Vehicle bolt loosening life prediction method and system based on vibration system model

Abstract

The invention provides a vehicle bolt loosening life prediction method and system based on a vibration system model, and relates to the technical field of bolt loosening life prediction, and the method comprises the steps: obtaining a bolt clamping force and related vibration data through a vibration rack test; establishing a two-degree-of-freedom vibration system dynamic model of the bolt connection structure; introducing an energy error index and a frequency domain distribution error index, and quantifying a matching degree between a simulation result in the two-degree-of-freedom vibration system dynamic model and actual test data; utilizing a multi-objective optimization algorithm and a particle swarm optimization algorithm to optimize relative stiffness and damping parameters of the two-degree-of-freedom vibration system dynamic model; and carrying out a bolt loosening vibration test, and analyzing the loosening damage and the service life of the bolt in combination with the optimized model parameters. The prediction precision of the two-degree-of-freedom vibration model is improved, the bolt loosening damage accumulation process is quantified, and the residual life of the bolt is predicted.

Description

Technical Field

[0001] This invention relates to the field of bolt loosening life prediction technology, and more specifically, to a method and system for predicting the loosening life of vehicle bolts based on a vibration system model. Background Technology

[0002] In engineering fields such as aerospace, automotive, rail transportation, and wind power, bolted connections are a common and critical fastening method, offering advantages such as good vibration resistance and convenient assembly and disassembly. However, under long-term dynamic loads such as vibration and impact, bolts are prone to loosening and failure. Furthermore, because the initial loosening is often concealed, it can easily lead to structural instability or even serious safety accidents.

[0003] To predict bolt loosening life in advance and avoid sudden failure, researchers typically use a combination of vibration testing and numerical simulation. Establishing a reasonable mechanical model (such as a single-degree-of-freedom or two-degree-of-freedom vibration system) is fundamental to predicting bolt loosening behavior. Current research has used simplified vibration models of bolted connection systems to simulate their dynamic response and attempted to compare these models with experimental data to verify their effectiveness. However, in actual modeling, the complex contact relationships between bolted connection interfaces make it difficult to accurately obtain the relative stiffness and damping parameters between different parts of the system, thus affecting the model's predictive accuracy.

[0004] Furthermore, existing methods for predicting bolt loosening life often rely on empirical formulas or static mechanical analysis, lacking in-depth modeling and quantitative assessment of bolt loosening mechanisms under dynamic conditions. Therefore, developing accurate methods for predicting bolt loosening life is crucial for structural health monitoring. Summary of the Invention

[0005] The purpose of this invention is to provide a method and system for predicting the loosening life of vehicle bolts based on a vibration system model, in order to improve the aforementioned problems. To achieve the above objective, the technical solution adopted by this invention is as follows:

[0006] In a first aspect, this application provides a method for predicting the loosening life of vehicle bolts based on a vibration system model, including:

[0007] Bolt clamping force and related vibration data were obtained through vibration table tests. The related vibration data included vibration acceleration data of the vibration table, test fixture and bolt connection structure.

[0008] Based on the obtained bolt clamping force and related vibration data, a two-degree-of-freedom vibration system dynamic model of the bolt connection structure is established.

[0009] By introducing energy error index and frequency domain distribution error index, the degree of matching between the simulation results and actual experimental data in the dynamic model of a two-degree-of-freedom vibration system is quantified, and the matching results are obtained.

[0010] The relative stiffness and damping parameters of the dynamic model of a two-degree-of-freedom vibration system are optimized using multi-objective optimization algorithm and particle swarm optimization algorithm to obtain the optimal solution set of relative stiffness and damping parameters.

[0011] Based on the matching results and the optimal set of relative stiffness and damping parameters, bolt loosening vibration tests were conducted. Combined with the optimized model parameters, the loosening damage and lifespan of the bolts were analyzed and predicted.

[0012] Preferably, the step of establishing a two-degree-of-freedom vibration system dynamic model of the bolted connection structure based on the obtained bolt clamping force and related vibration data includes:

[0013] Based on the arrangement of the test fixtures, the vibration direction is determined and the displacement variables of the vibration table, test fixtures, and bolted connection structure are defined. The masses of the vibration table, test fixtures, and bolted connection structure are set, and the first relative stiffness and first damping between the test fixtures and the vibration table, as well as the second relative stiffness and second damping between the bolted connection structure and the test fixture, are defined. Based on Newton's second law, and combined with the first relative stiffness, first damping, second relative stiffness, and second damping, the dynamic equations of the vibration table, test fixtures, and bolted connection structure are established, forming a preliminary two-degree-of-freedom system dynamic model.

[0014] Define the velocity variables of the vibration table, test fixture, and bolted connection structure. Substitute the velocity variables into the preliminary two-degree-of-freedom system dynamic model, replace the original displacement derivative term, update the preliminary two-degree-of-freedom system dynamic model, and by introducing velocity variables, form the final two-degree-of-freedom vibration system dynamic model that includes displacement and velocity.

[0015] Preferably, the optimization of the relative stiffness and damping parameters of the dynamic model of the two-degree-of-freedom vibration system using multi-objective optimization algorithm and particle swarm optimization algorithm to obtain the optimal solution set of relative stiffness and damping parameters includes:

[0016] Multi-objective optimization algorithm and particle swarm optimization algorithm are selected as parameter optimization tools. The parameters of the particle swarm optimization algorithm are initialized, including particle swarm size, initial position and velocity. The weight coefficients and constraints of the multi-objective optimization algorithm are configured. The running parameters of the optimization algorithm are set, including the number of iterations and convergence conditions.

[0017] The energy error index and frequency domain distribution error index are used as optimization objective functions to quantify the differences in root mean square values ​​and power spectral density between experimental data and model output, respectively. The first relative stiffness and first relative damping, and the second relative stiffness and second relative damping in the model established in the second step are set as optimization variables, and their initial value range and step size are set. The optimization variables are substituted into the model using the optimization algorithm to calculate the acceleration response of the model output, and the degree of matching between the model output and the experimental data is evaluated through the objective function.

[0018] In each iteration, the optimization variables are updated according to the rules of the optimization algorithm, the acceleration response of the model is recalculated, the objective function value is evaluated, and it is determined whether the optimization process meets the convergence condition. The convergence condition is that the rate of change of the objective function value is less than a set threshold or the preset number of iterations is reached. If it does not meet the condition, the next iteration continues. If it does meet the condition, the output is performed. When the optimization process meets the convergence condition, the optimal set of relative stiffness and damping parameters is extracted from the optimization algorithm, and the optimization process is completed, resulting in the optimal set of relative stiffness and damping parameters.

[0019] Secondly, this application also provides a vehicle bolt loosening life prediction system based on a vibration system model, comprising:

[0020] Acquisition module: used to acquire bolt clamping force and related vibration data through vibration table test, including vibration acceleration data of vibration table surface, test fixture and bolt connection structure;

[0021] The module is used to establish a two-degree-of-freedom vibration system dynamic model of the bolt connection structure based on the obtained bolt clamping force and related vibration data.

[0022] The acquisition module is used to introduce energy error index and frequency domain distribution error index, quantify the degree of matching between the simulation results in the dynamic model of the two-degree-of-freedom vibration system and the actual experimental data, and obtain the matching results;

[0023] Optimization module: Used to optimize the relative stiffness and damping parameters of a two-degree-of-freedom vibration system dynamic model using multi-objective optimization algorithm and particle swarm optimization algorithm, to obtain the optimal solution set of relative stiffness and damping parameters;

[0024] Prediction module: Based on the matching results and the optimal set of relative stiffness and damping parameters, conduct bolt loosening vibration tests, and analyze and predict bolt loosening damage and life by combining the optimized model parameters.

[0025] Thirdly, this application also provides a vehicle bolt loosening life prediction device based on a vibration system model, comprising:

[0026] Memory, used to store computer programs;

[0027] A processor is used to implement the steps of the vehicle bolt loosening life prediction method based on a vibration system model when executing the computer program.

[0028] Fourthly, this application also provides a readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the above-described method for predicting the loosening life of vehicle bolts based on a vibration system model.

[0029] The beneficial effects of this invention are as follows:

[0030] This invention addresses the problem of obtaining relative stiffness and damping parameters, which are difficult to obtain. By introducing two evaluation indicators, energy error and frequency domain distribution error, it uses an optimization algorithm to deduce the optimal parameter combination and finally combines it with DN curves to predict the bolt loosening life. It has strong engineering application value and promotion prospects.

[0031] This invention addresses the modeling error problem in bolted connection systems caused by the difficulty in obtaining parameters by combining experimental data-driven approaches, model parameter optimization, and damage accumulation analysis. It also provides a systematic prediction method for bolt loosening life under dynamic environments. The aim is to solve the problem of inaccurate bolt loosening life prediction caused by the difficulty in directly obtaining key parameters (relative stiffness, relative damping) and their significant impact on model accuracy. Specifically, it utilizes experimental data (DN curves, vibration response) plus quantitative evaluation indicators (energy error DIF). rms Frequency domain distribution error DIF freq The technical approach combining simulation and intelligent optimization algorithms (multi-objective optimization, particle swarm optimization) achieves the following: effectively identifying the matching degree between simulation and measured acceleration, and accurately identifying the optimal relative stiffness and damping parameters that conform to actual vibration conditions; using the optimized high-precision model and the DN curve obtained from experiments, reliable prediction of bolt loosening damage is achieved; ultimately, a reliable solution is provided for predicting and preventing loosening failure of bolted connection structures under random vibration environments in engineering.

[0032] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing embodiments of the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description, claims, and drawings. Attached Figure Description

[0033] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0034] Figure 1 This is a schematic diagram of the process for predicting the loosening life of vehicle bolts based on a vibration system model, as described in this embodiment of the invention.

[0035] Figure 2 This is a schematic diagram of the dynamic model of a two-degree-of-freedom system based on a vibration system model as described in an embodiment of the present invention;

[0036] Figure 3 This is a schematic diagram of a two-degree-of-freedom vibration system model of a bolted connection structure based on a vibration system model, as described in an embodiment of the present invention.

[0037] Figure 4 This is a schematic diagram of the optimization process of the multi-objective optimization algorithm based on the vibration system model described in this embodiment of the invention;

[0038] Figure 5 This is a schematic diagram of the Pareto front based on the vibration system model described in this embodiment of the invention;

[0039] Figure 6 This is a schematic diagram showing the distribution range of individual k1 and k2 in each region based on the vibration system model described in this embodiment of the invention;

[0040] Figure 7 This is a schematic diagram showing the distribution range of individuals c1 and c2 in each region based on the vibration system model described in this embodiment of the invention;

[0041] Figure 8 This is a schematic diagram of the vehicle bolt loosening life prediction system based on a vibration system model as described in an embodiment of the present invention;

[0042] Figure 9 This is a schematic diagram of the vehicle bolt loosening life prediction device based on a vibration system model as described in an embodiment of the present invention.

[0043] In the diagram: 701, Acquisition Module; 702, Establishment Module; 703, Obtaining Module; 704, Optimization Module; 705, Prediction Module; 800, Bolt Loosening Life Prediction Device; 801, Processor; 802, Memory; 803, Multimedia Component; 804, I / O Interface; 805, Communication Component. Detailed Implementation

[0044] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0045] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this invention, terms such as "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0046] Example 1:

[0047] This embodiment provides a method for predicting the loosening life of vehicle bolts based on a vibration system model.

[0048] In this invention, the traditional method for predicting bolt loosening life has the following key drawbacks:

[0049] 1. Key model parameters are difficult to obtain directly: The core parameters of a two-degree-of-freedom model are the relative stiffness and relative damping between the connection interfaces. These parameters represent the complex physical characteristics of bolted connections (such as contact, friction, and microslippage). They are highly nonlinear and cannot be obtained directly and accurately through theoretical calculations or simple measurements. Existing techniques typically rely on empirical estimations, simplifying assumptions, or limited test data to set these parameters, resulting in significant uncertainties in the model itself.

[0050] 2. The model's prediction accuracy is highly sensitive to parameters: Since relative stiffness and damping are the core inputs of the model, even small changes in them can significantly affect the vibration response (especially acceleration) output by the model. In existing technologies, using inaccurate parameters can lead to significant errors between the model simulation results and actual measurement results, making the model's predicted bolt loosening life unreliable.

[0051] 3. Parameter uncertainty affects prediction robustness: Although early methods (such as Gaussian process regression or basic deep learning models) attempted to predict loosening trends, they did not solve the parameter sensitivity problem. Different parameter combinations may output significantly different simulation results, which cannot be stably correlated with the actual damage state of the bolt.

[0052] 4. Lack of effective quantitative indicators for model calibration: Although it is known that model outputs (such as acceleration) need to match actual measured values, current technologies lack systematic and quantitative indicators to accurately evaluate and describe the degree of matching between simulated and measured accelerations in terms of overall energy level and frequency distribution characteristics. This makes calibrating model parameters and judging whether the model is "good" enough difficult and subjective.

[0053] 5. Low efficiency in model calibration and parameter optimization: Even when parameter inaccuracies are recognized, current technologies lack efficient methods to systematically explore the vast parameter space (different combinations of relative stiffness and damping) and automatically find the optimal parameter combination that makes the model output best match the measured data. Manual trial and error is inefficient and makes it difficult to find the globally optimal solution.

[0054] In summary, the core problem this invention addresses is that existing prediction methods based on two-degree-of-freedom models suffer from low model accuracy and unreliable prediction results due to the difficulty in obtaining key parameters (relative stiffness and damping) which have a significant impact on the results, coupled with a lack of effective quantitative evaluation indicators and efficient optimization methods. Therefore, the innovation of this invention lies in systematically solving these challenges of parameter identification and model calibration through experimental data, new evaluation indicators, and intelligent optimization algorithms.

[0055] Therefore, the core objective of this invention is to develop a more accurate and practical method for predicting the loosening life of bolted connection structures, solving the problem of predicting the loosening life of bolted connection systems under random vibration environments. This is achieved by establishing a method based on a two-degree-of-freedom vibration system model, combined with experimental data and intelligent optimization algorithms, to realize a high-precision quantitative assessment of bolt loosening damage, providing a scientific basis for the reliability design and life management of bolted connection structures in engineering applications. The problems to be solved are: 1. Difficulty in directly obtaining relative stiffness and damping parameters: In bolted connection systems, the relative stiffness and damping parameters between components such as the vibration table, test fixture, and connected parts are affected by factors such as the complexity of the contact surface and the assembly state, making direct measurement impossible through theoretical calculations or conventional methods. This leads to difficulties in setting dynamic model parameters and limits model accuracy. 2. Prediction error caused by model parameter sensitivity: The established two-degree-of-freedom vibration system model is highly sensitive to relative stiffness and damping parameters. Small parameter changes can cause significant deviations between simulation results (especially acceleration response) and actual measured values, directly affecting the reliability of the model's prediction of bolt loosening status. 3. How to quantify the matching degree between simulation and actual measurement: There is a lack of objective and quantitative standards to evaluate the degree of matching between the acceleration response obtained from simulation and the acceleration data measured in actual shaking table tests, making it difficult to effectively guide the identification and optimization of model parameters. Existing technologies lack indicators to quantify the matching degree between simulation results and measured data, making it difficult to guide the optimization and adjustment of model parameters. 4. How to obtain the optimal model parameters that conform to actual working conditions: In the absence of direct measurement methods and when the model is sensitive to parameters, an efficient and reliable method is needed to identify and determine a set of optimal relative stiffness and damping parameter combinations so that the model can most realistically reflect the dynamic behavior of bolted connection structures under actual vibration environments. 5. Bolt loosening life prediction relies on empirical formulas: Traditional methods often rely on static mechanical analysis or empirical formulas, failing to combine dynamic vibration test data and damage accumulation laws, leading to a disconnect between the life prediction results and actual working conditions.

[0056] See Figure 1 The figure shows that the method includes steps S100, S200, S300, S400 and S500.

[0057] S100. Obtain bolt clamping force and related vibration data through vibration table test, including vibration acceleration data of vibration table surface, test fixture and bolt connection structure.

[0058] Understandably, in this step, random vibration bench tests are conducted on the bolted connection structure to obtain data on bolt clamping force and vibration acceleration. The test object is the bolted connection structure on the bogie of a rail vehicle. The bolts used to connect the bolted connection structure and the tooling are 8.8 grade M16×2×120 high-strength bolts, made of 45 steel, with a tensile strength of 800MPa and a yield strength of 640MPa. The test is conducted on the Dongling ES-40-370-VT0505 multi-axis synchronous vibration test bench. First, the specially designed tooling is installed on the vibration table, and then the bolted connection structure is connected to the test tooling using M16 high-strength bolts. Simultaneously, an LVT-14TP-12T pressure sensor is connected in series with the bolt to monitor the real-time clamping force of the bolt.

[0059] In this embodiment, 1A314E accelerometers were arranged on the vibration table, test fixture, and bolted connection structure to collect vibration acceleration data at various points during the test. Before the test, the initial preload of the bolts was accurately controlled to 20 kN using a torque digital wrench and an LVT-14TP-12T pressure sensor. The test excitation was a three-wire random vibration acceleration test spectrum from the EN61373:2010 standard for shock and vibration testing, with a root mean square (RMS) value of 20 m / s² and a frequency range of 5–250 Hz. The test was stopped when the bolt clamping force decreased from the initial 20 kN to approximately 17.9 kN, representing about 89.5% of the initial preload. The acceleration data obtained from the test on the vibration table, test fixture, and bolted connection structure (i.e., the input acceleration signal of the two-degree-of-freedom vibration system of the bolted connection structure) were uniform and random, meeting the requirements of random vibration testing.

[0060] S200. Based on the obtained bolt clamping force and related vibration data, establish a two-degree-of-freedom vibration system dynamic model of the bolt connection structure.

[0061] It is understood that step S200 includes S201 and S202, wherein:

[0062] S201. Based on the arrangement of the test fixtures, determine the vibration direction and define the displacement variables of the vibration table, test fixtures and bolted connection structure. Set the mass of the vibration table, test fixtures and bolted connection structure, and define the first relative stiffness and first damping between the test fixtures and the vibration table, and the second relative stiffness and second damping between the bolted connection structure and the test fixture. Based on Newton's second law, and combining the first relative stiffness, first damping, second relative stiffness and second damping, establish the dynamic equations of the vibration table, test fixtures and bolted connection structure to form a preliminary two-degree-of-freedom system dynamic model.

[0063] S202. Define the velocity variables of the vibration table, test fixture, and bolted connection structure. Substitute the velocity variables into the preliminary two-degree-of-freedom system dynamic model, replace the original displacement derivative term, update the preliminary two-degree-of-freedom system dynamic model, and form the final two-degree-of-freedom vibration system dynamic model containing displacement and velocity by introducing velocity variables.

[0064] It should be noted that, based on the setup of the random vibration test fixture for the bolted connection structure in the first step, a two-degree-of-freedom system dynamic model along the vibration direction is established, such as... Figure 2 As shown in Formula (1). (Where a0 is the acceleration input to the vibration table, m0, m1, and m2 are the masses of the vibration table, the test fixture, and the bolted connection structure, respectively, x0, x1, and x2 are their displacements during vibration, k1 and c1 are the relative stiffness and relative damping between the test fixture and the vibration table, and k2 and c2 are the relative stiffness and relative damping between the bolted connection structure and the test fixture.)

[0065]

[0066] In the formula, m1 and m2 represent the masses of the test fixture and the bolted connection structure, respectively; x0, x1, and x2 represent the first, second, and third displacements generated by the vibration table, the test fixture, and the bolted connection structure during vibration; k1 and c1 represent the first relative stiffness and the first relative damping between the test fixture and the vibration table; and k2 and c2 represent the second relative stiffness and the second relative damping between the bolted connection structure and the test fixture. and Let x0, x1, and x2 be the first derivatives, representing the first velocity, the second velocity, and the third velocity, respectively. and These are the second derivatives of x0, x1, and x2, respectively, representing the first acceleration, the second acceleration, and the third acceleration.

[0067] Based on such Figure 2 Based on the two-degree-of-freedom system dynamic model of the bolted connection structure shown in formula (1), the final two-degree-of-freedom vibration system model of the bolted connection structure is established, as follows: Figure 3 As shown, (where v0, v1, and v2 represent the velocities of the vibration table, the test fixture, and the bolted connection structure, respectively). By inputting the acceleration signal a0 of the vibration table into this model, and then performing simulation based on the two-degree-of-freedom system dynamics model, the vibration displacements x1 and x2 of the test fixture and the bolted connection structure, as well as the relative displacement x2-x1 between them, can be obtained. Simultaneously, using this two-degree-of-freedom vibration system model, the vibration accelerations a1 and a2 of the test fixture and the bolted connection structure can also be output. Therefore, the simulation effect of this model can be evaluated from both displacement and acceleration perspectives.

[0068] S300 introduces energy error index and frequency domain distribution error index to quantify the degree of matching between simulation results and actual experimental data in the dynamic model of a two-degree-of-freedom vibration system, and obtains matching results.

[0069] Understandably, in this step, to reduce the acceleration error output by the two-degree-of-freedom vibration system model in the second step, an index for identifying the degree of acceleration consistency is proposed: Energy Error (DIF). rms Frequency domain distribution error DIF freq It is used to quantify the degree of matching between simulated acceleration and actual measured acceleration.

[0070] In this embodiment, when the two accelerations a1 and a2 simulated by the model match the two measured acceleration signals, the accuracy of the model can be proven to a certain extent. The matching of acceleration signals can be determined from two aspects. The first indicator measures the energy magnitude of the acceleration signal, specifically by calculating and comparing the difference in the root mean square (RMS) values ​​of the acceleration signals, which effectively quantifies the energy characteristics of the signal. The second indicator assesses the energy distribution of the acceleration signal. Acceleration signals with the same total energy will produce different effects and results under different loading methods; therefore, the energy distribution carried by the signal is also important. This is specifically obtained by calculating and comparing the difference in the power spectral density (PSD) of the acceleration signals.

[0071] S400. The relative stiffness and damping parameters of the dynamic model of the two-degree-of-freedom vibration system are optimized using multi-objective optimization algorithm and particle swarm optimization algorithm to obtain the optimal solution set of relative stiffness and damping parameters.

[0072] It is understood that step S400 includes S401, S402, and S403, wherein:

[0073] S401. Select multi-objective optimization algorithm and particle swarm optimization algorithm as parameter optimization tools, initialize the parameters of particle swarm optimization algorithm, including particle swarm size, initial position and velocity, configure the weight coefficients and constraints of multi-objective optimization algorithm, and set the running parameters of optimization algorithm, including the number of iterations and convergence conditions.

[0074] It should be noted that initializing the particle swarm optimization algorithm includes setting the particle swarm size, initial particle positions and velocities, and defining the parameters of the multi-objective optimization algorithm, such as weight coefficients and constraints. The algorithm's running parameters, such as the number of iterations and convergence conditions, are then configured to ensure that the optimization process can be completed within the limited computational resources.

[0075] S402. Using the energy error index and frequency domain distribution error index as optimization objective functions, the differences in root mean square values ​​and power spectral density between the experimental data and the model output are quantified respectively. The first relative stiffness and the first relative damping, as well as the second relative stiffness and the second relative damping in the model established in the second step, are set as optimization variables, and their initial value range and step size are set. The optimization variables are substituted into the model using the optimization algorithm to calculate the acceleration response of the model output, and the degree of matching between the model output and the experimental data is evaluated through the objective function.

[0076] It should be noted that the energy error and frequency domain distribution error proposed in the third step are used as the optimization objective functions. The energy error is quantified by calculating the difference between the root mean square (RMS) value of the experimentally measured acceleration signal and the root mean square value of the model-simulated acceleration signal; the frequency domain distribution error is quantified by calculating the difference between the power spectral density (PSD) of the experimentally measured acceleration signal and the power spectral density of the model-simulated acceleration signal.

[0077] S403. In each iteration, the optimization variables are updated according to the rules of the optimization algorithm, the acceleration response of the model is recalculated, the objective function value is evaluated, and it is determined whether the optimization process meets the convergence condition. The convergence condition is that the rate of change of the objective function value is less than a set threshold or the preset number of iterations is reached. If it is not met, the next iteration continues. If it is met, the output is performed. When the optimization process meets the convergence condition, the optimal relative stiffness and damping parameter solution set is extracted from the optimization algorithm, and the optimization process is completed to obtain the optimal relative stiffness and damping parameter solution set.

[0078] It should be noted that, through a multi-objective optimization algorithm, the four sets of parameters are abstracted into particles carrying four positional information and individuals carrying four decision variables. A Simulink simulation model is then used to simulate the corresponding accelerations a1 and a2. Subsequently, two consistency indices, DIF, between this set of acceleration signals and the measured acceleration signals are calculated. rms With DIF freq Then, based on the performance of the two main metrics, subsequent algorithm optimization operations are performed. The specific process is as follows: Figure 4 As shown.

[0079] Preliminary analysis revealed that the two criteria for matching the acceleration signal are contradictory optimization objectives; that is, there is no set of parameters k1, k2, c1, c2 that can satisfy DIF. rms With DIF freq Simultaneously optimizing to the minimum value is a typical multi-objective optimization problem. A multi-objective optimization algorithm can be used to optimize DIF... rms With DIF freq The Pareto front was obtained by calculating these two objective values, as follows: Figure 5As shown, this reveals the specific relationship between these two conflicting objective values ​​in the objective space. The optimization results show that the horizontal axis energy error DIF... rms The minimum value can be optimized to 0.017, which is close to 0; the vertical axis frequency domain distribution error DIF freq The minimum value can be optimized to around 0.13.

[0080] To comprehensively understand the energy error DIF rms Frequency domain distribution error DIF freq The effect of the two-degree-of-freedom system model on the selection Figure 5 The analysis will be conducted in three regions. Region 1 primarily considers the consistency of energy error, Region 2 primarily considers the consistency of frequency domain distribution error, and Region 3 considers the effects of both energy error and frequency domain distribution error in a balanced manner.

[0081] Before conducting a detailed exploration of the three regions using the particle swarm optimization algorithm, it is necessary to first determine the range of variation of the four parameters corresponding to each region, that is, to determine the solution space explored by the particle swarm optimization algorithm. For example... Figure 6 and Figure 7 As shown, based on the Pareto optimal solution set obtained in the multi-objective optimization algorithm, the specific parameters k1, k2, c1, and c2 of each individual in region 1, region 2, and region 3 can be obtained.

[0082] according to Figure 6 and Figure 7 The individual parameter values ​​shown are used to set the exploration solution space X range for regions one to three as follows, with each range corresponding to the exploration range of k1, k2, c1, and c2 from left to right.

[0083] Xlimite1=[130000,310000;7000000,18000000;90000,94000;135000,145000];

[0084] Xlimite2=[1800000,2100000;17000000,19000000;23000,25000;3000,4000];

[0085] Xlimite3=[2400000,3400000;28000000,31000000;29000,32000;2700,3200].

[0086] Within region one, the energy error DIF is used. rms The exploration aims to minimize the frequency domain distribution error DIF within region two. freq The exploration aims to minimize this error, focusing on the sum of energy error and frequency domain distribution error, DIF, within region three.rms +10DIF freq The goal is to optimize to the minimum. Here, the frequency domain distribution error is multiplied by 10 to ensure that the numerical changes of the two errors are on the same order of magnitude during particle exploration.

[0087] After a detailed exploration of the solution spaces in the three regions using the particle swarm optimization algorithm, the optimal position for region 1 was found to be (243870.9599, 16481629.8249, 92183.5018, 144897.7146), which was taken as parameter one. The optimal position for region 2 was (1829506.5888, 17830002.3427, 23353.687, 3552.3682), which was taken as parameter two. The optimal position for region 3 was (3255723.317, 30745926.4246, 30258.8645, 2768.1721), which was taken as parameter three.

[0088] Among them, the energy error DIF under parameter one rms The frequency domain distribution error DIF is 1.5125E-06. freq The energy error DIF under parameter two is 0.21338. rms The frequency domain distribution error DIF is 5.8631. freq The energy error DIF under parameter three is 0.13014. rms The frequency domain distribution error DIF is 2.9771. freq The value is 0.16023. Therefore, under the action of the three sets of parameters, the energy frequency domain distribution difference between the accelerations a1 and a2 simulated by the model and the experimentally measured acceleration signals is shown.

[0089] As can be seen, under parameter one, the simulated acceleration signal is completely consistent with the measured signal in terms of energy magnitude, but its frequency domain energy distribution is excessively concentrated in the 40–90 Hz band. Under parameter two, the simulated acceleration signal is basically consistent with the measured signal in terms of frequency domain energy distribution, but the simulated signal energy is lower, differing by 5.8631. Under parameter three, the simulated acceleration signal is basically consistent with the measured signal in terms of frequency domain energy distribution, and its energy magnitude is also closer, differing by only 2.9771.

[0090] Based on the matching results and the optimal set of relative stiffness and damping parameters, a bolt loosening vibration test was conducted using S500. Combined with the optimized model parameters, the bolt loosening damage and lifespan were analyzed.

[0091] Understandably, in step S500, firstly, a bolt loosening vibration test is conducted to obtain the bolt lateral displacement-loosening life curve (DN curve). Then, the optimal relative stiffness and damping parameter solution set (k1, k2, c1, and c2) obtained above is input into the established two-degree-of-freedom vibration system model of the bolt connection structure, thus obtaining the relative displacement x2-x1 between the bolt and the connected parts. Next, based on the rainflow counting method and the bolt loosening DN curve, rainflow counting is performed on the relative displacement of the bolt connection under random vibration to obtain the number of cycles at each relative displacement amplitude of the bolt connection. Then, a bolt loosening damage calculation model is established as shown in equations (3) and (4). Based on the bolt loosening damage calculation model, the bolt loosening damage value and loosening life are obtained.

[0092] To investigate the loosening life characteristics of bolts and quantitatively analyze the vibration of a two-degree-of-freedom vibration system in a bolted connection structure, it is necessary to obtain the relationship between the lateral relative displacement between the bolted components and the bolt loosening life. In this embodiment, an 8.8 grade M16×2×120 high-strength bolt was used as the test object. A bolt loosening vibration test was conducted using an MTS 809 tensile-torsional fatigue testing machine, and the bolt clamping force decay curves under various lateral relative displacement amplitudes were obtained. Furthermore, the number of cyclic vibrations experienced by the bolt when it reached 90% loosening under different relative displacement amplitudes was statistically analyzed, yielding the bolt lateral displacement-loosening life curve (DN curve). In a double logarithmic coordinate system, this curve exhibits the characteristics of two straight lines and a high-low cycle boundary.

[0093] The expression for the low-cycle loosening curve is:

[0094] d 6.59 N = 11.50

[0095] The expression for the high-cycle loosening curve is:

[0096] d 1.29 N = 1.25 × 10 4 (2)

[0097] In the formula, d is the lateral relative displacement, and N is the bolt loosening life.

[0098] Based on the linear cumulative damage theory, this invention first proposes the fundamental assumptions applicable to the linear cumulative bolt loosening model: when the cumulative displacement damage to the bolt reaches a critical threshold, its clamping force will decrease to 90% of the initial preload, at which point the bolt is considered to have loosened and failed. Under this assumption, if the displacement damage limit before 90% loosening is W, and the total number of cycles of relative displacement before loosening failure is N, then the displacement damage of one cycle n1 is W1, and there is a proportional relationship between the two, namely:

[0099]

[0100] If the relative displacements that cause the bolt to loosen are d1, d2, ..., d l At that time, according to the DN curve, the loosening life at each displacement amplitude level is N1, N2, ..., N l If the actual number of cycles for each displacement amplitude level is n1, n2, ..., n l Furthermore, when the total loosening damage value G reaches the limit value W, and the critical value for bolt loosening is set to 1, the bolt loosening damage calculation model can be expressed as:

[0101]

[0102] Inputting the three sets of parameters k1, k2, c1, and c2 obtained above into the two-degree-of-freedom vibration system model of the bolted connection structure established in the first step yields the relative displacement x2-x1 between the bolt and the connected parts. Then, based on the rainflow counting method and combined with the bolt loosening DN curve obtained in the sixth step, rainflow counting is performed on the relative displacement of the bolted connection under random vibration to obtain the number of cycles for each relative displacement amplitude of the bolted connection.

[0103] Based on the formula corresponding to low-to-high cycle loosening of the DN curve shown above, the loosening damage of bolts under the action of the above three parameters can be evaluated. First, based on the rainflow counting method, the rainflow counting diagrams of the relative displacement of the bolt connection corresponding to the three sets of parameters under random vibration conditions are obtained; then, based on the DN curve, the number of cycles of the bolt at each relative displacement amplitude is obtained; finally, based on the bolt loosening damage calculation model, the loosening damage values ​​of the bolt are obtained as follows: 0.2898 under parameter one, 1.4098 under parameter two, and 0.9348 under parameter three.

[0104] Therefore, under parameter three, the bolt loosening damage value is closest to 1 and does not exceed 1. This means that the bolt loosening damage value is closest to the loosening condition where the clamping force drops to 90% of the initial preload. (Energy error DIF) rms When the vibration parameters are dominant, the model excites more small relative displacements below 0.05 mm, thus the calculated bolt loosening damage value is underestimated. The frequency domain distribution error DIF is used as an example. freqThe vibration parameter two, obtained under the dominant condition, caused the model to generate a larger relative displacement, mainly between 0.1 and 0.2 mm, with a further relative displacement approaching 0.3 mm. Therefore, the calculated bolt loosening damage value was too high. Observing the rainflow counting diagram of the relative displacement under parameter three, it can be found that the distribution of the relative displacement amplitude is more even, without the relative displacement amplitude being mainly distributed in the high-cycle loosening range, or the situation where the relative displacement amplitude is too large and causes low-cycle loosening. The relative displacement amplitude is distributed at around 0.1 mm, so the calculated bolt loosening damage value is more reasonable and consistent with the actual vibration of the two-degree-of-freedom bolt connection system.

[0105] The main beneficial effects of this invention are reflected in the following aspects:

[0106] 1. Solved the problem of obtaining key parameters:

[0107] This paper directly addresses the core problem in engineering practice where the relative stiffness and damping between components of bolted connection systems are difficult to measure or calculate directly. It provides an indirect but effective approach: obtaining these key parameters through experimentation and optimization inversion.

[0108] 2. Improved model prediction accuracy and reliability:

[0109] By proposing the energy error DIF rms Frequency domain distribution error DIF freq These two quantitative indicators can scientifically and objectively evaluate the degree of matching between the output results of the simulation model (two-degree-of-freedom model) and the actual measurement data. The system quantifies the degree of matching between the simulation and the measured acceleration, providing an objective basis for assessing the loosening state.

[0110] Using multi-objective optimization and particle swarm optimization algorithms, the parameter space was systematically explored, and the optimal match between simulated and measured accelerations (i.e., minimizing DIF) was found. rms and DIF freq The optimal combination of relative stiffness and damping parameters.

[0111] This significantly reduces the model's sensitivity to initial parameter assumptions and greatly improves the accuracy of the two-degree-of-freedom vibration model in describing the dynamic response of real bolted connection systems.

[0112] 3. A practical link from vibration response to life prediction has been established:

[0113] The patented method does not study parameter identification in isolation, but rather integrates it closely with the ultimate goal of predicting bolt loosening life.

[0114] Preliminary experiments yielded bolt loosening-life curves (DN curves). Using optimized model parameters that accurately reflect the actual vibration of the system, combined with the DN curves, a quantitative assessment of bolt loosening damage was achieved. This provides a theoretical basis and practical tool for predicting the service life of bolts under vibration environments.

[0115] 4. Enhanced the applicability and guiding value of the project:

[0116] The entire method is based on data obtained from actual bench random vibration tests and bolt loosening tests, and has a solid engineering practice foundation. The final output of optimal parameters and loosening damage prediction results can provide direct reference for engineering structural design, health monitoring, and preventive maintenance, helping engineers to assess the reliability of bolted connections and optimize designs or develop maintenance strategies.

[0117] 5. Provides a systematic solution:

[0118] The patent demonstrates a complete closed-loop process: experimental data acquisition → model building and problem identification → evaluation index innovation → optimization algorithm to solve key parameters → damage prediction based on life curve.

[0119] This method is systematic, operable, and has the potential for widespread application. It can be applied to vibration analysis and life prediction problems of other bolted connection structures or more extensive mechanical connection structures that have similar difficulties in parameter identification.

[0120] Example 2:

[0121] like Figure 8 As shown, this embodiment provides a vehicle bolt loosening life prediction system based on a vibration system model. See [link to relevant documentation]. Figure 8 The system includes:

[0122] Acquisition module 701: used to acquire bolt clamping force and related vibration data through vibration table test, wherein the related vibration data includes vibration acceleration data of vibration table surface, test fixture and bolt connection structure;

[0123] Module 702: Used to establish a two-degree-of-freedom vibration system dynamic model of the bolt connection structure based on the obtained bolt clamping force and related vibration data;

[0124] Module 703: Used to introduce energy error index and frequency domain distribution error index, quantify the degree of matching between simulation results and actual experimental data in the dynamic model of a two-degree-of-freedom vibration system, and obtain matching results;

[0125] Optimization module 704: Used to optimize the relative stiffness and damping parameters of the dynamic model of a two-degree-of-freedom vibration system using multi-objective optimization algorithm and particle swarm optimization algorithm, so as to obtain the optimal solution set of relative stiffness and damping parameters;

[0126] Prediction module 705: Used to conduct bolt loosening vibration tests based on matching results and the optimal set of relative stiffness and damping parameters, and to analyze and predict bolt loosening damage and lifespan by combining optimized model parameters.

[0127] Specifically, the establishment module 702 includes:

[0128] Establishment Unit: Based on the arrangement of the test fixtures, this unit determines the vibration direction and defines the displacement variables of the vibration table, test fixtures, and bolted connection structure. It also sets the mass of the vibration table, test fixtures, and bolted connection structure, defines the first relative stiffness and first damping between the test fixture and the vibration table, and the second relative stiffness and second damping between the bolted connection structure and the test fixture. Based on Newton's second law, and combining the first relative stiffness, first damping, second relative stiffness, and second damping, it establishes the dynamic equations of the vibration table, test fixtures, and bolted connection structure, forming a preliminary two-degree-of-freedom system dynamic model.

[0129] The updated unit is used to define the velocity variables of the vibration table, test fixture, and bolted connection structure. The velocity variables are substituted into the preliminary two-degree-of-freedom system dynamic model, replacing the original displacement derivative terms, updating the preliminary two-degree-of-freedom system dynamic model, and by introducing velocity variables, forming the final two-degree-of-freedom vibration system dynamic model that includes displacement and velocity.

[0130] Specifically, the optimization module 704 includes:

[0131] The setting unit is used to select the multi-objective optimization algorithm and the particle swarm optimization algorithm as parameter optimization tools, initialize the parameters of the particle swarm optimization algorithm, including the particle swarm size, initial position and velocity, configure the weight coefficients and constraints of the multi-objective optimization algorithm, and set the running parameters of the optimization algorithm, including the number of iterations and convergence conditions.

[0132] The computational unit is used to quantify the differences between the root mean square values ​​and power spectral density of the experimental data and the model output, respectively, by using the energy error index and the frequency domain distribution error index as optimization objective functions. It sets the first relative stiffness and first relative damping, and the second relative stiffness and second relative damping in the model established in the second step as optimization variables, and sets their initial value range and step size. The optimization variables are substituted into the model using an optimization algorithm to calculate the acceleration response of the model output, and the degree of matching between the model output and the experimental data is evaluated through the objective function.

[0133] Iteration Judgment Unit: In each iteration, it updates the optimization variables according to the rules of the optimization algorithm, recalculates the acceleration response of the model, evaluates the objective function value, and determines whether the optimization process meets the convergence condition. The convergence condition is that the rate of change of the objective function value is less than a set threshold or the preset number of iterations is reached. If it does not meet the condition, it continues to the next iteration; if it does meet the condition, it outputs the result. When the optimization process meets the convergence condition, it extracts the optimal relative stiffness and damping parameter solution set from the optimization algorithm, thereby completing the optimization process and obtaining the optimal relative stiffness and damping parameter solution set.

[0134] It should be noted that the specific methods by which each module performs operations in the system described in the above embodiments have been described in detail in the embodiments related to the method, and will not be elaborated here.

[0135] Example 3:

[0136] Corresponding to the above method embodiments, this embodiment also provides a vehicle bolt loosening life prediction device based on a vibration system model. The vehicle bolt loosening life prediction device based on a vibration system model described below can be referred to in conjunction with the vehicle bolt loosening life prediction method based on a vibration system model described above.

[0137] Figure 9 This is a block diagram illustrating a vehicle bolt loosening life prediction device 800 based on a vibration system model, according to an exemplary embodiment. Figure 9 As shown, the vehicle bolt loosening life prediction device 800 based on a vibration system model includes a processor 801 and a memory 802. The device also includes one or more of a multimedia component 803, an I / O interface 804, and a communication component 805.

[0138] The processor 801 controls the overall operation of the vehicle bolt loosening life prediction device 800 based on the vibration system model to complete all or part of the steps in the aforementioned vehicle bolt loosening life prediction method based on the vibration system model. The memory 802 stores various types of data to support the operation of the vehicle bolt loosening life prediction device 800 based on the vibration system model. This data may include, for example, instructions for any application or method operating on the vehicle bolt loosening life prediction device 800 based on the vibration system model, as well as application-related data, such as contact data, sent and received messages, images, audio, video, etc. The memory 802 can be implemented using any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read-Only Memory (EPROM), Programmable Read-Only Memory (PROM), Read-Only Memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The multimedia component 803 may include a screen and an audio component. The screen may be, for example, a touchscreen, and the audio component is used to output and / or input audio signals. For example, the audio component may include a microphone for receiving external audio signals. The received audio signals may be further stored in the memory 802 or transmitted via the communication component 805. The audio component also includes at least one speaker for outputting audio signals. I / O interface 804 provides an interface between processor 801 and other interface modules, such as a keyboard, mouse, or buttons. These buttons can be virtual or physical. Communication component 805 is used for wired or wireless communication between the vibration system model-based vehicle bolt loosening life prediction device 800 and other devices. Wireless communication includes, for example, Wi-Fi, Bluetooth, Near Field Communication (NFC), 2G, 3G, or 4G, or a combination thereof. Therefore, the corresponding communication component 805 may include a Wi-Fi module, a Bluetooth module, or an NFC module.

[0139] In an exemplary embodiment, the vehicle bolt loosening life prediction device 800 based on a vibration system model may be implemented by one or more application-specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field programmable gate arrays (FPGAs), controllers, microcontrollers, microprocessors, or other electronic components to perform the above-described vehicle bolt loosening life prediction method based on a vibration system model.

[0140] In another exemplary embodiment, a computer-readable storage medium including program instructions is also provided. When executed by a processor, these program instructions implement the steps of the vehicle bolt loosening life prediction method based on a vibration system model described above. For example, the computer-readable storage medium may be the memory 802 including the program instructions described above. These program instructions may be executed by the processor 801 of the vehicle bolt loosening life prediction device 800 based on a vibration system model to complete the vehicle bolt loosening life prediction method based on a vibration system model described above.

[0141] Example 4:

[0142] Corresponding to the above method embodiments, this embodiment also provides a readable storage medium. The readable storage medium described below can be referred to in conjunction with the vehicle bolt loosening life prediction method based on vibration system model described above.

[0143] A computer program is stored on a readable storage medium, and when the computer program is executed by a processor, it implements the steps of the vehicle bolt loosening life prediction method based on a vibration system model in the above method embodiments.

[0144] Specifically, the readable storage medium can be a USB flash drive, a portable hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk, or any other readable storage medium capable of storing program code.

[0145] In summary, this invention obtains key data through experiments, conducts random vibration tests to acquire vibration response data of a two-degree-of-freedom system, and establishes a bolt loosening-life curve (DN curve) through bolt loosening tests, providing a foundation for damage accumulation modeling. It introduces error indices to quantify model matching, proposing energy error and frequency domain distribution error to evaluate the matching degree between simulated acceleration and measured data from the time and frequency domain perspectives, respectively. A multi-objective optimization algorithm is used to deduce optimal parameters: utilizing multi-objective optimization and particle swarm optimization algorithms, the influence of different relative stiffness and damping parameters on the error indices is explored, ultimately deriving the parameter combination that best matches actual working conditions. Finally, life prediction is achieved by combining the optimized two-degree-of-freedom vibration system model parameters with the DN curve to quantify the bolt loosening damage accumulation process and predict its remaining life.

[0146] In summary, the core benefits of this patent are: it innovatively combines experiments, quantitative evaluation indicators, and intelligent optimization algorithms to effectively overcome the engineering challenge of obtaining key dynamic parameters (relative stiffness and damping) of bolted connection systems, significantly improves the prediction accuracy of the two-degree-of-freedom vibration model, and successfully applies the accurate model to bolt loosening damage and life prediction, providing a reliable theoretical basis and practical prediction tool for engineering practice.

[0147] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0148] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for predicting the loosening life of vehicle bolts based on a vibration system model, characterized in that, include: Bolt clamping force and related vibration data were obtained through vibration table tests. The related vibration data included vibration acceleration data of the vibration table, test fixture and bolt connection structure. Based on the obtained bolt clamping force and related vibration data, a two-degree-of-freedom vibration system dynamic model of the bolt connection structure is established. By introducing energy error index and frequency domain distribution error index, the degree of matching between the simulation results and actual experimental data in the dynamic model of a two-degree-of-freedom vibration system is quantified, and the matching results are obtained. The relative stiffness and damping parameters of the dynamic model of a two-degree-of-freedom vibration system are optimized using multi-objective optimization algorithm and particle swarm optimization algorithm to obtain the optimal solution set of relative stiffness and damping parameters. Based on the matching results and the optimal set of relative stiffness and damping parameters, bolt loosening vibration tests were conducted. Combined with the optimized model parameters, the loosening damage and lifespan of the bolts were analyzed and predicted.

2. The method for predicting the loosening life of vehicle bolts based on a vibration system model according to claim 1, characterized in that, Based on the obtained bolt clamping force and related vibration data, a two-degree-of-freedom vibration system dynamic model of the bolted connection structure is established, including: Based on the arrangement of the test fixtures, the vibration direction is determined and the displacement variables of the vibration table, test fixtures, and bolted connection structure are defined. The masses of the vibration table, test fixtures, and bolted connection structure are set, and the first relative stiffness and first damping between the test fixtures and the vibration table, as well as the second relative stiffness and second damping between the bolted connection structure and the test fixture, are defined. Based on Newton's second law, and combined with the first relative stiffness, first damping, second relative stiffness, and second damping, the dynamic equations of the vibration table, test fixtures, and bolted connection structure are established, forming a preliminary two-degree-of-freedom system dynamic model. Define the velocity variables of the vibration table, test fixture, and bolted connection structure. Substitute the velocity variables into the preliminary two-degree-of-freedom system dynamic model, replace the original displacement derivative term, update the preliminary two-degree-of-freedom system dynamic model, and by introducing velocity variables, form the final two-degree-of-freedom vibration system dynamic model that includes displacement and velocity.

3. The method for predicting the loosening life of vehicle bolts based on a vibration system model according to claim 2, characterized in that, The calculation formula for the final two-degree-of-freedom vibration system dynamic model is as follows: In the formula, m1 and m2 represent the masses of the test fixture and the bolted connection structure, respectively; x0, x1, and x2 represent the first, second, and third displacements generated by the vibration table, the test fixture, and the bolted connection structure during vibration; k1 and c1 represent the first relative stiffness and the first relative damping between the test fixture and the vibration table; and k2 and c2 represent the second relative stiffness and the second relative damping between the bolted connection structure and the test fixture. and Let x0, x1, and x2 be the first derivatives, representing the first velocity, the second velocity, and the third velocity, respectively. and These are the second derivatives of x0, x1, and x2, respectively, representing the first acceleration, the second acceleration, and the third acceleration.

4. The method for predicting the loosening life of vehicle bolts based on a vibration system model according to claim 1, characterized in that, The energy error index and frequency domain distribution error index are introduced, and the calculation formula for the energy error index is as follows: DIF rms =(RMS exp1 -RMS sim1 ) 2 + (RMS exp2 -RMS sim2 ) 2 In the formula, DIF rms Represents energy error, RMS exp1,2 This represents the RMS value of the measured acceleration signal from the first test and the RMS value of the measured acceleration signal from the second test. sim1,2 This represents the RMS value of the acceleration signal from the first model simulation and the RMS value of the acceleration signal from the second model simulation. The formula for calculating the frequency domain distribution error index is as follows: In the formula, DIF freq PSD represents the frequency domain distribution error. exp1,2 This represents the measured acceleration signal PSD from the first experiment and the measured acceleration signal PSD from the second experiment. sim1,2 Let PSD represent the acceleration signal PSD of the first model simulation and the acceleration signal PSD of the second model simulation, and k represent the frequency domain range.

5. The method for predicting the loosening life of vehicle bolts based on a vibration system model according to claim 1, characterized in that, The relative stiffness and damping parameters of the dynamic model of the two-degree-of-freedom vibration system are optimized using multi-objective optimization algorithms and particle swarm optimization algorithms to obtain the optimal solution set of relative stiffness and damping parameters, including: Multi-objective optimization algorithm and particle swarm optimization algorithm are selected as parameter optimization tools. The parameters of the particle swarm optimization algorithm are initialized, including particle swarm size, initial position and velocity. The weight coefficients and constraints of the multi-objective optimization algorithm are configured. The running parameters of the optimization algorithm are set, including the number of iterations and convergence conditions. The energy error index and frequency domain distribution error index are used as optimization objective functions to quantify the differences in root mean square values ​​and power spectral density between experimental data and model output, respectively. The first relative stiffness and first relative damping, and the second relative stiffness and second relative damping in the model established in the second step are set as optimization variables, and their initial value range and step size are set. The optimization variables are substituted into the model using the optimization algorithm to calculate the acceleration response of the model output, and the degree of matching between the model output and the experimental data is evaluated through the objective function. In each iteration, the optimization variables are updated according to the rules of the optimization algorithm, the acceleration response of the model is recalculated, the objective function value is evaluated, and it is determined whether the optimization process meets the convergence condition. The convergence condition is that the rate of change of the objective function value is less than a set threshold or the preset number of iterations is reached. If it does not meet the condition, the next iteration continues. If it does meet the condition, the output is performed. When the optimization process meets the convergence condition, the optimal set of relative stiffness and damping parameters is extracted from the optimization algorithm, and the optimization process is completed, resulting in the optimal set of relative stiffness and damping parameters.

6. A vehicle bolt loosening life prediction system based on a vibration system model, wherein the vehicle bolt loosening life prediction method based on a vibration system model as described in claim 1 is characterized in that, include: Acquisition module: used to acquire bolt clamping force and related vibration data through vibration table test, including vibration acceleration data of vibration table surface, test fixture and bolt connection structure; The module is used to establish a two-degree-of-freedom vibration system dynamic model of the bolt connection structure based on the obtained bolt clamping force and related vibration data. The acquisition module is used to introduce energy error index and frequency domain distribution error index, quantify the degree of matching between the simulation results in the dynamic model of the two-degree-of-freedom vibration system and the actual experimental data, and obtain the matching results; Optimization module: Used to optimize the relative stiffness and damping parameters of a two-degree-of-freedom vibration system dynamic model using multi-objective optimization algorithm and particle swarm optimization algorithm, to obtain the optimal solution set of relative stiffness and damping parameters; Prediction module: Based on the matching results and the optimal set of relative stiffness and damping parameters, conduct bolt loosening vibration tests, and analyze and predict bolt loosening damage and life by combining the optimized model parameters.

7. The vehicle bolt loosening life prediction system based on a vibration system model according to claim 6, characterized in that, The establishment module includes: Establishment Unit: Based on the arrangement of the test fixtures, this unit determines the vibration direction and defines the displacement variables of the vibration table, test fixtures, and bolted connection structure. It also sets the mass of the vibration table, test fixtures, and bolted connection structure, defines the first relative stiffness and first damping between the test fixture and the vibration table, and the second relative stiffness and second damping between the bolted connection structure and the test fixture. Based on Newton's second law, and combining the first relative stiffness, first damping, second relative stiffness, and second damping, it establishes the dynamic equations of the vibration table, test fixtures, and bolted connection structure, forming a preliminary two-degree-of-freedom system dynamic model. The updated unit is used to define the velocity variables of the vibration table, test fixture, and bolted connection structure. The velocity variables are substituted into the preliminary two-degree-of-freedom system dynamic model, replacing the original displacement derivative terms, updating the preliminary two-degree-of-freedom system dynamic model, and by introducing velocity variables, forming the final two-degree-of-freedom vibration system dynamic model that includes displacement and velocity.

8. The vehicle bolt loosening life prediction system based on a vibration system model according to claim 6, characterized in that, The optimization module includes: The setting unit is used to select the multi-objective optimization algorithm and the particle swarm optimization algorithm as parameter optimization tools, initialize the parameters of the particle swarm optimization algorithm, including the particle swarm size, initial position and velocity, configure the weight coefficients and constraints of the multi-objective optimization algorithm, and set the running parameters of the optimization algorithm, including the number of iterations and convergence conditions. The computational unit is used to quantify the differences between the root mean square values ​​and power spectral density of the experimental data and the model output, respectively, by using the energy error index and the frequency domain distribution error index as optimization objective functions. It sets the first relative stiffness and first relative damping, and the second relative stiffness and second relative damping in the model established in the second step as optimization variables, and sets their initial value range and step size. The optimization variables are substituted into the model using an optimization algorithm to calculate the acceleration response of the model output, and the degree of matching between the model output and the experimental data is evaluated through the objective function. Iteration Judgment Unit: In each iteration, it updates the optimization variables according to the rules of the optimization algorithm, recalculates the acceleration response of the model, evaluates the objective function value, and determines whether the optimization process meets the convergence condition. The convergence condition is that the rate of change of the objective function value is less than a set threshold or the preset number of iterations is reached. If it does not meet the condition, it continues to the next iteration; if it does meet the condition, it outputs the result. When the optimization process meets the convergence condition, it extracts the optimal relative stiffness and damping parameter solution set from the optimization algorithm, thereby completing the optimization process and obtaining the optimal relative stiffness and damping parameter solution set.

9. A vehicle bolt loosening life prediction device based on a vibration system model, characterized in that, include: Memory, used to store computer programs; A processor, configured to execute the computer program to implement the vehicle bolt loosening life prediction method based on a vibration system model as described in any one of claims 1 to 5.

10. A readable storage medium, characterized in that: The readable storage medium stores a computer program that, when executed by a processor, implements the vehicle bolt loosening life prediction method based on a vibration system model as described in any one of claims 1 to 5.

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