Online prediction method for residual life of variable displacement piston pump

Abstract

The invention discloses an online prediction method for the residual life of a variable displacement piston pump, and the method comprises the following steps: collecting all leakage data of the variable displacement piston pump from the start of operation to failure under a periodic cycle working condition; calculating time domain features and frequency domain features according to the leakage rate data of each cycle working condition, and extracting multi-dimensional feature data representing degradation failure of the variable plunger pump; performing standardization processing on the multi-dimensional feature data by adopting a Z-score method; dimensionality reduction is carried out on the standardized multi-dimensional feature data by using a PCA algorithm, and multi-dimensional features are compressed into one-dimensional features to represent degradation features of each cycle condition; performing filtering processing on the one-dimensional features by using a Kalman filtering method, and obtaining a failure degradation feature curve of the variable plunger pump according to the filtered one-dimensional features; and extracting partial data of the characteristic curve, fitting the relationship between the degradation characteristics and the residual life through a plurality of models to obtain a prediction model, and predicting the residual life of the variable plunger pump by using the prediction model.

Description

Technical Field

[0001] This invention relates to the field of plunger pump life prediction technology, and more specifically, to a method for predicting the remaining life of a variable plunger pump. Background Technology

[0002] Variable displacement piston pumps are widely used in industries such as metallurgy, mining, petrochemicals, and shipbuilding. They are products with high control precision and long service life. Typically, tests on variable displacement piston pumps only last for a few hundred to a few thousand hours. During this period, the pump is far from reaching its failure state, making it impossible to obtain failure time data. For piston pumps, health status and life indicators are generally established based on volumetric efficiency, using volumetric efficiency as the evaluation standard for remaining life. By introducing solid particulate contaminants to accelerate the degradation process of the piston pump, vibration signals during operation are collected, and changes in volumetric efficiency during degradation are periodically tested. This establishes a relationship between characteristic values ​​and volumetric efficiency, enabling the prediction of remaining life.

[0003] However, under normal test or actual working conditions, it is difficult to test the volumetric efficiency during the operation of the plunger pump. Therefore, it is difficult to establish a life relationship model of the plunger pump based on the volumetric efficiency in actual practice.

[0004] Existing technologies mainly employ two types of prediction methods: Method 1 involves establishing a rigid-flexible-fluid coupling model of the plunger pump for simulation analysis to predict its remaining life; Method 2 uses spectral analysis data of hydraulic oil as the life characteristic information of the hydraulic pump and employs a grey support vector machine model to predict the pump's life. Method 1, based on simulation analysis rather than experimental data, predicts the theoretical remaining life of the plunger pump. Method 2, using hydraulic oil as the analysis object, is a common industrial approach; however, hydraulic oil can only indirectly reflect the internal mechanical wear of the hydraulic pump and is easily affected by interference from other systems in the oil circuit, influencing the judgment of the results. Summary of the Invention

[0005] The purpose of this invention is to overcome the defects and shortcomings of the prior art and provide an online prediction method for the remaining life of a variable displacement piston pump. By collecting leakage data of the variable displacement piston pump under cyclic operating conditions, fitting the relationship between degradation characteristics and remaining life, obtaining a prediction model through regression analysis, and using the prediction model to predict the remaining life of the variable displacement piston pump.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A method for online prediction of the remaining life of a variable displacement piston pump includes the following steps:

[0008] Collect all leakage data of the variable displacement piston pump under cyclic operating conditions from the start of operation until failure.

[0009] Based on the leakage data for each cycle, time-domain and frequency-domain features are calculated, and multi-dimensional feature data that can characterize the degradation and failure of the variable piston pump are extracted.

[0010] The Z-score method is used to standardize the multidimensional feature data to obtain standardized multidimensional feature data.

[0011] The PCA algorithm is used to reduce the dimensionality of the standardized multidimensional feature data, compressing the multidimensional features into one-dimensional features to represent the degradation features of each cycle condition.

[0012] The Kalman filter method is used to filter the one-dimensional features, and the failure degradation characteristic curve of the variable piston pump is obtained based on the filtered one-dimensional features.

[0013] Extract the characteristic curve data, fit the relationship between degradation characteristics and remaining life through multiple models to obtain a prediction model, and use the prediction model to predict the remaining life of the variable piston pump.

[0014] Furthermore, time-domain features include mean, standard deviation, root square amplitude, root mean square value, peak value, skewness, kurtosis, waveform factor, margin factor, shape factor, impulse factor, mean absolute value, absolute standard deviation, absolute skewness, absolute kurtosis, and skewness coefficient.

[0015] Furthermore, frequency domain characteristics include mean, frequency variance, skewness power spectrum, kurtosis power spectrum, frequency center, root variance, root mean square, average frequency of the over-time domain signal mean, stability coefficient, coefficient of variation, skewness, kurtosis, and standard deviation frequency.

[0016] Furthermore, the Z-score method is used to standardize the multidimensional feature data, resulting in standardized multidimensional feature data, specifically:

[0017] Different feature data are standardized using the Z-score method, and the feature data matrix is ​​centered to obtain... Its expression is as follows:

[0018] ;

[0019] In the formula, This is the first original value of the m-th feature group; This is the second original value of the m-th feature group; This is the nth original value of the mth feature group; This represents the average value of the m-th set of feature data; This represents the standard deviation of the m-th feature data set; Original value The value after standardization; Original value The value after standardization; Original value The value after standardization.

[0020] Furthermore, the PCA algorithm is used to reduce the dimensionality of the standardized multidimensional feature data, compressing the multidimensional features into one-dimensional features, specifically:

[0021] calculate covariance matrix ;

[0022] Calculate the covariance matrix eigenvalues Arrange them in descending order to form a projection matrix. Each of them Each is a 1×m dimensional vector. ;

[0023] Take the first feature value after sorting in descending order. The corresponding eigenvector , forming a projection matrix By using linear mapping, m-dimensional samples are transformed into 1-dimensional time-series samples, resulting in one-dimensional features. :

[0024] .

[0025] Furthermore, the one-dimensional features are filtered using the Kalman filter method, specifically as follows:

[0026] Given that X(0|0) and P(0|0) are initially 0, calculate the prior estimates:

[0027] ;

[0028] In the formula, X(k|k-1) represents the prior state estimate at time k; A represents the state transition matrix; X(k-1|k-1) is the posterior state estimate at time k−1; B is the control input matrix; U(k) is the control input vector; and W(k) is the process noise at time k.

[0029] ;

[0030] In the formula, P(k|k-1) is the prior error covariance matrix at time k, representing the uncertainty of the predicted state X(k|k-1); P(k-1|k-1) is the posterior error covariance matrix at time k−1, reflecting the accuracy of the estimation at the previous time; Q(k) is the process noise covariance matrix at time k, used to quantify the statistical characteristics of the process noise W(k); This represents the transpose of the state transition matrix A;

[0031] Update the Kalman gain Kg and posterior estimate:

[0032] ;

[0033] ;

[0034] ;

[0035] In the formula, The Kalman gain at time k is represented by H; H is the observation matrix. This represents the transpose of the observation matrix H; R is the observation noise covariance matrix, reflecting the measurement error of the leakage. The actual observation value at time k; according to The output value X(k|k) of the Kalman filter can then be calculated.

[0036] Furthermore, the characteristic curve data is extracted, and the relationship between degradation characteristics and remaining lifespan is fitted using multiple models, including:

[0037] Extract a period of data with significant monotonic changes before failure, and take the moment T0 in the characteristic curve where the remaining lifetime is determined to be 0 as t=0; the remaining lifetime corresponding to the time T1 before this moment is t=T0-T1.

[0038] The Kalman filter output value X and its corresponding remaining lifetime t are combined into a sample [t, X], and a linear regression analysis is performed. The linear model is as follows:

[0039] X = a1 + b1t;

[0040] In the formula, a1 and b1 are the fitting parameters of the linear model.

[0041] Furthermore, extracting the characteristic curve data and fitting the relationship between degradation characteristics and remaining lifespan using multiple models also includes:

[0042] Extract a period of data with significant monotonic changes before failure, and take the moment T0 in the characteristic curve where the remaining lifetime is determined to be 0 as t=0; the remaining lifetime corresponding to the time T1 before this moment is t=T0-T1.

[0043] The Kalman filter output value X and its corresponding remaining lifetime t are combined into a sample [t, X], and a power-law regression analysis is performed. The power-law model is as follows:

[0044] ;

[0045] In the formula, a2, b2, and c1 are the fitting parameters of the power model.

[0046] Furthermore, extracting the characteristic curve data and fitting the relationship between degradation characteristics and remaining lifespan using multiple models also includes:

[0047] Extract a period of data with significant monotonic changes before failure, and take the moment T0 in the characteristic curve where the remaining lifetime is determined to be 0 as t=0; the remaining lifetime corresponding to the time T1 before this moment is t=T0-T1.

[0048] The Kalman filter output value X and its corresponding remaining lifetime t are combined into a sample [t, X], and a logarithmic regression analysis is performed. The logarithmic model is as follows:

[0049] X = a³ + b³log(c²t + d¹);

[0050] In the formula, a3, b3, c2, and d1 are the fitting parameters of the logarithmic model.

[0051] Furthermore, extracting the characteristic curve data and fitting the relationship between degradation characteristics and remaining lifespan using multiple models also includes:

[0052] Extract a period of data with significant monotonic changes before failure, and take the moment T0 in the characteristic curve where the remaining lifetime is determined to be 0 as t=0; the remaining lifetime corresponding to the time T1 before this moment is t=T0-T1.

[0053] The Kalman filter output value X and its corresponding remaining lifetime t are combined into a sample [t, X], and regression analysis is performed using an exponential model. The exponential model is as follows:

[0054] ;

[0055] In the formula, a4, b4, c3, and d2 are the fitting parameters of the exponential model.

[0056] Compared with existing technologies, this invention collects all leakage data of a variable displacement piston pump under cyclic operating conditions from the start of operation until failure. Based on the leakage data of each cyclic operating condition, degradation features are extracted. Through feature extraction, filtering, regression fitting and other methods, the relationship between degradation features and remaining life is established to obtain a prediction model. The prediction model is used to predict and analyze the remaining life of this type of variable displacement piston pump under cyclic operating conditions. Attached Figure Description

[0057] Figure 1 This is a flowchart of the online prediction method for the remaining life of a variable piston pump according to the present invention.

[0058] Figure 2 This is a diagram showing the leakage data of a variable displacement piston pump under one cycle in the embodiment.

[0059] Figure 3This is a schematic diagram of the original average value and the Kalman filter output value in the embodiment. Detailed Implementation

[0060] The online prediction method for the remaining life of a variable displacement piston pump according to the present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0061] Please see Figure 1 This invention discloses an online prediction method for the remaining life of a variable displacement piston pump, comprising the following steps:

[0062] Collect all leakage data of the variable displacement piston pump under cyclic operating conditions from the start of operation until failure.

[0063] Based on the leakage data for each cycle, time-domain and frequency-domain features are calculated, and multi-dimensional feature data that can characterize the degradation and failure of the variable piston pump are extracted.

[0064] The Z-score method is used to standardize the multidimensional feature data to obtain standardized multidimensional feature data.

[0065] The PCA algorithm is used to reduce the dimensionality of the standardized multidimensional feature data, compressing the multidimensional features into one-dimensional features to represent the degradation features of each cycle condition.

[0066] The Kalman filter method is used to filter the one-dimensional features, and the failure degradation characteristic curve of the variable piston pump is obtained based on the filtered one-dimensional features.

[0067] Extract the characteristic curve data, fit the relationship between degradation characteristics and remaining life through multiple models to obtain a prediction model, and use the prediction model to predict the remaining life of the variable piston pump.

[0068] Specifically, the variable displacement piston pump operates under cyclic conditions, and all leakage data are periodically collected from the start of operation until failure under these cyclic conditions. For the leakage data of each cyclic condition, 16 time-domain features and 13 frequency-domain features are calculated to extract the corresponding multidimensional feature data.

[0069] Time-domain characteristics include mean, standard deviation, root square amplitude, root mean square value, peak value, skewness, kurtosis, waveform factor, margin factor, shape factor, impulse factor, mean absolute value, absolute standard deviation, absolute skewness, absolute kurtosis, and skewness coefficient.

[0070] Frequency domain characteristics include mean, frequency variance, skewness power spectrum, kurtosis power spectrum, frequency center, root variance, root mean square, average frequency of the over-time domain signal mean, stability coefficient, coefficient of variation, skewness, kurtosis, and standard deviation frequency.

[0071] The Z-score method is used to standardize the multidimensional feature data, resulting in standardized multidimensional feature data, as follows:

[0072] Different feature data are standardized using the Z-score method, and the feature data matrix is ​​centered to obtain... Its expression is as follows:

[0073] ;

[0074] In the formula, This is the first original value of the m-th feature group; This is the second original value of the m-th feature group; This is the nth original value of the mth feature group; This represents the average value of the m-th set of feature data; This represents the standard deviation of the m-th feature data set; Original value The value after standardization; Original value The value after standardization; Original value The value after standardization.

[0075] The PCA (Principal Component Analysis) algorithm is used to reduce the dimensionality of the standardized multidimensional feature data, compressing the multidimensional features into one-dimensional features. Specifically:

[0076] calculate covariance matrix ;

[0077] Calculate the covariance matrix eigenvalues Arrange them in descending order to form a projection matrix. Each of them ( Each of these is a 1×m dimensional vector;

[0078] Take the first feature value after sorting in descending order. The corresponding eigenvectors form the projection matrix. By using linear mapping, m-dimensional samples are transformed into 1-dimensional time-series samples, resulting in one-dimensional features. :

[0079] .

[0080] This invention extracts 29 features in the time and frequency domains from the leakage data of a variable displacement piston pump under cyclic operating conditions, and uses the PCA method to compress them into 1-dimensional features, characterizing each cyclic operating condition as a feature parameter, which retains as much of the dynamic and static features in the cyclic operating condition as possible.

[0081] The Kalman filter method is used to filter one-dimensional features, specifically as follows:

[0082] Given that X(0|0) and P(0|0) are initially 0, calculate the prior values:

[0083] ;

[0084] In the formula, X(k|k-1) represents the prior state estimate at time k, that is, the current state predicted based on the information at time k-1. A represents the state transition matrix, which describes how the state X(k−1|k−1) evolves from the previous state to the current state. In this embodiment, A=1 is set.

[0085] X(k-1|k-1) is the posterior state estimate at time k−1, i.e., the optimal estimate after correction based on the observation at the previous time. In this embodiment, the initial value at time 0 is set to X(0|0)=0. B is the control input matrix, which maps the external control quantity U(k) to the state space. In this embodiment, B=1. U(k) is the control input vector, representing the externally applied control quantity. In this embodiment, U(k)=0. W(k) is the process noise, representing uncertainty. In this embodiment, W(k)=0.

[0086] ;

[0087] In the formula, P(k|k-1) is the prior error covariance matrix, representing the uncertainty of the predicted state X(k|k-1). P(k-1|k-1) represents the posterior error covariance matrix at time k−1, reflecting the accuracy of the estimation at the previous time. Q(k) represents the process noise covariance matrix, quantifying the statistical nature of the process noise W(k). In this embodiment, Q(k) is set to 0.0001. This represents the transpose of the state transition matrix A.

[0088] Update the Kalman gain Kg and posterior estimate:

[0089] ;

[0090] ;

[0091] ;

[0092] Where H is the observation matrix, and in this embodiment, H=1; Let H represent the transpose of the observation matrix H; R is the observation noise covariance matrix, reflecting the measurement error of the leakage. In this embodiment, R = 0.01. The current observation value is given, and time k corresponds to a one-dimensional feature. The k-th data point. According to... The output value X(k|k) of the Kalman filter can then be obtained.

[0093] This invention employs Kalman filtering to smooth the eigenvalues, reducing the spikes in the eigenvalues. Based on the filtered one-dimensional features and combined with the runtime of the variable displacement piston pump, a curve is plotted to obtain the failure degradation characteristic curve of the variable displacement piston pump.

[0094] Extract a time segment of data where the monotonicity change is relatively obvious before the failure, denoted as T. RUL The moment T0 in the characteristic curve where the remaining lifetime is 0 is taken as t=0. The remaining lifetime corresponding to the time T1 before this moment is t=T0-T1. The output value X of the Kalman filter and its corresponding remaining lifetime t are combined into a sample [t,X], and regression analysis is performed using linear model, power model, logarithmic model, and exponential model, respectively.

[0095] The linear model is as follows:

[0096] X = a1 + b1t;

[0097] In the formula, a1 and b1 are the fitting parameters of the linear model.

[0098] The power model is:

[0099] ;

[0100] In the formula, a2, b2, and c1 are the fitting parameters of the power model.

[0101] The logarithmic model is:

[0102] X = a³ + b³log(c²t + d¹);

[0103] In the formula, a3, b3, c2, and d1 are the fitting parameters of the logarithmic model.

[0104] The exponential model is as follows:

[0105] ;

[0106] In the formula, a4, b4, c3, and d2 are the fitting parameters of the exponential model.

[0107] Substitute t into the fitted model and calculate the fitting result X at each time t. r(t). The mean absolute error (MAE) is used as the model evaluation metric, and the calculation formula is as follows:

[0108] ;

[0109] In the formula, X(t) is the Kalman filter output value, X r (t) represents the predicted value after substituting t into the fitted model.

[0110] The MAE value of the four models was calculated separately, and the model with the smallest MAE was selected as the "leakage amount-remaining life" relationship model, i.e., the prediction model.

[0111] The prediction model was applied to other online scenarios with the same operating conditions: When applying the above prediction model to another variable, a plunger pump, under the same operating conditions, features were extracted and standardized using the Z-score method, then Kalman filtering was used to filter the feature values. The results were then input into the selected fitting model to calculate the effective remaining life t. When t is less than T... RUL When the value is within the range, it is considered a valid remaining life prediction.

[0112] The following specific example illustrates the online prediction method for the remaining life of a variable displacement piston pump according to the present invention.

[0113] Accelerated degradation tests were designed and implemented on a variable displacement piston pump. All leakage data of the variable displacement piston pump were collected from the start of the test until failure, and leakage data for each cycle condition were extracted. Figure 2 As shown.

[0114] like Figure 3 As shown, feature extraction was performed on the leakage data for each cycle condition. After extraction from the time domain and frequency domain, 29-dimensional features were extracted. The Z-score method was used to standardize the different feature data, and then the PCA algorithm was used to reduce the dimensionality of the multi-dimensional features and compress them into 1-dimensional features. Kalman filtering was then performed, and the feature failure segment with significant changes in the last 36 hours was selected for regression analysis.

[0115] Taking the moment T0, where the remaining lifetime is 0, as t=0 in this characteristic curve segment, linear, power, logarithmic, and exponential regression models were performed based on the Kalman filter output value, and the MAE value of each model was calculated. The results show that the exponential model has the smallest MAE value, and its fitted model is:

[0116] ;

[0117] In the formula, 0 ≤ RUL ≤ 36.

[0118] The above exponential model was used as a prediction model and applied to the online remaining life prediction of another variable plunger pump under the same accelerated degradation test. The current Kalman filter output value was substituted into y, and the RUL value was obtained by solving the equation, which is the current remaining life of the plunger pump. The prediction results are shown in Table 1 below.

[0119] Table 1. Predicted Remaining Life of Piston Pump No. 2

[0120]

[0121] The prediction results show that the method of the present invention can make relatively accurate online predictions of the remaining life of a variable displacement piston pump under cyclic operating conditions, and the method itself is simple, effective and highly applicable.

[0122] In summary, this invention collects all leakage data of a variable displacement piston pump under cyclic operating conditions from the start of operation until failure. Based on the leakage data of each cyclic operating condition, degradation features are extracted. Through feature extraction, filtering, regression fitting, and other methods, the relationship between degradation features and remaining life is established to obtain a prediction model. The prediction model is then used to predict and analyze the remaining life of this type of variable displacement piston pump under cyclic operating conditions.

[0123] The above description is a detailed description of the preferred embodiments of the present invention. However, the embodiments are not intended to limit the scope of the patent application of the present invention. All equivalent changes or modifications made under the technical spirit disclosed in the present invention should fall within the patent scope covered by the present invention.

Claims

1. A method for online prediction of the remaining life of a variable displacement piston pump, characterized in that, Includes the following steps: Collect all leakage data of the variable displacement piston pump under cyclic operating conditions from the start of operation until failure. Based on the leakage data for each cycle, time-domain and frequency-domain features are calculated, and multi-dimensional feature data that can characterize the degradation and failure of the variable piston pump are extracted. The Z-score method is used to standardize the multidimensional feature data to obtain standardized multidimensional feature data. The PCA algorithm is used to reduce the dimensionality of the standardized multidimensional feature data, compressing the multidimensional features into one-dimensional features to represent the degradation features of each cycle condition. The Kalman filter method is used to filter the one-dimensional features, and the failure degradation characteristic curve of the variable piston pump is obtained based on the filtered one-dimensional features. Extract the characteristic curve data, fit the relationship between degradation characteristics and remaining life through multiple models to obtain a prediction model, and use the prediction model to predict the remaining life of the variable piston pump.

2. The online prediction method for the remaining life of a variable displacement piston pump according to claim 1, characterized in that, Time-domain characteristics include mean, standard deviation, root square amplitude, root mean square value, peak value, skewness, kurtosis, waveform factor, margin factor, shape factor, impulse factor, mean absolute value, absolute standard deviation, absolute skewness, absolute kurtosis, and skewness coefficient.

3. The online prediction method for the remaining life of a variable displacement piston pump according to claim 1, characterized in that, Frequency domain characteristics include mean, frequency variance, skewness power spectrum, kurtosis power spectrum, frequency center, root variance, root mean square, average frequency of the over-time domain signal mean, stability coefficient, coefficient of variation, skewness, kurtosis, and standard deviation frequency.

4. The online prediction method for the remaining life of a variable displacement piston pump according to claim 1, characterized in that, The Z-score method is used to standardize the multidimensional feature data, resulting in standardized multidimensional feature data, as follows: Different feature data are standardized using the Z-score method, and the feature data matrix is ​​centered to obtain... Its expression is as follows: ； In the formula, This is the first original value of the m-th feature group; This is the second original value of the m-th feature group; This is the nth original value of the mth feature group; This represents the average value of the m-th set of feature data; This represents the standard deviation of the m-th feature data set; Original value The value after standardization; Original value The value after standardization; Original value The value after standardization.

5. The online prediction method for the remaining life of a variable displacement piston pump according to claim 4, characterized in that, The PCA algorithm is used to reduce the dimensionality of the standardized multidimensional feature data, compressing the multidimensional features into one-dimensional features. Specifically: calculate covariance matrix ; Calculate the covariance matrix eigenvalues Arrange them in descending order to form a projection matrix. Each of them Each is a 1×m dimensional vector. ; Take the first feature value after sorting in descending order. The corresponding eigenvector , forming a projection matrix By using linear mapping, m-dimensional samples are transformed into 1-dimensional time-series samples, resulting in one-dimensional features. : 。 6. The online prediction method for the remaining life of a variable displacement piston pump according to claim 5, characterized in that, The Kalman filter method is used to filter one-dimensional features, specifically as follows: Given that X(0|0) and P(0|0) are initially 0, calculate the prior estimates: ； In the formula, X(k|k-1) represents the prior state estimate at time k; A represents the state transition matrix; X(k-1|k-1) is the posterior state estimate at time k−1; B is the control input matrix; U(k) is the control input vector; and W(k) is the process noise at time k. ； In the formula, P(k|k-1) is the prior error covariance matrix at time k, representing the uncertainty of the predicted state X(k|k-1); P(k-1|k-1) is the posterior error covariance matrix at time k−1, reflecting the accuracy of the estimation at the previous time; Q(k) is the process noise covariance matrix at time k, used to quantify the statistical characteristics of the process noise W(k); This represents the transpose of the state transition matrix A; Update the Kalman gain Kg and posterior estimate: ； ； ； In the formula, The Kalman gain at time k is represented by H; H is the observation matrix. This represents the transpose of the observation matrix H; R is the observation noise covariance matrix, reflecting the measurement error of the leakage. The actual observation value at time k; according to The output value X(k|k) of the Kalman filter can then be calculated.

7. The online prediction method for the remaining life of a variable displacement piston pump according to claim 1, characterized in that, Extracting characteristic curve data, and fitting the relationship between degradation characteristics and remaining lifespan using multiple models, including: Extract a period of data with significant monotonic changes before failure, and take the moment T0 in the characteristic curve where the remaining lifetime is determined to be 0 as t=0; the remaining lifetime corresponding to the time T1 before this moment is t=T0-T1. The Kalman filter output value X and its corresponding remaining lifetime t are combined into a sample [t, X], and a linear regression analysis is performed. The linear model is as follows: X = a1 + b1t; In the formula, a1 and b1 are the fitting parameters of the linear model.

8. The online prediction method for the remaining life of a variable displacement piston pump according to claim 1, characterized in that, Extracting characteristic curve data and fitting the relationship between degradation characteristics and remaining lifespan using multiple models also includes: Extract a period of data with significant monotonic changes before failure, and take the moment T0 in the characteristic curve where the remaining lifetime is determined to be 0 as t=0; the remaining lifetime corresponding to the time T1 before this moment is t=T0-T1. The Kalman filter output value X and its corresponding remaining lifetime t are combined into a sample [t, X], and a power-law regression analysis is performed. The power-law model is as follows: ； In the formula, a2, b2, and c1 are the fitting parameters of the power model.

9. The online prediction method for the remaining life of a variable displacement piston pump according to claim 1, characterized in that, Extracting characteristic curve data and fitting the relationship between degradation characteristics and remaining lifespan using multiple models also includes: Extract a period of data with significant monotonic changes before failure, and take the moment T0 in the characteristic curve where the remaining lifetime is determined to be 0 as t=0; the remaining lifetime corresponding to the time T1 before this moment is t=T0-T1. The Kalman filter output value X and its corresponding remaining lifetime t are combined into a sample [t, X], and a logarithmic regression analysis is performed. The logarithmic model is as follows: X = a³ + b³log(c²t + d¹); In the formula, a3, b3, c2, and d1 are the fitting parameters of the logarithmic model.

10. The method for online prediction of the remaining life of a variable displacement piston pump according to claim 1, characterized in that, Extracting characteristic curve data and fitting the relationship between degradation characteristics and remaining lifespan using multiple models also includes: Extract a period of data with significant monotonic changes before failure, and take the moment T0 in the characteristic curve where the remaining lifetime is determined to be 0 as t=0; the remaining lifetime corresponding to the time T1 before this moment is t=T0-T1. The Kalman filter output value X and its corresponding remaining lifetime t are combined into a sample [t, X], and regression analysis is performed using an exponential model. The exponential model is as follows: ； In the formula, a4, b4, c3, and d2 are the fitting parameters of the exponential model.

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