Multi-sensor signal fusion method for engine health index construction

Abstract

The invention discloses a multi-sensor signal fusion method for engine health index construction, and belongs to the field of residual life prediction, and the method comprises the steps: giving a description formula of a multi-sensor signal, and carrying out the data preprocessing through a maximum and minimum normalization method; establishing a degradation model based on a nonlinear Wiener process, and estimating unknown parameters of the model by using a maximum likelihood estimation algorithm; based on a sparse Bayesian algorithm, sensor selection and fusion coefficient calculation are realized at the same time; constructing an interactive feedback framework constructed by the health indexes; online updating of degradation model parameters is achieved according to the Bayesian theorem; and deducing the residual life probability density function to obtain an estimated value of the residual life of the engine. The multi-sensor signal fusion method for engine health index construction provided by the invention has important significance in accurately estimating the residual service life of the engine, reducing the engine fault risk and reducing the maintenance cost.

Description

Technical Field

[0001] The present invention relates to the technical field of remaining life prediction, and in particular to a multi-sensor signal fusion method for constructing engine health indicators. Background Art

[0002] The health status of the engine is directly related to the safety and reliability of the equipment. Accurately estimating the remaining service life of the engine is of great significance to reducing the risk of engine failure and reducing maintenance costs. As a typical multi-sensor device, how to construct a suitable health index based on multi-sensor signals is of great significance to the prediction of the remaining service life of the engine. For degraded devices with multi-sensor signals such as engines, existing methods do not consider the individual differences between a priori units, that is, all units share a set of sensor combinations and fusion coefficients. In addition, most existing methods divide sensor selection, health index construction, and remaining service life prediction into three isolated parts, which may result in the selected sensor being unable to form an optimal health index, and the constructed health index does not match the selected degradation model.

[0003] On the other hand, each sensor contains only partial degradation information, and different sensors may be correlated with each other, so using a single sensor may lead to inaccurate remaining life prediction. In contrast, treating all sensors as degradation-related sensors and assigning weights will produce information redundancy, which may increase computational complexity or be detrimental to fusion. Therefore, it is very important to remove useless sensors and select a reasonable sensor group for fusion. However, existing methods select sensors independently. The most common method at present is to select the sensor group related to degradation before constructing the health indicator. This method decides whether to select a sensor based on characteristics such as the monotonicity of a single sensor signal, and may not select the most relevant sensor group that affects the remaining life prediction. In addition, the usability of such methods is weakened when the trend of a single sensor signal does not increase or decrease significantly. Summary of the invention

[0004] The purpose of the present invention is to provide a multi-sensor signal fusion method for constructing engine health indicators to solve the problems existing in the background technology.

[0005] To achieve the above object, the present invention provides a multi-sensor signal fusion method for constructing engine health indicators, comprising the following steps:

[0006] S1. Give the description formula of multi-sensor signals and use the maximum and minimum normalization method to preprocess the data;

[0007] S2. A degradation model is established based on a nonlinear Wiener process, and the unknown parameters of the model are estimated using a maximum likelihood estimation algorithm, including the following steps:

[0008] S21, using nonlinear Wiener model to establish degradation model;

[0009] S22, estimating the prior parameters of the offline phase using the maximum likelihood estimation method;

[0010] S3, based on the sparse Bayesian algorithm, the sensor selection and fusion coefficient calculation are realized simultaneously;

[0011] S4, construct an interactive feedback framework for health indicator construction;

[0012] S5. Implement online update of degradation model parameters according to Bayesian theorem;

[0013] S6. Derivation of the remaining life probability density function to obtain an estimated value of the remaining life of the engine includes the following steps:

[0014] S61, obtaining a probability density function of the lifespan based on a nonlinear Wiener degradation model;

[0015] S62. Based on the relationship between the life span and the remaining life span, the probability density function of the remaining life span is solved.

[0016] Preferably, the description formula in S1 is as follows:

[0017] Suppose there are N degraded devices from the same batch for training from the beginning of operation to failure, each of which has P sensors; let the total life of the nth (n∈{1,...,N}) device be T Kn , the multi-sensor degradation data X of the nth device n as follows:

[0018]

[0019] in Indicates that the nth device at time t k (k∈{1,...,K n}) is the observation value of the pth (p∈{1,...,P}) sensor at time .

[0020] Preferably, in S1, the sensor data is preprocessed to the same scale by the maximum and minimum normalization method, which is expressed as:

[0021]

[0022] in and are normalized value and original value respectively; and are the minimum and maximum values ​​of the p-th sensor signal of the n-th device, respectively.

[0023] Preferably, the degradation model of S21 is:

[0024]

[0025] where y nk For the nth device at t k The degradation value at the moment; y n0 is the initial degenerate state; n and σ n are the drift coefficient and diffusion coefficient, respectively; is the nonlinear drift term; B(t k ) is the standard Brownian motion.

[0026] Preferably, the content of S22 is as follows:

[0027] set up According to the nonlinear Wiener model and the independent increment property of standard Brownian motion, is the constructed health index value, which obeys the multidimensional Gaussian distribution, where Y n The mean μ n and covariance Σ n Respectively expressed as:

[0028]

[0029] in:

[0030]

[0031]

[0032] Among them, n represents a vector composed of Ψ(t) at different times; represents; Ψ(t) represents the nonlinear link; Indicates time Ψ(t) at ;

[0033] Unknown parameters The log-likelihood function of is:

[0034]

[0035] in:

[0036]

[0037]

[0038] Among them, Σ n Represents health indicator Y n The covariance of Σn inverse; Represents Ω n The inverse of

[0039] Find the likelihood function The partial derivative of and set it equal to 0, we can further deduce The estimated value of is:

[0040]

[0041] Then substitute The value of , the likelihood function is:

[0042]

[0043] The above formula can be solved using the multidimensional search method "fminsearch" in MATLAB b n and The maximum likelihood estimate of .

[0044] Preferably, the content of S3 is as follows:

[0045] The multi-sensor data is fused into a one-dimensional health indicator as follows:

[0046]

[0047] Where Y n is the health indicator value of the nth device, is the fusion coefficient of the pth sensor, assuming is a function with variance α n ' p The hyperparameter α of the zero-mean Gaussian distribution np Generated. nk t k The observation noise at time and are the fusion coefficient vector and the noise vector respectively, assuming that the noise V n The variance is The zero-mean Gaussian distribution of

[0048] According to the sparse Bayes method:

[0049]

[0050] Among them, α n Indicated by The hyperparameter α np The vector composed of α n =[α n1 ,α n2 ,...,α nP]; W n The variance of W n The inverse of W n The mean of represents a diagonal matrix;

[0051] in:

[0052]

[0053]

[0054]

[0055] The hyperparameters in the formula and Update based on the fast marginal likelihood maximization algorithm:

[0056]

[0057]

[0058] x np Represents X n The p-th column vector of ;

[0059] Iterate equations (14) to (18) until the convergence criterion is met to complete the fusion coefficient vector W n The estimate of W n The sensors corresponding to all non-zero items in are the sensor group selected by the nth device, and the corresponding coefficients are the fusion coefficients used to construct the health indicator.

[0060] Preferably, in S4, interactive iteration between the degradation model and the health indicator construction process is selected until the root mean square error between the true value and the predicted value of the remaining life is minimized, and finally the fusion coefficient of the multi-sensor is determined.

[0061] Preferably, S5 content includes:

[0062] In order to make the degradation model fit the health indicator trajectory of the test unit more accurately, a sequential Bayesian method is used to update λ online when new data is obtained. According to the Bayesian theorem, λ is k The posterior distribution of the moment is:

[0063]

[0064] Further deduction shows that t k The mean value of time λ and variance for:

[0065]

[0066]

[0067] Preferably, the content of S61 is as follows:

[0068] Under the concept of first arrival time, let ω represent the failure threshold, and define the life and remaining life as:

[0069] T:=inf{t:Y(t)≥ω} (21)

[0070] L k :=inf{l k :(t k +l k )≥ω} (22)

[0071] The probability density function expression of the life based on the nonlinear Wiener degradation model is obtained as follows:

[0072]

[0073] Preferably, the content of S62 includes:

[0074] In order to find the remaining life, based on the relationship between life span and remaining life, the probability density function of the remaining life is:

[0075]

[0076] In this way, based on the probability density function of the remaining life, the estimated value of the remaining life at the current moment can be predicted.

[0077] Therefore, the present invention adopts the above-mentioned multi-sensor signal fusion method for constructing engine health indicators, which has the following beneficial effects:

[0078] (1) A new interactive feedback framework is established to iteratively obtain the fusion coefficient starting from the actual remaining life. The framework integrates sensor selection, nonlinear health indicator construction, and degradation modeling modules. In this framework, unlike existing methods that treat sensor selection as a separate part, the optimization objective is to minimize the root mean square error between the actual remaining life and the predicted remaining life.

[0079] (2) The selection of sensors is taken into account in the health index fusion framework, and the construction of the degradation model is also considered at the same time. This solves the problem that the sensor combination selected by the existing health index construction method cannot construct the optimal health index, and the constructed health index does not match the degradation model, resulting in low prediction accuracy. This is beneficial to improving the safety and reliability of engine use.

[0080] (3) Each a priori unit is assigned a different sensor combination and fusion coefficient, which fully reflects the individual differences between units and improves the accuracy of the remaining life.

[0081] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 It is a schematic diagram of a flow chart of an embodiment of the present invention;

[0083] Figure 2 Constructing a result graph for the engine health index of an embodiment of the present invention;

[0084] Figure 3 Graphs of probability density functions of the remaining life of an embodiment of the present invention; wherein (a) is the probability density function of the remaining life of test sample #7 of the data set DS01; (b) is the probability density function of the remaining life of test sample #8 of the data set DS01;

[0085] Figure 4 1 is a diagram of the remaining life estimation result of an embodiment of the present invention; wherein (a) is the average remaining life estimation value of test sample #7 of the data set DS01; and (b) is the average remaining life estimation value of test sample #8 of the data set DS01. DETAILED DESCRIPTION

[0086] 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.

[0087] See also Figure 1 , a multi-sensor signal fusion method for constructing engine health indicators, specifically comprising the following steps:

[0088] S1. Give the description formula of multi-sensor signals and use the maximum and minimum normalization method to preprocess the data;

[0089] Assume that there are N degraded devices from the same batch for training, each of which has P sensors. Let the total lifetime of the nth (n∈{1,...,N}) device be T Kn Therefore, the multi-sensor degradation data X of the nth device n It can be written as:

[0090]

[0091] in Indicates that the nth device at time t k (k∈{1,...,K n}) is the observation value of the pth (p∈{1,...,P}) sensor at time .

[0092] Since the amplitudes of raw data from different sensors are usually different, we choose to preprocess the sensor data to the same scale through the maximum and minimum normalization method, which can be expressed as:

[0093]

[0094] in and are the normalized value and the original value respectively, and are the minimum and maximum values ​​of the pth sensor signal of the nth device, respectively. All represent normalized data.

[0095] S2. A degradation model is established based on the nonlinear Wiener process, and the unknown parameters of the model are estimated using the maximum likelihood estimation algorithm, which includes the following steps:

[0096] S21, using nonlinear Wiener model to establish degradation model;

[0097] First, the nonlinear Wiener model is used to establish the degradation model:

[0098]

[0099] where y nk For the nth device at t k The degradation value at time, y n0 is the initial degenerate state, λ n and σ n are the drift coefficient and diffusion coefficient, respectively, is the nonlinear drift term, B(t k ) is a standard Brownian motion. For simplicity, it is assumed that the fitted degradation trend is growing and the initial degradation value is 0. This can be easily extended if necessary.

[0100] S22, estimating the prior parameters of the offline phase using the maximum likelihood estimation method;

[0101] Assumptions According to the nonlinear Wiener model and the independent increment property of the standard Brownian motion, is the constructed health index value, which obeys the multidimensional Gaussian distribution, where Y n The mean μ n and covariance Σ nCan be expressed as:

[0102]

[0103] in:

[0104]

[0105]

[0106] Among them, n represents a vector composed of Ψ(t) at different times; represents; Ψ(t) represents the nonlinear link; Indicates time Ψ(t) at .

[0107] Unknown parameters The log-likelihood function of is:

[0108]

[0109] in:

[0110]

[0111]

[0112] Among them, Σ n Represents health indicator Y n The covariance of Σ n inverse; Represents Ω n The inverse of.

[0113] Find the likelihood function The partial derivative of and set it equal to 0, we can further deduce The estimated value of is:

[0114]

[0115] Then substitute The value of , the likelihood function is:

[0116]

[0117] The above formula can be solved using the multidimensional search method "fminsearch" in MATLAB b n and The maximum likelihood estimate of .

[0118] S3. Based on the sparse Bayesian algorithm, the sensor selection and fusion coefficient calculation are realized simultaneously.

[0119] The multi-sensor data is fused into a one-dimensional health indicator as follows:

[0120]

[0121] Where Y n is the health indicator value of the nth device, is the fusion coefficient of the pth sensor, assuming is a function with variance α n ' p The hyperparameter α of the zero-mean Gaussian distribution np Generated. nk t k The observation noise at time and are the fusion coefficient vector and the noise vector respectively, assuming that the noise V n The variance is A zero-mean Gaussian distribution.

[0122] According to the sparse Bayes method, we have:

[0123]

[0124] Among them, α n Indicated by The hyperparameter α np The vector composed of α n =[α n1 ,α n2 ,...,α nP ]; W n The variance of W n The inverse of W n The mean of represents a diagonal matrix.

[0125] in:

[0126]

[0127]

[0128]

[0129] The hyperparameters in the formula and It can be updated based on the fast marginal likelihood maximization algorithm, namely:

[0130]

[0131]

[0132] x np Represents X n The p-th column vector of .

[0133] Then, equations (14) to (18) are iterated until the convergence criterion is met to complete the fusion coefficient vector W n The estimate of W n The sensors corresponding to all non-zero items in are the sensor group selected by the nth device, and the corresponding coefficients are the fusion coefficients used to construct the health index. In other words, we have completed the selection of sensors and the calculation of fusion coefficients at the same time through the sparse Bayesian algorithm.

[0134] S4. Construct an interactive feedback framework for health indicator construction.

[0135] In fact, the parameters of the degradation model, the health indicator value, and the failure threshold are all unknown at the beginning, so we choose to determine the fusion coefficient of multiple sensors through interactive iteration between the degradation model and the health indicator construction process until the root mean square error between the true value and the predicted value of the remaining life is minimized. This closed-loop feedback structure can ensure that the constructed health indicator matches the degradation model, and then select the most appropriate sensor group and failure threshold.

[0136] S5. Implement online update of degradation model parameters based on Bayesian theorem.

[0137] In order to make the degradation model fit the health indicator trajectory of the test unit more accurately, we adopt a sequential Bayesian method to update λ online when new data is obtained. According to the Bayesian theorem, λ is k The posterior distribution of the moment is:

[0138]

[0139] Further deduction shows that t k The mean value of time λ and variance for:

[0140]

[0141]

[0142] S6. Derivation of the remaining life probability density function to obtain an estimated value of the remaining life of the engine includes the following steps:

[0143] S61, obtaining a probability density function of the lifespan based on a nonlinear Wiener degradation model;

[0144] Under the concept of first arrival time, let ω represent the failure threshold, and define the life and remaining life as:

[0145] T:=inf{t:Y(t)≥ω} (22)

[0146] L k :=inf{l k :(t k +l k )≥ω} (23)

[0147] Then, the probability density function expression of the life based on the nonlinear Wiener degradation model can be obtained as:

[0148]

[0149] S62. Based on the relationship between the life span and the remaining life span, the probability density function of the remaining life span is solved.

[0150] In order to find the remaining life, based on the relationship between life span and remaining life, the probability density function of the remaining life is:

[0151]

[0152] In this way, based on the probability density function of the remaining life, the estimated value of the remaining life at the current moment can be predicted.

[0153] Based on MATLAB tools, NASA's engine dataset N-CMAPSS is used, and the subset DS01 is selected for illustration. This dataset contains measurements, virtual sensors, and operating status parameters. However, since the proposed method is purely data-driven, only sensor measurements are used as input. For the monitored signals, a total of 14 sensors are measured in the same working cycle. There are 6 training units and 4 test units in the DS01 subset. The power function form is selected as the nonlinear drift term of the Wiener degradation model, that is,

[0154] Figure 2-Figure 4 The engine health index construction results, remaining life probability density function and prediction result schematic diagram provided in this embodiment.

[0155] The method of this embodiment is compared with the existing advanced method, and the root mean square error RMSE and score Score are used to evaluate the performance of the remaining life prediction result. The calculation method is as follows:

[0156]

[0157]

[0158]

[0159] Where N total represents the total number of test data samples, and They represent the predicted remaining life and the actual remaining life respectively. The comparison methods include bidirectional long short-term memory network (bidirectional LSTM), long short-term memory network (LSTM) and deep neural network (DNN). The results are shown in Table 1, which can illustrate the applicability and effectiveness of the proposed method for engine remaining life prediction, that is, the health indicator construction framework we proposed is effective, and this method has high prediction accuracy.

[0160] Table 1 Performance comparison of remaining life prediction results

[0161] method Root mean square error RMSE Score Bidirectional LSTM 6.867 2.188e+06 LSTM 7.049 2.208e+06 DNN 6.950 - This method 6.639 2.027e+06

[0162] Therefore, the present invention adopts the above-mentioned multi-sensor signal fusion method for constructing engine health indicators, which is of great significance for accurately estimating the remaining service life of the engine, reducing the risk of engine failure and reducing maintenance costs.

[0163] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A multi-sensor signal fusion method for constructing engine health indicators, characterized in that: The following steps are involved: S1. Give the description formula of multi-sensor signals and use the maximum and minimum normalization method to preprocess the data; S2. A degradation model is established based on a nonlinear Wiener process, and the unknown parameters of the model are estimated using a maximum likelihood estimation algorithm, including the following steps: S21, using nonlinear Wiener model to establish degradation model; S22, estimating the prior parameters of the offline phase using the maximum likelihood estimation method; S3, based on the sparse Bayesian algorithm, the sensor selection and fusion coefficient calculation are realized simultaneously; S4, construct an interactive feedback framework for health indicator construction; S5. Implement online update of degradation model parameters according to Bayesian theorem; S6. Derivation of the remaining life probability density function to obtain an estimated value of the remaining life of the engine includes the following steps: S61, obtaining a probability density function of the lifespan based on a nonlinear Wiener degradation model; S62. Based on the relationship between the life span and the remaining life span, the probability density function of the remaining life span is solved.

2. A multi-sensor signal fusion method for constructing engine health indicators according to claim 1, characterized in that: The description formula in S1 is as follows: Suppose there are N degraded devices from the same batch for training from the beginning of operation to failure, each of which has P sensors; let the total life of the nth (n∈{1,...,N}) device be T Kn , the multi-sensor degradation data X of the nth device n as follows: in Indicates that the nth device at time t k (k∈{1,...,K n }) is the observation value of the pth (p∈{1,...,P}) sensor at time .

3. A multi-sensor signal fusion method for constructing engine health indicators according to claim 2, characterized in that: In S1, the sensor data is preprocessed to the same scale by the maximum and minimum normalization method, which is expressed as: in and are normalized value and original value respectively; and are the minimum and maximum values ​​of the p-th sensor signal of the n-th device, respectively.

4. A multi-sensor signal fusion method for constructing engine health indicators according to claim 3, characterized in that: The degradation model of S21 is: where y nk For the nth device at t k The degradation value at the moment; y n0 is the initial degenerate state; n and σ n are the drift coefficient and diffusion coefficient, respectively; is the nonlinear drift term; B(t k ) is the standard Brownian motion.

5. A multi-sensor signal fusion method for constructing engine health indicators according to claim 4, characterized in that: S22 content is as follows: set up According to the nonlinear Wiener model and the independent increment property of standard Brownian motion, is the constructed health index value, which obeys the multidimensional Gaussian distribution, where Y n The mean μ n and covariance Σ n Respectively expressed as: in: Among them, T n represents a vector composed of Ψ(t) at different times; represents; Ψ(t) represents the nonlinear link; Indicates time Ψ(t) at ; Unknown parameters b n , The log-likelihood function of is: in: Among them, Σ n Represents health indicator Y n The covariance of Σ n inverse; Represents Ω n The inverse of Find the likelihood function The partial derivative of and set it equal to 0, further derive The estimated value of is: Then substitute The value of , the likelihood function is:

6. A multi-sensor signal fusion method for constructing engine health indicators according to claim 5, characterized in that: The S3 content is as follows: The multi-sensor data is fused into a one-dimensional health indicator as follows: Where Y n is the health indicator value of the nth device, is the fusion coefficient of the pth sensor, let By a subject with variance α n ' p The hyperparameter α of the zero-mean Gaussian distribution np Generate, v nk t k The observation noise at time and are the fusion coefficient vector and the noise vector respectively, and the noise V n The variance is The zero-mean Gaussian distribution of According to the sparse Bayes method: Among them, α n Indicated by The hyperparameter α np The vector composed of α n =[α n1 ,α n2 ,...,α nP ]; W n The variance of W n The inverse of W n The mean of represents a diagonal matrix; in: The hyperparameters in the formula and Update based on the fast marginal likelihood maximization algorithm: x np Represents X n The p-th column vector of ; Iterate equations (14) to (18) until the convergence criterion is met to complete the fusion coefficient vector W n The estimate of W n The sensors corresponding to all non-zero items in are the sensor group selected by the nth device, and the corresponding coefficients are the fusion coefficients used to construct the health indicator.

7. A multi-sensor signal fusion method for constructing engine health indicators according to claim 6, characterized in that: In S4, the interactive iteration between the degradation model and the health indicator construction process is selected until the root mean square error between the true value and the predicted value of the remaining life is minimized, and the fusion coefficient of the multi-sensor is finally determined.

8. A multi-sensor signal fusion method for constructing engine health indicators according to claim 7, characterized in that: S5 content includes: In order to make the degradation model fit the health indicator trajectory of the test unit, a sequential Bayesian method is used to update λ online when new data is obtained. According to the Bayesian theorem, λ is k The posterior distribution of the moment is: Further deduction shows that t k The mean value of time λ and variance for:

9. A multi-sensor signal fusion method for constructing engine health indicators according to claim 8, characterized in that: S61 content is as follows: Under the concept of first arrival time, let ω represent the failure threshold, and define the life and remaining life as: T:=inf{t:Y(t)≥ω} (22) L k :=inf{l k :(t k +l k )≥ω} (23) The probability density function expression of the life based on the nonlinear Wiener degradation model is obtained as follows:

10. A multi-sensor signal fusion method for constructing engine health indicators according to claim 9, characterized in that: S62 content includes: Based on the relationship between life span and remaining life span, the probability density function of remaining life span is: According to the probability density function of the remaining life, the estimated value of the remaining life at the current moment is predicted.

Images