Method and system for predicting service life of rolling bearing in multiple failure modes based on Weibull distribution

Abstract

The invention discloses a method and a system for predicting the service life of a rolling bearing in multiple failure modes based on Weibull distribution, and relates to the technical field of rolling bearing service life prediction. In order to solve the problem that the service life discreteness of a rolling bearing is large due to multiple failure modes such as early failure, random failure and fatigue failure under different working conditions, the method comprises the following steps: firstly, determining first prediction time by using a random convolution kernel binary regression model, and dividing failure time data based on the first prediction time; a plurality of failure modes are identified by using Weibull distribution; secondly, through a particle filter (PF) dynamic updating mechanism and a soft resampling technology, improving a cell gate and a hidden state of a long and short term memory network (LSTM), constructing a particle filter and long and short term memory network (PF-LSTM) fusion prediction model, and enhancing adaptive capacity to complex working conditions; and finally, constructing a multi-criterion loss function by using the probability density function of the Weibull distribution and the mean square error again, and further improving the prediction precision of the PF-LSTM by integrating the traditional mean square error and the priori knowledge of the Weibull distribution. Experiments prove that the method provided by the invention can predict the service life of the rolling bearing in multiple failure modes, compared with a traditional LSTM method, the average absolute error is reduced by 13.69%, and in addition, compared with a CNN-LSTM model, the prediction average score is improved by 0.169.

Description

Technical Field

[0001] The present invention relates to the technical field of rolling bearing life prediction, and in particular to a method and system for predicting the life of a rolling bearing under multiple failure modes. Background Art

[0002] As the core component of rotating machinery, once a rolling bearing fails, it will have a significant impact on the operation of the entire machine and may even cause a devastating accident. [1] Accurately predicting the remaining useful life (RUL) of rolling bearings can help reduce the occurrence of catastrophic accidents. Therefore, the research on the prediction of RUL of rolling bearings is of great significance. The life of rolling bearings is affected by many factors such as manufacturing defects, incorrect installation, instantaneous impact, seasonal environmental changes, regular maintenance, equipment operation history and load changes. These factors interact with each other, leading to the occurrence of various failure modes such as early failure, random failure and fatigue failure. [2] Because each failure mode has its own unique characteristics, the bearing life distribution presents a significant discrete problem. Therefore, solving the problem of multiple failure modes of rolling bearings is particularly critical for RUL prediction.

[0003] Rolling bearing RUL prediction methods are divided into two categories: model-driven and data-driven methods. [3] The model-driven approach is to establish a mathematical model by summarizing the failure mechanism, so as to make a unified prediction. The data-driven approach is to collect, group, integrate data, and form an automated decision-making model through training and fitting. [4] In practice, bearing operating conditions are complex and highly variable. Model-driven approaches require extensive expert knowledge to establish effective prediction models. However, data-driven approaches, when sufficient full-life data is available, typically enable models to more accurately detect, classify, and predict different failure modes. Therefore, this paper chooses a data-driven approach for bearing RUL prediction.

[0004] Data-driven methods include machine learning methods and statistical data-driven methods [5] Deep learning methods have many advantages over traditional RUL prediction technologies. First, deep learning has strong feature extraction capabilities due to its own learning ability. [6] Secondly, deep learning can provide insights into the correlation patterns between signal characteristics and device health status, thereby establishing a complex mapping relationship between the two, which is conducive to analyzing diverse health monitoring data. [7]. It can be seen that the introduction of deep learning in the field of RUL prediction has brought many new methods to this field. Reference [8] proposed a novel temporal convolutional neural network, which uses soft threshold denoising to achieve RUL prediction with good generalization ability. Reference [9] proposed a rolling bearing RUL prediction method based on deep transfer autoencoder, which achieved high prediction accuracy. Reference

[10] proposed a new gated recurrent unit neural network with dual attention gates, which was verified by experiments to be able to accurately predict the RUL of rolling bearings.

[0005] Compared to traditional machine learning methods, deep learning methods can better solve the problem of bearing life prediction when training on complete data for a single failure mode. However, in actual engineering, bearing failures often involve multiple failure modes. To solve this problem, statistical data-driven methods have emerged.

[0006] The statistical data driven model can flexibly adapt to the diverse equipment failure modes, thus effectively reflecting the status under various actual working conditions. In order to accurately estimate the RUL of the equipment, the researchers cleverly constructed a statistical data driven model to quantify its probability distribution characteristics.

[11] Specifically, by characterizing the system behavior and degradation process using parameterized models, the evolution of equipment performance over time can be revealed. Therefore, introducing statistical data-driven methods into the field of RUL prediction can provide a new solution for this field.

[12] .

[0007] Statistical data driven methods include degradation statistical data driven and failure statistical data driven

[13] . The Wiener process is one of the most commonly used degradation statistics driven methods. Reference

[14] proposed a Wiener-based comprehensive prediction method for the RUL of rolling bearings with multiple failure modes, which can handle multiple failure modes and improve prediction accuracy. Reference

[15] proposed a scale-mixed Wiener prediction method, which achieved good results in terms of prediction accuracy and reliability. Reference

[16] proposed a multi-stage jump degradation model based on the Wiener process to describe multiple failure modes, and the effectiveness of the proposed method was verified by experiments.

[0008] The above-mentioned degradation statistics driven method can effectively solve the RUL prediction problem of rolling bearings under multiple failure modes, but the parameters of the Wiener process usually have no intuitive physical meaning and are difficult to explain the failure mode of the system. Among the failure statistics driven methods, Weibull distribution, as a widely used probability distribution model, has good flexibility and can effectively adapt to and describe different types of fault distributions, especially in the field of life analysis. Reference

[17] proposed a RUL prediction method based on Weibull-frailty model reliability analysis to describe the failure mode and life distribution of the system. Reference

[18] proposed a ball bearing multi-failure behavior identification and RUL prediction method based on clustering and change point detection algorithm, which successfully achieved the identification of multiple failure modes and showed good prediction performance. Reference

[19] proposed a Weibull accelerated failure time regression model suitable for bearing RUL prediction under multiple working conditions. The model takes into account working condition parameters and working condition monitoring signals when estimating parameters, thereby achieving good prediction accuracy.

[0009] While the aforementioned Weibull distribution method can effectively explain the failure modes and life distribution characteristics of a system, it lacks a clear distinction between different failure modes. This can lead to biased estimates of Weibull distribution parameters, thus affecting the accuracy of life prediction. Furthermore, the Weibull distribution typically assumes fixed parameters and cannot effectively handle parameter variations under multiple failure modes, further complicating its application in bearing life prediction.

[0010] Therefore, the problem of life discreteness of rolling bearings caused by multiple failure modes under different working conditions needs to be solved urgently. Summary of the Invention

[0011] The technical problems to be solved by the present invention are:

[0012] The present invention addresses the problem that rolling bearings may face multiple failure modes such as early failure, random failure and fatigue failure under different working conditions, which leads to large life dispersion and affects the accuracy of rolling bearing life prediction. It further provides a rolling bearing life prediction method and system under multiple failure modes based on Weibull distribution.

[0013] The technical solution adopted by the present invention to solve the above technical problems is:

[0014] A method for predicting the life of a rolling bearing under multiple failure modes based on Weibull distribution, the method comprising:

[0015] Step 1: Data preprocessing

[0016] First, the time series lifespan data is fed into a random convolution kernel binary regression network to determine the FPT. Second, the time intervals to the first equipment failure are recorded based on the FPT points and integrated to form a failure time dataset. Finally, when analyzing the failure time data, the data is divided into different failure modes by calculating the ratio of the failure time data to the total lifespan of the equipment.

[0017] Step 2: Feature Extraction

[0018] For each failure mode, the data is first divided into time windows and each window is downsampled to reduce the data volume. Secondly, the continuous wavelet transform is used to extract the signal characteristics at different frequencies and time scales, generating a two-dimensional wavelet coefficient matrix. This matrix is used to capture the multi-scale characteristics of the signal and provide fault indication information. Finally, the wavelet coefficients are logarithmically transformed and normalized to enhance feature contrast and unify the scale.

[0019] Step 3: Multiple Failure Mode Identification

[0020] The characteristic data of the same failure mode is input into the Weibull distribution for analysis to determine the specific failure mode based on the shape parameter; when the shape parameter β is less than 1, this indicates an early failure mode; when β = 1, it indicates a random failure mode; when β > 1, it is identified as a fatigue failure mode, thereby identifying the specific failure mode;

[0021] Step 4: Training the PF-LSTM model

[0022] Based on steps two and three, the spectral features of different failure modes are respectively input into the PF-LSTM network to obtain RUL prediction models for three different failure modes. During the training process, a custom loss function combining the Weibull distribution and the traditional loss function is used to evaluate the prediction accuracy, and the parameters are updated through the Adam optimization algorithm. After multiple iterative optimizations, a dynamic RUL prediction model that adapts to different failure modes is obtained.

[0023] Step 5: Lifespan prediction

[0024] The frequency domain features of the non-full-life unlabeled data to be predicted are extracted through continuous wavelet transform, and then the failure mode is determined using Weibull distribution. Finally, these features are input into the corresponding PF-LSTM dynamic life prediction model to obtain the final prediction results.

[0025] The present invention has the following beneficial technical effects:

[0026] This paper addresses the problem of large life dispersion caused by various failure modes, including premature failure, random failure, and fatigue failure, that rolling bearings may face under different operating conditions. The method first uses a random convolution kernel binary regression model to determine the first prediction time, then partitions the failure time data based on this prediction time and uses the Weibull distribution to identify multiple failure modes. Secondly, through a particle filter (PF) dynamic update mechanism and soft resampling technology, the unit gates and hidden states of a long short-term memory (LSTM) network are improved to construct a particle filter and long short-term memory (PF-LSTM) fusion prediction model, enhancing its adaptability to complex operating conditions. Finally, the probability density function and mean squared error of the Weibull distribution are used again to construct a multi-criteria loss function. This combines the traditional mean squared error with prior knowledge of the Weibull distribution to further improve the prediction accuracy of the PF-LSTM. Experimental verification shows that the proposed method can predict rolling bearing life under multiple failure modes, reducing the mean absolute error by 13.69% compared to the traditional LSTM method and improving the average prediction score by 0.169 compared to the CNN-LSTM model.

[0027] This paper proposes a new rolling bearing life prediction method using the Weibull distribution to identify device failure modes. This method combines a particle filter (PF) with a long short-term memory (LSTM) network to form a PF-LSTM prediction model. This method deeply integrates the cell state and hidden state of the LSTM with the particle weights in the particle filter, and uses soft resampling technology to construct a novel composite particle structure. It also proposes a method for establishing a domain-specific loss function based on prior knowledge. This effectively addresses the discrete life of rolling bearings caused by multiple failure modes under different operating conditions, further improving prediction accuracy.

[0028] The contributions and main innovations of the present invention are as follows:

[0029] (1) A random convolution kernel binary regression model is proposed and the first prediction time is determined. The failure time data is divided accordingly to prepare for the identification of multiple failure modes.

[0030] (2) In order to solve the problem of multiple failure modes that are common in rolling bearings under complex working conditions, this study uses the Weibull distribution to fit the failure time data and uses the change law of the shape parameters after fitting to achieve accurate identification of different failure modes.

[0031] (3) A PF-LSTM rolling bearing RUL prediction method is proposed. This method uses the particle filter dynamic update mechanism to improve the unit gate and hidden state update strategy of LSTM, and combines the soft resampling technology to construct a PF-LSTM fusion prediction model, thereby enhancing the adaptability to complex working conditions.

[0032] (4) A multi-criteria loss function is constructed based on the Weibull distribution to optimize the training process of the PF-LSTM model. By combining the probability density function of the Weibull distribution with the mean square error, prediction models for different failure modes are constructed.

[0033] Experimental studies on two datasets verify that the proposed method has high prediction accuracy and exhibits good generalization ability under different working conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 This is the block diagram of the random convolution kernel binary regression model; Figure 2 It is a bathtub curve graph; Figure 3 This is the LSTM unit structure diagram; Figure 4 This is the network architecture diagram of particle filter and LSTM; Figure 5 This is a flowchart of the rolling bearing life prediction method based on multiple failure modes of Weibull distribution; Figure 6 This is a photo of the PHM2012 rolling bearing test bench; Figure 7 This is the classification result diagram of the bearing 1_3FPT prediction model; Figure 8 The distribution diagram of different failure modes; Figure 9 is the wavelet transform image of bearing 3_1, Figure 10 is the wavelet transform image of bearing 1_3, Figure 11 is the wavelet transform image of bearing 1_4; Figure 12 This is the Weibull distribution fitting result diagram for the early failure mode. Figure 13 This is the Weibull distribution fitting result diagram for random failure mode. Figure 14 This is the Weibull distribution fitting result diagram for fatigue failure mode; Figure 15 This is a diagram showing the training effect of the prediction model; Figure 16 is the wavelet transform image of bearing 2_3, Figure 17 This is the fitting result diagram of the Weibull distribution of bearing 3_3. Figure 18 The degradation state curve and prediction result diagram of bearing 2_3; Figure 19 This is a comparison curve of the degradation state curve of bearing 2_3; Figure 20 A bar chart comparing the performance evaluation index values of different models (PHM2012 dataset); Figure 21 Comparison chart of the results of multi-criteria loss function and traditional loss function (%); Figure 22A comparison chart of performance evaluation index values for single failure and multiple failure mode models; Figure 23 This is a comparison diagram of the degradation curve of bearing 2_5; Figure 24 A comparison chart of performance evaluation index values of different algorithm models (XJTU-SY dataset). DETAILED DESCRIPTION

[0035] Combined with attachment Figure 1-24 The implementation of the rolling bearing life prediction method under multiple failure modes based on Weibull distribution is described as follows:

[0036] 1 Identification of multiple failure modes

[0037] 1.1 Using random convolution kernel to determine the first prediction time

[0038] 1.1.1 Random Convolution Kernel

[0039] ROCKET is a method that transforms time series data through random convolution kernels and uses the transformed features as a basis to train linear classifiers.

[20] The random convolution kernel parameter settings are shown in Table 1.

[0040] Table 1 Parameters of random convolution kernel

[0041]

[0042] As can be seen from Table 1, each parameter is randomly selected, thus generating a large number of random convolution kernels. For each convolution kernel, the algorithm extracts two key features: maximum value and positive value ratio. Among them, the maximum value feature captures the peak information in the convolution result, while the positive value ratio reflects the proportion of positive numbers in the convolution result. These features are aggregated and used as the input of the classifier. The specific structure is as follows Figure 1 shown.

[0043] 1.1.2 First prediction time

[0044] Rolling bearings are in a healthy state at the beginning of operation, and then at a certain point in time, an initial failure occurs and the bearing enters a degraded state. In order to accurately determine this critical first prediction time (FPT),

[21] , according to the method in Section 1.1.1, the time series data is classified to achieve the division between normal state and fault state.,This method can identify the time of occurrence of the initial fault and thus determine the FPT,,providing a reliable basis for subsequent failure mode identification and life prediction.

[0045] The training preset labels are:

[0046]

[0047] Among them, y FPT represents the health status label in the FPT prediction task, where 0 represents a healthy state and 1 represents an unhealthy state. x represents the current position, n represents the total number of data sets, and p represents the confidence interval. Different p values have different effects on different bearings. Based on experience, a p value of 3% to 10% generally yields good results. In this paper, the confidence interval p is set to 5%.

[0048] 1.2 Obtaining failure time data

[0049] Based on the FPT points determined in Section 1.1, time-to-failure data is defined as the entire period from the first fault to the complete failure of the bearing. This data systematically collects and analyzes the bearing's performance throughout its degradation phase, providing data support for subsequent Weibull distribution modeling. In this way, time-to-failure data not only reflects the initial failure characteristics of a bearing but also documents its complete degradation history until the end of its life, which is crucial for identifying multiple failure modes.

[0050] 1.3 Failure mode identification based on Weibull distribution

[0051] 1.3.1 Bathtub Curve

[0052] By utilizing the prior knowledge of rolling bearings and collecting failure time data in Section 1.2, we can better understand the different failure modes of equipment during its life cycle. The bathtub curve is a classic model that describes the changing trend of the failure rate of equipment during its life cycle. The curve consists of three stages: the first stage is the infancy, during which the failure rate is high but drops rapidly, usually caused by manufacturing defects, design problems or installation errors; the second stage is the stable period, when the failure rate is low and relatively stable, the equipment performs normally, and the failure is mainly caused by random factors; the third stage is the old age period, as the equipment begins to experience material fatigue and wear, the failure rate gradually increases. The changes in failure rates through the above stages form a bathtub shape, so it is called the bathtub curve. Specifically, Figure 2 shown.

[0053] 1.3.2 Weibull distribution

[0054] Weibull distribution can flexibly describe the changing trends of different types of failure rates and is widely used in equipment life prediction, failure mode identification and other fields.

[22] The probability density function (PDF) of the Weibull distribution can describe the lifespan distribution of different devices or systems. Specifically, it is shown in Equation (2).

[0055]

[0056] Where D is the failure time data, η is the scale parameter, which represents the characteristic life at a specific time point, and β is the shape parameter, which determines the shape of the distribution.

[0057] The key to describing the failure rate trend using the Weibull distribution lies in its shape parameter, β, which determines how the failure rate changes over time. When β < 1, the Weibull distribution indicates a decreasing failure rate, suitable for infancy; when β = 1, the failure rate is stable, conforming to an exponential distribution, suitable for stable periods; and when β > 1, the failure rate increases, suitable for older age. By adjusting the shape parameter β, the Weibull distribution can fit the three stages of the bathtub curve, capturing the failure rate characteristics of different stages, thereby providing theoretical support for the prediction of the RUL of rolling bearings and further providing a data foundation for failure mode identification.

[0058] 1.3.3 Classification of failure modes

[0059] By combining the failure characteristics revealed by the bathtub curve and the statistical model provided by the Weibull distribution, this paper divides the failure modes of rolling bearings into three types: early failure, random failure, and fatigue failure. The specific classification is as follows:

[0060] Failure Mode 1: When the ratio of the failure time data to the total time is greater than 2 / 3, the fault is classified as an early failure mode. This mode represents the failure of the equipment in the early stages due to design defects or material problems.

[0061] Failure Mode 2: When the ratio of failure time data to total time is between 1 / 3 and 2 / 3, the fault is classified as a random failure mode. This mode is associated with sudden, unforeseen events.

[0062] Failure Mode 3: When the ratio of the failure time data to the total time is less than 1 / 3, the fault is classified as a fatigue failure mode. This mode indicates that the equipment fails due to fatigue after a long period of operation.

[0063] 2 Prediction model of particle filter and LSTM fusion

[0064] The prediction model of particle filter and LSTM fusion, that is, the PF-LSTM fusion prediction model, is described as follows:

[0065] 2.1 LSTM Network Model

[0066] LSTM is a variant of recurrent neural network. By introducing a gating mechanism, LSTM can capture long-term dependencies in time series and is suitable for modeling the degradation process of rolling bearings. Figure 3 shown.

[0067] Although LSTM performs well in network structure design and time series data modeling, its performance is limited when faced with complex working conditions with multiple failure modes. Therefore, it is particularly important to combine other methods to enhance the performance of the model.

[0068] 2.2 Particle Filter Algorithm

[0069] Due to the complexity of failure modes, rolling bearing data often exhibits nonlinear and non-Gaussian characteristics. Although LSTM performs well in processing time series data, it has limitations when facing complex nonlinear and non-Gaussian distributed data. Therefore, this paper introduces particle filtering.

[0070] Particle filtering is a Monte Carlo method based on the Bayesian framework. It provides an effective method for estimating the state of nonlinear and non-Gaussian systems by using a set of random samples to approximate the posterior distribution of the system state.

[23] The specific mathematical models are shown in Equations (3) and (4).

[0071] x t =f(x t-1 ,u t-1 ) (3)

[0072] y t =h(x t ,v t ) (4)

[0073] Wherein, the time variable is t. f(·) and h(·) are the transfer functions of the system state value and the observed quantity. t and y t is the system state and measurement value at time t, u t-1 and v t is the white noise in the model.

[0074] 2.3 Prediction Algorithm of Particle Filter and LSTM Fusion

[0075] Although particle filtering is good at handling multiple failure modes in theory, its computational efficiency and stability are not as good as LSTM. Therefore, this paper proposes a PF-LSTM dynamic update mechanism prediction method with soft resampling technology. This method improves the control gate update strategy by building a nonlinear relationship between LSTM and particle filtering. While overcoming the multiple failure mode problem, it also completes the dynamic update of rolling bearing life prediction tasks. Figure 4 shown.

[0076] The specific contents are as follows:

[0077] (1) Define the representation of particles. The memory state of each particle includes the hidden state h j,t, the cell state of the particle c j,t and the particle weight w j,t Therefore, the particle set represents

[0078] (2) Update the memory state of the particle

[0079] 1. Introducing randomness: adding noise to the candidate values of the particle's cell state.

[0080]

[0081] ζ j,t ~N(0,Σ j,t )(6)

[0082] Σ j,t =W Σ [h j,t-1 ,x t ]+b Σ (7)

[0083] 2. Memory status update

[0084] h i,t =f tr (h i,t-1 ,u t (x t ),ζ i,t ) (8)

[0085]

[0086] (3) Particle weight update

[0087] Update particle weights based on observation data

[0088] w i,t =ηf obs (o t (x t ),h i,t )w i,t-1 (10)

[0089] f obs is a learned function that calculates the weight of a particle given an observation. η is a normalization factor.

[0090] (4) Soft resampling

[0091] In order to avoid particle degeneration (i.e. the weights of most particles are close to zero), soft resampling is used to generate a new set of particles:

[0092]

[0093] Here, α is a tuning parameter, usually set to 0.5.

[0094]

[0095] (5) Output prediction

[0096] The prediction results of the particles are aggregated to obtain the final prediction value.

[0097] (6) Repeat steps 2, 3, 4, and 5 until convergence or the maximum number of iterations is reached.

[0098] 3 Multi-criteria loss function based on Weibull distribution

[0099] In rolling bearing life prediction, an accurate loss function is crucial for model training. While traditional loss functions are intuitive and easy to implement, they are inadequate for dealing with complex failure modes. To address this, this paper proposes a multi-criteria loss function based on the Weibull distribution. This function aims to fully exploit the failure mode information provided by the Weibull distribution and optimize prediction accuracy by leveraging multiple traditional loss functions.

[0100] Weibull distribution can effectively fit the failure data of equipment, and its probability density function is shown in formula (2).

[0101] Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and Root Mean Squared Logarithmic Error (RMLSE) are commonly used loss functions in regression models.

[24] As shown in formula (13)-formula (15):

[0102]

[0103]

[0104]

[0105] Among them, Ns is the number of test samples, A i represents the actual RUL value of the i-th test sample, and P i Indicates the predicted RUL value of the same test sample.

[0106] In order to combine the failure mode information of Weibull distribution and the advantages of various traditional loss functions, this paper designs a multi-criteria comprehensive loss function, as shown in Equations (16) to (20).

[0107]

[0108]

[0109]

[0110] A i =F(A i )+1 (19)

[0111] P i =F(P i )+1 (20)

[0112] Among them, N s is the number of test samples, A i represents the actual RUL value of the i-th test sample, and P i Indicates the predicted RUL value of the same test sample.

[0113] 4 Dynamically updated rolling bearing life prediction method under multiple failure modes

[0114] The flowchart of the rolling bearing life prediction method under multiple failure modes based on Weibull distribution is as follows: Figure 5 As shown, the steps are as follows:

[0115] (1) Data preprocessing

[0116] First, the time series lifespan data is fed into a random convolution kernel binary regression network to determine the FPT. Second, the time intervals to the first equipment failure are recorded based on the FPT points and integrated to form a failure time dataset. Finally, when analyzing the failure time data, the data is divided into different failure modes by calculating the ratio of the failure time data to the total lifespan of the equipment. This is described in detail in Section 1.3.2.

[0117] (2) Feature extraction

[0118] For each failure mode, the data is first divided into time windows and downsampled within each window to reduce the data volume. Next, a continuous wavelet transform is used to extract signal features at different frequency and time scales, generating a two-dimensional wavelet coefficient matrix. This matrix captures the multi-scale characteristics of the signal and provides fault indication information. Finally, the wavelet coefficients are logarithmically transformed and normalized to enhance feature contrast and unify scale, thereby improving feature extraction quality and model prediction capabilities.

[0119] (3) Multiple failure mode identification

[0120] Based on (2), the characteristic data of the same failure mode is input into the Weibull distribution for analysis to determine the specific failure mode based on the shape parameter. Specifically, when the shape parameter β < 1, this indicates an early failure mode; when β = 1, it indicates a random failure mode; when β > 1, it indicates a fatigue failure mode. Thus, the specific failure mode is identified.

[0121] (4) Training of PF-LSTM model

[0122] Based on (2) and (3), the spectral features of different failure modes are input into the PF-LSTM network to obtain RUL prediction models for three different failure modes. During the training process, a custom loss function combining the Weibull distribution and the traditional loss function is used to evaluate the prediction accuracy, and the parameters are updated using the Adam optimization algorithm. After multiple iterative optimizations, a dynamic RUL prediction model that adapts to different failure modes is obtained.

[0123] (5) Lifespan prediction

[0124] The frequency domain features of the non-full-life unlabeled data to be predicted are extracted through continuous wavelet transform, and then the failure mode is determined using Weibull distribution. Finally, these features are input into the corresponding PF-LSTM dynamic life prediction model to obtain the final prediction results.

[0125] 5 Application and Analysis

[0126] 5.1 Experimental Dataset

[0127] 5.1.1 PHM2012 Rolling Bearing Dataset

[0128] To verify the proposed method, experiments were carried out based on PHM2012 bearing data, such as Figure 6 The Figure 6 PHM2012 rolling bearing test bench. Accelerated degradation experiments were conducted on rolling bearings under different operating conditions, and the changes in vibration signals were recorded. The test was terminated when the amplitude of the vibration signal exceeded 20g. Data was recorded every 10 seconds for a duration of 0.1s at a sampling frequency of 25.6kHz. The recorded vibration signals were divided into horizontal and vertical directions. The experiment used horizontal vibration data. The data set contained 17 sets of data at three different speeds. Eight full-life data sets were used to establish the prediction model, and the remaining nine non-full-life data sets were used for bearing RUL prediction tasks, as shown in Table 2. Specific information for the three operating conditions is shown in Table 3.

[0129] Table 2 PHM2012 experimental data

[0130]

[0131] Table 3 Specific information of three operating conditions

[0132]

[0133] 5.2 Evaluation Metrics

[0134] This paper uses the "model performance evaluation index" that focuses on measuring the prediction accuracy and stability of the model and the "prediction result evaluation index" that focuses on measuring the performance of the method in actual application scenarios to comprehensively evaluate the performance of the proposed method.

[0135] 5.2.1 Model performance evaluation indicators

[0136] MSE, RMSE, and RMSLE are commonly used metrics for evaluating prediction model performance. Based on these metrics, a new model performance evaluation metric, the multi-criteria loss function, is proposed. This metric combines the Weibull distribution with MSE, RMSE, and RMSLE. It ignores lead or lag predictions and focuses on the accuracy and stability of the model's prediction of the degradation state at each sampling point. Specifically, this is shown in Equations (16) to (20).

[0137] 5.2.2 Forecast result evaluation indicators

[0138] The prediction result evaluation index takes into account the advanced prediction and the lagging prediction to measure the performance of the method in the actual application scenario. The evaluation index is provided by the PHM2012 bearing data challenge, as shown in formula (21).

[0139]

[0140] Among them, A i Defined as:

[0141]

[0142] Among them, Er i is the prediction error, as shown in formula (23).

[0143]

[0144] If the predicted RUL value is higher or lower than the actual value, it should be considered differently: if Er ≤ 0, it is a lagged forecast; if Er > 0, it is a lead forecast. For industrial production and life, the risk of leading forecast is low, while the risk of lagged forecast is higher.

[0145] 5.3 Experimental Results Analysis

[0146] 5.3.1 FPT prediction results

[0147] Input the rolling bearing data set described in 5.1.1 into Figure 3 In the random convolution kernel binary regression model shown in Figure 2. As described in Section 2.1, the confidence interval p = 5%, according to formula (1), the first 5% of the life data are marked as healthy, and the last 5% are marked as unhealthy. The final output of the model is 0 or 1, indicating the predicted value of the healthy state. Taking bearing 1_3 as an example, the classification results of the FPT prediction model are visualized, as shown in the following figure. Figure 7 shown.

[0148] Depend on Figure 7 It can be seen that the intersection of the healthy state and the unhealthy state is a suspicious FPT point. At this time, the random convolution kernel binary regression model cannot clearly distinguish the healthy state of the bearing. The point where the unhealthy state appears for the first time for a length of p is taken as the final predicted FPT point to ensure that the bearing enters the degraded state. Similarly, the final prediction results of the FPT of all bearings can be obtained, as shown in Table 4.

[0149] Table 4 FPT prediction results

[0150]

[0151] Table 4 shows that bearing 1_2 enters a degraded state in the latter half of its lifespan data, whereas bearing 2_2 enters a degraded state at the beginning of its lifespan data. This means that the proportion of normal conditions in the lifespan data of different bearings varies significantly. The same applies to other bearings.

[0152] 5.3.2 Generating Failure Time Data

[0153] According to the FPT prediction results obtained in 5.3.1, the sum of the time from the start of operation to the first failure of the bearing and the failure time data is the full life operation time, so the time to obtain the FPT is equivalent to obtaining the failure time data, as shown in Table 5.

[0154] Table 5 Failure time data

[0155]

[0156] 5.3.3 Failure mode classification

[0157] According to the failure time data obtained in 5.3.2, taking bearing 1_1 as an example, the time when the first failure occurred is between 1 / 3 and 2 / 3 of the total life, which belongs to the second failure mode. The failure modes of other training sets are shown in Table 6.

[0158] Table 6 Identification of failure modes

[0159]

[0160] In order to eliminate the differences in different feature dimensions, the present invention uses a standardization method to preprocess the above data. First, principal component analysis is used to reduce the computational complexity and reduce the data dimension to 50 dimensions. Then, in order to visualize the distribution of high-dimensional data, t-SNE is used to further reduce the data to 2 dimensions; at the same time, data enhancement technology is used to improve the diversity of the data. Finally, a two-dimensional scatter plot is used to show the relationship between the data distribution after dimensionality reduction and different failure modes. Figure 8 shown.

[0161] Depend on Figure 8 As can be seen, the figure shows the two-dimensional visualization results after dimensionality reduction using t-SNE. Each point represents a bearing fault sample, and the two coordinate axes represent the two principal components after dimensionality reduction. Different colors correspond to different failure modes, and the color bar shows the identity of each failure mode. The t-SNE algorithm clusters similar fault samples together, and the distribution differences between different failure modes are highlighted.

[0162] The data set is re-divided according to Table 6, as shown in Table 7.

[0163] Table 7 PHM2012 experimental data

[0164]

[0165] 5.3.4 Vibration failure analysis

[0166] First, the vibration signal is divided into time windows and each window is downsampled. Second, the continuous wavelet transform is used to extract the signal features at different frequencies and time scales, obtaining a two-dimensional wavelet coefficient matrix. Finally, the wavelet coefficients are logarithmically transformed and normalized to enhance the contrast of the features and unify the scale. Taking bearing 3_1, bearing 1_3, and bearing 1_2 as examples, the specific Figure 9 、 10 , as shown in 11.

[0167] from Figure 9 It can be seen that the red characteristic of bearing 3_1 is prominent at the beginning, and the fault level reaches a peak, which belongs to the early failure mode. This is often due to defects in bearing manufacturing, such as impurities in raw materials or insufficient processing precision, which makes it overwhelmed and fails frequently as soon as it is put into use.

[0168] Look again Figure 10 Bearing 1_3 remained nearly constant red throughout the entire process, and the fault severity remained stable, indicating a typical random failure mode. In actual operation, complex and unpredictable factors such as temperature fluctuations, uneven lubrication, and external shocks intertwine, causing the failure to occur randomly and without any pattern.

[0169] And analysis Figure 11It was found that the color of the red area of bearing 1_4 gradually deepened from the beginning to the end, which means that it was continuously subjected to alternating stress during long-term operation, and the internal microstructure continued to accumulate damage. The degree of failure increased over time, showing a fatigue failure mode.

[0170] In summary, the images extracted through wavelet transform provide a key basis for in-depth insights into bearing failure modes. Figures 12 to 14 The different characteristics presented reveal the inherent logic of different bearing failures.

[0171] 5.3.5 Failure Mode Identification

[0172] Input the features obtained in 5.3.4 into the Weibull distribution, as follows Figure 12 、 Figure 13 、 Figure 14 shown.

[0173] from Figure 12 、 Figure 13 as well as Figure 14 It can be seen that the early failure mode, random failure mode and fatigue failure mode correspond to the cases where the shape parameter of the Weibull distribution is less than 1, equal to 1 and greater than 1, respectively, which reflects that the Weibull distribution can well identify multiple failure modes.

[0174] 5.3.6 Prediction Model

[0175] After extracting features from the vibration signals of the same failure mode through wavelet transform, they are input into the prediction model PF-LSTM to obtain the prediction model under the failure mode. Taking the early failure mode as an example, the specific Figure 15 shown.

[0176] 5.3.7 Lifespan Prediction

[0177] After constructing a personalized prediction model for each failure mode, we first use wavelet transform to analyze the test data, extract key feature vectors, input them into the Weibull distribution to lock the failure mode, and then connect them to the corresponding prediction model to obtain the final prediction result. Taking test data 2_3 as an example, we input the test data 2_3 into the wavelet transform to extract features. Figure 16 shown.

[0178] The above characteristics are input into the Weibull distribution to identify the failure mode, as shown in the following example: Figure 17 shown.

[0179] pass Figure 17It can be seen that the Weibull distribution shape parameter of bearing 3_3 is 0.932, which is less than 1, indicating that the bearing is in the early failure mode. Therefore, the characteristics of bearing 2_3 are input into the early failure mode prediction model, and the degradation state scatter plot of bearing 2_3 and the final prediction result of bearing 2_3 are obtained as shown in the figure below. Figure 18 shown.

[0180] Depend on Figure 18 It can be seen that the final predicted point for bearing 2_3 is 20371, which means the final predicted damage time is 20370s. Given that the current time of bearing 2_3 is 11600s and the actual damage time is 19540s, its actual RUL value and predicted RUL value are the difference between the actual damage time and the predicted damage time and the current time, namely: 7940s and 8770s, respectively. The final prediction error can be calculated according to formula (11) and is -10.47%. Similarly, the final prediction results and prediction errors for the remaining test set data can be obtained, as shown in Table 8.

[0181] Table 8 RUL prediction results of different bearings

[0182]

[0183] 5.3.8 Ablation Experiment

[0184] To verify the effectiveness of the proposed method, ablation experiments were conducted on the particle filter and long short-term memory network models. While other conditions remained unchanged, all errors were adjusted to the range of 0–1. The results were evaluated based on the number of particles, soft resampling, the use of the ReLU activation function, and batch normalization. The proposed method used a PF-LSTM model with 30 particles, soft resampling, and a BN-ReLU structure. The results are shown in Table 9.

[0185] Table 9 Comparison of performance evaluation indicators

[0186]

[0187] Table 9 shows that the PF-LSTM model exhibits optimal performance when the number of particles is set to 30. In addition, the experimental results show that the application of soft resampling technology can further improve the performance of the model. The combination of batch normalization and ReLU activation function has a positive impact on the training process of PF-LSTM.

[0188] 5.3.9 Comparative Experiment

[0189] Experiment 1: Comparison of prediction models under multiple failure modes

[0190] To verify the effectiveness of the proposed method, the PF-LSTM network was compared with LSTM and CNN-LSTM respectively.

[0191] (1) Visual analysis of degradation state curve

[0192] The performance evaluation index values of each model are calculated based on the relationship between the predicted value and the true label of each point on the bearing degradation state curve. Therefore, the degradation state curve can intuitively reflect the model performance. Taking bearing 2_3 as an example, the degradation state curves obtained by different prediction models are visualized and compared. Figure 19 shown.

[0193] (2) Analysis of model performance evaluation indicators

[0194] In order to verify that the proposed PF-LSTM prediction model has significantly improved the prediction tasks of different failure mode test sets, the average values of the performance evaluation indicators of the three different prediction models under multiple failure modes are compared, as shown in Table 10. The corresponding bar charts are shown in Table 10. Figure 20 shown.

[0195] Table 10 Comparison of model performance evaluation index values of different methods

[0196]

[0197] Table 10 and Figure 20 The performance of models constructed using three different methods with multiple evaluation metrics for different failure modes is evaluated. It is clear that the PF-LSTM method significantly improves performance across all failure modes compared to the LSTM ablation method, demonstrating the effectiveness of the particle filter algorithm in improving the LSTM unit gate and hidden state update strategies.

[0198] (3) Analysis of evaluation indicators of prediction results

[0199] In order to verify the superiority of the proposed PF-LSTM prediction model in actual application scenarios, the prediction errors and scores of different prediction models are compared in Table 11.

[0200] Table 11 Comparison of RUL prediction error and score results (%)

[0201]

[0202] Table 11 shows the RUL prediction results of 9 bearings, where the mean absolute error represents the average accuracy of the prediction without considering the lead and lag predictions, and the average score represents the comprehensive performance of the method in the actual scenario.

[0203] As can be seen from the table:

[0204] (1) The prediction method in this paper reduces the average absolute error by 8.32% and improves the average score by 0.556 compared with CNN-LSTM, which proves the effectiveness of the improved prediction model method.

[0205] (2) Compared with the LSTM method, the proposed method has a good prediction score, with the average absolute error reduced by 13.79% and the average score increased by 0.611, which proves that particle filtering has a good effect in overcoming the problem of multiple failure modes and realizing the life prediction of multiple failure modes.

[0206] (3) In summary, the PF-LSTM method for predicting the life of rolling bearings under multiple failure modes proposed in this paper has advantages and disadvantages in terms of maximum and minimum absolute errors compared with CNN-LSTM and LSTM, and has obvious improvements in comprehensive performance; the average absolute errors of life prediction compared with the two methods are reduced by 8.32% and 13.79% respectively, and the average scores are increased by 0.556 and 0.611 respectively; at the same time, compared with references

[17] and

[18] , the average absolute errors of this method are reduced by 5.50% and 2.44% respectively, and the average scores are increased by 0.108 and 0.053 respectively. This further verifies the significant advantages of this method in RUL prediction.

[0207] Experiment 2: Comparison between multi-criteria loss function and traditional loss function

[0208] In order to verify the advantage of Weibull distribution as a loss function, the Weibull distribution is combined with MSE, RMSE, and RMLSE, as shown in Table 12. Each failure mode is taken as 1 to obtain the percentage. Taking failure mode 1 as an example, the corresponding bar chart is as follows: Figure 20 shown.

[0209] Table 12 Comparison of the results of multi-criteria loss function and traditional loss function (%)

[0210]

[0211] Through Table 12 and Figure 21 It can be clearly seen that the multi-criteria loss function combining Weibull distribution with traditional loss function is smaller than the traditional loss function, indicating that the loss function proposed in this paper has obvious advantages.

[0212] Experiment 3: Comparative experiment of single failure mode and multiple failure modes

[0213] To fully demonstrate the necessity of addressing multiple failure modes in rolling bearing life prediction research, this paper systematically compares the complex operating conditions and failure processes of multiple failure modes with those of a single failure mode without failure mode identification. During this analysis, all other conditions remained the same, with only the failure mode (multiple failure modes versus a single failure mode) being varied. The average values of the performance evaluation indicators of the PF-LSTM prediction model were compared. The relevant data are shown in Table 13.

[0214] Table 13 Comparison of performance evaluation index values of multiple failure mode and single failure mode models

[0215]

[0216] Table 13 and Figure 22 The performance of the models constructed using three different methods with multiple evaluation indicators for different failure modes is evaluated. It can be clearly seen that the minimum Weibull-MSE is for failure mode 3, the minimum Weibull-RMSE is for failure mode 1, and the minimum Weibull-RMLSE is for failure mode 1, demonstrating the necessity of addressing multiple failure modes and the effectiveness of the proposed method.

[0217] 5.3.10 Experimental Verification on the XJTU-SY Dataset

[0218] To verify the generalization capability of the proposed rolling bearing life prediction method based on the Weibull distribution under multiple failure modes, the XJTU-SY bearing dataset was used as a generalization experiment. This dataset consists of three data sets, all of which present full-life cycle data. Each data set contains full-life cycle vibration data for four bearings. Each sampling period lasts for 1 second, and the sampling frequency is set at 20 kHz, resulting in a data file containing 20,480 sampling points. The bearings were partitioned similarly to the PHM2012 dataset, with full-life data from eight bearings used as the training set and partial-life data from the remaining seven bearings used as the test set. The detailed information is shown in Table 14.

[0219] Table 14 Experimental data of XJTU-SY dataset

[0220]

[0221] Following the same experimental and dataset settings as the PHM2012 bearing dataset, the prediction model method in this paper is compared with the LSTM and CNN-LSTM prediction model methods.

[0222] (1) Visual analysis of degradation state curve

[0223] Taking bearing 2_5 as an example, the degradation state curves obtained by different algorithms are visualized and compared. Figure 23 shown.

[0224] Depend on Figure 23 It can be seen that for prediction task 2_5, the degradation state curve of the test set of the proposed algorithm on the XJTU-SY dataset still has good accuracy and stability, while the degradation state curves of CNN-LSTM and LSTM deviate relatively greatly from the true value, indicating that the PF-LSTM model trained on different datasets still maintains good model performance.

[0225] (2) Analysis of model performance evaluation indicators

[0226] Comparison of performance evaluation index values of each model of the three prediction model methods Figure 24 shown.

[0227] (3) Analysis of evaluation indicators of prediction results

[0228] The comparison of prediction errors and scores of the three prediction models is shown in Table 15.

[0229] Table 15 Comparison of RUL prediction error and score results (%)

[0230]

[0231]

[0232] Depend on Figure 24 As can be seen from Table 15, in the experimental results of the XJTU-SY bearing dataset, the PF-LSTM method proposed in this paper has significant advantages over the LSTM method and the CNN-LSTM method, further proving that the method in this paper can demonstrate good generalization ability on different bearing datasets.

[0233] 6 Conclusion

[0234] (1) A multi-failure mode identification method is proposed, which uses bearing degradation data from different time periods to reveal different failure modes. Through Weibull distribution vibration failure analysis, it is proved that there are indeed multiple failure modes in the experimental data set.

[0235] (2) A dynamic update mechanism prediction method for PF-LSTM is proposed. This method improves the control gate update strategy by constructing a nonlinear relationship between LSTM and particle filtering, and combines soft resampling technology to complete the dynamic update rolling bearing life prediction task. After experimental verification, the algorithm reduced the mean absolute error by 13.79% and 8.32% compared with the LSTM and CNN-LSTM models in each failure mode, and improved the average score by 0.214 and 0.159, respectively. The Weibull-MSE, Weibull-RMSE, and Weibull-RMSLE values were all significantly reduced, proving that the algorithm can better learn the data characteristics of different failure modes.

[0236] (3) Based on (2), a multi-criteria loss function combining Weibull distribution and mean square error is proposed. This function can use the characteristics of Weibull distribution to guide model training, improve the model's prediction ability in different failure modes, and improve the accuracy. Experimental verification shows that the Weibull-MSE, Weibull-RMSE, and Weibull-RMSLE of the proposed method are at least 0.0172, 0.0235, and 0.0203 lower than the loss function performance of the traditional life prediction method, respectively, proving the effectiveness of the proposed method.

[0237] (4) A multi-failure mode rolling bearing life prediction method based on the Weibull distribution is proposed. This method can establish an effective life prediction model under different operating conditions when facing the large life discreteness problem caused by multiple failure modes. Experimental verification shows that the Weibull-MSE, Weibull-RMSE, and Weibull-RMSLE values of the proposed method are at least 0.0001, 0.0043, and 0.0036 lower than those of the single failure mode life prediction method, demonstrating the necessity of addressing multiple failure modes and the effectiveness of the proposed method.

[0238] The experiment used two rolling bearing vibration datasets for research, but did not validate other types of data. Furthermore, compared with single-failure-mode life prediction methods, multi-failure-mode life prediction methods exhibited weaker stability. This will be a key area of future research.

[0239] The references cited in this invention are listed as follows:

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Claims

1. A method for predicting the life of rolling bearings under multiple failure modes based on Weibull distribution, characterized in that: The method comprises: Step 1: Data preprocessing First, the time series lifespan data is fed into a random convolution kernel binary regression network to determine the FPT. Second, the time intervals to the first equipment failure are recorded based on the FPT points and integrated to form a failure time dataset. Finally, when analyzing the failure time data, the data is divided into different failure modes by calculating the ratio of the failure time data to the total lifespan of the equipment. Step 2: Feature Extraction For each failure mode, the data is first divided into time windows and each window is downsampled to reduce the data volume. Secondly, the continuous wavelet transform is used to extract the signal characteristics at different frequencies and time scales, generating a two-dimensional wavelet coefficient matrix. This matrix is used to capture the multi-scale characteristics of the signal and provide fault indication information. Finally, the wavelet coefficients are logarithmically transformed and normalized to enhance feature contrast and unify the scale. Step 3: Multiple Failure Mode Identification The characteristic data of the same failure mode is input into the Weibull distribution for analysis to determine the specific failure mode based on the shape parameter; when the shape parameter β is less than 1, this indicates an early failure mode; when β=1, it indicates a random failure mode; when β>1, it is identified as a fatigue failure mode, thereby identifying the specific failure mode; Step 4: Training the PF-LSTM model Based on steps two and three, the spectral features of different failure modes are respectively input into the PF-LSTM network to obtain RUL prediction models for three different failure modes. During the training process, a custom loss function combining the Weibull distribution and the traditional loss function is used to evaluate the prediction accuracy, and the parameters are updated through the Adam optimization algorithm. After multiple iterative optimizations, a dynamic RUL prediction model that adapts to different failure modes is obtained. Step 5: Lifespan prediction The frequency domain features of the non-full-life unlabeled data to be predicted are extracted through continuous wavelet transform, and then the failure mode is determined using Weibull distribution. Finally, these features are input into the corresponding PF-LSTM dynamic life prediction model to obtain the final prediction results.

2. The method for predicting the life of a rolling bearing under multiple failure modes based on Weibull distribution according to claim 1, characterized in that: The multiple failure mode identification is specifically as follows: Step 3.1: Use random convolution kernel to determine the first prediction time FPT The training preset labels are: Among them, y FPT represents the health status label in the FPT prediction task, 0 represents healthy state and 1 represents unhealthy state; x represents the current position, n represents the total number of data groups, and p represents the confidence range; different p values have different effects on different bearings, and p ranges from 3% to 10%; Step 3.2: Obtain failure time data Based on the determined FPT point, the failure time data is defined as the entire period from the first fault to the complete failure of the bearing. The failure time data is used to collect and analyze the performance of the bearing throughout the degradation stage, providing data support for subsequent Weibull distribution modeling; Step 3. Failure mode identification based on Weibull distribution The probability density function PDF for Weibull distribution describes the life distribution, as shown in formula (2): Where D is the failure time data, η is the scale parameter, which represents the characteristic life at a specific time point; β is the shape parameter, which determines the shape of the distribution; The key to describing the failure rate trend in the Weibull distribution lies in its shape parameter β, which determines how the failure rate changes over time. When β < 1, the Weibull distribution indicates a decreasing failure rate, which is suitable for infancy. When β = 1, the failure rate of the Weibull distribution is stable, conforming to the exponential distribution, and is suitable for stable periods. When β > 1, the failure rate increases, which is suitable for old age. By adjusting the shape parameter β, the Weibull distribution can fit the three stages of the bathtub curve, capturing the failure rate characteristics of different stages, and providing a data basis for the RUL prediction and failure mode identification of rolling bearings. By combining the failure characteristics revealed by the bathtub curve and the statistical model provided by the Weibull distribution, the failure modes of rolling bearings are divided into three types: early failure, random failure, and fatigue failure. The specific classification is as follows: Failure Mode 1: When the ratio of the failure time data to the total time is greater than 2 / 3, the fault is classified as an early failure mode. This mode represents failure of the equipment in the early stages due to design defects or material problems. Failure Mode 2: When the ratio of the failure time data to the total time is between 1 / 3 and 2 / 3, the fault is classified as a random failure mode; this mode is associated with sudden, unforeseen events; Failure mode 3: When the ratio of failure time data to total time is less than 1 / 3, the fault is classified as fatigue failure mode; this mode indicates that the equipment fails due to fatigue after long-term operation.

3. The method for predicting the life of a rolling bearing under multiple failure modes based on Weibull distribution according to claim 2, characterized in that: The prediction model of particle filter and LSTM fusion (PF-LSTM fusion prediction model) is: The PF-LSTM dynamic update mechanism using soft resampling technology completes the dynamic update of rolling bearing life prediction task, as follows: (1) Define the representation of particles: the memory state of each particle includes the hidden state h of the particle j,t , the cell state of the particle c j,t and the particle weight w j,t , particle set representation (2) Update the memory state of the particle 1. Introducing randomness: Adding noise to the candidate values of the particle's cell state: g j,t ~N(0,Σ j,t ) (6) Σ j,t =W Σ [h j,t-1 ,x t ]+b Σ (7) 2. Memory status update: h i,t =f tr (h i,t-1 ,u t (x t ),ζ i,t ) (8) (3) Particle weight update: Update particle weights based on observation data w i,t =ηf obs (of t (x t ),h i,t ) i,t-1 (10) f obs is a learned function used to calculate the weight of a particle given an observation value, and η is a normalization factor; (4) Soft resampling To avoid particle degeneration, soft resampling is used to generate a new set of particles: Among them, α is the adjustment parameter, (5) Output prediction Summarize the prediction results of the particles to get the final prediction value; (6) Repeat steps (2), (3), (4), and (5) until convergence or the maximum number of iterations is reached.

4. The method for predicting the life of a rolling bearing under multiple failure modes based on Weibull distribution according to claim 3, characterized in that: The multi-criteria loss function based on Weibull distribution is specifically: By using the failure mode information provided by the Weibull distribution and optimizing the prediction accuracy through a variety of traditional loss functions, the Weibull distribution can effectively fit the failure data of the equipment, and its probability density function is shown in formula (2); The traditional loss function is a commonly used loss function in regression models: mean square error (MSE), root mean square error (RMSE), and root mean square logarithmic error (RMLSE), as shown in equations (13) to (15): Among them, Ns is the number of test samples, A i represents the actual RUL value of the i-th test sample, and P i Represents the predicted RUL value of the same test sample; A multi-criteria comprehensive loss function is designed to integrate the failure mode information of Weibull distribution and the advantages of various traditional loss functions, as shown in Equations (16) to (20): A i =F(A i )+1 (19) P i =F(P i )+1 (20) Among them, N s is the number of test samples, A i represents the actual RUL value of the i-th test sample, and P i Represents the predicted RUL value of the same test sample.

5. The method for predicting the life of a rolling bearing under multiple failure modes based on Weibull distribution according to claim 4, characterized in that: The trust margin p is 5% and the tuning parameter α is set to 0.

5.

6. A rolling bearing life prediction system based on Weibull distribution under multiple failure modes, characterized by: The system has a program module corresponding to the steps of any one of claims 1 to 5, and executes the steps of the method for predicting the life of a rolling bearing under multiple failure modes based on Weibull distribution during operation.

7. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and the computer program is configured to implement the steps of a rolling bearing life prediction method under multiple failure modes based on Weibull distribution according to any one of claims 1 to 5 when called by a processor.

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