A rolling bearing vibration signal prediction method based on an improved kingfisher optimization network model

Abstract

The present application relates to the technical field of industrial production safety monitoring, and particularly relates to a rolling bearing vibration signal prediction method based on an improved kingfisher optimization network model, comprising: obtaining a vibration signal of a target rolling bearing and constructing a time series; performing variational mode decomposition on the time series of the vibration signal to obtain a plurality of components; inputting the components into a pre-constructed signal prediction model to output a prediction result of the vibration signal, wherein the signal prediction model is constructed based on an improved kingfisher optimization algorithm optimizing a bidirectional gate recurrent unit, and the improved kingfisher optimization algorithm is constructed by introducing a Bloch unit sphere coordinate quantum bit coding mechanism, a local grid clustering selection strategy, a fly-away predator strategy and an improved multi-difference Cauchy mutation strategy in the kingfisher optimization algorithm. The present application enhances the generalization ability of the model through multi-strategy optimization, and significantly improves the prediction accuracy and robustness of the rolling bearing vibration signal.

Description

Technical Field

[0001] This invention relates to the field of industrial production safety monitoring technology, and in particular to a method for predicting rolling bearing vibration signals based on an improved kingfisher optimized network model. Background Technology

[0002] Rolling bearings are one of the key basic components in heavy rotating equipment, widely used in chemical, mining, and energy industries. Due to their long-term operation under high loads and harsh conditions, rolling bearings are among the most vulnerable parts of such equipment. Failures can significantly reduce production efficiency, potentially causing system safety issues and even personal injury or death. Therefore, accurate prediction of rolling bearing vibration signals is crucial for equipment condition monitoring and fault early warning.

[0003] In the early stages of bearing failure, the fault characteristics typically manifest as weak vibration signals. Influenced by complex operating conditions and noise interference, these vibration signals often exhibit significant nonlinearity and non-stationarity, posing considerable challenges to accurate prediction. Existing research commonly employs signal decomposition techniques including Empirical Mode Decomposition (EMD) and its improved versions, such as Integrated Empirical Mode Decomposition (IMD) and Fully Adaptive Noise Ensemble Empirical Mode Decomposition (MAD). However, when processing complex signals using these methods, issues such as mode aliasing, residual noise, and reliance on manual, empirically set noise intensity can arise. Variational Mode Decomposition (VMD) mitigates the mode aliasing problem to some extent, but it requires an empirically preset number of decomposition modes. Setting the number too small can easily lead to mode aliasing, while setting it too large introduces redundant components and significantly increases computational costs.

[0004] In terms of optimization algorithms, the Kingfisher Optimization Algorithm (PKO), as a biomimetic intelligent optimization algorithm, has good global search capabilities, but it has certain shortcomings in practical applications: unstable individual quality during population initialization, lack of diversity, population activity decline leading to search stagnation in the later stages of the algorithm, premature convergence due to local optima in the later stages of the algorithm, and poor overall convergence performance.

[0005] In deep time series modeling, Bidirectional Gated Recurrent Unit (BiGRU) networks have been widely used for time series prediction due to their strong context modeling capabilities. However, existing studies often use default or empirically set network structure parameters, which can easily lead to problems such as excessively large model parameters resulting in increased model complexity, overfitting, and excessively high training costs; or insufficient model parameters resulting in insufficient model expressive power and decreased prediction accuracy. Summary of the Invention

[0006] The purpose of this invention is to provide a rolling bearing vibration signal prediction method based on an improved kingfisher optimization network model, which solves the problems in the prior art such as insufficient prediction accuracy due to the nonlinearity and non-stationarity of vibration signals, certain shortcomings of the kingfisher optimization algorithm in practical applications, and the influence of BiGRU network parameters on prediction performance due to reliance on empirical settings. This effectively improves the prediction accuracy of rolling bearing vibration signals and the convergence stability of the model.

[0007] To achieve the above objectives, the present invention provides the following solution:

[0008] A method for predicting rolling bearing vibration signals based on an improved kingfisher optimized network model includes:

[0009] The vibration signal of the target rolling bearing is acquired and constructed as a time series;

[0010] The time series of the vibration signal is subjected to variational mode decomposition to obtain several components;

[0011] The component is input into a pre-constructed signal prediction model, and the prediction result of the vibration signal is output. The signal prediction model is constructed based on the improved kingfisher optimization algorithm to optimize the bidirectional gated cyclic unit. The improved kingfisher optimization algorithm is constructed by introducing the Bloch unit spherical coordinate qubit encoding mechanism, local grid clustering selection strategy, fly-away predator strategy and improved multi-difference Cauchy mutation strategy into the kingfisher optimization algorithm.

[0012] Optionally, variational mode decomposition is performed on the time series of the vibration signal to obtain several components, including:

[0013] The number of components of the variational mode decomposition is determined based on the center frequency distribution of the vibration signal, and a variational constraint model is constructed with the goal of minimizing the sum of the estimated bandwidths of each mode component.

[0014] By introducing a penalty factor and Lagrange multipliers, the variational constraint model is transformed into an unconstrained form. The alternating direction multiplier method is used to iteratively update the signal, center frequency, and Lagrange multipliers of each modal component until convergence is achieved, thereby obtaining several intrinsic modal components and a residual component, and the sum of all components is equal to the vibration signal.

[0015] Optionally, the signal prediction model is constructed by optimizing the bidirectional gated cyclic unit based on the improved kingfisher optimization algorithm, including:

[0016] An improved kingfisher optimization algorithm is used to jointly optimize the number of neurons in the hidden layer of the bidirectional gated recurrent unit, the learning rate, and the L2 regularization coefficient to obtain the signal prediction model.

[0017] The signal prediction model is used to model and predict each component separately, obtain the predicted values ​​of each component, and then reconstruct the final predicted vibration signal. The final predicted vibration signal is:

[0018]

[0019] In the formula, u′ s Represents the prediction result of the s-th intrinsic mode component, with subscripts s = 1, 2, ..., k. Res′ represents the prediction result of the residual component, S(n) is the final predicted value of the vibration signal, and k is the number of intrinsic mode components.

[0020] Optionally, the improved kingfisher optimization algorithm can be constructed by introducing a Bloch unit spherical coordinate qubit encoding mechanism, a local grid clustering selection strategy, a predator-avoidance strategy, and an improved multi-difference Cauchy mutation strategy into the kingfisher optimization algorithm, including:

[0021] S3.1. By introducing the Bloch unit spherical coordinate qubit encoding mechanism and the local grid clustering selection strategy, the initial population is obtained, and then proceed to S3.2.

[0022] S3.2, Conduct the exploration and development phases of the kingfisher, and proceed to S3.3 after completion. The exploration phase simulates the kingfisher's natural circling and perching behavior, and the development phase simulates the kingfisher's dive attack behavior on prey.

[0023] S3.3, Conduct the partial escape phase of the kingfisher, and after completion, proceed to S3.4. The partial escape phase simulates the temporary communal behavior between the kingfisher and the otter, and incorporates the strategy of flying away from the predator.

[0024] S3.4 Introduce an improved multi-difference Cauchy mutation strategy, wherein the improved multi-difference Cauchy mutation strategy includes a multi-difference mutation structure, a linearly decreasing mutation probability, a Cauchy factor, an adaptive control factor, and a boundary bounce mechanism.

[0025] Optionally, by introducing the Bloch unit spherical coordinate qubit encoding mechanism and the local grid clustering selection strategy, the initial population can be obtained as follows:

[0026] Define the state of a qubit and map it to three-dimensional Bloch unit spherical coordinates;

[0027] Let P be the i-th individual in the population. i The optimization problem has a dimension of n, and for individual P i Each dimension generates Bloch unit spherical coordinates;

[0028] The Bloch unit spherical coordinates are decomposed into coordinate components in three directions to obtain P. iCandidates in three directions;

[0029] The candidate individuals located in the Bloch unit spherical coordinate interval are mapped to the variable range of the optimization problem, and the candidate individuals that have completed the mapping in the three directions are merged into an expanded candidate individual set. The fitness value of all candidate individuals in the set is calculated.

[0030] Select two dimensions d from the search space dimensions. x d y The grid cells are divided at equal intervals, and individuals are selected within each grid based on their fitness values ​​to obtain a set of candidate individuals for each grid.

[0031] Merge all candidate individuals selected within the grid and control the population size according to the preset size. If the number of individuals is insufficient, randomly supplement the unselected candidate individuals to the target size. If the number of individuals exceeds the limit, retain the top N best individuals in ascending order of fitness value.

[0032] Optionally, the location of individual kingfisher populations during the exploration phase is updated based on their resting or circling behavior, using the following method:

[0033]

[0034] in, and These represent the current position and the updated position of the i-th individual during the exploration phase, respectively. The position of the Qth individual is randomly selected during the exploration phase, where Q is not equal to i. N is the population size, α is a random perturbation vector that follows a normal distribution, the T parameter is used to control the population's habitat or hovering behavior, o indicates element-wise multiplication, and t is the time step.

[0035] Optionally, the location of individual kingfisher populations during the development phase is updated based on hunting ability, and the update method is as follows:

[0036]

[0037] in, and These represent the current position and the updated position of the i-th individual during the development phase, respectively. represents the position of the individual with the best fitness value at the current stage of development, HA represents hunting ability, B is the position update variable, o is the decay factor, α is a random perturbation vector that follows a normal distribution, ⊙ represents element-wise multiplication, N is the population size, and t is the time step.

[0038] Optionally, the location of individual kingfisher populations exhibiting temporary commensal behavior during the local escape phase is updated based on predation efficiency, using the following method:

[0039]

[0040] in, and Let these represent the current position and the updated position of the i-th individual in the temporary symbiotic behavior, respectively. and Let U and V represent the positions of the Uth and Vth individuals randomly selected during the temporary commensal behavior, respectively, where U is not equal to V and V is not equal to i. Let rand represent a random value in the interval [0, 1]. Let α be a random perturbation vector that follows a normal distribution. Let o be a decay factor. Let ⊙ represent element-wise multiplication. Let PE be the predation efficiency of the kingfisher during the temporary commensal behavior. Let abs(·) be the absolute value operation. Let t be the time step.

[0041] Optionally, the method for updating the individual positions of the kingfisher population by incorporating the strategy of flying away from predators during the local escape phase is as follows:

[0042]

[0043] in, and Let represent the current position and the updated position of the i-th individual in the strategy of flying away from the predator, respectively. denoted by , where α is a random perturbation vector following a normal distribution, ⊙ represents element-wise multiplication, K represents random selection of 1 or 2, rand represents a random value in the interval [0, 1], PE is the predation efficiency of the kingfisher in the temporary commensal behavior, and t is the time step.

[0044] Optionally, the improved multi-difference Cauchy mutation strategy includes:

[0045] By introducing Cauchy factors, adaptive control factors, and a multi-difference mutation structure, new kingfisher individuals are generated. If a new kingfisher individual exceeds the variable boundary, a boundary bounce mechanism is used to correct its position. The individual is updated based on its fitness value to obtain the final retained individual position. The position update method for generating the new kingfisher individuals is as follows:

[0046]

[0047] in, and Let these represent the current position and the updated position of the i-th individual in the improved multi-difference Cauchy mutation strategy, respectively. This indicates the position of the individual with the best current fitness value in the improved multi-difference Cauchy mutation strategy. This represents the positions of the A, B, and Cth individuals randomly selected in the improved multi-difference Cauchy mutation strategy, where A is not equal to B, C is not equal to i, F is the Cauchy factor, and B... tr1 is an adaptive control factor, r1 is a random number uniformly distributed in the interval [0, 1], rand represents a random value in the interval [0, 1], r1 and rand are independent of each other, t is the time step, Max_Iter is the maximum number of iterations, and p is the mutation probability that decreases with iteration.

[0048] The beneficial effects of this invention are as follows:

[0049] (1) In the initialization stage of the kingfisher optimization algorithm, the present invention introduces the Bloch unit spherical coordinate qubit encoding mechanism and local grid clustering selection strategy, which expands the coverage of the search space and significantly enhances the diversity and quality of the initial population compared with the existing random initialization strategy.

[0050] (2) This invention integrates a predator-avoidance strategy into the local escape phase of the kingfisher optimization algorithm, using the globally optimal individual as the guiding direction to provide directional perturbation and dynamic development compensation for the local escape phase. Compared with existing local escape phases, this strategy can significantly improve the algorithm's development capability and convergence efficiency in the mid-to-late stages of iteration;

[0051] (3) In the later stage of the kingfisher optimization algorithm, the present invention introduces an improved multi-difference Cauchy mutation strategy. By combining the multi-difference mutation structure, Cauchy factor, adaptive control factor and mutation probability that decreases with iteration, the ability of individuals to escape local optima is effectively enhanced, and the diversity and local optimization accuracy of the algorithm in the later iteration are improved. At the same time, the combination of boundary bounce mechanism and individual update strategy based on fitness value further improves the stability and solution quality of the algorithm.

[0052] (4) This invention utilizes the improved Kingfisher Optimization (IPKO) algorithm to jointly optimize the number of hidden layer neurons, learning rate, and L2 regularization coefficient of the BiGRU network, effectively avoiding underfitting or overfitting problems caused by manual parameter tuning. Compared with existing optimization algorithms, the improved algorithm (IPKO) can achieve more efficient global search and convergence control in the parameter space of the network model, significantly improving the fitting accuracy and generalization ability of the BiGRU network in the prediction of non-stationary vibration signals. Attached Figure Description

[0053] 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.

[0054] Figure 1 This is a flowchart of a rolling bearing vibration signal prediction method based on an improved kingfisher optimization network model according to an embodiment of the present invention;

[0055] Figure 2 This is a flowchart of the improved kingfisher optimization algorithm according to an embodiment of the present invention;

[0056] Figure 3 This is a flowchart of the population initialization process based on Bloch unit spherical coordinate qubit encoding according to an embodiment of the present invention;

[0057] Figure 4 This is a flowchart of the partial escape phase of the kingfisher in accordance with the strategy of merging flight away from predators, as described in an embodiment of the present invention.

[0058] Figure 5 This is a flowchart of the improved multi-difference Cauchy mutation strategy according to an embodiment of the present invention;

[0059] Figure 6 This is a flowchart of the BiGRU network parameter optimization based on the improved kingfisher optimization algorithm according to an embodiment of the present invention.

[0060] Figure 7 This is a schematic diagram of the IPKO-BiGRU network model structure according to an embodiment of the present invention;

[0061] Figure 8 This is a three-dimensional visualization of the test functions selected from the CEC2017 standard test function set in this embodiment of the invention;

[0062] Figure 9 The graph shows the convergence curve comparison results of the IPKO algorithm and the comparative optimization algorithm on the selected test functions according to the embodiments of the present invention. Among them, (a) is the convergence result on the CEC2017-F1 test function, (b) is the convergence result on the CEC2017-F8 test function, (c) is the convergence result on the CEC2017-F12 test function, and (d) is the convergence result on the CEC2017-F22 test function.

[0063] Figure 10 This is a variational mode decomposition result diagram of the vibration signal of the compressor drive end bearing in an embodiment of the present invention;

[0064] Figure 11 This is a comparison chart of the results of the IPKO-BiGRU model and the PKO-BiGRU model in bearing vibration signal prediction according to an embodiment of the present invention. Detailed Implementation

[0065] 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.

[0066] 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.

[0067] This embodiment provides a method for predicting rolling bearing vibration signals based on an improved kingfisher optimized network model, including:

[0068] The vibration signal of the target rolling bearing is acquired and constructed as a time series;

[0069] The time series of the vibration signal is subjected to variational mode decomposition to obtain several components;

[0070] The component is input into a pre-constructed signal prediction model, and the prediction result of the vibration signal is output. The signal prediction model is constructed based on the improved kingfisher optimization algorithm to optimize the bidirectional gated cyclic unit. The improved kingfisher optimization algorithm is constructed by introducing the Bloch unit spherical coordinate qubit encoding mechanism, local grid clustering selection strategy, fly-away predator strategy and improved multi-difference Cauchy mutation strategy into the kingfisher optimization algorithm.

[0071] Specifically, this embodiment uses the improved Kingfisher Optimization (IPKO) algorithm to jointly optimize the number of hidden layer neurons, learning rate, and L2 regularization coefficient of the Bidirectional Gated Recurrent Unit (BiGRU) network, constructing a signal prediction model (IPKO-BiGRU), effectively avoiding the underfitting or overfitting problems caused by manual parameter tuning. Figure 1 As shown, the specific steps include:

[0072] S1: Obtain the vibration signal of the rolling bearing and construct the time series f(t);

[0073] S2: The vibration signal time series is decomposed using the variational mode decomposition method to obtain k intrinsic mode components and one residual component, wherein the sum of each component is equal to the original signal, and the sum of the estimated bandwidths of all intrinsic mode components is minimized.

[0074] S3: Based on the Kingfisher Optimization Algorithm (PKO), the Bloch unit spherical coordinate qubit encoding mechanism, local grid clustering selection strategy, predator-avoidance strategy, and improved multi-difference Cauchy mutation strategy are introduced to construct the improved Kingfisher Optimization Algorithm (IPKO).

[0075] S4: By improving the Kingfisher Optimization Algorithm (IPKO), the number of neurons in the hidden layer of the Bidirectional Gated Recurrent Unit (BiGRU) network, the learning rate, and the L2 regularization coefficient are jointly optimized to establish a signal prediction model (IPKO-BiGRU). The decomposed components are predicted and the final vibration signal prediction result is obtained through reconstruction.

[0076] In step S2 of this embodiment, the number of components of the variational mode decomposition is determined based on the center frequency distribution of the vibration signal, and a variational constrained model is constructed with the goal of minimizing the sum of the estimated bandwidths of each modal component. The variational constrained model is transformed into an unconstrained form by introducing a penalty factor and Lagrange multipliers. The signal, center frequency, and Lagrange multipliers of each modal component are iteratively updated using the alternating direction multiplier method until convergence, obtaining several intrinsic modal components and one residual component, where the sum of all components equals the vibration signal. Specifically, the following sub-steps are included:

[0077] Step S2.1 Construct the variational constraint model, the corresponding formula of which is as follows:

[0078]

[0079] Among them, u s Let ω be the s-th intrinsic mode component, with subscripts s = 1, 2, ..., k, where k is the number of intrinsic mode components. s The center frequency of the intrinsic modal component. Here, δ(t) is the Hilbert transform kernel, δ(t) is the Dixlade function, J is the imaginary unit, and * represents the convolution operation. Here, f is a complex exponential modulation term used to modulate the signal to baseband or for frequency domain analysis, and f is the original vibration signal time series. This represents the first-order partial derivative with respect to time t. Let ∑ be the square of the L2 norm, and let ∑ denote the summation.

[0080] Step S2.2 transforms the constrained problem into an unconstrained problem. In step S2.1, a penalty factor β and a Lagrange multiplier λ are introduced, resulting in the following formula:

[0081]

[0082] in, The expression represents the Lagrange function, * represents the convolution operation, and <·> represents the inner product operation.

[0083] Step S2.3 Update parameter u alternately using the alternating direction multiplier method. s w s , λ:

[0084]

[0085] in, and Let u represent the updated values ​​of the s-th intrinsic mode component and the center frequency in the (i+1)th iteration, respectively. e The e-th eigenmode component is the eigenmode component other than the s-th eigenmode component. λ represents the summation of all intrinsic mode components except for the s-th intrinsic mode component. I+1 Let λ represent the (i+1)th iteration of the Lagrange multipliers. I This represents the i-th iteration of the Lagrange multipliers. Represents the integral over the range from 0 to ∞. Let f(t) and u represent respectively. s (t), λ(t), λ I+1 (t), λ I The expression of (t) and h(t) in the frequency domain, where τ is the update factor and h is the auxiliary variable;

[0086] Iteration termination condition: Where ε is the preset convergence accuracy threshold.

[0087] Step S2.4 Determine the number of intrinsic mode components k in the variational mode decomposition method based on the center frequency distribution, and calculate the residual components res:

[0088] Where f(t) is the time series of the original bearing vibration signal, u s Let s represent the s-th intrinsic mode component, with subscripts s = 1, 2, ..., k, where k is the number of intrinsic mode components.

[0089] In this embodiment, step S3 is as follows: Figure 2 As shown, the specific steps include the following:

[0090] Step S3.1 Population Initialization. In the initialization phase of the kingfisher optimization algorithm, the Bloch unit spherical coordinate qubit encoding mechanism and the local grid clustering selection strategy are introduced to jointly generate an initial population with stable quality and diversity;

[0091] Step S3.2 Modeling the kingfisher's exploration and development behaviors. In each iteration, the kingfisher population is guided to perform exploration and development behaviors with probabilities of 80% and 20%, respectively. In the exploration phase, the kingfisher's natural circling and perching behaviors are simulated to achieve periodic perturbations and directional jumps, thereby enhancing its global search capabilities. In the development phase, the kingfisher's dive-attack behavior against prey is simulated to enhance the local convergence ability of the optimal solution region.

[0092] Step S3.3 Modeling the behavior of the kingfisher during the local escape phase. After completing step S3.2, the population enters a temporary symbiotic phase simulating the kingfisher and otter. In the temporary symbiotic behavior during this phase, the strategy of flying away from the predator is integrated. When the kingfisher cannot form a symbiotic relationship with the otter, the individual with the best fitness value in the current iteration is used as a guide to provide directional perturbation and dynamic development compensation for the local escape phase, thereby improving the algorithm's development capability and convergence efficiency in the mid-to-late iterations.

[0093] Step S3.4 introduces an improved multi-difference Cauchy mutation strategy. After completing step S3.3, by introducing a multi-difference mutation structure, linearly decreasing mutation probability, Cauchy factor, adaptive control factor, and boundary bounce mechanism, irregular mutations with strong leaps and clear directional guidance are achieved, thereby improving the diversity and local optimization accuracy of the population in later iterations.

[0094] In this embodiment, step S3.1 is as follows: Figure 3 As shown, the specific steps include the following:

[0095] Step S3.1.1 defines the state of the qubit, and its corresponding formula is as follows:

[0096]

[0097] Here, |0> and |1> are quantum computing bases, and θ=π×r and φ=2π×r are the polar angle and azimuth angle of real numbers, respectively. and The probability amplitudes corresponding to the ground states |0> and |1>, e iφ Represents phase information, where r is a uniformly distributed random number in the interval [0, 1].

[0098] The quantum state is mapped to three-dimensional Bloch unit spherical coordinates, and the corresponding formula is as follows:

[0099]

[0100] Step S3.1.2 Let the i-th individual in the population be P. i The optimization problem has a dimension of n, and for individual P i Each dimension generates Bloch unit spherical coordinates, with the following encoding structure:

[0101]

[0102] Where N is the population size;

[0103] Step S3.1.3 decomposes the above Bloch unit spherical coordinates into three coordinate components, where: x = cosφsinθ, y = sinφsinθ, z = cosθ; from this, P can be obtained. iCandidate individuals in the x, y, and z directions:

[0104]

[0105] in, These represent candidate individuals for the i-th individual in the x, y, and z directions, respectively, and are treated as independent candidate individuals participating in optimization, thereby achieving a coding expansion capability equivalent to 3 times the initial population size during the population initialization stage;

[0106] Step S3.1.4 maps the candidate individuals located within the Bloch unit spherical coordinate interval to the variable range of the optimization problem. Let the lower and upper bounds of the j-th variable in the optimization problem be [a...]. j b j The mapping relationship is as follows:

[0107]

[0108] Where, x ij y ij z ij Let represent the component values ​​of the i-th candidate individual in the Bloch unit spherical coordinate interval in the j-th optimization problem dimension, respectively. These represent the corresponding values ​​of the above component values ​​mapped to the variable range of the optimization problem. The subscripts i = 1, 2, ..., N represent individual indices, and the subscripts j = 1, 2, ..., n represent the dimensions of the optimization problem.

[0109] The candidate individuals that have completed mapping in the three directions are merged into an expanded set of candidate individuals:

[0110]

[0111] in, Let P1′, P2′, ..., P′ be the expanded set of candidate individuals. 3N This represents a candidate individual, with a population size of 3N after Bloch unit ball encoding expansion;

[0112] Calculate the fitness values ​​of all candidate individuals: f i =fitness(P i ′), i = 1, ..., 3N;

[0113] Step S3.1.5 Select two dimensions d in the search space dimension D. x d y Divide the grid into cells and select individuals within each cell;

[0114] Define the spacing between grid boundary points:

[0115]

[0116] Where G is the number of grid cells; l x , l y and u x ,u y d are the dimensions respectively x d y The lower and upper bounds, where the subscripts x and y represent the x-dimension and y-dimension, respectively;

[0117] Define the set of mesh boundary points:

[0118] edges x ={x0,x1,…,x G},x g =l x +gΔx,g=0,1,2,...,G;

[0119] edges y ={y0,y1,…,y G},y g =l y +gΔy,g=0,1,2,...,G;

[0120] Among them, edges x and edges y They represent the dth time respectively x and d y The set of grid boundary points in dimension x g and y g They represent the dth time respectively x and the dth y Grid boundary points in a dimension;

[0121] Set of individuals within a grid area:

[0122]

[0123] Among them, P i ′ indicates that it falls on the (x)th g y g The i-th individual in ) grids, x g-1 ≤X i,dx <x g Indicates that the i-th individual is in dimension d x The value on is greater than the boundary point x g-1 And less than the boundary point x g R d Indicates a grid area;

[0124] Let the (x)th g y g The set of individual indices within each grid is The number of individuals is m:

[0125]

[0126] Sort individuals within the grid in ascending order of fitness value:

[0127]

[0128] in, This represents the fitness value of the i-th individual, and the subscript m indicates its rank after sorting by fitness value;

[0129] The elite set is composed of individuals with the highest fitness values ​​(E) within the grid.

[0130]

[0131] in, This indicates that the fitness value of the i-th individual within the grid is j-th. For floor operations, Ensure that at least one elite individual is selected within the grid;

[0132] Randomly select individuals from the remaining individuals in the grid to form a non-elite set:

[0133]

[0134] Where, min(E, mE) means that the number of random selections should be as consistent as possible with the number of elites;

[0135] Merge the above elite and non-elite sets:

[0136] After completing all grid clustering selections, the candidate individual sets within all grids are merged and controlled according to the preset population size N: if the number of individuals is insufficient, they are randomly added to the target size from the unselected candidate individual set; if the number of individuals exceeds the limit, the top N best individuals are retained in ascending order of fitness value.

[0137] In this embodiment, step S3.2 specifically includes the following sub-steps:

[0138] Step S3.2.1 During the exploration phase, based on the habitat or circling behavior of the kingfisher population, the location of individual kingfishers in the population is updated according to the following formula:

[0139]

[0140] α = 2 × randn(1, Dim) - 1;

[0141] in, and These represent the current position and the updated position of the i-th individual during the exploration phase, respectively. This represents the Qth individual position randomly selected during the exploration phase, where Q is not equal to i. N is the population size, α is a random perturbation vector following a normal distribution, the T parameter is used to control the population's habitat or hovering behavior, and ⊙ represents element-wise multiplication.

[0142] T-parameters of population habitat status:

[0143]

[0144] Crest_angles = 2π × rand;

[0145] Where exp(·) represents the natural exponential function, Max_Iter is the maximum number of iterations, t is the time step, BF is a constant value of 8, cos(·) represents the cosine function, Crest_angles is used to simulate the crest angle, and rand represents a random value in the interval [0, 1].

[0146] T-parameters of the population hovering state:

[0147]

[0148] Wherein, PKO_Fitness(j) and PKO_Fitness(i) are the fitness values ​​of the Qth individual and the ith individual, respectively, and beating_rate is used to simulate the wingbeat frequency;

[0149] Step S3.2.2 During the development phase, based on the hunting ability of the kingfisher, the formula for updating the individual location of the kingfisher population is as follows:

[0150]

[0151] α = 2 × randn(1, Dim) - 1;

[0152] in, and These represent the current position and the updated position of the i-th individual during the development phase, respectively. This represents the position of the individual with the best fitness value in the current development phase. PKO_Fitness(i) and Best_Fitness represent the fitness value of the i-th individual and the best individual in the current iteration of the development phase, respectively. HA represents hunting ability, rand represents a random value in the interval [0,1], b is the position update variable, randn represents a random variable that follows a normal distribution, o is the decay factor, exp(·) represents the natural exponential function, Max_iter is the maximum number of iterations, t is the time step, α is a random perturbation vector that follows a normal distribution, ⊙ represents element-wise multiplication, and N is the population size.

[0153] In this embodiment, step S3.3 is as follows: Figure 4 As shown, the specific steps include the following:

[0154] Step S3.3.1 During the temporary cohabitation phase between the kingfisher and the otter, based on the kingfisher's predation efficiency, if rand > (1-PE), the individual positions of the kingfisher population are updated according to the following formula:

[0155]

[0156] α = 2 × randn(1,Dim) - 1;

[0157]

[0158] in, and Let these represent the current position and the updated position of the i-th individual in the temporary symbiotic behavior, respectively. and Let U and V represent the positions of the U-th and o-th individuals randomly selected during the temporary commensal behavior, respectively, where U is not equal to V and not equal to i. `abs(·)` performs the absolute value operation, `rand` represents a random value in the interval [0, 1], α is a normally distributed random perturbation vector, `randn` represents a normally distributed random variable, `o` is the decay factor, `exp(·)` represents the natural exponential function, `max_Iter` is the maximum number of iterations, `t` is the time step, and `PE` is the predation efficiency of the kingfisher during the temporary commensal behavior. max and PE min The constant values ​​are 0.5 and 0, respectively, and ⊙ represents element-wise multiplication.

[0159] Step S3.3.2 If rand < (1-PE), incorporate the strategy of flying away from predators, and update the individual positions of the kingfisher population according to the following formula:

[0160]

[0161] α = randn(1, Dim);

[0162] K = round(1 + rand(1, 1));

[0163] in, and Let represent the current position and the updated position of the i-th individual in the strategy of flying away from the predator, respectively. denoted as the position of the individual with the best fitness value in the fly-away-from-predator strategy, α is a random perturbation vector following a normal distribution, randn represents a random variable following a normal distribution, ⊙ represents element-wise multiplication, K represents randomly selecting 1 or 2, rand represents a random value in the interval [0, 1], and PE is the predation efficiency of the kingfisher in the temporary commensal behavior.

[0164] In this embodiment, step S3.4 introduces Cauchy factors, adaptive control factors, and a multi-difference mutation structure to calculate the mutation probability p that decreases with iteration. A judgment is made based on the random number rand. If rand is not less than p, the original individual position is retained; if rand is less than p, multi-difference Cauchy mutation is performed to obtain the mutated individual position and determine if it exceeds the bounds. If it does, a boundary bounce mechanism is used to correct the position before calculating the fitness of the mutated individual; if it does not exceed the bounds, the fitness of the mutated individual is directly calculated. It is then determined whether the fitness of the mutated individual is better than the fitness of the original individual. If it is better, the individual position is updated; if not, the original individual position is retained. Figure 5 As shown, the specific steps include the following:

[0165] Step 3.4.1 If rand is less than p, the update formula for generating a new kingfisher individual is as follows:

[0166]

[0167]

[0168] in, and Let these represent the current position and the updated position of the i-th individual in the improved multi-difference Cauchy mutation strategy, respectively. This indicates the position of the individual with the best current fitness value in the improved multi-difference Cauchy mutation strategy. This represents the randomly selected A, B, and C-th individual positions in the improved multi-difference Cauchy mutation strategy, where A is not equal to B, C is not equal to i, and B... t is the adaptive control factor, cos(·) represents the cosine function, Max_Iter is the maximum number of iterations, t is the time step, p is the mutation probability that decreases with iteration, F is the Cauchy factor, tan(·) represents the tangent function, r1 represents a random number uniformly distributed in the interval [0, 1], and r1 and rand are independent of each other.

[0169] Step 3.4.2 If the newly generated individual exceeds the variable boundary, the position is corrected using the boundary bounce mechanism:

[0170]

[0171] in, and Let represent the updated position and the corrected position of the i-th individual in the improved multi-difference Cauchy mutation strategy, respectively; UB and LB are the upper and lower boundaries of the variables in the optimization problem, respectively.

[0172] Step 3.4.3 Update based on the individual's fitness value after mutation:

[0173]

[0174] in, This represents the current position of the i-th individual in the improved multi-difference Cauchy mutation strategy. and Let X′ represent the updated and corrected positions of the i-th individual in the improved multi-difference Cauchy mutation strategy, respectively. i (t+1) represents the final position of the individual retained in the improved multi-difference Cauchy mutation strategy. f(·) is the fitness value calculation function. When the fitness value of the newly generated individual and the corrected individual is better than that of the original individual, the individual is replaced; otherwise, the original individual is retained to ensure stable convergence of the algorithm.

[0175] In this embodiment, step S4 is as follows: Figure 6 As shown, the specific steps include the following:

[0176] Step S4.1 uses the Improved Kingfisher Optimization Algorithm (IPKO) to jointly optimize the number of hidden layer neurons, learning rate, and L2 regularization coefficient of the Bidirectional Gated Recurrent Unit (BiGRU) network, thereby obtaining the IPKO-BiGRU network model. The structure of the IPKO-BiGRU network model is as follows: Figure 7 As shown.

[0177] The optimization process is as follows:

[0178] Step S4.1.1 Initialize BiGRU parameters and IPKO parameters;

[0179] Step S4.1.2 Initialize the parameter combination (number of hidden layer neurons, learning rate, and L2 regularization coefficient) within the search range;

[0180] Step S4.1.3 Perform initial model training and evaluate model performance and loss;

[0181] Step S4.1.4 Save the current optimal model and parameter combination, update the combined parameters, return to step S4.1.3 to execute the next round of model training, evaluate the model characteristics and loss, until the termination condition is reached, and update the optimal model and parameter combination.

[0182] Step S4.2 Using the IPKO-BiGRU network model, process each component u1, u2, ..., u obtained from variational mode decomposition. k Res is used for modeling and prediction to obtain the predicted values ​​u′ of each component. s And Res′, the final predicted vibration signal S(n) is reconstructed according to the following formula:

[0183]

[0184] In the formula, u′ sRepresents the prediction result of the s-th intrinsic mode component, with subscripts s = 1, 2, ..., k. Res′ represents the prediction result of the residual component, S(n) is the final predicted value of the vibration signal, and k is the number of intrinsic mode components.

[0185] The simulation verification is as follows:

[0186] Simulation Calculation Analysis Example 1:

[0187] To verify the performance of the improved kingfisher optimization algorithm (IPKO) constructed in this embodiment, the following functions were selected from the CEC2017 standard test function set: a unimodal function (F1) to test the algorithm's local convergence speed and optimization accuracy under conditions without local extrema; a multimodal function (F8) to test the algorithm's global search ability and ability to escape local optimum traps when there are many local extrema; a mixed function (F12) to evaluate the algorithm's adaptive ability and convergence stability in complex mixed function search spaces; and a composite function (F22) to test the algorithm's global optimization ability, robustness, and generalization performance under highly nonlinear and strongly disturbed backgrounds. The three-dimensional visualization of the selected functions is shown below. Figure 8 As shown.

[0188] The performance of the IPKO algorithm was compared with seven existing mainstream optimization algorithms, including: Kingfisher Optimization (PKO), Hlobaloid Optimization (HLOA), Goose Optimization (GOOSE), Chernobyl Catastrophe Optimizer (CDO), Great White Shark Optimization (WSO), Slime Mucin Optimization (SMA), and Particle Swarm Optimization (PSO). Simulation parameters were set as follows: optimization problem dimension 30, population size N = 50, maximum number of iterations Max_Iter = 1000. To ensure fairness, all algorithms were run under the same initial parameter configuration and constraints, and the optimal fitness value and convergence trend were recorded.

[0189] Figure 9 The results show the convergence curves of the IPKO algorithm and seven mainstream optimization algorithms on the selected test function. Figure 9 (a) and (b) show that the IPKO 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 9 (c) and (d) show that the IPKO algorithm can still maintain a stable convergence trend when facing a search space with complex function structure and high noise interference. It exhibits strong global search ability, convergence stability and robustness, and has obvious advantages in high-complexity optimization problems.

[0190] Simulation Calculation Analysis Example 2:

[0191] To further evaluate the generalization ability and statistical significance of the improved kingfisher optimization algorithm (IPKO) constructed in this embodiment across different types of optimization problems, a comparative experimental platform was built based on the CEC2022 standard test functions. This test function set covers 12 single-objective real-valued optimization functions, including unimodal, multimodal, shift / rotation, and non-separation functions, effectively simulating the complex search space and high-dimensional nonlinear characteristics in practical engineering, and is widely used to evaluate the versatility and robustness of optimization algorithms.

[0192] The IPKO algorithm was compared with seven existing mainstream optimization algorithms, including Kingfisher Optimizer (PKO), Hlore-O-A (HLOA), Goose Optimizer (GOOSE), Chernobyl Catastrophe Optimizer (CDO), Great White Shark Optimizer (WSO), Slime Mucin Optimizer (SMA), and Particle Swarm Optimization (PSO). Experimental parameters were set as follows: 10-dimensional optimization problem, population size N = 50, and maximum number of iterations Max_Iter = 500. To reduce the impact of experimental randomness, each algorithm was run independently 50 times on each test function, and the mean fitness value was used as the evaluation metric. The Friedman nonparametric rank-sum test was used to statistically rank the mean fitness values ​​of each algorithm across all test functions. This method is a nonparametric statistical test used to analyze the significant performance differences of multiple algorithms across multiple test tasks.

[0193] Table 1 shows the average Friedman ranking of the IPKO algorithm and seven existing mainstream optimization algorithms on the CEC2022 standard test function set. The IPKO algorithm achieved the lowest average rank (1.5417) among all algorithms, significantly outperforming the second-ranked PKO algorithm (3.1677). Further analysis reveals that the IPKO algorithm exhibits faster convergence speed, higher optimization accuracy, and smaller performance fluctuations across multiple test functions, demonstrating strong robustness and stability.

[0194] Table 1

[0195] algorithm IPKO PKO HLOA GOOSE CDO WSO SMA PSO Rank average 1.54 3.17 5.67 7.67 7.92 3.58 3.92 3.63 Ranking 1 2 6 7 8 3 5 4

[0196] Application examples:

[0197] Taking the vibration signal of the compressor drive end bearing collected in a certain city in December 2022 as an example, the method proposed in this implementation will be further explained. The data is acquired at a sampling frequency of once per minute, and 1440 data points can be collected per day, which is sufficient to comprehensively reflect the operating status of the compressor drive end bearing.

[0198] The collected vibration signals from the compressor drive bearing were used to construct a time series, and variational mode decomposition (VMD) was employed for data preprocessing. During decomposition, the number of intrinsic mode components (IMCs) was determined based on the principle of uniform center frequency distribution and the constraint that the sum of all components equals the original signal. Ultimately, the time series was decomposed into 7 IMCs and 1 residual component, with a penalty factor set to 2000. The resulting components were divided into training and testing sets in an 8:2 ratio and then uniformly normalized. The decomposition results are shown below. Figure 10 As shown.

[0199] The improved kingfisher optimization algorithm (IPKO) constructed in this invention is used to jointly optimize the number of hidden layer neurons, learning rate, and L2 regularization coefficient of the BiGRU network, thereby obtaining the IPKO-BiGRU network model.

[0200] The population size of the kingfisher is set to N=6, the maximum number of iterations Max_Iter=80, the gating structure uses the sigmoid activation function, the state update uses the tanh activation function, and the root mean square error (RMSE) on the test set is used as the optimization objective function to guide the optimization algorithm to search for the optimal parameter combination.

[0201] To verify the superiority of the IPKO-BiGRU model, normalized training and test sets were input into the IPKO-BiGRU model and the comparison model PKO-BiGRU for training and prediction. The prediction results of each component were then denormalized and reconstructed to obtain the final prediction results for the test set, as shown below. Figure 11 As shown. To ensure fairness in the comparison, both models were run under the same parameter configuration.

[0202] To intuitively evaluate the predictive performance of the two models, the root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and coefficient of determination (R²) were selected. 2 Four indicators are used as evaluation criteria. Among them, RMSE reflects the overall deviation between the model's predicted values ​​and the original signal; the smaller the value, the higher the overall reconstruction accuracy of the model. MAE represents the mean 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, assessing the model's prediction accuracy on a relative scale. 2 The value measures how well the model fits the real data; the closer the value is to 1, the better the fit.

[0203] The prediction results of the two models are shown in Table 2. The IPKO-BiGRU model outperforms the PKO-BiGRU model in all evaluation metrics. Specifically, the RMSE of IPKO-BiGRU is 0.0213, lower than that of PKO-BiGRU (0.0269), indicating a smaller overall prediction error; the MAE value decreased from 0.0222 to 0.0177, showing a significant reduction in the average bias; and the MAPE decreased from 0.2787 to 0.2210, indicating a significant improvement in relative error at different numerical scales. Furthermore, the R-value of the IPKO-BiGRU model... 2 Reaching 0.9663, higher than PKO-BiGRU's 0.9500, indicates that it has better performance in signal trend fitting and structure reconstruction, and can more accurately reflect the true change law of vibration signal.

[0204] Table 2

[0205] Model RMSE MAE MAPE <![CDATA[R 2 ]]> PKO-BiGRU 0.0269 0.0222 0.2787 0.9500 IPKO-BiGRU 0.0213 0.0177 0.2210 0.9663

[0206] 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 rolling bearing vibration signal prediction method based on an improved kingfisher optimization network model, characterized in that, The method comprises the following steps: acquiring a vibration signal of a target rolling bearing and constructing a time series; performing variational mode decomposition on the time series of the vibration signal to obtain a plurality of components; inputting the components into a pre-constructed signal prediction model to output a prediction result of the vibration signal, wherein the signal prediction model is constructed based on an improved kingfisher optimization algorithm optimizing a bidirectional gated recurrent unit, and the improved kingfisher optimization algorithm is constructed by introducing a Bloch unit sphere coordinate quantum bit coding mechanism, a local grid clustering selection strategy, a fly-away predator strategy and an improved multi-difference Cauchy mutation strategy into a kingfisher optimization algorithm; The improved kingfisher optimization algorithm constructed by introducing the Bloch unit sphere coordinate quantum bit coding mechanism, the local grid clustering selection strategy, the fly-away predator strategy and the improved multi-difference Cauchy mutation strategy into the kingfisher optimization algorithm comprises: S3.1, by introducing the Bloch unit sphere coordinate quantum bit coding mechanism and the local grid clustering selection strategy, an initial population is obtained, and S3.2 is entered; S3.2, the exploration stage and the development stage of the kingfisher are carried out, and after completion, S3.3 is entered, wherein the exploration stage simulates the natural circling and habitat behavior of the kingfisher, and the development stage simulates the diving attack behavior of the kingfisher to the prey; S3.3, the local escape stage of the kingfisher is carried out, and after completion, S3.4 is entered, wherein the local escape stage simulates the temporary cohabitation behavior of the kingfisher and the otter, and fuses the fly-away predator strategy; S3.4, the improved multi-difference Cauchy mutation strategy is introduced, wherein the improved multi-difference Cauchy mutation strategy comprises a multi-difference mutation structure, a linearly decreasing mutation probability, a Cauchy factor, an adaptive control factor and a boundary bounce mechanism; By introducing the Bloch unit sphere coordinate quantum bit coding mechanism and the local grid clustering selection strategy, an initial population is obtained, and S3.2 is entered; The state of the quantum bit is defined and mapped to the three-dimensional Bloch unit sphere coordinate; Let the population be the first Individuals The dimension of the optimization problem is For individuals Each dimension generates Bloch unit spherical coordinates; The Bloch unit sphere coordinates are disassembled into three directional coordinate components, and the following is obtained Three directional candidate individuals The candidate individuals located in the Bloch unit sphere coordinate interval are mapped to the variable range of the optimization problem, and the candidate individuals in the three directions are combined into an extended candidate individual set, and the fitness values of all candidate individuals in the set are calculated; Select two dimensions from the search space dimensions. , The grid cells are divided at equal intervals, and individuals are selected within each grid based on their fitness values ​​to obtain a set of candidate individuals for each grid. All the candidate individuals screened in the grid are combined, and the population size is controlled according to the preset population size. If the number of individuals is insufficient, the target size is supplemented randomly from the set of unselected candidate individuals; if the number of individuals is excessive, the top optimal individuals are reserved in ascending order of fitness values. The improved multi-difference Cauchy mutation strategy is introduced, wherein the improved multi-difference Cauchy mutation strategy comprises a multi-difference mutation structure, a linearly decreasing mutation probability, a Cauchy factor, an adaptive control factor and a boundary bounce mechanism; The new kingfisher individual is generated by introducing the Cauchy factor, the adaptive control factor and the multi-difference mutation structure, if the new kingfisher individual exceeds the variable boundary, the boundary bounce mechanism is used to correct the position, and the individual update is judged according to the fitness value of the new kingfisher individual to obtain the final reserved individual position, wherein the position update method for generating the new kingfisher individual is: ； ； ； ； wherein, and respectively represent the current position and the updated position of the i-th individual in the improved multi-difference Cauchy mutation strategy, represents the position of the individual with the optimal fitness value in the improved multi-difference Cauchy mutation strategy, , represents the position of the randomly selected i-th individual in the improved multi-difference Cauchy mutation strategy, , is not equal to is not equal to is not equal to , is a Cauchy factor, is an adaptive control factor, is a random number uniformly distributed in the interval [0, 1], represents a random value in the interval [0, 1], and are mutually independent, and t is a time step, is the maximum number of iterations, is a mutation probability that decreases with iteration.​​​​ 2. The rolling bearing vibration signal prediction method based on the improved kingfisher optimization network model according to claim 1, characterized in that, The variational mode decomposition is performed on the time series of the vibration signal to obtain a plurality of components, which comprises: determining the number of components of the variational mode decomposition according to the central frequency distribution of the vibration signal, and constructing a variational constraint model with the sum of the bandwidths of each modal component as the target; The variational constraint model is converted into an unconstrained form by introducing a penalty factor and a Lagrange multiplier, and each modal component signal, center frequency and Lagrange multiplier are iteratively updated by using an alternating direction multiplier method until convergence is achieved, thereby obtaining several eigenmodal components and a residual component, and the sum of all components is equal to the vibration signal.

3. The rolling bearing vibration signal prediction method based on the improved kingfisher optimization network model according to claim 1, characterized in that, The signal prediction model is constructed based on an improved kingfisher optimization algorithm and a bidirectional gated recurrent unit, and the method comprises the following steps: The network hidden layer neuron number, learning rate and L2 regularization coefficient of the bidirectional gated recurrent unit are jointly optimized by using the improved kingfisher optimization algorithm, and the signal prediction model is obtained. The signal prediction model is used for modeling and predicting each component respectively, and the final predicted vibration signal is obtained after the predicted values of the components are reconstructed. ； wherein represents the prediction result of the th eigemodal component, the subscript , represents the prediction result of the residual component, is the final prediction value of the vibration signal, is the number of eigemodal components.

4. The rolling bearing vibration signal prediction method based on the improved kingfisher optimization network model according to claim 1, characterized in that, The position of the kingfisher population individual in the exploration stage is updated according to the habitat or hovering behavior state, and the updating method is as follows: ； wherein, with denote the current and updated position of the i-th individual in the exploration phase, denote the current and updated position of the i-th individual in the exploration phase, denote the randomly selected position of the i-th individual in the exploration phase, denote the randomly selected position of the i-th individual in the exploration phase, is not equal to , is the population size, is a random perturbation vector following a normal distribution, is a parameter used to control the population's habitat or hovering behavior, denotes element-wise multiplication, t is the time step.

5. The rolling bearing vibration signal prediction method based on the improved kingfisher optimization network model according to claim 1, characterized in that, The position of the kingfisher population individual in the development stage is updated according to the hunting ability, and the updating method is as follows: ； wherein, with denote the current position of the i-th individual and the updated position of the i-th individual, respectively, denote the current position of the i-th individual and the updated position of the i-th individual, respectively, denote the position of the individual with the best fitness value in the development stage, denote the hunting ability, is a position update variable, is a decay factor, is a random perturbation vector subject to a normal distribution, denotes element-wise multiplication, is the population size, and t is the time step.

6. The rolling bearing vibration signal prediction method based on the improved kingfisher optimization network model according to claim 1, characterized in that, The position of the kingfisher population individual in the temporary symbiotic behavior in the local escape stage is updated according to the predation efficiency, and the updating method is as follows: ； wherein, and denote the current and updated positions of the i-th individual in the temporary symbiotic behavior, respectively, and denote the randomly selected positions of the i-th and j-th individuals in the temporary symbiotic behavior, respectively, is not equal to is not equal to , denotes an interval random value, is a random disturbance vector following a normal distribution, is a decay factor, denotes element-wise multiplication, is the predation efficiency of the kingfisher in the temporary symbiotic behavior, is an absolute value operation, and t is the time step.​​​ 7. The rolling bearing vibration signal prediction method based on the improved kingfisher optimization network model according to claim 1, characterized in that, The position of the kingfisher population individual in the local escape stage and the fusion flying away from the predator strategy is updated as follows: ； wherein, with denote the current position and the updated position of the i-th individual in the flee-from-predator strategy, respectively, denote the current position and the updated position of the i-th individual in the flee-from-predator strategy, respectively, denote the position of the individual with the optimal fitness value in the flee-from-predator strategy, is a random perturbation vector following a normal distribution, denotes element-wise multiplication, denotes a random selection of 1 or 2, denotes an interval random value, is the predation efficiency of the great tit in the temporary mutualistic behavior, and t is the time step.

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