A bearing vibration signal two-stage decomposition and prediction method and system based on an improved optimization algorithm

Abstract

This invention relates to a two-level decomposition and prediction method and system for bearing vibration signals based on an improved optimization algorithm. The method includes: acquiring vibration signal data and preprocessing it to obtain an initial sequence; using an improved center collision optimization algorithm to optimize the jump-oscillation mode decomposition parameters and variational mode decomposition parameters respectively to obtain the optimal first-level decomposition parameters and the optimal second-level decomposition parameters, thereby constructing a first-level decomposition model and a second-level decomposition model; inputting the initial sequence into the first-level decomposition model to obtain the jump component, oscillation component, and residual component of the first-level decomposition, and calculating the complexity evaluation index of the oscillation component and the residual component to obtain the high-frequency component and the low-frequency component; inputting the reconstructed high-frequency sequence corresponding to the high-frequency component into the second-level decomposition model to obtain the modal component and the second-level residual component of the second-level decomposition; inputting the jump component, low-frequency component, modal component, and second-level residual component into the prediction model to obtain the final bearing vibration signal prediction result.

Description

Technical Field

[0001] This invention relates to the field of rotating machinery condition monitoring and intelligent prediction technology, and in particular to a two-level decomposition and prediction method and system for bearing vibration signals based on an improved optimization algorithm. Background Technology

[0002] Rolling bearings are critical components in mechanical equipment, and their performance directly affects the stability and operating efficiency of the equipment. Due to long-term operation and load variations, rolling bearings are prone to wear, fatigue, and other failures, which in turn cause changes in vibration signals. Therefore, monitoring and analyzing the vibration signals of rolling bearings is an important means of equipment health management and fault diagnosis.

[0003] In signal prediction, hybrid models combine signal decomposition with prediction and have been widely used to improve prediction accuracy. Commonly used signal decomposition methods, such as Empirical Mode Decomposition (EMD) and its improved versions (ICEEMD, ICEEMDAN), perform well in handling non-stationary signals, but still face problems such as mode aliasing, residual noise, and reliance on manual experience. Variational Mode Decomposition (VMD) was proposed to alleviate these problems, especially in terms of mode aliasing and noise, but VMD can only extract oscillatory components from the signal and cannot handle transition components. Jump-Oscillatory Mode Decomposition (JMD) can extract both oscillation and transition components simultaneously, but requires tuning additional parameters, increasing the complexity of the method and relying on manual adjustment. In addition, existing hybrid models usually perform only one decomposition, making it difficult to fully capture the multiple components in the signal, especially the details in the high-frequency part, affecting prediction accuracy.

[0004] In time series forecasting modeling, Bidirectional Gated Recurrent Unit Networks (BiGRU) are widely used due to their excellent context modeling capabilities. However, existing studies often rely on empirically set hyperparameters, which can easily lead to overfitting or insufficient model expressive power. Therefore, optimizing the hyperparameters of BiGRU has become a key challenge in improving prediction accuracy and generalization ability.

[0005] Center Collision Optimization (CCO) is a physics-based global optimization algorithm with strong global search capabilities, widely used in signal decomposition and hyperparameter optimization of deep learning models. However, CCO also has some shortcomings in practical applications: uneven initial population distribution may reduce search efficiency; performing the same collision update in each iteration may distribute computational resources, reducing the ability to focus on key regions; and the algorithm is prone to stalling during iteration, affecting optimization results and search efficiency. Summary of the Invention

[0006] To address the problems existing in the prior art, the present invention aims to provide a two-level decomposition and prediction method and system for bearing vibration signals based on an improved optimization algorithm. By improving the optimization algorithm and optimizing the parameters of signal processing technology and deep learning model, the prediction accuracy, system stability and optimization efficiency of bearing vibration signals are effectively improved, which has high engineering application value.

[0007] To achieve the above objectives, the present invention provides the following solution: A two-level decomposition and prediction method for bearing vibration signals based on an improved optimization algorithm includes: Vibration signal data of the centrifugal compressor drive end bearing during operation is acquired, and the vibration signal data is preprocessed to obtain an initial sequence; An improved center collision optimization algorithm is used to optimize the jump-oscillation mode decomposition parameters and variational mode decomposition parameters respectively, to obtain the optimal first-level decomposition parameters and the optimal second-level decomposition parameters; the improved center collision optimization algorithm is obtained by introducing a Latin hypercube sampling strategy, a focus selection strategy and a guided collision strategy; A first-level decomposition model is constructed using the optimal first-level decomposition parameters. The initial sequence is input into the first-level decomposition model to obtain the jump components, oscillation components, and residual components of the first-level decomposition. The complexity evaluation index of the oscillation components and the residual components is calculated to obtain the high-frequency components and low-frequency components. A second-level decomposition model is constructed using the optimal second-level decomposition parameters. The reconstructed high-frequency sequence of the high-frequency components is input into the second-level decomposition model to obtain the modal components and second-level residual components of the second-level decomposition. The jump component, the low-frequency component, the modal component, and the second-order residual component are input into the prediction model to obtain the prediction results of each component; the prediction model is constructed by the optimal combination of prediction hyperparameters obtained by the improved center collision optimization algorithm for the hyperparameter optimization of the bidirectional gated cyclic unit network; The prediction results of each component are processed by signal reconstruction and inverse normalization to obtain the final bearing vibration signal prediction result.

[0008] Optionally, the improved center collision optimization algorithm includes: The center collision optimization algorithm incorporates a Latin hypercube sampling strategy, a focus selection strategy, and a guided collision strategy to update the individual positions in the population: By using the hierarchical probability sampling method of the Latin hypercube sampling strategy, each search interval is divided into several equally probable sub-intervals, and sampling points are randomly selected in each probability sub-interval. The initial population is then generated through random permutation and combination. The initial population is divided into a first population and a second population according to the current spatial allocation ratio. Individuals in the first population are subjected to a center collision strategy in the original space. The individual positions are updated by simulating a random pair collision mechanism between individuals in the population, so as to cause the individuals in the first population to generate random perturbations in the search space and move towards the high-quality region. The covariance matrix of the second population is used and eigenvalue decomposition is performed to obtain an orthogonal transformation matrix. The original space is orthogonally transformed and mapped to a decorrelation space through the orthogonal transformation matrix. The center collision strategy is performed in the decorrelation space to update the individual positions. The updated individuals are then mapped back to the original space. Greedy selection is performed on the updated individuals in the original space and the decorrelation space. If the fitness of the updated individual is better than that of the original individual, the updated individual is retained and the count of individuals that successfully produce better offspring in the corresponding space is increased. Otherwise, the original individual is retained. Based on the individual count statistics and the individual allocation ratio of the two spaces in the previous round, the proportion of population individuals allocated to the original space and the decorrelation space in the next iteration is adaptively adjusted. Based on the focused selection strategy, a two-dimensional evaluation mechanism based on spatial topological location and potential energy distribution is constructed to differentiate and screen individuals in the updated population, obtaining high-potential-energy individuals and centrally stagnant individuals. A gravitational field is constructed through the guided collision strategy to perform directional updates on the high-potential-energy individuals. The average distance of the individuals in the population relative to the population centroid is calculated through a population diversity monitoring mechanism. When the average distance is lower than a preset diversity threshold, it is determined that the population diversity is insufficient and there is a risk of premature convergence. Therefore, multiple individuals farthest from the centroid are selected as spatial anchor points to construct a repulsive force vector pointing outward from the centroid, so as to cause the centrally stagnant individuals to break out of their current stagnant state.

[0009] Optionally, the Latin hypercube sampling strategy includes: ; in, Indicates the first The individual in the first Initial position on the dimension and They represent the first Lower and upper bounds of a dimensional variable. Indicates the first A random permutation function in dimension 1 is used to determine the nth dimension. The sub-interval number to which each individual is assigned in this dimension. This indicates the population size, i.e., the total number of individuals. To show obedience Uniformly distributed random numbers are used to perform random sampling within an assigned sub-interval.

[0010] Optionally, performing a greedy selection on the original space and the updated individuals in the decorrelation space includes: ; ; ; in, and They represent the first time. In each iteration, the success update counters for both the original space and the decorrelation space are initialized to 1. For the fitness calculation function, and These represent the central collision phase, respectively. The current location and updated location of each individual and These represent the relevant spatial stages. The current location and updated location of each individual and They represent the first The final successful update count result is obtained from the original space and the decorrelation space after the round of iterations.

[0011] Optionally, adaptively adjusting the ratio of individuals in the population allocated to the original space and the decorrelation space in the next iteration includes: ; ; ; ; in, and They represent the first time. The distribution ratio of individuals in the original space and the decorrelation space of the population in each iteration. and They respectively represent the use for the first The distribution ratio of individuals in the original space and the decorrelation space of the population in each iteration. This indicates that the initial individual assignments in the original space and the decorrelation space are the same during the first iteration. This indicates that the population distribution ratio between the original space and the decorrelation space in each iteration is limited to the range of 30%-70%.

[0012] Optionally, constructing a two-dimensional evaluation mechanism based on spatial topological location and potential energy distribution based on the focused selection strategy to perform differential screening of individuals in the updated population includes: Calculate the geometric centroid of the population and determine the Euclidean distance between each individual in the population and the geometric centroid; The Euclidean distance is used to measure the spatial deviation of individuals in the search space, the topological location characteristics of individuals are obtained, and the two-dimensional evaluation mechanism is constructed by combining the individual fitness value to classify and screen individuals in the population.

[0013] Optionally, constructing a gravitational field through the guided collision strategy to perform targeted updates on the high-potential individual includes: ; in, and These represent the current position and the updated position of the high-potential-energy individual during the guided collision phase, respectively. and These represent the positions of individuals randomly selected from the top 10% of the fitness-ranked elite individuals and the top 50% of the fitness-ranked secondary elite individuals, respectively, during the guided collision phase. and for Random values ​​within the interval The convergence factor decreases linearly with the number of iterations. It is a Gaussian random perturbation with a mean of zero.

[0014] Optionally, causing the centrally stationary individual to break free from its current stagnant state by constructing a repulsive force vector pointing outward from the center of mass includes: ; in, and These represent the current and updated positions of the individual stranded at the center during the guided collision phase, respectively. Indicates the first The position of the geometric centroid of the population at the next iteration and This indicates the relationship between the population and the centroid during the guided collision phase. The positions of the two individuals with the greatest distance. and for Random values ​​within the interval The convergence factor decreases linearly with the number of iterations. It is a Gaussian random perturbation with a mean of zero.

[0015] To achieve the above objectives, the present invention also provides a two-level decomposition and prediction system for bearing vibration signals based on an improved optimization algorithm, comprising: The data acquisition and preprocessing module is used to acquire vibration signal data during the operation of the centrifugal compressor drive end bearing, and to preprocess the vibration signal data to obtain an initial sequence. The decomposition and optimization module is used to optimize the jump-oscillation mode decomposition parameters and variational mode decomposition parameters respectively using an improved center collision optimization algorithm to obtain the optimal first-level decomposition parameters and the optimal second-level decomposition parameters. The improved center collision optimization algorithm is obtained by introducing a Latin hypercube sampling strategy, a focus selection strategy, and a guided collision strategy. A first-level decomposition model is constructed using the optimal first-level decomposition parameters. The initial sequence is input into the first-level decomposition model to obtain the jump components, oscillation components, and residual components of the first-level decomposition. The complexity evaluation index of the oscillation components and the residual components is calculated to obtain the high-frequency components and low-frequency components. A second-level decomposition model is constructed using the optimal second-level decomposition parameters. The reconstructed high-frequency sequence of the high-frequency components is input into the second-level decomposition model to obtain the modal components and second-level residual components of the second-level decomposition. The signal prediction and reconstruction module is used to input the jump component, the low-frequency component, the modal component and the second-order residual component into the prediction model to obtain the prediction results of each component; the prediction model is constructed by the optimal combination of prediction hyperparameters obtained by the improved center collision optimization algorithm for hyperparameter optimization of the bidirectional gated cyclic unit network; The prediction results of each component are processed by signal reconstruction and inverse normalization to obtain the final bearing vibration signal prediction result.

[0016] The beneficial effects of this invention are as follows: (1) The improved center collision optimization algorithm proposed in this invention improves upon the problems of uneven population initialization, scattered computational resources for collision updates, and algorithm stagnation in the traditional center collision optimization algorithm by introducing a Latin hypercube sampling strategy, a focusing selection strategy, and a guided collision strategy. It enhances the global search capability and convergence stability of decomposition parameters and prediction model hyperparameter optimization, strengthens parameter adaptation capability, and thus improves the optimization efficiency and overall system stability in the process of vibration signal decomposition and prediction model construction.

[0017] (2) The present invention utilizes an improved center collision optimization algorithm to optimize the key parameters of jump-oscillation mode decomposition and variational mode decomposition respectively, so that the decomposition process has stronger adaptability, improves mode separation degree and reduces mode aliasing phenomenon; on this basis, the complex vibration signal is characterized by a "two-level decomposition" structure, thereby improving the separation effect of multi-scale features of complex vibration signal and reducing the interference of signal nonlinearity and complexity on subsequent prediction modeling.

[0018] (3) The present invention evaluates the complexity of the oscillation components and residual components obtained by the first-level decomposition by using the entropy-type complexity evaluation index, and sorts the components according to the complexity evaluation index value corresponding to each component. The high-frequency components with higher complexity are selected for reconstruction, so that the second-level decomposition focuses on further refining the complex high-frequency components, thereby reducing the complexity propagation effect of high-frequency components and improving the decomposition efficiency and the accuracy of high-frequency feature characterization.

[0019] (4) This invention utilizes an improved center collision optimization algorithm to optimize the hyperparameters of the bidirectional gated cyclic unit network, thereby improving the rationality of the parameter configuration and convergence stability of the prediction model. At the same time, the jump components and low-frequency components of the first-level decomposition, as well as the modal components and second-level residual components of the second-level decomposition, are input into the optimized prediction model for component prediction, and the prediction results are reconstructed, thereby improving the accuracy of vibration signal prediction, reducing prediction error fluctuations, and improving the stability and reliability of bearing vibration signal prediction in engineering applications. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is a flowchart of a two-level decomposition and prediction method for bearing vibration signals based on an improved optimization algorithm, according to an embodiment of the present invention. Figure 2 This is a schematic diagram of a two-level decomposition and prediction system for bearing vibration signals based on an improved optimization algorithm, according to an embodiment of the present invention. Figure 3 The graph shows the convergence curves of the LFGCCO algorithm and seven advanced optimization algorithms in this embodiment of the invention on the selected test functions; (a) is the convergence result on the F1 test function, (b) is the convergence result on the F10 test function, (c) is the convergence result on the F18 test function, and (d) is the convergence result on the F28 test function. Figure 4 This is the first-level decomposition result of the initial sequence in an embodiment of the present invention; Figure 5 This is the result of the secondary decomposition of the reconstructed high-frequency sequence in an embodiment of the present invention; Figure 6 This is a comparison chart of the results of the LFGCCO-JMD-VMD-BiGRU model of this invention with three comparative models in bearing vibration signal prediction; Figure 7This is a comparison chart of the results of the LFGCCO-JMD-VMD-BiGRU model, the LFGCCO-JMD-BiGRU model, and the LFGCCO-VMD-BiGRU model in bearing vibration signal prediction according to embodiments of the present invention. Detailed Implementation

[0022] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0023] This embodiment discloses a two-level decomposition and prediction method for bearing vibration signals based on an improved optimization algorithm, including: Vibration signal data of the centrifugal compressor drive end bearing during operation is acquired, and the vibration signal data is preprocessed to obtain an initial sequence; Based on the traditional center collision optimization algorithm, an improved center collision optimization algorithm is constructed by introducing a Latin hypercube sampling strategy, a focus selection strategy, and a guided collision strategy. The improved center collision optimization algorithm is used to optimize the parameters of the jump-oscillation mode decomposition, determine the optimal first-level decomposition parameters, and construct a first-level decomposition model based on the optimal first-level decomposition parameters; the initial sequence is input into the first-level decomposition model to obtain the jump component, oscillation component and residual component of the first-level decomposition. The complexity evaluation index of the oscillation component and residual component obtained from the first-level decomposition is calculated, and the complexity evaluation index values ​​of each component are sorted. Based on the sorting results, the components with higher complexity are selected as high-frequency components and the components with lower complexity are selected as low-frequency components. The high-frequency components are reconstructed to obtain the reconstructed high-frequency sequence. The improved center collision optimization algorithm is used to optimize the parameters of variational mode decomposition, determine the optimal second-level decomposition parameters, and construct a second-level decomposition model based on the optimal second-level decomposition parameters; the reconstructed high-frequency sequence is input into the second-level decomposition model to obtain the modal components and second-level residual components of the second-level decomposition. The improved center collision optimization algorithm is used to optimize the hyperparameters of the bidirectional gated recurrent unit network, determine the optimal combination of prediction hyperparameters, and construct a prediction model based on the optimal combination of prediction hyperparameters. The jump components and low-frequency components of the first-level decomposition, as well as the modal components and second-level residual components of the second-level decomposition, are input into the prediction model to obtain the prediction results of each component. The prediction results of each component are then processed for signal reconstruction, and the reconstructed signals are inversely normalized to obtain the final bearing vibration signal prediction results.

[0024] Further, the vibration signal data is preprocessed to obtain an initial sequence including: The collected vibration signal data is normalized to map the vibration signal amplitude to a preset numerical range in order to reduce the impact of different dimensions on the subsequent decomposition and prediction process. Furthermore, the improved center collision optimization algorithm includes: The initialization phase, the center collision phase, the decorrelated space phase, the space allocation phase, the focus selection phase, and the guided collision phase; in: In the initialization phase, a Latin hypercube sampling strategy is used to initialize the population position in the search space, and hierarchical probability sampling is used to ensure the orthogonality and uniformity of the population in each dimension in the search space. The central collision phase updates the population's individual positions by simulating random pair collisions between individuals in the original space, causing individuals to generate random perturbations in the search space and move towards high-quality areas; In the de-relevant space stage, the population is mapped to the base space through orthogonal transformation, and the individual positions are updated in the base space using a center collision strategy; During the spatial allocation phase, the distribution ratio of individuals in the population in the two spaces is adaptively adjusted based on the update effects in the original space and the decorrelation space. The selection phase focuses on building a two-dimensional evaluation mechanism based on physical location and potential energy to screen out individuals with high potential energy and individuals that remain in the center. During the guided collision phase, differentiated dynamic update mechanisms are constructed for the high-potential individuals and the centrally stranded individuals to update their positions, thereby accelerating the development speed of the high-potential individuals and enhancing the exploration capabilities of the centrally stranded individuals. Furthermore, constructing the first-level decomposition model includes: Determine the parameters to be optimized for jump-oscillation mode decomposition and set their search range. The parameters to be optimized include, but are not limited to, the number of oscillation components, oscillation constraint parameters, jump constraint parameters, jump component control parameters, penalty coefficient scaling parameters, and other parameters that affect the stability, decomposition accuracy, and frequency band division effect of mode decomposition. The operational control parameters of the improved center collision optimization algorithm are determined, wherein the operational control parameters include population size parameters, maximum number of iterations parameters, and other parameters used to control the optimization search process, adjust the search space exploration capability, and convergence speed; The improved center collision optimization algorithm is used to iteratively optimize the parameters to be optimized. Different parameter combinations are evaluated by a preset fitness function, and the parameter combination with the best fitness is determined as the optimal first-level decomposition parameters. The fitness function is used to characterize at least one of decomposition quality, modal separation degree or decomposition stability. A first-level decomposition model is constructed based on the optimal first-level decomposition parameters, and the initial sequence is decomposed to obtain the jump component, oscillation component and residual component of the first-level decomposition.

[0025] Furthermore, the reconstructed high-frequency sequence includes: Calculate the complexity evaluation index of the oscillatory component and residual component of the first-level decomposition, wherein the complexity evaluation index includes, but is not limited to, information entropy, sample entropy, permutation entropy, fuzzy entropy or other indexes that can characterize the complexity characteristics of the signal. The complexity evaluation index values ​​corresponding to each component are sorted, and the complexity of each component is grouped according to the sorting results. Select the components with larger complexity evaluation index values ​​in the sorting results as high-frequency components. The components identified as high-frequency components are subjected to signal reconstruction processing to obtain a reconstructed high-frequency sequence, wherein the signal reconstruction processing includes at least one of linear superposition or weighted fusion of the high-frequency components. Furthermore, the second-order decomposition mode components and second-order residual components are obtained, including: Determine the parameters to be optimized in variational mode decomposition and set their search range. The variables to be optimized include, but are not limited to, the number of modal components, penalty factor, reconstruction error tolerance parameter, center frequency initialization control parameter, and iteration termination threshold control parameter, which are used to adjust the number of modal components, bandwidth constraint strength, and algorithm convergence accuracy. The operational control parameters of the improved center collision optimization algorithm are determined, wherein the operational control parameters include population size parameters, maximum number of iterations parameters, and other parameters used to control the optimization search process, adjust the search space exploration capability, and convergence speed; The improved center collision optimization algorithm is used to iteratively optimize the parameters to be optimized. The performance of different parameter combinations is evaluated by a preset fitness function. The parameter combination with the best fitness is determined as the optimal second-level decomposition parameters. The fitness function is used to characterize at least one of the following: mode separation effect, signal reconstruction error, noise suppression capability, or decomposition stability. A second-level decomposition model is constructed based on the optimal second-level decomposition parameters, and the reconstructed high-frequency sequence is decomposed to obtain the modal components and second-level residual components of the second-level decomposition.

[0026] Furthermore, determining the optimal combination of prediction hyperparameters and constructing the prediction model includes: Determine the hyperparameters to be optimized for the bidirectional gated recurrent unit network and set its search range. The hyperparameters to be optimized include, but are not limited to, the number of hidden layer units, the learning rate, the regularization control, the batch size, the number of network layers, and other parameters that affect the prediction accuracy, training stability, and convergence performance of the network. The operational control parameters of the improved center collision optimization algorithm are determined, wherein the operational control parameters include population size parameters, maximum number of iterations parameters, and other parameters used to control the optimization search process, adjust the search space exploration capability, and convergence speed; The improved center collision optimization algorithm is used to iteratively optimize the hyperparameters to be optimized. The performance of different hyperparameter combinations is evaluated by a preset loss function or performance evaluation index, and the hyperparameter combination with the best performance is determined as the optimal prediction model parameters. The loss function or performance evaluation index is used to characterize at least one of prediction error, model fitting ability or prediction stability. A prediction model is constructed based on the parameters of the optimal prediction model.

[0027] Furthermore, the final bearing vibration signal prediction results include: The jump components and low-frequency components of the first-level decomposition, as well as the modal components and second-level residual components of the second-level decomposition, are input into the prediction model to obtain the prediction results for each component. The prediction results of each component are processed by signal reconstruction, and the reconstructed signal is inversely normalized to obtain the final bearing vibration signal prediction result. The signal reconstruction process includes at least one of linear superposition or weighted fusion.

[0028] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0029] like Figure 1 As shown, this embodiment provides a two-level decomposition and prediction method for bearing vibration signals based on an improved optimization algorithm, including the following steps: S1: Acquire vibration signal data of the centrifugal compressor drive end bearing during operation, and preprocess the vibration signal data to obtain an initial sequence; S2: Based on the traditional center collision optimization algorithm, a Latin hypercube sampling strategy, a focus selection strategy, and a guided collision strategy are introduced to improve the algorithm mechanism and construct an improved center collision optimization algorithm. S3: The improved center collision optimization algorithm is used to optimize the parameters of the jump-oscillation mode decomposition, determine the optimal first-level decomposition parameters, and construct a first-level decomposition model based on the optimal first-level decomposition parameters; the initial sequence is input into the first-level decomposition model to obtain the jump component, oscillation component and residual component of the first-level decomposition. S4: Calculate the complexity evaluation index of the oscillation component and residual component obtained from the first-level decomposition, and sort the complexity evaluation index values ​​corresponding to each component. Based on the sorting results, select the components with higher complexity as high-frequency components and the components with lower complexity as low-frequency components; reconstruct the high-frequency components to obtain the reconstructed high-frequency sequence. S5: The improved center collision optimization algorithm is used to optimize the parameters of variational mode decomposition, determine the optimal second-level decomposition parameters, and construct a second-level decomposition model based on the optimal second-level decomposition parameters; the reconstructed high-frequency sequence is input into the second-level decomposition model to obtain the modal components and second-level residual components of the second-level decomposition; S6: The improved center collision optimization algorithm is used to optimize the hyperparameters of the bidirectional gated recurrent unit network, determine the optimal combination of prediction hyperparameters, and construct a prediction model based on the optimal combination of prediction hyperparameters. S7: Input the jump component and low-frequency component of the first-level decomposition, as well as the modal component and second-level residual component of the second-level decomposition, into the prediction model to obtain the prediction results of each component. Then, perform signal reconstruction processing on the prediction results of each component and perform inverse normalization on the reconstructed signal to obtain the final bearing vibration signal prediction result.

[0030] In this embodiment, step S1 includes acquiring vibration signal data during the operation of the centrifugal compressor drive end bearing, and normalizing the vibration signal data to map the vibration signal amplitude to a preset numerical range, so as to reduce the influence of different dimensions on the subsequent decomposition and prediction process and obtain an initial sequence.

[0031] The normalization process employs a maximum-minimum normalization method, and its normalization formula is as follows: (1); in, For the first A normalized value, For the first One original vibration signal data, and These are the maximum and minimum values ​​in the original vibration signal data; Normalization makes the numerical distribution of vibration signal data more concentrated and consistent in scale, which helps to improve the convergence speed and numerical calculation stability of subsequent decomposition algorithms and prediction models, and reduces the impact of numerical fluctuations on the model training process.

[0032] In this embodiment, the improved center collision optimization algorithm constructed in step S2 includes six stages: initialization stage, center collision stage, decorrelation space stage, space allocation stage, focus selection stage, and guided collision stage.

[0033] Step S2.1 Initialization Phase. In traditional random initialization methods, the initial distribution of individuals in the search space may exhibit clustering or gaps, affecting the algorithm's early exploration capability and overall convergence performance. To improve the uneven initial population distribution, this embodiment introduces a Latin Hypercube Sampling (LHS) strategy to initialize the population within the search space. LHS uses stratified probability sampling to divide each dimension of the search interval into several equally probable sub-intervals, and randomly samples a point within each sub-interval, thereby ensuring uniform coverage and orthogonality of samples in each dimension. The mathematical expression for Latin Hypercube Sampling is as follows: (2); in, Indicates the first The individual in the first Initial position on the dimension and They represent the first Lower and upper bounds of a dimensional variable. Indicates the first A random permutation function in dimension 1 is used to determine the nth dimension. The sub-interval number to which each individual is assigned in this dimension. This indicates the population size, i.e., the total number of individuals. To show obedience Uniformly distributed random numbers are used to perform random sampling within an assigned sub-interval.

[0034] This strategy can effectively improve the spatial coverage of the initial population and enhance the global search capability of the algorithm in the early stages.

[0035] Step S2.2 Center Collision Phase. After initialization, the population is divided into two parts according to the current spatial allocation ratio. One part of the individuals executes the center collision strategy in the Original Space (OS). The individual positions are updated by simulating a random pairwise collision mechanism between individuals, causing random perturbations in the search space and moving towards high-quality regions. The center collision update formula in the original space is as follows: (3); in, and These represent the central collision phase, respectively. The current location and updated location of each individual , , and These represent the points where the center collision phase is randomly selected from the population and has a fitness better than the current point. The position of each individual and These represent the positions of different individuals randomly selected from the population during the center collision phase. for Random values ​​within the interval These are collision control variables used to determine the strategy employed for updating individual positions. This is an adjustment coefficient that dynamically changes with iteration, used to balance the exploratory and exploitative capabilities during the search process. and It is given by the following formula: (4); (5); in, Indicates the current iteration number. This indicates the maximum number of iterations of the algorithm. Indicates in Uniformly generated random numbers within the interval.

[0036] Step S2.3 Decorrelated Space Stage. When the population only executes the center-collision strategy in the original space, there may be correlations between variables in each dimension, leading to redundancy in search directions. To reduce the coupling effect of correlations between variables in the original space on search directions, a covariance matrix is ​​constructed based on a subset of individuals and eigenvalue decomposition is performed to obtain an orthogonal transformation matrix, which is used to establish a decorrelated space (DS). Subsequently, according to the current space allocation ratio, another subset of individuals is mapped from the original space to the decorrelated space, where the center-collision strategy is executed to update their positions. The updated individuals are then mapped back to the original space, thereby achieving collaborative search between the population in the two spaces.

[0037] The process of constructing the relevant space is as follows: First, in the current iteration, the individuals in the population are sorted in ascending order according to their fitness values, and the individuals in the bottom half of the fitness ranking are selected, i.e., those with poor fitness. Individuals; construct a data matrix based on the selected individuals. ,in For the sample size, The population size; The dimension of the variable; To eliminate the impact of mean bias on covariance calculation, the data matrix is... Centralized processing: (6); Where 1 is a column vector consisting entirely of 1s. It is the data mean vector. This is the data matrix after centralization.

[0038] Using the centralized data matrix To calculate the covariance matrix : (7); Wherein, the covariance matrix Used to characterize the correlation structure between variables in each dimension. for The transpose of .

[0039] For covariance matrix Perform eigenvalue decomposition: (8); Among them, feature vector Indicates the direction in the decorrelated space, eigenvalues This indicates the magnitude of the variance in these directions; All feature vectors Composition of eigenvector matrix : (9); eigenvector matrix This forms an orthogonal transformation basis from the original space to the decorrelation space.

[0040] population Mapping to the dereferenced space (DS): (10); in, To represent the population in the relevant space; Execute the center collision update strategy in the relevant space: (11); in, and These represent the relevant spatial stages. The current location and updated location of each individual , , and These represent random selections from the population at relevant spatial stages, with fitness better than the current [number] [unit]. The position of each individual and These represent the locations of different individuals randomly selected from the population during the relevant spatial stages. for Random values ​​within the interval These are collision control variables used to determine the strategy employed for updating individual positions. This is an adjustment coefficient that dynamically changes with iteration, used to balance the exploratory and exploitative capabilities during the search process. and It is given by the following formula: (12); (13); in, Indicates the current iteration number. This indicates the maximum number of iterations of the algorithm. Indicates in Uniformly generated random numbers within the interval.

[0041] Since the variables are no longer correlated, the update directions are more independent, which helps to improve search efficiency.

[0042] After updating the position in the relevant space, the transpose of the eigenvector matrix is ​​used. Map the updated individuals back to the original space: (14); in, This indicates the position after mapping back to the original space. Indicates the relevant spatial stage. The position of each individual after being updated by the central collision strategy.

[0043] By constructing and mapping the aforementioned decorrelation space, the interference of correlation between variables can be effectively reduced, the independence of search direction can be improved, and invalid search paths can be reduced, thereby accelerating the convergence speed of the algorithm and improving the global optimization capability.

[0044] Step S2.4 Spatial Allocation Phase. A greedy selection process is performed on the updated individuals in both the original space and the decorrelational space. If the fitness of the updated individual is better than that of the unupdated individual, the updated individual is retained, and the count of individuals successfully producing better offspring in the corresponding space is increased; otherwise, the original individual is retained. Furthermore, based on the statistical results of successfully updated individuals in the original space and the decorrelational space, and combined with the individual allocation ratio between the two spaces in the previous round, the proportion of population individuals allocated to the original space and the decorrelational space in the next iteration is adaptively adjusted. This tilts search resources towards the currently more effective space while maintaining collaborative search between the two spaces.

[0045] The greedy selection formula is as follows: (15); (16); (17); in, and They represent the first time. In each iteration, the success update counters for both the original space (OS) and the decorrelation space (DS) are initially initialized to 1. For the fitness calculation function, and These represent the central collision phase, respectively. The current location and updated location of each individual and These represent the relevant spatial stages. The current location and updated location of each individual and They represent the first The final successful update count is obtained from the original space (OS) and the decorrelation space (DS) after the round of iterations.

[0046] The formula for updating the spatial population individual allocation ratio is as follows: (18); (19); (20); (twenty one); in, and They represent the first time. The distribution ratio of individuals in the original space and the decorrelation space of the population in each iteration. and They respectively represent the use for the first The distribution ratio of individuals in the original space and the decorrelation space of the population in each iteration. This indicates that the initial individual assignments in the original space and the decorrelation space are the same during the first iteration. This indicates that the population distribution ratio between the original space and the decorrelation space in each iteration is limited to the range of 30%-70%.

[0047] Step S2.4 Focused Selection Phase. In traditional center collision optimization algorithms, all individuals adopt a homogeneous update mechanism, meaning that all individuals in the population perform the same form of collision update in each iteration. This approach easily leads to the dispersion of computational resources in complex multimodal search environments, reducing the algorithm's ability to focus on key regions and thus affecting the overall optimization efficiency. To improve the adaptability of the population in complex search spaces, this embodiment introduces a focused selection strategy, which constructs a two-dimensional evaluation mechanism based on spatial topological location and potential energy distribution to perform differentiated screening of population individuals.

[0048] In the t-th iteration, the geometric centroid of the population is first calculated. : (twenty two); in, Indicates the first The geometric centroid of the population in the search space at each iteration is used to characterize the overall spatial distribution center of the population. Indicates the number of individuals in the population. Indicates the first The location of an individual in the search space This represents the summation of the position vectors of all individuals in the population.

[0049] Then, the Euclidean distance between each individual and the population centroid is calculated: (twenty three); in, Indicates the first The Euclidean distance between an individual and the geometric centroid of the population. Indicates the first The location of an individual in the search space Indicates the first The position of the geometric centroid of the population at the next iteration This represents the L2 norm of a vector, i.e., the method for calculating Euclidean distance.

[0050] The Euclidean distance is used to measure the degree of spatial deviation of an individual in the search space, thereby reflecting the topological location characteristics of the individual.

[0051] Based on the spatial location information, and combined with the fitness value of individuals, a two-dimensional evaluation mechanism of "spatial location-potential energy" is constructed to classify and screen individuals in the population.

[0052] In this process, individuals in the population are sorted in ascending order according to their fitness values; the higher the fitness value, the higher the potential energy of the individual, and the worse the quality of its solution.

[0053] Based on the above assessment mechanism, two key individuals were identified: (1) individuals with high potential energy. Individuals ranked last in fitness have the highest fitness value and are located in the high-potential region of the search space. These individuals are of poor quality and have significant room for improvement, making them priority targets for adjustment; (2) Centrally relegated individuals Individuals whose fitness is close to the population centroid but have not reached the global optimum. These individuals are spatially close to the population center but do not exhibit superior fitness, indicating that they may be stuck in a local optimum. Therefore, external perturbations need to be applied in subsequent iterations to enhance their ability to escape local optima.

[0054] By employing the aforementioned focused selection strategy, key individuals that significantly impact population quality can be accurately identified in each iteration, enabling a differentiated update mechanism. This improves the algorithm's search efficiency in complex multimodal problems and provides a basis for directional updates in the subsequent guided collision phase.

[0055] Step S2.5 Guided Collision Phase. High-potential individuals are selected during the focused selection phase. and individuals stranded in the center Subsequently, this embodiment constructs differentiated dynamic update mechanisms for the two types of individuals, aiming to accelerate the development speed of high-potential individuals and enhance the exploration capabilities of centrally stranded individuals. Considering high potential energy individuals Since no effective high-quality information has been accumulated during historical iterations, this embodiment employs a guided collision mode based on multi-level elite memory for targeted updates. Specifically, the fitness values ​​of individuals in the population are sorted in ascending order, and individuals ranked in the top 10% are divided into a top-tier elite set, while individuals ranked in the top 50% but not in the top 10% are divided into a secondary elite set. Subsequently, the positions of elite individuals are randomly selected from the top-tier and secondary elite sets to construct a gravitational field to guide the update of high-potential-energy individuals.

[0056] Top elites gathered: (twenty four); Secondary elites gathering: (25); in, This represents the top elite group, consisting of individuals ranked in the top 10% by fitness. This represents the secondary elite group, consisting of individuals ranked in the top 50% by fitness but not in the top 10%. Represents an individual The fitness ranking is sorted in ascending order. Indicates population size, This indicates the rounding up operation.

[0057] High potential energy individuals The update formula is: (26); in, and These represent the current position and the updated position of the high-potential-energy individual during the guided collision phase, respectively. and These represent the positions of individuals randomly selected from the top 10% of the fitness-ranked elite individuals and the top 50% of the fitness-ranked secondary elite individuals, respectively, during the guided collision phase. and for Random values ​​within the interval The convergence factor decreases linearly with the number of iterations. It is a Gaussian random perturbation with a mean of zero.

[0058] Through the aforementioned update mechanism, high-potential-energy individuals move in a directional manner under the combined influence of the multi-level gravitational fields constructed by top-tier and second-tier elite individuals, thereby accelerating their approach to high-quality search areas and improving the overall convergence efficiency and search accuracy of the population.

[0059] To avoid premature convergence during the algorithm's iteration, this embodiment introduces a population diversity monitoring mechanism. In each iteration, the average distance of an individual in the population relative to the population centroid is calculated as an indicator of population distribution dispersion. When the average centroid distance falls below a preset diversity threshold... At this point, the population is deemed to have insufficient diversity, posing a risk of premature convergence. Diversity threshold. The calculation formula is as follows: (27); in, and They represent the first Lower and upper bounds of a dimensional variable. Indicates the current iteration number. This indicates the maximum number of iterations of the algorithm. Represents norm operations.

[0060] When premature convergence is detected in the population, this embodiment employs a reverse discrete collision mode based on geometric repulsion to target the centrally stranded individuals. Dynamic adjustments are made. Specifically, the two individuals furthest from the centroid are selected. and As a spatial anchor point, a repulsive force vector is constructed pointing outward from the center of mass, causing the individual to remain at the center. Break free from the current stagnant state. (Centralized, stranded individual) The update formula is: (28); in, and These represent the current and updated positions of the individual stranded at the center during the guided collision phase, respectively. Indicates the first The position of the geometric centroid of the population at the next iteration and This indicates the relationship between the population and the centroid during the guided collision phase. The positions of the two individuals with the greatest distance. and for Random values ​​within the interval The convergence factor decreases linearly with the number of iterations. It is a Gaussian random perturbation with a mean of zero.

[0061] In this embodiment, the specific process of step S3 includes: The improved center collision optimization algorithm (LFGCCO) is used to iteratively optimize the parameters to be optimized in jump-oscillation mode decomposition (JMD). Different parameter combinations are evaluated by a preset fitness function, and the parameter combination with the best fitness is determined as the optimal first-level decomposition parameters. A first-level decomposition model is constructed based on the optimal first-level decomposition parameters, and the initial sequence is decomposed using the first-level decomposition model to obtain the jump component, oscillation component and residual component of the first-level decomposition.

[0062] Specifically, determine the parameters to be optimized in JMD and their search range, including: oscillation mode constraint parameters ( ), number of oscillating components ( ), jump constraint parameters ( ), regulatory factors ( ) and minimum jump height parameter ( Simultaneously, the operating control parameters of the LFGCCO algorithm are set, including population size and maximum number of iterations; the initialization mechanism of LFGCCO is used to randomly generate the positions of individuals in the population, and each individual in the population corresponds to a set of JMD parameter combinations. Substituting each set of parameters into the JMD method, the initial sequence is decomposed to obtain multiple sets of jump components, oscillation components, and residual components. This embodiment uses the minimum envelope entropy as the fitness function to evaluate the decomposition effect of JMD under different parameter combinations. During the iteration process, LFGCCO updates the individual positions of the population through its six stages, thereby achieving dynamic optimization of the JMD parameter combinations. Each iteration performs parameter updates, signal decomposition, fitness calculation, and optimal individual recording. When the maximum number of iterations is reached or the termination condition is met, the parameter combination with the optimal fitness is output as the optimal first-level decomposition parameters; a first-level decomposition model is constructed based on the optimal first-level decomposition parameters; the initial sequence is input into the first-level decomposition model for decomposition processing to obtain the jump components, oscillation components, and residual components of the first-level decomposition.

[0063] JMD achieves the synchronous decomposition of oscillatory and abrupt components by constructing a joint variational optimization model that combines oscillatory mode bandwidth constraints with abrupt component sparsity constraints. The specific steps are as follows: Construct a joint variational constraint optimization model: (29); in, Indicates the first Each oscillation component, subscript , The number of oscillating components. Indicates the first The center frequency of each oscillation component This represents the jump component function to be optimized. Indicates the jump component at time t. The value of , These are oscillation mode constraint parameters. express Analytical signal form, Indicates the first The oscillation component at time... The value of , It is a complex exponential frequency shift factor. Represents the imaginary unit. These are jump constraint parameters. This indicates the jump amplitude control parameter. This represents the minimum jump height parameter. This indicates that a summation operation is being performed. Represents the time variable The partial derivative operation, The square of the L2 norm, This represents integration. It is the L2 norm. This represents the penalty function used to characterize the sparsity of jump transitions. This represents the initial sequence.

[0064] To solve To address the issue of non-differentiable terms, an auxiliary variable is introduced. Furthermore, the Lagrange multiplier method is used to transform the original constrained optimization problem into an optimization form that is easier to solve: (30); in, Represents the augmented Lagrange function. An auxiliary variable is introduced to represent the time derivative of the jump component. For auxiliary variables at time The value of , The Lagrange multipliers representing signal reconstruction constraints, The Lagrange multipliers representing the signal reconstruction constraints at time t = 0. The value of , Represents the Lagrange multipliers for auxiliary variable constraints. The Lagrange multipliers representing the auxiliary variable constraints at time t = 1 The value of , To increase the weight of the Lagrange penalty, This represents the inner product operation. Indicates the initial sequence at time [time]. The value of , It is a regulating factor.

[0065] Alternating updates using the alternating direction multiplier method (ADMM) , ,λ, , , : (31); (32); (33); (34); (35); (36); in, and They represent the first The oscillation component and the center frequency are in the... The update value for the next iteration. Indicates except the first The summation of all oscillation components other than the first oscillation component. and Indicates the Lagrange multiplier at the 1st The update value for the next iteration. For step size parameters, Indicates the jump component at the th The update value for the next iteration. It is a first-order difference operator matrix. It is the transpose matrix of the first-order difference operator. It is the identity matrix. To increase the weight of the Lagrange penalty, Indicates the auxiliary variable in the th... The update value for the next iteration. For intermediate calculation variables, , , , , They represent , , , , Representation in the frequency domain, Indicates except the first Besides the oscillation component, other oscillation components at time 1 The value of , This represents the inverse operation of a matrix. For frequency variables, jump constraint parameters With augmented Lagrange penalty weights The ratio of .

[0066] The iteration stops when the convergence condition is met, and the obtained As the final transition components, the obtained each As the final oscillation component, the convergence condition formula is as follows: (37); in, To preset the convergence threshold, and They represent the first Second and third The signal reconstruction result obtained from the next iteration. The calculation method is as follows: (38); The residual component is obtained by calculating the difference between the original signal and the reconstructed signal. : (39); Through the aforementioned joint variational optimization model and ADMM iterative mechanism, JMD can effectively separate impact or step change components while preserving the periodic vibration characteristics of the signal. This avoids the pseudo-mode phenomenon caused by traditional decomposition methods based solely on the narrowband oscillation assumption mistakenly modeling jump changes as oscillation modes. Combined with LFGCCO's global optimization of key parameters, the decomposition accuracy and stability can be further improved, enhancing the reliability of complex non-stationary vibration signal analysis and providing a clearer feature basis for subsequent complexity screening and secondary decomposition.

[0067] In this embodiment, the specific process of step S4 includes: calculating the complexity evaluation index of the oscillation component and residual component obtained by the first-level decomposition, sorting the complexity evaluation index values ​​corresponding to each component, selecting the components with higher complexity as high-frequency components and the components with lower complexity as low-frequency components according to the sorting results; reconstructing the high-frequency components to obtain the reconstructed high-frequency sequence.

[0068] Specifically, after the first-level decomposition, oscillation components and residual components are obtained. To measure the complexity of each component, this embodiment calculates a complexity evaluation index for each component, preferably using sample entropy as the time series complexity evaluation index. Sample entropy is used to measure the randomness and complexity of a time series; a larger value indicates a more complex sequence and stronger randomness; a smaller value indicates a more regular sequence and more obvious structure. The formula for calculating sample entropy is: (40); in, For embedded dimensions, For similarity tolerance, For sequence length, Indicates similarity tolerance The lower dimension is The probability of matching vector pairs. Indicates similarity tolerance The lower dimension is The probability of matching vector pairs.

[0069] The sample entropy values ​​corresponding to each component are sorted in ascending order, and the components with larger sample entropy values ​​are selected as high-frequency components, while the remaining components are selected as low-frequency components. The sorting and selection method can be based on proportions, such as the last 50% or the last k components after sorting the sample entropy values, or it can be dynamically determined based on the statistical characteristics of the training samples.

[0070] The components identified as high-frequency components are reconstructed to obtain a reconstructed high-frequency sequence. Preferably, the signal reconstruction is performed using a linear superposition method, that is, all high-frequency components are summed and combined, and its expression is: (41); in, For the reconstructed high-frequency sequence, For the first The component that is determined to be high frequency, This represents the number of high-frequency components.

[0071] By using the above reconstruction method, high-frequency components with high complexity are integrated in a concentrated manner, providing a more focused input signal for subsequent secondary decomposition, thereby improving decomposition efficiency and the degree of decomposition refinement.

[0072] In this embodiment, the specific process of step S5 includes: The improved center collision optimization algorithm (LFGCCO) is used to iteratively optimize the parameters to be optimized in variational mode decomposition (VMD). Different parameter combinations are evaluated by a preset fitness function, and the parameter combination with the best fitness is determined as the optimal secondary decomposition parameters. A secondary decomposition model is constructed based on the optimal secondary decomposition parameters, and the reconstructed high-frequency sequence is decomposed into secondary components and secondary residual components using the secondary decomposition model to obtain the secondary decomposition modal components and secondary residual components.

[0073] Specifically, the parameters to be optimized in variational mode decomposition (VMD) and their search range are determined, including: the number of modal components ( ) and penalty factor ( Simultaneously, the operating control parameters of the LFGCCO algorithm are set, including population size and maximum number of iterations; the positions of individuals in the population are randomly generated using the LFGCCO algorithm, with each individual corresponding to a set of VMD parameter combinations. Substituting each set of parameters into the VMD method, the reconstructed high-frequency sequence is decomposed to obtain corresponding multiple sets of modal components and second-order residual components. This embodiment uses minimum envelope entropy as the fitness function to evaluate the decomposition effect of VMD on the reconstructed high-frequency sequence under different parameter combinations. During the iteration process, LFGCCO updates the individual positions of the population through its core stage, realizing dynamic optimization of the VMD parameter combination. Each iteration performs parameter updates, signal decomposition, fitness calculation, and optimal parameter recording. When the maximum number of iterations is reached or the termination condition is met, the parameter combination with the best fitness is output as the optimal second-order decomposition parameters. Based on the obtained optimal second-order decomposition parameters, a second-order decomposition model is constructed; the reconstructed high-frequency sequence is input into the second-order decomposition model to obtain the modal components and second-order residual components of the second-order decomposition.

[0074] VMD decomposes the input signal into several narrowband modal components with specific center frequencies by constructing a variational constrained optimization model. The specific steps are as follows: Construct a variational constrained optimization model: (42); in, For the first Each modal component, subscript , The number of modal components. For the first The center frequency of each modal component For the Dirac impulse function, Represents the Hilbert transform kernel function. The imaginary unit, For convolution operations, For the reconstructed high-frequency sequence, Represents the time variable The partial derivative operation, The square of the L2 norm, To express summation, Pi is a constant. For the first Each modal component at time... The value of .

[0075] In the above-mentioned constrained problem, a penalty factor is introduced. and Lagrange multipliers This transforms a constrained problem into an unconstrained problem: (43); in, As a penalty factor, For Lagrange multipliers, Represent the Lagrange function, For convolution operations, This indicates the inner product operation.

[0076] Alternating Directional Multiplier Method (ADMM) is used to update parameters. , , : (44); (45); (46); in, and They represent the first The modal component and the center frequency at the ... The update value for the next iteration. Indicates except the first The summation of all modal components other than the first modal component. The first Lagrange multiplier represents the first... iteration The first Lagrange multiplier represents the first... iteration This represents integration. , , They represent , , Representation in the frequency domain, For the reconstructed high-frequency sequence at time... The value of , For the Lagrange multipliers at time The value of , For frequency variables, This is the step size parameter; The iteration stops when the following convergence condition is met, and the obtained results are... The final modal components of the second-order decomposition. The convergence condition formula is as follows: (47); in, The preset convergence threshold is used; Calculate the second-order residual components : (48); The VMD parameter optimization mechanism based on LFGCCO optimization described above enables the two-level decomposition model to achieve adaptive optimization in terms of the number of modes and bandwidth constraint parameters, thereby improving the decomposition accuracy of high-frequency components, enhancing mode separation capability, and reducing mode aliasing. Combined with the complexity screening mechanism in step S4, the two-level decomposition focuses on refining complex high-frequency components, thereby improving the stability of the overall two-level decomposition structure and its multi-scale feature representation capability.

[0077] In this embodiment, the specific process of step S6 includes: using the improved center collision optimization algorithm (LFGCCO) to iteratively optimize the key hyperparameters of the bidirectional gated recurrent unit (BiGRU) network, evaluating different parameter combinations through a preset fitness function, determining the hyperparameter combination with the best fitness as the optimal prediction hyperparameter, and constructing a prediction model based on the optimal prediction hyperparameter.

[0078] Specifically, the jump components and low-frequency components of the first-level decomposition, and the modal components and second-level residual components of the second-level decomposition, are divided into training and testing sets according to a preset ratio. Preferably, the ratio is 8:2. Then, the hyperparameters to be optimized in the BiGRU network and their search range are determined, including the number of neurons, L2 regularization coefficient, and learning rate. Simultaneously, the population size and maximum number of iterations for the LFGCCO algorithm are set. The positions of individuals in the population are randomly generated using the LFGCCO algorithm, with each individual corresponding to a set of BiGRU hyperparameter combinations. This hyperparameter combination is used to construct the BiGRU network structure. Subsequently, the BiGRU network is trained using the training set, and the model performance under different hyperparameter combinations is evaluated using the minimum root mean square error (RMSE) as the fitness function. The formula for calculating RMSE is: (49); in, and They represent the first The true and predicted values ​​of each sample Indicates the number of sample data.

[0079] During the iteration process, LFGCCO continuously updates the individual positions of the population according to its core stage mechanism, thereby achieving dynamic optimization of the BiGRU hyperparameter combination. The hyperparameter update, model training, and fitness evaluation processes are repeated until the maximum number of iterations is reached or the termination condition is met. At this point, the hyperparameter combination with the best fitness is output as the globally optimal prediction hyperparameter, and the final prediction model is built based on this optimal prediction hyperparameter.

[0080] Among them, the number of neurons is used to control the model capacity and feature representation ability; the L2 regularization coefficient is used to constrain the weight size and reduce the risk of overfitting; and the learning rate is used to control the parameter update step size during model training.

[0081] By using LFGCCO to perform global collaborative optimization of the above BiGRU hyperparameters, the limitations of manual empirical parameter tuning can be avoided, the rationality and stability of model parameter configuration can be improved, and a model foundation can be provided for the prediction of each component in subsequent steps.

[0082] In this embodiment, the specific process of step S7 includes: The test set obtained in step S6 is input into the prediction model. Time series prediction is performed on the jump components and low-frequency components obtained from the first-level decomposition, and the modal components and second-level residual components obtained from the second-level decomposition, to obtain the prediction results corresponding to each component. Subsequently, signal reconstruction processing is performed on the prediction results of each component, and the reconstructed signal is inversely normalized to obtain the final bearing vibration signal prediction result. Preferably, the signal reconstruction is achieved by linear superposition, and its expression is: (50); in, This represents the final reconstructed predicted sequence of bearing vibration signals. Indicates the first The prediction results for each component, This indicates the number of components involved in the reconstruction.

[0083] like Figure 2 As shown, the present invention also provides a two-level decomposition and prediction system for bearing vibration signals based on an improved optimization algorithm, comprising: The data acquisition and preprocessing module is used to acquire vibration signal data during the operation of the centrifugal compressor drive end bearing, and to preprocess the vibration signal data to obtain an initial sequence. An improved algorithm building module is introduced to improve the algorithm mechanism by introducing Latin hypercube sampling strategy, focus selection strategy and guided collision strategy on the basis of traditional center collision optimization algorithm, and constructing an improved center collision optimization algorithm. The first-level decomposition optimization module is used to optimize the parameters of the jump-oscillation mode decomposition using the improved center collision optimization algorithm, determine the optimal first-level decomposition parameters, and construct a first-level decomposition model based on the optimal first-level decomposition parameters; the initial sequence is input into the first-level decomposition model to obtain the jump component, oscillation component and residual component of the first-level decomposition. The high-frequency component screening and reconstruction module is used to calculate the complexity evaluation index of the oscillation components and residual components obtained from the first-level decomposition, sort the complexity evaluation index values ​​corresponding to each component, select the components with higher complexity as high-frequency components and the components with lower complexity as low-frequency components according to the sorting results, and reconstruct the high-frequency components to obtain the reconstructed high-frequency sequence. The second-level decomposition optimization module is used to optimize the parameters of variational mode decomposition using the improved center collision optimization algorithm, determine the optimal second-level decomposition parameters, and construct a second-level decomposition model based on the optimal second-level decomposition parameters; the reconstructed high-frequency sequence is input into the second-level decomposition model to obtain the modal components and second-level residual components of the second-level decomposition; The prediction model building module is used to optimize the hyperparameters of the bidirectional gated recurrent unit network using the improved center collision optimization algorithm, determine the optimal combination of prediction hyperparameters, and build a prediction model based on the optimal combination of prediction hyperparameters. The signal prediction and reconstruction module is used to input the jump components and low-frequency components of the first-level decomposition, as well as the modal components and second-level residual components of the second-level decomposition, into the prediction model to obtain the prediction results of each component. The module then performs signal reconstruction processing on the prediction results of each component and performs inverse normalization on the reconstructed signal to obtain the final bearing vibration signal prediction result.

[0084] This embodiment also provides a computer-readable storage medium storing a computer program that is executed by a processor to implement a two-level decomposition and prediction method for bearing vibration signals based on an improved optimization algorithm.

[0085] The simulation verification is as follows: Simulation Analysis Example 1: To verify the optimization performance of the Improved Center Collision Optimization Algorithm (LFGCCO) proposed in this embodiment, the LFGCCO algorithm is compared with seven advanced optimization algorithms on representative functions in the CEC2017 benchmark function set. The unimodal function F1, multimodal function F10, mixed function F18, and composite function F28 are selected as test objects. The unimodal function is used to evaluate the algorithm's convergence speed and optimization accuracy under conditions without local extrema; the multimodal function is used to evaluate the algorithm's global search capability and ability to escape local optima under conditions with a large number of local extrema; the mixed function is used to evaluate the algorithm's adaptive capability and convergence stability in complex search spaces; and the composite function is used to evaluate the algorithm's global optimization capability and robustness under highly nonlinear and strongly disturbed environments. The algorithms compared include Center Collision Optimization (CCO), Improved Snow Melting Optimization (ISAO), Improved Rime Optimization (IRIME), Improved Crayfish Optimization (ICOA), Improved Sparrow Search Optimization (DLSSA), Co-evolutionary Multi-Swarm Particle Swarm Optimization (CMPSO), and Adaptive Accelerated Particle Swarm Optimization (AAPSO). In the simulation experiments, the optimization problem dimension was set to 10, the population size to 20, and the maximum number of evaluations to 4000. To ensure fairness in the experimental comparison, all algorithms were run under the same parameter settings and constraints, and the optimal fitness value and convergence curve were recorded for performance analysis.

[0086] Figure 3 The results show the convergence curves of the LFGCCO algorithm and seven advanced optimization algorithms on the selected test function. Figure 3 (a) and (b) show that the LFGCCO algorithm maintains strong population diversity during the iteration process, effectively avoids getting trapped in local optima, and ultimately outperforms the comparison algorithms in terms of convergence accuracy, convergence speed, and optimal solution quality. Figure 3 (c) and (d) show that the LFGCCO algorithm can still maintain a stable convergence trend when facing a search space with complex function structures and high noise interference. It exhibits strong global search ability, convergence stability and robustness, and has obvious advantages in high-complexity optimization problems.

[0087] Example 2: Simulation Analysis: To evaluate the generalization ability and robustness of the proposed Improved Center Collision Optimization Algorithm (LFGCCO) in different types of optimization problems, a simulation experimental platform was built based on the CEC2022 benchmark test function set. This test function set contains 12 single-objective real-valued optimization functions, covering various types such as unimodal functions, multimodal functions, offset / rotation functions, and non-separating functions, effectively simulating complex search spaces and high-dimensional nonlinear optimization problems. In the experiment, the LFGCCO algorithm was compared with seven advanced optimization algorithms: Center Collision Optimization Algorithm (CCO), Improved Snow Melting Algorithm (ISAO), Improved Rime Optimization Algorithm (IRIME), Improved Crayfish Optimization Algorithm (ICOA), Improved Sparrow Search Algorithm (DLSSA), Co-evolutionary Multi-Swarm Particle Swarm Optimization Algorithm (CMPSO), and Adaptive Accelerated Particle Swarm Optimization Algorithm (AAPSO). The experimental parameters were set as follows: optimization problem dimension 10, population size 50, and maximum number of evaluations 50,000. To reduce the impact of randomness on the experimental results, each algorithm was run independently 30 times on each test function, and the mean fitness value was used as the performance evaluation metric. Furthermore, the Friedman nonparametric rank-sum test was used to statistically rank and analyze the mean fitness values ​​of each algorithm across all test functions to further evaluate the performance differences between the different algorithms.

[0088] Table 1 shows the average Friedman rank of the LFGCCO algorithm and seven existing advanced optimization algorithms on the CEC2022 standard test function set. The results show that the LFGCCO algorithm achieves the lowest average rank (1.83) among all algorithms, significantly outperforming the second-ranked CMPSO algorithm (3.50). Compared to the CCO algorithm (average rank of 4.17), the LFGCCO algorithm demonstrates a significant improvement, ultimately improving its ranking by nearly two places. It exhibits faster convergence speed, higher optimization accuracy, and smaller performance fluctuations, reflecting its strong robustness and stability.

[0089] Table 1 Application Example: This embodiment uses the vibration signal of a compressor drive end bearing collected in a certain city as an example to illustrate the method proposed in this invention. First, 1500 consecutive sampling points are selected from the collected vibration signal data as research samples, and these vibration signals are normalized by maximum and minimum values ​​to obtain an initial sequence.

[0090] Next, the improved center collision optimization algorithm (LFGCCO) proposed in this invention is used to optimize the parameters of jump-oscillatory mode decomposition (JMD). The optimized parameters include the oscillatory mode constraint parameters (…). ), number of oscillating components ( ), jump constraint parameters ( ), regulatory factors ( ) and minimum jump height parameter ( Specifically, the LFGCCO population size was set to N=30, the maximum number of iterations Max_Iter=20, and the minimum envelope entropy was used as the optimization objective function. Through this optimization, the optimal combination of first-order decomposition parameters was obtained, as shown in Table 2. A first-order decomposition model was constructed based on the optimal parameters, and the initial sequence was input into the model for decomposition to obtain the first-order decomposition results, as shown in Table 2. Figure 4 As shown.

[0091] Table 2 The sample entropy values ​​of the oscillation components and residual components obtained from the first-level decomposition were further calculated as evaluation indicators of signal complexity, and the results are shown in Table 3. The sample entropy values ​​of each component were sorted in ascending order, and the components were divided into high-frequency and low-frequency components based on the sorting results. Components with larger sample entropy values ​​indicate higher signal complexity and usually correspond to high-frequency oscillation components; while components with smaller sample entropy values ​​indicate lower signal complexity and usually correspond to low-frequency components. Based on the sorting results of the sample entropy values, the latter half of the components with larger sample entropy values ​​were identified as high-frequency components, and the remaining components were identified as low-frequency components. The components identified as high-frequency were reconstructed to obtain the reconstructed high-frequency sequence.

[0092] Table 3 Subsequently, the improved center collision optimization algorithm (LFGCCO) was used to optimize the parameters of variational mode decomposition (VMD), including the number of modal components. ) and penalty factor ( The LFGCCO population size was set to N=30, and the maximum number of iterations Max_Iter=20. The minimum envelope entropy was used as the optimization objective function. After optimization, the optimal combination of second-order decomposition parameters was obtained, as shown in Table 4. A second-order decomposition model was constructed based on the optimal parameters, and the reconstructed high-frequency sequence was input into the model for decomposition to obtain the second-order decomposition results, as shown in Table 4. Figure 5 As shown.

[0093] Table 4 After completing the two-level decomposition, the jump components and low-frequency components obtained from the first-level decomposition, as well as the modal components and second-level residual components obtained from the second-level decomposition, are divided into training and testing sets in an 8:2 ratio.

[0094] Furthermore, the improved center collision optimization algorithm (LFGCCO) was used to optimize the key hyperparameters of the bidirectional gated recurrent unit network (BiGRU). The optimized hyperparameters included the number of neurons, the L2 regularization coefficient, and the learning rate. The LFGCCO population size was set to P=10, and the maximum number of iterations Max_Iter=100. The BiGRU network was trained using the training set, and the optimal combination of prediction hyperparameters was obtained by minimizing the root mean square error (RMSE) as the fitness function, as shown in Table 5. A prediction model was then constructed based on these optimal prediction hyperparameters.

[0095] Table 5 Finally, the test set is input into the prediction model for time series prediction to obtain the prediction results for each component. The prediction results are then reconstructed and inversely normalized to obtain the final prediction result for the bearing vibration signal.

[0096] To verify the effectiveness of this invention, multiple sets of comparative experiments were designed. The models compared included: (1) CCO-JMD-VMD-BiGRU model: The center collision optimization algorithm (CCO) is used to optimize the JMD and VMD parameters, and the decomposition results are input into the BiGRU network optimized by CCO for vibration signal prediction. (2) ISAO-JMD-VMD-BiGRU model: The improved snow ablation algorithm (ISAO) is used to optimize the JMD and VMD parameters, and the decomposition results are input into the ISAO-optimized BiGRU network for vibration signal prediction. (3) ICOA-JMD-VMD-BiGRU model: The improved crayfish optimization algorithm (ICOA) is used to optimize the JMD and VMD parameters, and the decomposition results are input into the ICOA-optimized BiGRU network for vibration signal prediction. Finally, the bearing vibration signal prediction results of each model group were obtained, such as... Figure 6 As shown. To ensure the fairness of the comparative experiments, all experiments were conducted under the same parameter configuration and equipment conditions.

[0097] To intuitively evaluate the prediction performance, root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and coefficient of determination (R²) were selected as evaluation metrics. RMSE reflects the overall deviation between the model's predicted values ​​and the original signal; a smaller value indicates higher overall reconstruction accuracy. MAE represents the average absolute deviation between the predicted and true values, directly reflecting the overall error level. MAPE represents the average percentage of prediction error relative to the true value, used to assess the model's prediction accuracy on a relative scale. R²... 2The value measures how well the model fits the real data; the closer the value is to 1, the better the fit.

[0098] The evaluation metrics for each group of experiments are shown in Table 6. The LFGCCO-JMD-VMD-BiGRU model outperformed the comparison models in all evaluation metrics. Specifically, the RMSE of the LFGCCO-JMD-VMD-BiGRU model was 0.0163, which was 46.4%, 46.4%, and 64.1% lower than that of the CCO-JMD-VMD-BiGRU, ISAO-JMD-VMD-BiGRU, and ICOA-JMD-VMD-BiGRU models, respectively, indicating that the present invention has a significant advantage in overall prediction accuracy. Meanwhile, the MAE index also showed a significant reduction, further verifying the effectiveness of the model in reducing prediction errors. The significant increase in the R² value indicates that the LFGCCO-JMD-VMD-BiGRU model has a higher trend fit to the vibration signal. In summary, the LFGCCO-JMD-VMD-BiGRU model exhibits superior performance in terms of overall prediction accuracy, error reduction, and signal trend fitting for vibration signals.

[0099] Table 6 The formula for calculating the percentage reduction is as follows: (51); To further analyze the impact of two-level decomposition on the prediction accuracy of vibration signals, two simplified models were designed for comparison: (1) LFGCCO-JMD-BiGRU model: The JMD parameters are optimized using LFGCCO, and the decomposition results are input into the LFGCCO-optimized BiGRU network for vibration signal prediction. This model performs only one decomposition, decomposing the signal through the LFGCCO-optimized JMD.

[0100] (2) LFGCCO-VMD-BiGRU model: The VMD parameters are optimized using LFGCCO, and the decomposition results are input into the LFGCCO-optimized BiGRU network for vibration signal prediction. This model performs only one decomposition, decomposing the signal through the LFGCCO-optimized VMD.

[0101] Finally, the bearing vibration signal prediction results of each model group are obtained as follows: Figure 7As shown in Table 7, the evaluation metrics for each experimental group are presented. The results indicate that the LFGCCO-JMD-VMD-BiGRU model outperforms both the LFGCCO-JMD-BiGRU and LFGCCO-VMD-BiGRU models in all evaluation metrics. Specifically, the RMSE and MAE of the LFGCCO-JMD-VMD-BiGRU model are 0.0163 and 0.0133, respectively, representing reductions of 65.1% and 65.2% compared to the LFGCCO-JMD-BiGRU model, and 69.5% and 68.3% compared to the LFGCCO-VMD-BiGRU model. Simultaneously, the R² of the LFGCCO-JMD-VMD-BiGRU model reaches 0.9818, representing improvements of 15.5% and 22.1% compared to the LFGCCO-JMD-BiGRU and LFGCCO-VMD-BiGRU models, respectively, indicating a better fit to the real data. This verifies the effectiveness of the two-level decomposition method of this invention in improving model prediction accuracy.

[0102] Table 7 The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A two-level decomposition and prediction method for bearing vibration signals based on an improved optimization algorithm, characterized in that, include: Vibration signal data of the centrifugal compressor drive end bearing during operation is acquired, and the vibration signal data is preprocessed to obtain an initial sequence; An improved center collision optimization algorithm is used to optimize the jump-oscillation mode decomposition parameters and variational mode decomposition parameters respectively, to obtain the optimal first-level decomposition parameters and the optimal second-level decomposition parameters; the improved center collision optimization algorithm is obtained by introducing a Latin hypercube sampling strategy, a focus selection strategy and a guided collision strategy; A first-level decomposition model is constructed using the optimal first-level decomposition parameters. The initial sequence is input into the first-level decomposition model to obtain the jump components, oscillation components, and residual components of the first-level decomposition. The complexity evaluation index of the oscillation components and the residual components is calculated to obtain the high-frequency components and low-frequency components. A second-level decomposition model is constructed using the optimal second-level decomposition parameters. The reconstructed high-frequency sequence of the high-frequency components is input into the second-level decomposition model to obtain the modal components and second-level residual components of the second-level decomposition. The jump component, the low-frequency component, the modal component, and the second-order residual component are input into the prediction model to obtain the prediction results of each component; the prediction model is constructed by the optimal combination of prediction hyperparameters obtained by the improved center collision optimization algorithm for the hyperparameter optimization of the bidirectional gated cyclic unit network; The prediction results of each component are processed by signal reconstruction and inverse normalization to obtain the final bearing vibration signal prediction result.

2. The two-level decomposition and prediction method for bearing vibration signals based on an improved optimization algorithm according to claim 1, characterized in that, The improved center collision optimization algorithm includes: The center collision optimization algorithm incorporates a Latin hypercube sampling strategy, a focus selection strategy, and a guided collision strategy to update the individual positions in the population: By using the hierarchical probability sampling method of the Latin hypercube sampling strategy, each search interval is divided into several equally probable sub-intervals, and sampling points are randomly selected in each probability sub-interval. The initial population is then generated through random permutation and combination. The initial population is divided into a first population and a second population according to the current spatial allocation ratio. Individuals in the first population are subjected to a center collision strategy in the original space. The individual positions are updated by simulating a random pair collision mechanism between individuals in the population, so as to cause the individuals in the first population to generate random perturbations in the search space and move towards the high-quality region. The covariance matrix of the second population is used and eigenvalue decomposition is performed to obtain an orthogonal transformation matrix. The original space is orthogonally transformed and mapped to a decorrelation space through the orthogonal transformation matrix. The center collision strategy is performed in the decorrelation space to update the individual positions. The updated individuals are then mapped back to the original space. Greedy selection is performed on the updated individuals in the original space and the decorrelation space. If the fitness of the updated individual is better than that of the original individual, the updated individual is retained and the count of individuals that successfully produce better offspring in the corresponding space is increased. Otherwise, the original individual is retained. Based on the individual count statistics and the individual allocation ratio of the two spaces in the previous round, the proportion of population individuals allocated to the original space and the decorrelation space in the next iteration is adaptively adjusted. Based on the focused selection strategy, a two-dimensional evaluation mechanism based on spatial topological location and potential energy distribution is constructed to differentiate and screen individuals in the updated population, obtaining high-potential-energy individuals and centrally stagnant individuals. A gravitational field is constructed through the guided collision strategy to perform directional updates on the high-potential-energy individuals. The average distance of the individuals in the population relative to the population centroid is calculated through a population diversity monitoring mechanism. When the average distance is lower than a preset diversity threshold, it is determined that the population diversity is insufficient and there is a risk of premature convergence. Therefore, multiple individuals farthest from the centroid are selected as spatial anchor points to construct a repulsive force vector pointing outward from the centroid, so as to cause the centrally stagnant individuals to break out of their current stagnant state.

3. The two-level decomposition and prediction method for bearing vibration signals based on an improved optimization algorithm according to claim 2, characterized in that, The Latin hypercube sampling strategy includes: ； in, Indicates the first The individual in the first Initial position on the dimension and They represent the first Lower and upper bounds of a dimensional variable. Indicates the first A random permutation function in dimension 1 is used to determine the nth dimension. The sub-interval number to which each individual is assigned in this dimension. This indicates the population size, i.e., the total number of individuals. To show obedience Uniformly distributed random numbers are used to perform random sampling within an assigned sub-interval.

4. The two-level decomposition and prediction method for bearing vibration signals based on an improved optimization algorithm according to claim 2, characterized in that, Performing a greedy selection on the original space and the updated individuals in the decorrelation space includes: ； ； ； in, and They represent the first time. In each iteration, the success update counters for both the original space and the decorrelation space are initialized to 1. For the fitness calculation function, and These represent the central collision phase, respectively. The current location and updated location of each individual and These represent the relevant spatial stages. The current location and updated location of each individual and They represent the first The final successful update count result is obtained from the original space and the decorrelation space after the round of iterations.

5. The two-level decomposition and prediction method for bearing vibration signals based on an improved optimization algorithm according to claim 2, characterized in that, Adaptively adjusting the ratio of individuals in the population allocated to the original space and the decorrelation space in the next iteration includes: ； ； ； ； in, and They represent the first time. The distribution ratio of individuals in the original space and the decorrelation space of the population in each iteration. and They respectively represent the use for the first The distribution ratio of individuals in the original space and the decorrelation space of the population in each iteration. This indicates that the initial individual assignments in the original space and the decorrelation space are the same during the first iteration. This indicates that the population distribution ratio between the original space and the decorrelation space in each iteration is limited to the range of 30%-70%.

6. The two-level decomposition and prediction method for bearing vibration signals based on an improved optimization algorithm according to claim 2, characterized in that, Based on the aforementioned focused selection strategy, a two-dimensional evaluation mechanism based on spatial topological location and potential energy distribution is constructed to perform differential screening of individuals in the updated population, including: Calculate the geometric centroid of the population and determine the Euclidean distance between each individual in the population and the geometric centroid; The Euclidean distance is used to measure the spatial deviation of individuals in the search space, the topological location characteristics of individuals are obtained, and the two-dimensional evaluation mechanism is constructed by combining the individual fitness value to classify and screen individuals in the population.

7. The two-level decomposition and prediction method for bearing vibration signals based on an improved optimization algorithm according to claim 2, characterized in that, The high-potential-energy individual is updated in a targeted manner by constructing a gravitational field through the guided collision strategy, which includes: ； in, and These represent the current position and the updated position of the high-potential-energy individual during the guided collision phase, respectively. and These represent the positions of individuals randomly selected from the top 10% of the fitness-ranked elite individuals and the top 50% of the fitness-ranked secondary elite individuals, respectively, during the guided collision phase. and for Random values ​​within the interval The convergence factor decreases linearly with the number of iterations. It is a Gaussian random perturbation with a mean of zero.

8. The two-level decomposition and prediction method for bearing vibration signals based on an improved optimization algorithm according to claim 2, characterized in that, By constructing a repulsive force vector pointing outward from the center of mass, the centrally stationary individual is prompted to break free from its current stagnant state, including: ； in, and These represent the current and updated positions of the individual stranded at the center during the guided collision phase, respectively. Indicates the first The position of the geometric centroid of the population at the next iteration and This indicates the relationship between the population and the centroid during the guided collision phase. The positions of the two individuals with the greatest distance. and for Random values ​​within the interval The convergence factor decreases linearly with the number of iterations. It is a Gaussian random perturbation with a mean of zero.

9. A two-level decomposition and prediction system for bearing vibration signals based on an improved optimization algorithm, implemented according to any one of claims 1-8, characterized in that, include: The data acquisition and preprocessing module is used to acquire vibration signal data during the operation of the centrifugal compressor drive end bearing, and to preprocess the vibration signal data to obtain an initial sequence. The decomposition and optimization module is used to optimize the jump-oscillation mode decomposition parameters and variational mode decomposition parameters respectively using an improved center collision optimization algorithm to obtain the optimal first-level decomposition parameters and the optimal second-level decomposition parameters. The improved center collision optimization algorithm is obtained by introducing a Latin hypercube sampling strategy, a focus selection strategy, and a guided collision strategy. A first-level decomposition model is constructed using the optimal first-level decomposition parameters. The initial sequence is input into the first-level decomposition model to obtain the jump components, oscillation components, and residual components of the first-level decomposition. The complexity evaluation index of the oscillation components and the residual components is calculated to obtain the high-frequency components and low-frequency components. A second-level decomposition model is constructed using the optimal second-level decomposition parameters. The reconstructed high-frequency sequence of the high-frequency components is input into the second-level decomposition model to obtain the modal components and second-level residual components of the second-level decomposition. The signal prediction and reconstruction module is used to input the jump component, the low-frequency component, the modal component and the second-order residual component into the prediction model to obtain the prediction results of each component; the prediction model is constructed by the optimal combination of prediction hyperparameters obtained by the improved center collision optimization algorithm for hyperparameter optimization of the bidirectional gated cyclic unit network; The prediction results of each component are processed by signal reconstruction and inverse normalization to obtain the final bearing vibration signal prediction result.

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