critical value, is the critical value of the parameter at which failure occurs.

[0020] The present invention has the following advantages: 1. By collecting and integrating available historical measurement data, a dynamic multi-output relevance vector machine prediction model (DMO-RVM) is established to predict the sensor observation value. Based on this value, the state / parameter double particle filter (DPF) is used to predict the system state and hidden health parameters, and further realize K-step forward prediction of the state and health parameters, and predict the remaining life from the current moment to the moment of system failure.

[0021] 2. Establish the initial dynamic prediction model DMO-RVM based on historical data and conduct k The measured prediction value is obtained by step-forward prediction to improve the adaptability of the MO-RVM model to system state changes, thereby improving the accuracy of the prediction. On this basis, the DPF realizes the prediction of state and health parameters. The design goal of DPF is to solve the convergence of the estimator so that it can achieve the true optimal estimation.

[0022] 3. Compared with the traditional particle filter that estimates the state parameters and then makes a judgment on the health monitoring scheme, the dual particle filter can realize the joint estimation of the state and health parameters. When the health parameters are directly monitored, the failure threshold is easier to obtain and more intuitive. At the same time, compared with the prediction scheme based on the physical model and the data-driven algorithm, the hybrid prediction method has stronger practicality and stability, and can more accurately predict the remaining life of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 : Schematic diagram of the process of the present invention.

[0024] Figure 2 : Schematic diagram of the principle of dual particle filter.

[0025] Figure 3 : Schematic diagram of dynamically updating sample monitoring window.

[0026] Figure 4 : Schematic diagram of the probability density distribution of remaining life prediction. The actual remaining life is 220.

[0027] Figure 5 : Schematic diagram of the probability density distribution of remaining life prediction. The actual remaining life is 460.

[0028] Figure 6 : Schematic diagram of the probability density distribution of remaining life prediction. The actual remaining life is 740.

[0029] Figure 7 : Schematic diagram of remaining life prediction under high pressure compressor fouling.

[0030] Figure 8 : Schematic diagram of the measurement data prediction and health parameter prediction process based on the dynamic model.

[0031] Fig. 9 : Schematic diagram of the updating process of some measurement values ​​under fouling damage.

[0032] Fig.10 : Schematic diagram of dynamic estimation measurement values ​​under fouling damage.

[0033] Fig.11 : Comparison of long-term predictions of measurements based on DMO-RVM and ARMA. DETAILED DESCRIPTION

[0034] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0035] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0036] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features of the embodiments may be combined with each other.

[0037] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0038] In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inside", "outside", etc. indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, or the positions or positional relationships in which the product of the invention is usually placed when in use, or the positions or positional relationships commonly understood by those skilled in the art, which are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", etc. are only used to distinguish the description, and cannot be understood as indicating or implying relative importance.

[0039] In the description of the present invention, it is also necessary to explain that, unless otherwise clearly specified and limited, the terms "set", "install", "connect", and "connect" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two elements. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0040] refer to Figure 1-10 As shown, one embodiment of the present invention is: The method for predicting the remaining life of an aircraft engine based on a dual particle filter hybrid includes the following steps: Step 1: Data preprocessing and model building: Select states for calculation and estimation x , observe sensor measurements y and health parameters θ , conduct MO-RVM modeling for each existing measurement data and establish the initial n y A MO-RVM prediction model.

[0041] Among them, the status , where T CC is the combustion chamber temperature, N1 and N2 are the shaft speeds connecting the high-pressure turbine and the high-pressure compressor, and connecting the low-pressure turbine and the low-pressure compressor, respectively, P LT , P CC , P LC and P HT Represent the pressures of the low-pressure turbine, combustion chamber, low-pressure compressor and high-pressure turbine respectively.

[0042] Observe sensor measurements , where T HC , T LC , T HT and TLT are the outlet temperatures of the high-pressure compressor, low-pressure compressor, high-pressure turbine and low-pressure turbine respectively. P HC Indicates the high pressure compressor pressure.

[0043] Health parameters , including the efficiency of the high-pressure compressor (HC), low-pressure compressor (LC), high-pressure turbine (HT), and low-pressure turbine (LT) and flow . Perform MO-RVM modeling on each existing initial measurement data to obtain n y The initial prediction models are: , according to the formula:

[0044] The initial k-step forward prediction results are obtained through iteration: .

[0045] Step 2: Based on the prediction results of the prediction model, decide whether to dynamically update the model: Determine whether the MO-RVM model needs to be updated based on the state update rules. If the result shows that an update is required, a DMO-RVM model will be further established, and then the sensor observation values ​​will be predicted. If no dynamic update is required, the prediction will be performed directly.

[0046] According to the state update rule, it is determined whether the MO-RVM model under the current data window m needs to be updated. The state update rule is determined by the gap between the predicted measurement value and the actual measurement value. The gap between the predicted measurement value and the actual measurement value is quantified using the Mahalanobis distance. The Mahalanobis distance of single-point comparison is defined as:

[0047] Where Σ is the covariance matrix of the multidimensional random variable, μ is the mean of the reference sample, is the matrix transpose, and x is the measured value. The larger the Mahalanobis distance is, the farther the distance between the observation point and the sample is. Therefore, when the Mahalanobis distance in the above formula is greater than the threshold, the MO-RVM prediction model is updated.

[0048] First, the data window to be updated is selected. Second, the Mahalanobis distances of all measured values ​​in the monitoring window are calculated. Finally, the prediction model is updated using the following judgment criteria.

[0049] No. Measurements in the monitoring window m The average value of the lower Mahalanobis distance is ,when n Any of the average distances is greater than the threshold And it is greater than the average Mahalanobis distance of the previous window times, it is determined that an update is needed, and the judgment rules are as follows:

[0050] Where: is the threshold 1, used to determine the size of the distance, is threshold 2; used to determine the speed of the distance change rate; Since there is no need to n The prediction model of each measurement value is updated. Therefore, sub-rules are established under the above judgment rules for secondary judgment. The sub-rules are as follows:

[0051] Where: σ 3 is the secondary decision threshold, and , when the above sub-rules are met, it is determined that there is no need to Road update.

[0052] Step 3: Predict health parameters: Use the state / health parameter dual particle filter to predict the system state and hidden health parameters based on the sensor observations predicted in step 2, and achieve k-step forward prediction of the state and health parameters. The k-step forward state and health parameter prediction is achieved through iteration, and the prediction process is as follows: For the time step : (1) Perform r-step forward prior state prediction: according to Predict a priori state particles, where is t+r The particle noise added to the state particles at all times has a distribution that conforms to , and They are t+ r- Status at moment 1 x and health parameters θ An estimated value of according to Estimate the prior state covariance matrix; (2) Perform r-step forward posterior state prediction: By resampling, we calculate ,get t+r Status at all times x Estimate filter weights ,in, for The probability density function of Approximate posterior state distribution calculation in, Nreg is the regularization quantity, Depend on Calculated; According to the filter weight Resample the state estimation particles, which is done with The obtained posterior state estimate distribution after approximate resampling is , is the Dirac function; according to Approximate a posteriori state estimates; (3) Perform the first r-step forward posterior parameter prediction: Calculate the corrected output prediction error , is a nonlinear equation between the state, health parameters and measurements; Calculate correction parameters ,in, is the adaptive coefficient in the calibration process, For the j Jacobian determinant of the particle; The kernel shrinkage algorithm is used to calculate the first step posterior parameter prediction: , A is the contraction matrix, , is the noise distribution added to each particle; (4) Perform the second r-step forward posterior parameter prediction: Compute parameter estimates filter weights To resample, The first posterior parameter distribution is approximated as follows ; Predicting particles based on resampling parameters After resampling, the approximate posterior parameter prediction distribution is , Get the posterior parameter prediction , Calculate the posterior parameter prediction covariance as: ; According to the above prediction process, the predicted measurement data is used and resampling is maintained for future moments to generate a health parameter particle probability density function predicted k steps forward.

[0053] Step 4: Remaining life prediction: Based on the predicted health parameter values ​​obtained in step 3, the probability density distribution of the predicted health parameters is plotted. By plotting the probability density function of the health parameter prediction particles in the DPF, the moment with the highest probability is obtained, which is the estimated remaining life.

[0054] Based on the predicted health parameter values ​​obtained in step 3, the probability density distribution of the predicted health parameter is plotted. For D-dimensional data x, the health parameter particle probability density function The calculation formula is:

[0055] in, μ is the mean of x, Σ is the covariance of x, and x is the health parameter of the engine. At this time, it is assumed that the data follows a Gaussian distribution. By plotting the probability density function of the health parameter prediction particle in the DPF, the moment with the maximum probability is obtained, which is considered to be the estimated remaining life.

[0056] Step 4: When calculating the remaining life of the system through the obtained health parameters, it is also necessary to determine the time when the failure occurs. The remaining life RUL (t) at time t is calculated as follows:

[0057] , Where: is the time when any relevant parameter reaches the critical value, is the critical value of the parameter at which failure occurs. Once one of the parameters reaches the critical value, maintenance operations must be performed. Here, it should be noted that the critical value is very important for failure determination. In most application problems, an exact value is usually not selected as an estimate of the remaining life, but a predicted confidence interval or probability distribution of the remaining life is given.

[0058] The effect of the present invention is further illustrated by the following experiments: 1. Experimental conditions: The present invention applies the prediction algorithm to the twin-shaft turbofan engine developed by Meskin et al. The model establishes a Simulink model by considering the nonlinear dynamic characteristics of both rotor dynamics and volume dynamics. By assuming an adiabatic process, the model calculates the pressure and temperature of the intake system in the engine intake duct. For the low-pressure compressor, the pressure ratio (π LC ) is calculated by the volume dynamics between the high-pressure compressor and the low-pressure compressor. The rotor speed (N1) is obtained by performing an energy balance calculation on the low-pressure shaft connecting the low-pressure compressor and the low-pressure turbine. Once the pressure ratio and speed are calculated, the corrected mass flow rate and efficiency can be obtained from the performance diagram, thereby obtaining the temperature rise. Similar to the low-pressure compressor, for the high-pressure compressor, the pressure is obtained by volume dynamics, and the speed (N2) is obtained by solving the energy balance of the high-pressure shaft connecting the high-pressure compressor and the high-pressure turbine. Finally, the pressure ratio of the high-pressure turbine is obtained by the volume dynamics between the high and low-pressure turbines, and the pressure ratio of the low-pressure turbine is obtained by the volume dynamics calculation of the low-pressure turbine.

[0059] 2. Experimental content: (1) Introduction to the experimental data set: First, we need to select the state, health parameters and measurement parameters for calculation and estimation. As state. Where T CC is the combustion chamber temperature, N1 and N2 are the shaft speeds connecting the high-pressure turbine and the high-pressure compressor, and connecting the low-pressure turbine and the low-pressure compressor, respectively, P LT , P CC , P LC and P HT Represent the pressures of the low-pressure turbine, combustion chamber, low-pressure compressor and high-pressure turbine respectively.

[0060] choose As the observed sensor measurement value, T HC 、T LC 、T HT and T LT Respectively represent the outlet temperatures of the high-pressure compressor, low-pressure compressor, high-pressure turbine and low-pressure turbine. In addition, the health parameters include the efficiency of the high-pressure compressor (HC), low-pressure compressor (LC), high-pressure turbine (HT) and low-pressure turbine (LT). and flow , that is, health parameters

[0061] (2) Data processing: In the high-pressure compressor fouling damage experiment, it is assumed that there are 100 data (1 second) of measured values ​​as known inputs to establish the initial model of DMO-RVM and obtain the initial estimated values ​​of the measured values. When new measured data is collected, the Mahalanobis distance between the estimated value of the DMO-RVM prediction model and the measured value is determined to determine whether to update the DMO-RVM model. Fig. 9 As shown, the dynamic model DMO-RVM of the measured value N1 is updated three times, at 8.6 seconds, 11.4 seconds and 13.4 seconds respectively; the measured value T HT After two updates, it is located at 9.2 seconds and 12 seconds. The DMO-RVM update time of other measured values ​​is shown in the following table. The total number of updates is four times. This total number of updates refers to the unified update number for all measured values, that is, the DMO-RVM update of different measured values ​​at the same time is counted as one.

[0062] In the following table, T LC and T HC No update is required, the reason can be seen from Fig.10 The measured value T LC and T HCThe initial prediction value has a high accuracy and is very close to the actual measurement value, so there is no need to update it. The final estimated value obtained by the dynamic update mechanism of the 8 sets of measurement values ​​is as follows Fig.10 As shown, it can be seen that the estimated values ​​all fall within the 95% confidence interval of the measured values. When the estimated value is about to exceed this interval, the DMO-RVM model will be updated through the dynamic update mechanism to calculate the new estimated value.

[0063]

[0064] (3) Analysis of experimental results: First, the DMO-RVM and ARMA algorithms are used to model and predict the initial 100 data (1 second), as shown in Fig.11 It can be seen that compared with the ARMA algorithm, the DMO-RVM algorithm has more outstanding long-term prediction ability.

[0065] Secondly, in order to verify the influence of the dynamic measurement value prediction method based on the DMO-RVM algorithm on the remaining life estimation, Figure 7 The results of the remaining life estimation under the dynamic update of the measurement values ​​by the DMO-RVM algorithm and the ARMA algorithm under degradation caused by high-pressure compressor fouling are compared in the paper. In general, the remaining life estimated by the hybrid prediction method is more accurate than the data-driven prediction method, and the long-term remaining life estimation is more accurate when the DMO-RVM algorithm is used for dynamic estimation of the measurement values, that is, when there is less process data, the DMO-RVM-based hybrid prediction method is more accurate than the ARMA-based hybrid prediction method.

[0066] Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments, or to make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for predicting the remaining life of an aircraft engine based on a dual particle filter hybrid method, characterized in that: The following steps are involved: Step 1: Data preprocessing and model building: Select states for calculation and estimation x , observe sensor measurements y and health parameters θ , conduct MO-RVM modeling for each existing measurement data and establish the initial n y MO-RVM prediction model; Step 2: According to the prediction results of the prediction model, decide whether to dynamically update the model: determine whether the MO-RVM model needs to be updated according to the state update rule. If the judgment result shows that it needs to be updated, then the DMO-RVM model will be further established, and then the sensor observation value will be predicted. If no dynamic update is required, the prediction will be made directly. Step 3: Predict health parameters: Use the state / health parameter dual particle filter to predict the system state and hidden health parameters based on the sensor observations predicted in step 2, and achieve state and health parameter prediction. k Step forward prediction; Step 4: Remaining life prediction: Based on the predicted health parameter values ​​obtained in step 3, the probability density distribution of the predicted health parameters is plotted. By plotting the probability density function of the health parameter prediction particles in the DPF, the moment with the highest probability is obtained, which is the estimated remaining life.

2. The method for predicting the remaining life of an aircraft engine based on a dual particle filter hybrid method according to claim 1, characterized in that: In step 1, MO-RVM modeling is performed on each existing initial measurement data to obtain n y The initial prediction models are: , according to the formula: The initial k-step forward prediction results are obtained through iteration: .

3. The method for predicting the remaining life of an aircraft engine based on a dual particle filter hybrid method according to claim 1, characterized in that: The state update rule in step 2 is determined by the gap between the predicted measurement value and the actual measurement value. The gap between the predicted measurement value and the actual measurement value is quantified using the Mahalanobis distance. The Mahalanobis distance for single-point comparison is defined as: Where Σ is the covariance matrix of the multidimensional random variable, μ is the mean of the reference sample, is the matrix transpose, and x is the measured value.

4. The method for predicting the remaining life of an aircraft engine based on a dual particle filter hybrid method according to claim 1, characterized in that: The judgment criteria in step 2 are as follows: Measurements in the monitoring window m The average value of the lower Mahalanobis distance is ,when n Any of the average distances is greater than the threshold And it is greater than the average Mahalanobis distance of the previous window times, it is determined that an update is needed, and the judgment rules are as follows: Where: is the threshold value 1, is the threshold 2; since it is not necessary to n The prediction model of each measurement value is updated. Therefore, sub-rules are established under the above judgment rules for secondary judgment. The sub-rules are as follows: Where: σ 3 is the secondary decision threshold, and , when the above sub-rules are met, it is determined that there is no need to Road update.

5. The method for predicting the remaining life of an aircraft engine based on a dual particle filter hybrid method according to claim 1, characterized in that: In step 3, the prediction process is as follows: For the time step : (1) Perform r-step forward prior state prediction: according to Predict a priori state particles, where is t+r The particle noise added to the state particles at all times has a distribution that conforms to , and They are t+r- Status at moment 1 x and health parameters θ estimated value; based on Estimate the prior state covariance matrix; (2) Perform r-step forward posterior state prediction: By resampling, calculate get t+r Status at all times x Estimate filter weights ,in, for The probability density function of Compute the approximate posterior state distribution: ,in, Nreg is the regularization quantity, Depend on Calculated; According to the filter weight Resample the state estimation particles, which is done with The obtained posterior state estimate distribution after approximate resampling is , is the Dirac function; according to Approximate a posteriori state estimates; (3) Perform the first r-step forward posterior parameter prediction: Calculate the corrected output prediction error , is a nonlinear equation between the state, health parameters and measurements; Calculate correction parameters ,in, is the adaptive coefficient in the calibration process, For the j Jacobian determinant of the particle; The kernel shrinkage algorithm is used to calculate the first step posterior parameter prediction: , A is the contraction matrix, ， is the noise distribution added to each particle; (4) Perform the second r-step forward posterior parameter prediction: Compute parameter estimates filter weights To resample, Approximate the first posterior parameter distribution as follows ; Predicting particles based on resampling parameters After resampling, the approximate posterior parameter prediction distribution is , Get the posterior parameter prediction Calculate the posterior parameter prediction covariance as ; According to the above prediction process, the predicted measurement data is used and resampling is maintained for future moments to generate a health parameter particle probability density function predicted k steps forward.

6. The method for predicting the remaining life of an aircraft engine based on a dual particle filter hybrid method according to claim 5, characterized in that: In step 4, for the D-dimensional data x, the health parameter particle probability density function The calculation formula is: ; in, μ is the mean of x, Σ is the covariance of x, and x is the health parameter of the engine.

7. The method for predicting the remaining life of an aircraft engine based on a dual particle filter hybrid method according to claim 1, characterized in that: In step 4, the remaining life RUL (t) at time t is calculated as follows: ; ， Where: is the time when any relevant parameter reaches the critical value, is the critical value of the parameter at which failure occurs.

Images