Reliability Evaluation and Remaining Life Prediction Method Based on Multi-Source Degradation Data Fusion

Abstract

The present invention relates to the technical field of equipment health prediction, and discloses a reliability evaluation and remaining life prediction method based on multi-source degradation data fusion, including: preprocessing multi-source degradation data; fitting the preprocessed multi-source degradation data into a one-dimensional health index through a set fusion coefficient for modeling; using the maximum likelihood estimation method to estimate the parameters of the degradation model; considering the random failure threshold, obtaining the expected value of equipment life prediction, and obtaining the actual fusion coefficient of the equipment health index through the minimum value of the sum of the mean square errors of life prediction; fitting the preprocessed multi-source degradation data into the actual one-dimensional health index of the equipment according to the actual fusion coefficient; obtaining the probability distribution function of the equipment life; deriving the probability distribution expression of the remaining life of the equipment under the influence of the random failure threshold, and obtaining the predicted remaining life and reliability of the equipment. This method can effectively improve the accuracy and precision of reliability evaluation and remaining life prediction.

Description

Technical Field

[0001] The present invention relates to the technical field of equipment health prediction, and in particular to a reliability assessment and remaining life prediction method based on multi-source degradation data fusion. Background Art

[0002] With the continuous advancement of science and technology, equipment in cutting-edge manufacturing, aerospace, national defense and military fields is becoming increasingly large-scale, diversified, integrated and complex. Accurately grasping the health status of such equipment, scientifically predicting the future development trend of the health status, and formulating targeted maintenance and support plans are effective means to ensure its long-term stable operation, which is of great significance to achieving industrial upgrading, improving the national economy, and maintaining national defense security. In order to ensure the reliability and safety of the operation of large-scale high-tech equipment, Prognostics and Health Management (PHM) technology came into being and attracted widespread attention from researchers.

[0003] The collection of equipment degradation data and the prediction of remaining life are the core points of PHM technology. With the popularization and development of sensor technology and Internet of Things technology, it has become possible to fully set up sensors for large-scale high-tech equipment and obtain massive state monitoring information. However, how to scientifically use the multi-source degradation information obtained, accurately model the degradation process and predict its remaining life has become a realistic challenge that needs to be solved urgently. At present, the remaining life prediction methods based on multi-source degradation data can be mainly divided into two categories. The first category is to perform degradation modeling and remaining life prediction for different sensor monitoring degradation data separately, and then formulate rules to determine the overall remaining life; however, this method ignores the correlation between different sensor monitoring degradation data, and it is difficult to reflect the overall degradation law of the equipment, resulting in low prediction performance. The second category is to screen and fuse all monitoring degradation data based on data fusion methods, and then conduct degradation modeling and remaining life prediction research; this method takes into account both the "individuality" of single sensor monitoring degradation data and the "commonality" of overall equipment degradation, and can obtain more ideal remaining life prediction results.

[0004] According to different data fusion methods, the remaining life prediction methods based on data fusion can be divided into many types. Among them, directly fusing multiple sensor monitoring degradation data into a single health index (Health Index, HI) is a popular method. This method has the following advantages: First, by constructing a one-dimensional health index, the analysis of multivariate degradation problems can be transformed into the analysis of univariate degradation problems, which not only helps to reduce the complexity of modeling, but also can directly apply the existing rich research results on univariate degradation problems; second, different degradation models can be selected for different sensor monitoring degradation data and integrated into the health index to improve the flexibility and pertinence of the method; third, the fused health index realizes the continuous visualization of the equipment degradation process, which is of great significance in the actual use link, helps decision makers to fully grasp the overall degradation process and current degradation status of the equipment, and plays an important role in boosting decision-making confidence. Many research results have emerged around the construction of health indicators at home and abroad. Liu et al. established a general path model of health indicators with the minimum variance of model fitting error and failure threshold as the accurate criterion for determining the fusion coefficient, and realized the prediction of remaining life. Zhao Guangshe et al. established a criterion for determining product health indicators based on Euclidean distance, and studied the degradation modeling and remaining life prediction of equipment based on the Wiener process. Peng Kaixiang et al. extracted features from multi-source degradation data by training a deep belief network (DBN) to determine its health indicators, and on this basis used a hidden Markov model (HMM) to perform degradation modeling and remaining life prediction. However, the above methods all regard the construction process of health indicators and the degradation modeling and remaining life prediction process of health indicators as two independent parts, which may lead to mismatches between the constructed health indicators and the degradation models used, reducing the accuracy of remaining life prediction. In response to the shortcomings of the above studies, Ren Ziqiang et al. and Li Tianmei et al. proposed a multi-source data-driven digital-analog linkage remaining life prediction method, which considers the construction and prediction processes of health indicators simultaneously and improves the accuracy of remaining life prediction.

[0005] Further analysis shows that the above-mentioned digital-analog linkage remaining life prediction method sets the failure threshold corresponding to the health index as a fixed value. In the existing research on univariate degradation problems, the important influence of random failure threshold on the remaining life prediction results has been widely discussed and confirmed. In view of the fact that the current research on digital-analog linkage remaining life prediction methods has not yet discussed the impact of random failure threshold, this paper proposes a multi-source degradation data fusion and remaining life prediction method considering random failure threshold. Based on the Wiener process considering random failure threshold, the degradation model of sensor monitoring degradation data and fused health index is constructed; and the fusion coefficient is determined based on the minimum mean square error and life prediction criterion. Furthermore, the parameters of the health index degradation model are estimated offline and updated online based on the maximum likelihood principle and Bayesian principle. Then, the analytical expression of the remaining life probability distribution under the influence of random failure threshold is derived according to the full probability formula. Finally, verification analysis is carried out based on the Commercial Modular Aero Propulsion System Simulation (C-MAPSS) data set publicly provided by NASA. Summary of the invention

[0006] The present invention provides a reliability assessment and remaining life prediction method based on multi-source degradation data fusion, which can solve the above problems in the prior art.

[0007] The present invention provides a reliability assessment and remaining life prediction method based on multi-source degradation data fusion, including:

[0008] S1. Preprocessing the multi-source degradation data obtained by monitoring;

[0009] S2, fitting the preprocessed multi-source degradation data into a one-dimensional health index through the set fusion coefficient, and using the Wiener process to model the preprocessed multi-source degradation data according to the one-dimensional health index;

[0010] S3. Use the maximum likelihood estimation method to estimate the parameters of the degradation model: drift coefficient, diffusion coefficient and random failure threshold;

[0011] S4. Considering the random failure threshold, the expected value of the equipment life prediction is obtained, and the actual fusion coefficient of the equipment health index is obtained through the minimum value of the mean square error of the life prediction;

[0012] S5, fitting the preprocessed multi-source degradation data according to the actual fusion coefficient to obtain the actual one-dimensional health index of the equipment;

[0013] S6. Obtain the probability distribution function of the equipment life according to the actual one-dimensional health index of the equipment, drift coefficient, diffusion coefficient and random failure threshold;

[0014] S7. Update the drift coefficient online according to Bayes' principle;

[0015] S8. Considering the drift coefficient, according to the probability distribution function of the equipment life, deduce the probability distribution expression of the remaining life of the equipment under the influence of the random failure threshold, and obtain the predicted remaining life and reliability of the equipment.

[0016] Furthermore, the preprocessing in the above step S1 includes:

[0017] If we let Y i,j,k represent the degradation data obtained by the j-th type of sensor in the i-th equipment at the k-th monitoring moment, then let represent the corresponding degradation data after filtering, and i = 1, 2, …, N; j = 1, 2, …, M; k = 1, 2, …, Ki;

[0018] Let D i,j,k represent the degradation data after normalization, and the specific normalization method is:

[0019]

[0020] where, represents all the degradation data corresponding to the j-th type of sensor in the entire degradation dataset, which is equivalent to all the monitoring data obtained by this type of sensor during the full life cycle of different equipment; min(·) and max(·) respectively represent taking the minimum and the maximum.

[0021] Furthermore, the above step S2 specifically includes: Modeling the preprocessed degradation data using the Wiener process, we get:

[0022]

[0023] where, D i,j (0) represents the degradation data corresponding to the j-th type of sensor in the i-th equipment at the initial moment; is the drift coefficient corresponding to the j-th type of sensor in the i-th equipment; is the corresponding diffusion coefficient; B(t) is a standard Brownian motion and satisfies B(t) ∼ N(0, t);

[0024] Let X i,k represent the health index corresponding to the i-th equipment at the k-th monitoring moment, then:

[0025] X i,k = g(D i,k , ω) (3)

[0026] where, D i,k = [D i,1,k , D i,2,k , …, Di,M,k , representing all the degradation data of the device; ω = [ω1, ω2, …, ω M represents the fusion coefficient; g(·) represents the fusion function;

[0027] The health index is solved by the method of linear fusion,

[0028] X i,k = D i,k ·ω′ (4)

[0029] where ω′ represents the transpose of the fusion coefficient vector ω;

[0030] From the basic properties of the Wiener process, it is known that the health index X obtained based on the linear fusion method i,k also follows the Wiener process, that is, X i,k satisfies:

[0031] X i,k = X i (t k ) = X i (0) + λ i t k + σ B B(t k ) (5)

[0032] where X i (0) represents the initial health index of the i-th device; λ i and σ B represent the corresponding drift and diffusion coefficients.

[0033] Furthermore, the above step S3 specifically includes:

[0034] The estimation of the degradation model parameters includes the following steps:

[0035] The increment of the device health index should satisfy the normal distribution, that is and ΔX i,k = X i,k - X i,k-1 , Δt k = t k - Δt k-1 , let t0 = 0, X i,0 = X i,1 , thus obtaining the profile likelihood function of the health index increment ΔX i,k as:

[0036]

[0037] The maximum likelihood estimation method is used to solve the degradation model parameters λ i and Taking the partial derivatives of equation (6) with respect to λ respectivelyi The partial derivative with respect to and set it equal to zero to obtain:

[0038]

[0039]

[0040] Then, equations (7) and (8) are the calculation formulas for the estimated values of λ i and ;

[0041] Estimating the random failure threshold includes the following steps:

[0042] For a specific device, the degradation amount of the health index corresponding to its failure is defined as the failure threshold of the device. Then is equivalent to the failure threshold corresponding to the i-th device. The randomness of the failure threshold is represented by a normal distribution, that is where S represents the random failure threshold of the device;

[0043] Based on the above analysis, the profile likelihood function corresponding to the random failure threshold is:

[0044]

[0045] Using the maximum likelihood estimation method, we get:

[0046]

[0047]

[0048] Furthermore, the above steps S4 - S6 specifically include:

[0049] According to Lemma 1: If Z ~ N(μ, σ 2 ), A ∈ R, B ∈ R + , then the following equation holds;

[0050]

[0051] The probability expression of the Wiener process life distribution under the condition of a fixed failure threshold is:

[0052]

[0053] where X i,0 = X i (0) represents the initial value of the device health index;

[0054] f(·) represents the probability density function. Based on the total probability formula, the probability distribution corresponding to the device life considering the random failure threshold is:

[0055]

[0056] If the random failure threshold S of the device satisfies a normal distribution, and let Z = S - X i,0 , then Let's assume A = λ i t, Then, using Lemma 1, the equivalent expression of Equation (14) is obtained as follows:

[0057]

[0058] Based on Equation (15), the expected value of the device life is obtained as:

[0059]

[0060] Further analysis shows that Equation (16) is equivalent to I1 - I2, where:

[0061]

[0062]

[0063] where, F i (t) is the cumulative distribution function of the life;

[0064] From the properties of the cumulative distribution function, we have F i (+∞) = 1, then Equation (18) is equivalent to

[0065] Let Substituting it into Equation (17), we get:

[0066]

[0067] In engineering practice, the variance of the random failure threshold is usually extremely small and approaches zero. Then, based on the basic properties of definite integrals, the approximate expression of Equation (19) is obtained as:

[0068]

[0069] Let Substituting it into Equation (20), we get:

[0070]

[0071] The integral term in Equation (21) is the standard form for solving the expected value of the inverse Gaussian distribution. Therefore, we have:

[0072]

[0073] The expected value of the device life considering the random failure threshold is obtained as:

[0074]

[0075] Let denote the true life of the device, then the mean square error of life prediction is expressed as:

[0076]

[0077] Taking the minimum value of Equation (24), the actual fusion coefficient of the device health index is obtained.

[0078] Furthermore, the above step S7 specifically includes:

[0079] Assume that the health indexes of the target device at times 1 to t k are respectively X 1:k ={X1, X2, …, X k}, then its degradation model is expressed as:

[0080] X k = X(t k ) = X(0) + λt k + σ B B(t k ) (25)

[0081] Let the drift coefficient λ satisfy to reflect the differences in degradation among different devices. In the remaining life prediction step, the drift coefficient is updated. According to Bayes' theorem, we have:

[0082]

[0083]

[0084] where the initial values of the mean and variance of the drift coefficient are respectively:

[0085]

[0086]

[0087] Furthermore, the above step S8 specifically includes:

[0088] The probability distribution expression of the remaining life of the device considering the random effect of the drift coefficient is:

[0089]

[0090] where l k denotes the remaining life at time t k ;

[0091] If the influence of the random failure threshold is considered, then S - Xk satisfies the normal distribution and follows If we let Z = S - X k , A = μ λ,k l k ; Based on the total probability formula and using Lemma 1, we get:

[0092]

[0093] Considering the expected remaining life of the device under the condition of the random failure threshold, that is, the predicted remaining life is:

[0094]

[0095] Similarly, the reliability of the device is obtained as:

[0096]

[0097] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0098] 1) Fusing multi-source degradation data to construct a health index can realize the full utilization of monitoring data, effectively reduce the one-sidedness of the description of the overall degradation process by single-sensor data, and reduce the uncertainty of remaining life prediction;

[0099] 2) In the process of determining the health index, ignoring the random failure threshold will reduce the effectiveness of the health index determination method, resulting in the difficulty of the fused health index to accurately reflect the true degradation law of the device and reducing the accuracy of remaining life prediction;

[0100] 3) In the process of reliability evaluation and remaining life prediction, considering the random failure threshold can effectively reduce the prediction error and improve the method performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0101] Figure 1 It is a schematic diagram of the relationship between degradation data and health index of the reliability evaluation and remaining life prediction method based on multi-source degradation data fusion provided by the present invention.

[0102] Figure 2 It is a health index failure threshold distribution diagram in the reliability evaluation and remaining life prediction method based on multi-source degradation data fusion provided by the present invention.

[0103] Figure 3 It is a Ps30 failure threshold distribution diagram in the reliability evaluation and remaining life prediction method based on multi-source degradation data fusion provided by the present invention.

[0104] Figure 4(a) is a remaining life prediction result diagram of M0 and M1 in the reliability evaluation and remaining life prediction method based on multi-source degradation data fusion provided by the present invention.

[0105] Figure 4(b) is a graph showing the predicted remaining useful life of M0 and M2 in the reliability assessment and remaining useful life prediction method based on multi-source degradation data fusion provided by the present invention.

[0106] Figure 5 It is a schematic diagram of the predicted remaining useful life of M0, M1, and M2 in the reliability assessment and remaining useful life prediction method based on multi-source degradation data fusion provided by the present invention.

[0107] Figure 6 It is the main process block diagram of the reliability assessment and remaining useful life prediction method based on multi-source degradation data fusion provided by the present invention. Specific embodiments

[0108] The following combines the attached Figures 1-6 , and describes in detail a specific embodiment of the present invention, but it should be understood that the protection scope of the present invention is not limited by the specific embodiment.

[0109] Aiming at the problem that the existing remaining useful life prediction method for fusing multi-source degradation data ignores the influence of the random failure threshold, the present invention proposes a method for fusing multi-source degradation data and predicting the remaining useful life considering the random failure threshold. First, a criterion for determining the fusion coefficient considering the random failure threshold is established to fuse multi-source degradation data into a single health index; secondly, a degradation model of the obtained health index is established using a Wiener process with linear drift, and the unknown parameters of the model are solved using the maximum likelihood estimation method and updated based on the Bayesian principle; then, an analytical expression of the probability distribution of the remaining useful life under the influence of the random failure threshold is derived based on the total probability formula; finally, taking the degradation data of an aero-engine as an example for analysis, it is proved that the method proposed in this paper can effectively improve the accuracy and precision of the remaining useful life prediction and has engineering application value.

[0110] The reliability assessment and remaining useful life prediction method based on multi-source degradation data fusion provided by the embodiments of the present invention includes the following steps:

[0111] I. Pretreatment of degradation data

[0112] Affected by factors such as equipment operating environment interference and sensor production process defects, the degradation data obtained by sensor monitoring often contains many interference signals, resulting in the obtained degradation data deviating from the true degradation trajectory and affecting the accuracy of modeling and prediction. In addition, considering the different physical meanings and dimensions of the degradation data monitored by different sensors of the same equipment, directly fusing them is likely to generate large errors and have an adverse impact on the prediction results. To address the above problems, the present invention first preprocesses the multi-source degradation data obtained by monitoring at the initial stage of constructing the health index, and the specific method can be summarized as "filtering + normalization".

[0113] ① If we let Y i,j,k represent the degradation data obtained by the j - th type of sensor in the i - th device at the k - th monitoring moment, then let represent the corresponding degradation data after filtering processing, where i = 1, 2, …, N; j = 1, 2, …, M; k = 1, 2, …, Ki. Among them, common filtering methods can adopt Gaussian filtering, median filtering, etc.

[0114] ② Let D i,j,k represent the degraded device after normalization processing, and the specific normalization method is:

[0115]

[0116] Among them, represents all the degradation data corresponding to the j - th type of sensor in the entire degradation dataset, which is equivalent to all the monitoring data obtained by this type of sensor during the full - life cycle of different devices; min(·) and max(·) respectively represent taking the minimum and the maximum.

[0117] It can be easily known from Equation (1) that D i,j,k ∈[0, 1] and D i,j,k is dimensionless. Therefore, in subsequent analysis, the health indicators and related parameters of the device have no unit.

[0118] II. Degradation Data Modeling

[0119] The present invention uses the Wiener process to model the pre - processed degradation data, and we get:

[0120]

[0121] Among them, D i,j (0) represents the degradation data corresponding to the j - th type of sensor in the i - th device at the initial moment; is the drift coefficient corresponding to the j - th type of sensor in the i - th device; is the corresponding diffusion coefficient; B(t) is a standard Brownian motion, and it satisfies B(t) ∼ N(0, t).

[0122] Let X i,k represent the health indicator corresponding to the i - th device at the k - th monitoring moment, then:

[0123] X i,k = g(D i,k , ω) (3)

[0124] Among them, D i,k = [D i,1,k , D i,2,k , …, D i,M,k ; ω = [ω1, ω2, …, ωM represents the fusion coefficient vector; represents the fusion function.

[0125] The present invention uses a linear fusion method to solve the health index, then Equation (3) can be expressed as: g(·)

[0126] X i,k = D i,k ·ω′ (4)

[0127] where ω′ represents the transpose of the fusion coefficient vector ω.

[0128] It is easy to know from the basic properties of the Wiener process that the health index X obtained based on the linear fusion method i,k also follows a Wiener process, that is, X i,k satisfies:

[0129] X i,k = X i (t k ) = X i (0) + λ i t k + σ B B(t k ) (5)

[0130] where X i (0) represents the initial health index of the i-th device; λ i and σ B represent the corresponding drift and diffusion coefficients.

[0131] III. Degradation Parameter Estimation

[0132] Affected by factors such as the operating environment, production process, and usage method, the degradation of different individuals of the same type of equipment has significant randomness. One manifestation is the randomness of the "process" of degradation, that is, the parameter values corresponding to the degradation models of different devices are not the same; the other manifestation is the randomness of the "result" of degradation, that is, the failure thresholds corresponding to different devices vary. In order to obtain the estimated values of the equipment degradation parameters, the present invention analyzes around two parts: the degradation model parameters and the random failure threshold.

[0133] (1) Degradation Model Parameter Estimation

[0134] The Wiener process is an independent increment process. From its basic properties, it can be known that the increment of the equipment health index should satisfy a normal distribution, that is And ΔX i,k = X i,k - X i,k-1 , Δt k = t k - Δt k-1 . For the convenience of analysis, this article sets t0 = 0, X i,0 = Xi,1 Thus, the increment of the health index ΔX can be obtained. i,k The profile likelihood function of is:

[0135]

[0136] The present invention uses the maximum likelihood estimation method to solve the degradation model parameter λ. i and Taking the partial derivatives of Equation (6) with respect to λ respectively and setting them equal to zero, we get: i and The partial derivatives with respect to and setting them equal to zero gives:

[0137]

[0138]

[0139] Then, Equations (7) and (8) are the calculation formulas for the estimated values of λ and. i and The calculation formula for the estimated value.

[0140] (2) Estimation of the random failure threshold

[0141] For a specific device, the degradation amount of the health index corresponding to its failure is often defined as the failure threshold of the device. Then, is equivalent to the failure threshold corresponding to the i-th device. The present invention uses a normal distribution to represent the randomness of the failure threshold, that is, where S represents the random failure threshold of the device.

[0142] Based on the above analysis, it is easy to obtain that the profile likelihood function corresponding to the random failure threshold is:

[0143]

[0144] Using the maximum likelihood estimation method, we get:

[0145]

[0146]

[0147] IV. Determination of the fusion coefficient

[0148] The present invention proposes a fusion coefficient determination criterion, and establishes a fusion coefficient determination model with the goal of minimizing the mean square error of life prediction. To solve the probability distribution function of the device life affected by the random failure threshold, the present invention gives Lemma 1.

[0149] Lemma 1: If Z ~ N(μ, σ 2 ), A ∈ R, B ∈ R + , then the following equation holds.

[0150]

[0151] The probability expression of the lifetime distribution of the Wiener process under the condition of a fixed failure threshold is specifically as follows:

[0152]

[0153] where X i,0 = X i (0) represents the initial value of the equipment health index; f(·) represents the probability density function.

[0154] Furthermore, based on the total probability formula, the probability distribution corresponding to the equipment lifetime considering the random failure threshold can be obtained as:

[0155]

[0156] If the random failure threshold S of the equipment satisfies the normal distribution and let Z = S - X i,0 , then it can be known that Let's assume A = λ i t, Then, by using Lemma 1, the equivalent expression of Equation (14) can be obtained as:

[0157]

[0158] Based on Equation (15), the expected value of the equipment lifetime can be obtained as:

[0159]

[0160] Further analysis shows that Equation (16) can be equivalent to I1 - I2, where:

[0161]

[0162]

[0163] where F i (t) is the cumulative distribution function of the lifetime.

[0164] From the property of the cumulative distribution function, it can be obtained that F i (+∞) = 1, then Equation (18) is equivalent to Let Substituting it into Equation (17) gives:

[0165]

[0166] In engineering practice, the variance of the random failure threshold is usually extremely small and approaches zero. Then, based on the basic property of definite integral, the approximate expression of Equation (19) can be obtained as:

[0167]

[0168] Let Substituting it into Equation (20), we can get:

[0169]

[0170] Further analysis shows that the integral term in Equation (21) is in the standard form for solving the expectation of the inverse Gaussian distribution. Therefore, we can get:

[0171]

[0172] Based on the above analysis, the expected value of the device life considering the random failure threshold is:

[0173]

[0174] Let represent the true life of the device. Then the mean square error sum of life prediction can be expressed as:

[0175]

[0176] Taking the minimum value of Equation (24), the fusion coefficient of the device health index can be obtained. Further analysis shows that taking the minimum value of Equation (24) is equivalent to an unconstrained multi-variable non-linear programming problem. Therefore, the fminunc function in MATLAB can be used to solve it.

[0177] V. Online Parameter Update

[0178] Assume that the health indexes of the target device corresponding to the time from 1 to t k are X 1:k ={X1, X2,... X k}. Then its degradation model can be expressed as:

[0179] X k =X(t k ) = X(0) + λt k + σ B B(t k ) (25)

[0180] In order to more accurately characterize the degradation law of the device, the drift coefficient λ is often made to satisfy to reflect the differences in degradation among different devices. In the remaining life prediction link, in order to further improve the prediction accuracy, the drift coefficient is often updated. According to the Bayesian principle, its update process is:

[0181]

[0182]

[0183] Among them, the initial values of the mean and variance of the drift coefficient are respectively:

[0184]

[0185]

[0186] VI. Derivation of remaining life distribution

[0187] Probability distribution expression of the remaining life of the device when considering the random effect of the drift coefficient:

[0188]

[0189] If the influence of the random failure threshold is considered, then S - X k obeys the normal distribution and follows If we let Z = S - X k , A = μ λ,k l k . Based on the total probability formula and using Lemma 1, we can obtain:

[0190]

[0191] Among them, l k represents the remaining life at time t k ;

[0192] Furthermore, the expected value and reliability of the remaining life of the device under the condition of considering the random failure threshold are respectively:

[0193]

[0194]

[0195] E(l k ) is also called the predicted remaining life and is often used to measure the quality of the prediction result.

[0196] This invention conducts analysis based on the C - MAPSS dataset publicly released by NASA. Among them, the specific research object is selected as all the training set data corresponding to the FD001 subset. This dataset contains a total of full - life - cycle degradation data of 100 aero - engines monitored by 21 different sensors. The monitoring data information corresponding to different sensors is shown in Table 1.

[0197] Table 1 Sensor monitoring data information

[0198]

[0199]

[0200] The monitoring data is preprocessed using the degradation data preprocessing method proposed in the present invention. Among them, the Gaussian filtering method is selected for filtering, and the window width is set to 20. On this basis, the degradation data monitored by different sensors is normalized. Through analysis, it can be seen that after normalization, the six types of monitored degradation data, namely the total temperature at the fan inlet, the fan inlet pressure, the engine pressure ratio, the burner fuel-air ratio, the required fan speed, and the required corrected fan speed, are always zero, indicating that these six types of data have no influence on the fusion result of the health indicators. To simplify the calculation, in subsequent studies, the above six types of data are excluded from the research object.

[0201] For the convenience of comparative analysis, the multi-source degradation data fusion and remaining life prediction method considering the random failure threshold proposed in the present invention is denoted as M0, and the multi-source degradation data fusion and remaining life prediction method without considering the random failure threshold is denoted as M1. In addition, the present invention also sets the remaining life prediction method based on univariate degradation data under the influence of the random failure threshold as a control group, denoted as M2. In M2, the selection of sensor degradation data is carried out according to the Pearson correlation coefficient standard. If the absolute value of the Pearson correlation coefficient of a certain type of degradation data is larger, it indicates that the correlation between this type of data and the Wiener process is better. The static pressure at the outlet of the high-pressure compressor of the engine has the largest absolute value of the Pearson correlation coefficient among the 21 groups of sensor-monitored degradation data. Therefore, the present invention selects the static pressure at the outlet of the high-pressure compressor as the univariate degradation data for analysis. The fusion coefficients determined according to different methods are shown in Table 2. Under the condition of determining the fusion coefficients, the health indicator fusion can be carried out. The present invention takes the 8th engine in the FD001 training set as an example for illustration, and its corresponding degradation data and the fused health indicators are as Figure 1 shown.

[0202] Table 2 Results of determining fusion coefficients

[0203]

[0204] From Figure 1 it can be seen that the degradation processes of different performance parameters of the engine and its health indicators are significantly non-monotonic. Therefore, it is suitable to use the Wiener process to model its degradation. Based on the degradation parameter estimation method proposed in the present invention, the engine degradation parameters can be estimated, and the specific results are shown in Table 3.

[0205] Table 3 Estimated values of degradation parameters

[0206]

[0207] Figure 2 And Figure 3The quantile-quantile plots (i.e., Q-Q plots) of the overall distribution of the failure thresholds of 100 engines in the M0 method and the M2 method against the normal distribution are respectively given. From Figure 2 and Figure 3 it can be seen that the failure thresholds corresponding to the engine health index and the static pressure at the outlet of the high-pressure compressor are basically distributed on a straight line, which can show that the failure thresholds of the engine health index and the static pressure at the outlet of the high-pressure compressor (P s30 ) both follow the normal distribution. This proves the rationality of the assumption in the present invention that the engine failure threshold follows the normal distribution.

[0208] Based on the estimated values of the degradation parameters, the remaining useful life of the engine can be predicted by using the method proposed in the present invention. The 8th engine in the FD001 training set ( Figure 1 as shown) is selected as the target device for verification analysis, and the specific remaining useful life prediction results are shown in Figure 4. As can be seen from Figure 4(a), the probability density curve of the remaining useful life corresponding to M0 can completely cover the true remaining useful life of the target device, while the distribution curve of the remaining useful life corresponding to M1 cannot completely cover the true remaining useful life of the target device. For example, at the operating times of 105 and 120 cycles, which indicates that M0 has higher accuracy in predicting the remaining useful life than M1. As can be seen from Figure 4(b), the probability density curves of the remaining useful life corresponding to M0 and M1 can both completely cover the true remaining useful life of the target device, but the probability distribution curve of the remaining useful life corresponding to M0 is more concentrated than that of M2, indicating that the prediction uncertainty of M0 is smaller than that of M2, which shows that the prediction accuracy of M0 is higher than that of M2.

[0209] To further prove that the data fusion and remaining useful life prediction method considering the random failure threshold proposed in the present invention has more advantages in prediction performance, the present invention gives the predicted values, predicted 95% confidence intervals, and predicted absolute errors of the remaining useful life of the target device at different operating times, as shown in detail in Figure 5 and Table 4.

[0210] Table 4 95% Confidence Intervals and Absolute Errors of Remaining Useful Life Prediction

[0211]

[0212]

[0213] From Figure 5It can be seen that in the early stage of engine operation, the performance of M0, M1, and M2 in predicting the remaining useful life is generally poor. The main reason for the large prediction error in this stage is the relatively large prediction uncertainty caused by the small amount of monitoring data. As the operation time extends and the amount of acquired monitoring data increases, the prediction accuracy gradually improves. In the late stage of engine operation, all three methods can accurately predict the remaining useful life. By analyzing Table 4, it can be found that in the middle and late stages of engine operation (operation time greater than 60 cycles), the absolute error of RUL corresponding to M0 is significantly smaller than that of M1, indicating that the prediction accuracy of M1 is better, which shows the necessity of considering the random failure threshold in the process of health index fusion and remaining useful life prediction. At the same time, the prediction confidence interval of RUL corresponding to M0 is generally narrower than that of M2, indicating that M0 has lower prediction uncertainty while ensuring prediction accuracy, which shows that fusing multi-source sensor data has more advantages than single-sensor data in improving the prediction accuracy of the remaining useful life.

[0214] The above discloses only several specific embodiments of the present invention. However, the embodiments of the present invention are not limited thereto, and any changes that can be conceived by those skilled in the art should fall within the protection scope of the present invention.

Claims

1. A reliability evaluation and remaining life prediction method based on multi-source degradation data fusion, characterized in that, It includes the following steps: S1. Preprocess the multi-source degradation data obtained by monitoring; S2. Fit the preprocessed multi-source degradation data into a one-dimensional health index through a set fusion coefficient. According to the one-dimensional health index, use the Wiener process to model the preprocessed multi-source degradation data; S3. Use the maximum likelihood estimation method to estimate the parameters of the degradation model: drift coefficient, diffusion coefficient, and random failure threshold; S4. Considering the random failure threshold, obtain the expected value of the equipment life prediction. Through the minimum value of the sum of the mean square errors of the life prediction, obtain the actual fusion coefficient of the equipment health index; S5. Fit the preprocessed multi-source degradation data into the actual one-dimensional health index of the equipment according to the actual fusion coefficient; S6. According to the actual one-dimensional health index of the equipment, drift coefficient, diffusion coefficient, and random failure threshold, obtain the probability distribution function of the equipment life; S7. Based on the Bayesian principle, perform online update on the drift coefficient; S8. Considering the drift coefficient, according to the probability distribution function of the equipment life, deduce the probability distribution expression of the remaining life of the equipment under the influence of the random failure threshold, and obtain the predicted remaining life of the equipment and the reliability of the equipment; The preprocessing in step S1 includes: If we let Y i,j,k represent the degradation data obtained by the j-th type of sensor in the i-th device at the k-th monitoring moment, then let represent the corresponding degradation data after filtering, and i = 1, 2, …, N; j = 1, 2, …, M; k = 1, 2, …, Ki; Let D i,j,k represent the degraded data after normalization, and the specific normalization method is as follows: Among them, represents all the degradation data corresponding to the j-th type of sensor in the entire degradation dataset, which is equivalent to all the monitoring data obtained by this type of sensor during the full life cycle of different devices; min(·) and max(·) respectively represent taking the minimum and the maximum; Step S2 specifically includes: Using the Wiener process to model the preprocessed degradation data, we get: Among them, D i,j (0) represents the degradation data corresponding to the j-th type of sensor of the i-th device at the initial moment; is the drift coefficient corresponding to the j-th type of sensor of the i-th device; is the corresponding diffusion coefficient; B(t) is a standard Brownian motion and satisfies B(t) ~ N(0, t); Let X i,k represent the health index corresponding to the i-th device at the k-th monitoring moment, then: X i,k = g(D i,k , ω) (3) Among them, D i,k = [D i,1,k , D i,2,k , …, D i,M,k , represents all the degradation data of the device; ω = [ω1, ω2, …, ω M represents the fusion coefficient; g(·) represents the fusion function; Solve the health index by using the method of linear fusion, X i,k = D i,k · ω′(4) where ω′ represents the transpose of the fusion coefficient vector ω; According to the basic properties of the Wiener process, the health index X obtained based on the linear fusion method i,k also follows a Wiener process, that is, X i,k satisfies: X i,k = X i (t k ) = X i (0) + λ i t k + σ B B(t k ) (5) Among them, X i (0) represents the initial health index of the i-th device; λ i and σ B represent the corresponding drift and diffusion coefficients; Step S3 specifically includes: The estimation of the degradation model parameters includes the following steps: The increment of the device health indicator should satisfy a normal distribution, that is and ΔX i,k = X i,k - X i,k-1 , Δt k = t k - Δt k-1 , let t0 = 0, X i,0 = X i,1 , thus obtaining the profile likelihood function of the health indicator increment ΔX i,k as: Solve the degradation model parameter λ using the maximum likelihood estimation method i and Take the partial derivatives of Equation (6) with respect to λ i and respectively, and set them equal to zero to obtain: Then equations (7) and (8) are the calculation formulas for the estimated values of λ i and respectively. The estimation of the random failure threshold includes the following steps: For a specific device, the degradation amount of the corresponding health indicator at the time of its failure is defined as the failure threshold of the device. Then is equivalent to the failure threshold corresponding to the i-th device. The normal distribution is used to represent the randomness of the failure threshold, that is where S represents the random failure threshold of the device; Based on the above analysis, the profile likelihood function corresponding to the random failure threshold is: Using the maximum likelihood estimation method, we get: Steps S4 - S6 specifically include: According to Lemma 1: If \(Z\sim N(\mu,\sigma 2 ^2)\), \(A\in R\), \(B\in R + \), then the following equation holds; The probability expression of the life distribution of the Wiener process under the condition of a fixed failure threshold is: Among them, X i,0 = X i (0) represents the initial value of the device health indicator; f(·) represents the probability density function. Based on the total probability formula, the probability distribution corresponding to the equipment life considering the random failure threshold is: If the random failure threshold S of the equipment satisfies the normal distribution, and Z ＝ SX i,0 ,but Let A = λ i t, Then, using Lemma 1, we can get the equivalent expression of formula (14): Based on Equation (15), the expectation of the equipment life is obtained as: Further analysis shows that Equation (16) is equivalent to I1 - I2, where: where, F i (t) is the cumulative distribution function of the lifetime; From the properties of the cumulative distribution function, we have F i (+∞) = 1, then Equation (18) is equivalent to Let Substituting it into Equation (17), we get: In engineering practice, the variance of the random failure threshold is usually extremely small and approaches zero. Then, based on the basic properties of definite integrals, the approximate expression of Equation (19) is obtained as follows: Let Substituting into Equation (20), we get: The integral term in Equation (21) is the standard form for solving the expectation of the inverse Gaussian distribution. Therefore, we get: The expected value of the equipment life considering the random failure threshold is: Let represent the true life of the device, then the mean square error of life prediction is expressed as: Take the minimum value of Equation (24) to obtain the actual fusion coefficient of the equipment health index.

2. The reliability evaluation and remaining life prediction method based on multi-source degradation data fusion according to claim 1, characterized in that, Step S7 specifically includes: Suppose the health indicators corresponding to the target device at times 1 to t k are respectively X 1:k ={X1, X2, …, X k}, then its degradation model is expressed as: X k = X(t k ) = X(0) + λt k + σ B B(t k ) (25) Let the drift coefficient λ satisfy To reflect the differences in degradation between different devices, during the remaining useful life prediction process, the drift coefficient is updated. According to Bayes' theorem, we have: where the initial values of the mean and variance of the drift coefficient are respectively:

3. The reliability assessment and remaining life prediction method based on multi-source degradation data fusion according to claim 2, characterized in that, Step S8 specifically includes: The probability distribution expression of the remaining life of the equipment considering the random effect of the drift coefficient is: where, l k represents the remaining life at time k t; If the influence of the random failure threshold is considered, then S - X k follows a normal distribution and obeys If we let Z = S - X k , A = μ λ,k l k ; Based on the total probability formula and using Lemma 1, we have: Considering the expectation of the remaining life of the equipment under the condition of the random failure threshold, that is, the predicted remaining life is: Similarly, the reliability of the equipment is obtained as:

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