Trajectory Similarity-Based Remaining Life Prediction Method Based on Slow Feature Information Gain Ratio

Abstract

This invention discloses a trajectory similarity-based remaining life prediction method based on slow feature information gain ratio. First, multi-dimensional condition monitoring data of the entire lifecycle of decommissioned equipment is acquired. Slow feature analysis is then applied to the condition monitoring data after feature filtering and normalization. Next, the optimal feature vector for data fusion is obtained by combining the generalized eigenvalue of a matrix with the definition of slow feature information gain ratio. The processed multi-dimensional condition monitoring data of the decommissioned unit is multiplied with the optimal feature vector to obtain a health index curve. The same feature filtering, feature normalization, nonlinear expansion, and matrix whitening are then applied to the degradation curve of the multi-dimensional condition monitoring data of in-service machinery to obtain its corresponding health index curve. A specified segment of this curve is matched with the health index curve; the curve segment that meets the similarity filtering requirements provides the remaining life prediction result for the in-service equipment. This invention can be applied to various complex mechanical equipment with full lifecycle condition monitoring data.

Description

Technical Field

[0001] This invention relates to the technology for predicting the remaining life of mechanical equipment, and more particularly to a method for predicting the remaining life of equipment based on trajectory similarity using slow feature information gain ratio. Background Technology

[0002] With the rapid development of sensor networks, the Industrial Internet, and cloud computing technologies, monitoring the operational status of mechanical equipment, and storing and processing massive amounts of data have become possible. In this context, condition-based maintenance (DPM) technology is gradually becoming the mainstream of equipment maintenance and health management. Unlike periodic maintenance and fail-safe maintenance, DPM analyzes monitoring data of mechanical equipment to obtain health status indicators and then formulates corresponding maintenance plans, maximizing the equipment's usability. Accurate remaining life prediction is a key aspect of DPM technology. Remaining life prediction methods based on equipment degradation trajectory similarity are an important category of remaining life prediction technologies. They combine data-driven approaches, model interpretability, and ease of real-time deployment, and are increasingly widely used in industrial big data scenarios. Constructing effective health indicators is crucial for degradation trajectory similarity methods. Traditional data-driven and statistical learning methods neglect the mining of trajectory difference information in their obtained health indicators, making it difficult to combine these indicators with subsequent trajectory similarity matching processes to obtain accurate remaining life prediction results. Summary of the Invention

[0003] The purpose of this invention is to address the shortcomings of existing technologies by providing a trajectory similarity-based remaining lifetime prediction method based on slow feature information gain ratio. This method, based on a data fusion strategy using slow feature information gain ratio, can construct health indicators that conform to equipment degradation characteristics while also containing information on degradation trend differences, thus improving the remaining lifetime prediction accuracy of this type of algorithm. It can be used to enhance the performance of equipment remaining lifetime prediction in industrial big data scenarios. The specific technical solution is as follows:

[0004] A trajectory similarity-based remaining lifetime prediction method based on slow feature information gain ratio, which is divided into an offline training phase and an online monitoring phase;

[0005] The offline training phase specifically includes:

[0006] (1) Acquire the status monitoring data of M similar mechanical devices from operation to failure collected by multi-dimensional sensors. When the status monitoring data is non-process data, use feature extraction method to extract the feature quantity of the degradation process; when the status monitoring data is process data, the status monitoring data is directly used as the feature quantity of the degradation process.

[0007] (2) The characteristic quantities of the degradation process are screened and normalized according to the operating conditions;

[0008] (3) For the feature quantities of the normalized degradation process, based on the slow feature solution framework and the definition of information gain ratio index, the feature fusion vector is obtained by solving the matrix generalized eigenvalues.

[0009] (4) Based on the feature fusion vector and the nonlinear expansion function in the slow feature solution framework, M original health index curves are obtained;

[0010] (5) Based on the local slope value of the original health index curve, define the healthy stage and the degenerative stage, and save the original health index curve of the degenerative stage to the degenerative trajectory curve library.

[0011] The online monitoring phase includes:

[0012] S1: Acquire the status monitoring data of in-service mechanical equipment up to the current stage of operation, and perform the same feature extraction, feature filtering and normalization processing as in the offline stage;

[0013] S2: Based on the feature vectors obtained in the offline stage and the nonlinear expansion function in the slow feature solution framework, the health index curve of in-service equipment is obtained;

[0014] S3: Use a time window to extract the health index curve of in-service equipment, and calculate the similarity between the extracted time window curve and the M original health index curves obtained in the offline stage segment by segment. Select the curve segment in each original health index curve whose similarity with the extracted time window curve is greater than a set threshold as the prediction reference sample.

[0015] S4: Obtain the remaining lifetime prediction results based on the final prediction reference sample.

[0016] Furthermore, for the feature quantities of the normalized degradation process, based on the slow feature solving framework and the definition of the information gain ratio index, the feature fusion vector is obtained by solving the matrix generalized eigenvalues, which is achieved through the following sub-steps:

[0017] (1) The normalized feature x i,j,k The nonlinear extended feature z is obtained by performing nonlinear extension function expansion and whitening. i,j',k =whiten(h(x) i,j,k )); where i represents the i-th decommissioned equipment, j represents the j-th feature dimension, j' represents the j-th nonlinearly expanded feature dimension, k represents the k-th monitoring time step, h() represents the nonlinear expansion function, and whiten() represents the whitening operation;

[0018] (2) The data z after augmentation and whitening were processed using a linear combination. i,j',k Dimensional fusion is performed to obtain the fused health indicator value d. i,k =z i,j',kω, where ω is the fusion weight;

[0019] (3) Define the slow feature information gain ratio (SNR) s :

[0020]

[0021] Among them, D e D is a feature range matrix used to record the difference between the initial and final values. e Each row represents a decommissioned unit, and each column represents the multidimensional condition monitoring characteristics after nonlinear expansion, as expressed in equation (2):

[0022]

[0023] In equation (1), 1 represents a column vector consisting entirely of 1s, and Q = (IO / M) / (M-1)Δt∈R M×M It is a symmetric matrix, Δt is the length of the analysis of variance, O is a square matrix of all 1s, I is the identity matrix, and Z is a symmetric matrix. M,j The matrix that records the j+1th reciprocal value before failure is expressed as shown in equation (3):

[0024]

[0025] In formula (1) The first-order difference matrix of the nonlinear expansion variables of the i-th decommissioned unit is expressed as shown in equation (4):

[0026]

[0027] (4) Make Equation (1) can be simplified to:

[0028] Aω=λBω (5)

[0029] Where λ=SNR s ;

[0030] (5) Solve formula (2) to obtain the maximum value of λ. max That is, SNR s The maximum value of ω is the optimal feature fusion vector ω. * .

[0031] Furthermore, based on the feature fusion vector and the nonlinear expansion function in the slow feature solving framework, M original health indicator curves are obtained through the following sub-steps:

[0032] (1) via d i,j * =z i,j,k ω *The health index value d of the i-th decommissioned equipment at the j-th monitoring time step was calculated. i,j * ;

[0033] (2) Based on d i,j * Draw the original health indicator curve.

[0034] Furthermore, based on three evaluation indicators—monotonicity, trend, and correlation—feature screening is performed on the characteristic quantities of the degradation process, and data that simultaneously meets these three evaluation indicators are selected for subsequent operations.

[0035] Furthermore, the formula for calculating the similarity between the extracted time window curve and the M original health indicator curves obtained in the offline phase is as follows:

[0036]

[0037] Among them, t o This serves as the starting point for the predicted reference segment on the original health index curve. This indicates the difference between the in-service equipment and the m-th decommissioned equipment at time t. o The similarity value at any given moment; Let λ be the Euclidean distance of the m-th predicted reference segment, and λ be the distance magnification factor.

[0038] Furthermore, step S4 of the online monitoring phase is implemented through the following sub-steps:

[0039] (4.1) Calculate the set of remaining predicted lifetime values ​​{ERL} for each predicted reference segment. m}:

[0040] ERL m =EoL m -t o -ΔT (7)

[0041] Among them, EoL m t represents the service life of the m-th decommissioned device. o The starting point of the predicted reference segment on the original health index curve; ΔT represents the length of the time window;

[0042] (4.2) The 3σ criterion is used to remove outliers from the set of remaining lifetime predictions in (4.1) to obtain remaining lifetime predictions within the normal range;

[0043] (4.3) Based on the predicted remaining useful life within the normal range, calculate the final predicted remaining useful life (RUL) of the in-service equipment:

[0044]

[0045] in, This represents the similarity value after passing the similarity screening.

[0046] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0047] (1) When constructing equipment health indicators, the remaining life prediction method of the present invention expands the feature fusion space by nonlinear extension, and obtains the optimal data fusion weight based on the proposed slow feature information gain ratio criterion and the solution of the generalized eigenvalue of the matrix. Finally, it obtains health indicators that can accurately characterize the degradation features of equipment and highlight the differences in degradation trends. Combined with the subsequent similarity matching process, it can significantly improve the remaining life prediction performance of the method of the present invention.

[0048] (2) The data fusion process of the method of the present invention does not require the use of a linear regressor, and has a simpler model implementation and deployment process.

[0049] (3) This invention can be widely used in the condition monitoring and remaining life prediction of complex mechanical equipment and their key components, such as turbofan engines, precision injection molding machines and die casting machines. Attached Figure Description

[0050] Figure 1 This is a flowchart illustrating the overall implementation of the present invention;

[0051] Figure 2 This is a flowchart of the process for obtaining the optimal feature vector in this invention;

[0052] Figure 3 This is a diagram of the feature selection process of the present invention;

[0053] Figure 4 This is a graph showing the health indicator results obtained by this invention;

[0054] Figure 5 This is a diagram showing the results of the similarity matching process of this invention;

[0055] Figure 6 This is the remaining lifetime prediction result obtained by the present invention. Detailed Implementation

[0056] The present invention will be described in detail below with reference to the accompanying drawings and preferred embodiments. The objectives and effects of the present invention will become clearer as a result. The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only for explaining the present invention and are not intended to limit the present invention.

[0057] Existing similarity-based life expectancy prediction processes consist of two parts: offline construction of a health indicator curve library and online life expectancy prediction. The degradation indicator curve library construction process proposed in this invention differs from traditional health indicator construction methods by adding the mining of information on differences in degradation trajectory trends. This results in the acquired health indicators exhibiting significant differences in degradation rates, which is beneficial for obtaining more accurate life expectancy prediction results in conjunction with the subsequent similarity matching process. The specific implementation process is as follows: Figure 1 As shown:

[0058] I. Offline Training Phase

[0059] Step 1: Acquire state monitoring data from M similar mechanical devices that have been running until failure, collected by multi-dimensional sensors, and save them as time series data according to the given monitoring time steps; when the state monitoring data is non-process data, i.e., data obtained by high-frequency sampling, such as vibration signals and acoustic emission signals, feature extraction methods (such as time-domain feature extraction and frequency-domain feature extraction methods) are used to extract the feature quantities of the degradation process; when the state monitoring data is process data, i.e., data obtained by low-frequency sampling, such as temperature, pressure, flow rate, etc., the state monitoring data is directly used as the feature quantities of the degradation process.

[0060] Step 2: Feature filtering is performed on the characteristic quantities of the degradation process, and normalization is performed according to the operating conditions.

[0061] Among them, the original multidimensional monitoring data is screened based on evaluation indicators such as monotonicity, trend, and correlation. Evaluation indicators for each degradation feature are calculated, and indicators that exceed the given monotonicity, trend, and correlation thresholds are used as degradation indicators that pass the screening.

[0062] For the filtered multidimensional state monitoring data {x i,j,k}, where i is the i-th failed unit, with values ​​{1, 2, ..., M}, and j is the j-th monitoring time step, with values ​​{1, ..., EoL}. i}, where k is the k-th degenerative feature with values ​​{1,2,...,l}, obtained by z-score normalization according to operating conditions.

[0063] Step 3: For the feature quantities of the normalized degradation process, based on the slow feature solution framework and the definition of the information gain ratio index, the feature fusion vector is obtained by solving the matrix generalized eigenvalues.

[0064] (1) The normalized feature x i,j,k The nonlinear extended feature z is obtained by performing nonlinear extension function expansion and whitening. i,j',k =whiten(h(x) i,j,k)); where i represents the i-th decommissioned device, j represents the j-th feature dimension, j' represents the j-th nonlinearly expanded feature dimension, k represents the k-th monitoring time step, h() represents the nonlinear expansion function, and whiten() represents the whitening operation.

[0065] (2) The data z after augmentation and whitening were processed using a linear combination. i,j',k Dimensional fusion is performed to obtain the fused health indicator value d. i,k =z i,j',k ω, where ω is the fusion weight.

[0066] (3) Define the slow feature information gain ratio (SNR) s :

[0067]

[0068] Where R is the range feature of the fusion feature. For the health index obtained after fusion, it is desirable that its initial value and the final value have a large difference, that is, a large range value. This is the mean of the slow eigenvalues ​​of the fusion feature. The slow eigenvalue is the square of the first-order difference. For a health indicator curve with a given range of values, a smaller mean of the slow eigenvalues ​​indicates that the first-order difference is more evenly distributed, meaning the trend difference in the degradation process is smaller. This is less conducive to obtaining similar degradation trajectory matching results through the trajectory similarity algorithm; conversely, a larger mean corresponds to a larger trend difference, which is beneficial for obtaining similar degradation trajectory matching segments in subsequent similarity matching stages. Δt This describes the variance distribution near the endpoint of the fusion characteristic, where Δt is the time period near the endpoint. For the optimized health index, we hope that the values ​​of different units near the failure time are similar, i.e., a smaller variance value. In summary, we expect to obtain a smaller denominator and a larger numerator, meaning that the fusion-based health index should have the maximum SNR. s value.

[0069] D e D is a feature range matrix used to record the difference between the initial and final values. e Each row represents a decommissioned unit, and each column represents the multidimensional condition monitoring characteristics after nonlinear expansion, as expressed in equation (2):

[0070]

[0071] In equation (1), 1 represents a column vector consisting entirely of 1s, and Q = (IO / M) / (M-1)Δt∈R M×M It is a symmetric matrix, Δt is the length of the analysis of variance, O is a square matrix of all 1s, I is the identity matrix, and Z is a symmetric matrix. M,j The matrix that records the j+1th reciprocal value before failure is expressed as shown in equation (3):

[0072]

[0073] In formula (1) The first-order difference matrix of the nonlinear expansion variables of the i-th decommissioned unit is expressed as shown in equation (4):

[0074]

[0075] (4) Make Equation (1) can be simplified to:

[0076] Aω=λBω (5)

[0077] Where λ=SNR s ;

[0078] (5) Solve formula (2) to obtain the maximum value of λ. max That is, SNR s The maximum value of ω is the optimal feature fusion vector ω. * .

[0079] Step 4: Based on the feature fusion vector and the nonlinear expansion function in the slow feature solving framework, obtain M original health indicator curves. This is achieved through the following sub-steps:

[0080] (1) via d i,j * =z i,j,k ω * The health index value d of the i-th decommissioned equipment at the j-th monitoring time step was calculated. i,j * ;

[0081] (2) Based on d i,j * Draw the original health indicator curve.

[0082] Step 5: Based on the local slope value of the original health index curve, define the healthy stage and the degenerative stage, and save the original health index curve of the degenerative stage to the degenerative trajectory curve library.

[0083] A dynamic slope determination method is used, which considers the time when the slope value first reaches a given threshold within a fixed time period as the degradation initiation point. Will The subsequent curves, after smoothing, yield the degenerate trajectory curve library Ω. DI .

[0084] II. Online Monitoring Phase

[0085] S1: Acquire the status monitoring data of in-service mechanical equipment up to the current stage of operation, and perform the same feature extraction, feature filtering and normalization processing as in the offline stage;

[0086] S2: Based on the feature vectors obtained in the offline stage and the nonlinear expansion function in the slow feature solution framework, the health index curve of in-service equipment is obtained;

[0087] S3: Extract health indicator curves of in-service equipment using time windows, and calculate the similarity between the extracted time window curves and the M original health indicator curves obtained in the offline phase segment by segment. Select the curve segments in each original health indicator curve whose similarity to the extracted time window curve is greater than a set threshold as prediction reference samples; this is specifically accomplished through the following sub-steps:

[0088] (3.1) Set the time window length ΔT for the health index curve of in-service equipment, and use this time window length to segment the degradation trend curve of the health index. Calculate the Euclidean distance between the curves within multiple time windows of the original health index curve and the curves within the time windows of the in-service equipment health index curve. Select the original health index curve segment with the smallest Euclidean distance as the prediction reference segment, with its starting point being t. o Calculate the similarity between M original health indicator curves and the health indicator curves of in-service equipment.

[0089]

[0090] Among them, t o This serves as the starting point for the predicted reference segment on the original health index curve. This indicates the difference between the in-service equipment and the m-th decommissioned equipment at time t. o The similarity value at any given moment; Let λ be the Euclidean distance of the m-th predicted reference segment, and λ be the distance magnification factor.

[0091] (3.2) Use the original health index curves whose similarity satisfies the following relationship as the prediction reference sample;

[0092]

[0093] Where γ is the similarity screening coefficient.

[0094] S4: Obtain the remaining lifetime prediction results based on the final prediction reference sample. Details are as follows:

[0095] (4.1) Calculate the set of remaining predicted lifetime values ​​{ERL} for each predicted reference segment. m}:

[0096] ERL m =EoL m -t o-ΔT

[0097] Among them, EoL m t represents the service life of the m-th decommissioned device. o The starting point of the predicted reference segment on the original health index curve; ΔT represents the length of the time window;

[0098] (3.2) The 3σ criterion is used to remove outliers from the set of remaining lifetime predictions in (4.1) to obtain remaining lifetime predictions within the normal range;

[0099] (3.3) Based on the predicted remaining useful life within the normal range, calculate the final predicted remaining useful life (RUL) of the in-service equipment:

[0100]

[0101] in, This represents the similarity value after passing the similarity screening.

[0102] The following is a specific application example to demonstrate the effectiveness of the remaining lifetime prediction method of the present invention.

[0103] In this implementation example, the aero-engine turbofan simulation dataset provided by NASA is used. This dataset is based on an aero-engine simulation system built using MATLAB and its Simulink module. This system can simulate and calculate the operation-to-failure process of aero-engines in different initial degradation states by setting different initial conditions, and records process data, such as 21-dimensional condition monitoring data including temperature, pressure, and flow of each key module. The dataset consists of multiple training and test sets. The training sets contain monitoring data throughout the engine's entire lifecycle, while the test sets contain multi-dimensional condition monitoring data of engines that have not yet reached a failure state. Using engine unit #5 in the FD001 test set as in-service mechanical equipment, the remaining life prediction process is performed based on the multi-dimensional condition monitoring data from 100 units in the FD001 training set, from operation to failure.

[0104] In the offline feature selection phase, the thresholds for the three evaluation indicators—monotonicity, trend, and correlation—are 0.78, 0.5, and 0.25, respectively. Features that pass the selection process must simultaneously be greater than or equal to the thresholds corresponding to all three indicators. For example... Figure 2 As shown, feature filtering is performed on the original 21-dimensional degenerate features to obtain 8-dimensional degenerate features. For the filtered multi-dimensional degenerate features {x}... i,j,k ,i=1,2,...,100,j=1,2,...,EoL iLet k = 1, 2, ..., 8, where i represents the i-th decommissioned unit and takes the value {1, 2, ..., 100}, and j represents the monitoring time step and takes the value {1, 2, ..., EoL}. i}, where k represents the k-th degenerate feature, with values ​​ranging from 1, 2, ..., 8. The filtered features are obtained after z-score normalization.

[0105] Based on the slow feature analysis solution framework and the definition of slow feature information gain ratio, the optimal feature fusion vector ω* is obtained using the matrix generalized eigenvalue solution process, such as... Figure 3 As shown. A second-order nonlinear expansion function h() is used to nonlinearly expand the normalized data to obtain... The degenerate data dimension before expansion is 8, and the data dimension after expansion is 44, meaning that k' takes values ​​in the range {1, 2, ..., 44}. The degenerate features after nonlinear expansion are then whitened to obtain the processed degenerate features. Based on Aω=λ max Solving for the generalized eigenvalues ​​Bω yields the optimal weights ω* for data fusion. This is based on the data fusion process d. i,t =z i,j,k' ω* Obtain the health indicators of the retired system.

[0106] Using a dynamic slope determination method, the monitoring time step in which the slope value first reaches 0.05 within a fixed time period (ΔT = 30) is determined as the degradation initiation point t. i d , will t i d The curve after -ΔT is smoothed using kernel smoothing to obtain the degenerate trajectory curve library Ω. DI ,like Figure 4 As shown.

[0107] During the online monitoring phase, for the in-service test unit #5, the status monitoring data of the current phase is used to first obtain 8-dimensional degradation features based on the feature screening results of the offline phase, and then z-score normalization is performed based on the statistical features of the offline phase. After nonlinear expansion and whitening, the data is multiplied with the optimal feature fusion vector ω* to obtain the health index curve of the in-service equipment.

[0108] A sliding time window of length ΔT = 30 was used to extract the health indicator curve of test unit #5. The extracted time window curve was then compared segment by segment with 100 original health indicator curves obtained in the offline phase. During the similarity calculation, the distance amplification factor λ = 0.02 was used. Segments of each original health indicator curve with a similarity greater than the similarity screening threshold γ = 0.9 to the in-service unit's health indicator curve within the extracted time window were selected as preliminary prediction reference samples. The similarity matching results for test unit #5 are shown below. Figure 5 It can be seen that the local degradation trends of #01, #03, and #14 in the training units that meet the similarity screening process are similar to the degradation trends of the units in the final stage of the test, and their respective predicted remaining lifetimes (ERL) are similar. m The values ​​of 88, 89, and 90 are respectively, all very close to the actual predicted remaining lifetime of 91 for test unit #5, demonstrating the effectiveness of the proposed method in constructing health indicators. Predictions were made for all test units, and the predicted remaining lifetime for all test units is shown below. Figure 6 The prediction results are sorted according to the actual remaining lifetime. The remaining lifetime prediction results of the proposed method on the overall test set are close to the actual remaining lifetime values, and most of the prediction results are within the allowable error range ([-13,10]), which reflects the effectiveness of the proposed method.

[0109] Furthermore, Table 1 presents a comparison of the remaining life expectancy prediction results obtained by the method proposed in this invention and other methods under the same similarity matching rules. The prediction error of the method proposed in this invention (evaluated using the root mean square error, i.e., RMSE) is significantly smaller than that of similar methods, demonstrating the effectiveness of the health indicator construction method proposed in this invention. In addition, the first three methods obtain target health indicators and require the use of a linear regressor to map them to the final health indicator curve, while the data fusion process of the method proposed in this invention does not require a linear regressor, resulting in a simpler model implementation and deployment process.

[0110] Table 1 compares the model prediction performance of the proposed method with other methods.

[0111]

Claims

1. A trajectory similarity-based remaining lifetime prediction method based on slow feature information gain ratio, characterized in that, This method consists of an offline training phase and an online monitoring phase; The offline training phase specifically includes: (1) Acquire the status monitoring data of M similar mechanical devices from operation to failure collected by multi-dimensional sensors. When the status monitoring data is non-process data, use feature extraction method to extract the feature quantity of the degradation process; when the status monitoring data is process data, the status monitoring data is directly used as the feature quantity of the degradation process. (2) The characteristic quantities of the degradation process are screened and normalized according to the operating conditions; (3) For the feature quantities of the normalized degradation process, based on the slow feature solution framework and the definition of information gain ratio index, the feature fusion vector is obtained by solving the matrix generalized eigenvalue. (4) Based on the feature fusion vector and the nonlinear expansion function in the slow feature solution framework, M original health index curves are obtained; (5) Based on the local slope value of the original health index curve, define the healthy stage and the degenerative stage, and save the original health index curve of the degenerative stage to the degenerative trajectory curve library. The online monitoring phase includes: S1: Acquire the status monitoring data of in-service mechanical equipment up to the current stage of operation, and perform the same feature extraction, feature filtering and normalization processing as in the offline stage; S2: Based on the feature vectors obtained in the offline stage and the nonlinear expansion function in the slow feature solution framework, the health index curve of in-service equipment is obtained; S3: Use a time window to extract the health index curve of in-service equipment, and calculate the similarity between the extracted time window curve and the M original health index curves obtained in the offline stage segment by segment. Select the curve segment in each original health index curve whose similarity with the extracted time window curve is greater than a set threshold as the prediction reference sample. S4: Obtain the remaining lifetime prediction results based on the final prediction reference sample; For the feature quantities of the normalized degradation process, based on the slow feature solving framework and the definition of the information gain ratio index, the feature fusion vector is obtained by solving the matrix generalized eigenvalues, which is achieved through the following sub-steps: (1) The normalized feature x i,j,k The nonlinear extended feature z is obtained by performing nonlinear extension function expansion and whitening. i,j',k =whiten(h(x) i,j,k )); where i represents the i-th decommissioned equipment, j represents the j-th feature dimension, j' represents the j-th nonlinearly expanded feature dimension, k represents the k-th monitoring time step, h() represents the nonlinear expansion function, and whiten() represents the whitening operation; (2) The data z after augmentation and whitening were processed using a linear combination. i,j',k Dimensional fusion is performed to obtain the fused health indicator value d. i,k =z i,j',k ω, where ω is the fusion weight; (3) Define the slow feature information gain ratio (SNR) s : Among them, D e D is a feature range matrix used to record the difference between the initial and final values. e Each row represents a decommissioned unit, and each column represents the multidimensional condition monitoring characteristics after nonlinear expansion, as expressed in equation (2): In equation (1), 1 represents a column vector consisting entirely of 1s, and Q = (IO / M) / (M-1)Δt∈R M×M It is a symmetric matrix, Δt is the length of the analysis of variance, O is a square matrix of all 1s, I is the identity matrix, and Z is a symmetric matrix. j The matrix that records the j+1th reciprocal value before failure is expressed as shown in equation (3): In formula (1) The first-order difference matrix of the nonlinear expansion variables of the i-th decommissioned unit is expressed as shown in equation (4): (4) Make Equation (1) can be simplified to: Aω=λBω (5) Where λ=SNR s ; (5) Solve formula (2) to obtain the maximum value of λ. max That is, SNR s The maximum value of ω is the optimal feature fusion vector ω. * .

2. The trajectory similarity remaining lifetime prediction method based on slow feature information gain ratio according to claim 1, characterized in that, Based on the feature fusion vector and the nonlinear expansion function in the slow feature solving framework, M original health indicator curves are obtained through the following sub-steps: (1) via d i,j * =z i,j,k ω * The health index value d of the i-th decommissioned equipment at the j-th monitoring time step was calculated. i,j * ; (2) Based on d i,j * Draw the original health indicator curve.

3. The trajectory similarity remaining lifetime prediction method based on slow feature information gain ratio according to claim 1, characterized in that, Based on three evaluation indicators—monotonicity, trend, and correlation—feature screening is performed on the characteristic quantities of the degradation process, and data that simultaneously meets all three evaluation indicators are selected for subsequent operations.

4. The trajectory similarity remaining lifetime prediction method based on slow feature information gain ratio according to claim 1, characterized in that, The formula for calculating the similarity between the extracted time window curve and the M original health indicator curves obtained in the offline phase is as follows: Among them, t o This serves as the starting point for the predicted reference segment on the original health index curve. This indicates the difference between the in-service equipment and the m-th decommissioned equipment at time t. o The similarity value at any given moment; Let λ be the Euclidean distance of the m-th predicted reference segment, and λ be the distance magnification factor.

5. The trajectory similarity remaining lifetime prediction method based on slow feature information gain ratio according to claim 1, characterized in that, Step S4 of the online monitoring phase is implemented through the following sub-steps: (4.1) Calculate the set of remaining predicted lifetime values ​​{ERL} for each predicted reference segment. m }: ERL m =EoL m -t o -ΔT (7) Among them, EoL m t represents the service life of the m-th decommissioned device. o The starting point of the predicted reference segment on the original health index curve; ΔT represents the length of the time window; (4.2) The 3σ criterion is used to remove outliers from the set of remaining lifetime predictions in (4.1) to obtain remaining lifetime predictions within the normal range; (4.3) Based on the predicted remaining useful life within the normal range, calculate the final predicted remaining useful life (RUL) of the in-service equipment: in, This represents the similarity value after passing the similarity screening.

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