Nonlinear damping ratio prediction method of composite component under multi-factor coupling, computer device and computer program product

Abstract

The application relates to a composite component nonlinear damping ratio prediction method under multi-factor coupling, a computer device and a computer program product, and relates to the technical field of computers. The method comprises the following steps: obtaining test data sets of sample composite components under different environmental conditions and load actions and preprocessing; a finite element model is established and calibrated to generate numerical simulation data, which is combined with the test data to form a training data set; a damping ratio physical relationship expression is established based on the energy dissipation principle; a genetic programming algorithm is adopted to perform symbolic regression on the training data set and the physical relationship expression as a base function, and an iteration optimization is performed to generate a nonlinear damping ratio prediction model that fuses physical constraints; and parameters of a target composite component are input into the model to output a damping ratio prediction value, so that the problem of insufficient damping ratio prediction accuracy of the composite component under multi-factor coupling and damage evolution can be effectively solved, and the reliability of structure dynamic performance evaluation is improved.

Description

Technical Field

[0001] This application relates to the field of computer technology, specifically to a method for predicting the nonlinear damping ratio of composite components under multi-factor coupling, computer equipment, and computer program products. Background Technology

[0002] With the rapid development of infrastructure such as marine engineering, cross-sea bridges, and offshore wind power, composite components made of composite materials, concrete, and steel are widely used due to their excellent mechanical properties and durability. In the dynamic analysis and seismic assessment of these structures, the damping ratio is a key parameter determining the dynamic response amplitude, comfort evaluation, and safety verification. Currently, research on the damping characteristics of such composite components typically employs experimental methods based on the free decay method or hysteresis tests to obtain data, or uses finite element software to establish numerical models for simulation analysis. In engineering practice and theoretical research, experimental data under different environmental conditions (such as salt spray concentration and erosion time) and load conditions are often collected. Combined with material constitutive relations and energy dissipation principles, attempts are made to construct correlation models between the damping ratio and stress level, damage state, and geometric parameters to serve the full life-cycle performance assessment of the structure.

[0003] However, in the existing technology, due to the complex material composition of composite components and the highly nonlinear interface behavior, the damping ratio exhibits significant time-varying and multi-factor coupling characteristics. Existing estimation methods are difficult to accurately describe its evolution under the combined action of long-term environmental erosion and cyclic loading, resulting in large deviations in the dynamic response prediction results. There is a lack of high-precision prediction methods that can simultaneously integrate physical mechanisms and data characteristics. Summary of the Invention

[0004] This application provides a nonlinear damping ratio prediction method for composite components under multi-factor coupling, which can solve the technical problems of insufficient damping ratio prediction accuracy and lack of physical mechanism support in the face of multi-factor coupling and damage evolution in the existing technology.

[0005] In a first aspect, embodiments of this application provide a method for predicting the nonlinear damping ratio of a composite component under multi-factor coupling effects. The method is executed by a computer and includes the following steps: Step S1: Obtain the test dataset, which is obtained by measuring the damping characteristics of the sample composite component under different environmental conditions and loads; wherein, the sample composite component is composed of a composite material layer, a concrete layer and a steel pipe, the environmental conditions include seawater erosion cycle and salt solution concentration, the loads include normal loads, and the damping characteristic measurement includes measuring the damping ratio of the component at different damage stages by using the free decay method and / or hysteresis test method; Step S2: Perform data preprocessing on the experimental dataset to construct a standardized small sample dataset; Step S3: Establish and calibrate the finite element model of the sample composite component, calibrate the finite element model by comparing the experimental results, and perform parametric analysis based on the calibrated model to generate numerical simulation data under different working conditions. Step S4: Merge the standardized small sample dataset with the numerical simulation data into a training dataset, calculate the energy consumption per unit volume of the component based on the hysteresis curve in the training dataset, and establish a physical relationship expression for the damping ratio with stress, material parameters and damage degree as independent variables according to the principle of energy dissipation. Step S5: Using the genetic programming algorithm, with the training dataset as the target data and the physical relationship expression of the damping ratio as the basis function, a symbolic regression is performed to iteratively optimize and generate a nonlinear damping ratio prediction model that integrates physical constraints; Step S6: Input the material properties, geometric parameters, environmental conditions and load conditions of the target composite component into the nonlinear damping ratio prediction model, and output the predicted damping ratio value of the target composite component under the current damage state; wherein, the target composite component and the sample composite component have the same material composition and structural form.

[0006] Preferably, step S2 involves preprocessing the experimental dataset to construct a standardized small sample dataset, including: Using the Pearson correlation coefficient, key features with a correlation higher than a preset threshold with the damping ratio were selected from the experimental dataset; Z-score standardization is performed on the numerical features among the selected key features to unify the units of measurement; One-hot encoding is performed on the categorical features among the selected key features to convert them into numerical form.

[0007] Preferably, step S5, which involves using a genetic programming algorithm to perform symbolic regression to generate a nonlinear damping ratio prediction model, specifically includes: Step S51: Initialization, randomly generate several candidate formulas to form an initial formula group. Each candidate formula is composed of predefined construction units, which include at least variables, operators, constants and functions. Step S52: Fitness evaluation. Using mean squared error as the fitness function, calculate the error between the predicted value and the actual damping ratio of each candidate formula on the training dataset, and use the calculated error value as the prediction accuracy evaluation result of the candidate formula. Step S53: Selection and Evolution. Based on the prediction accuracy evaluation results, select one or more candidate formulas with the smallest prediction error as excellent individuals; perform crossover operations on the excellent individuals to exchange some of their structures, and / or perform mutation operations to randomly change their operators or functions, thereby generating a new generation of candidate formula population. Step S54: Iteration and convergence judgment. Repeat the fitness evaluation steps S52 and S53, and monitor in real time whether the preset convergence condition is met. The preset convergence condition includes any one of the following: the number of iterations reaches the preset maximum number of iterations, or the error value calculated by the fitness function is lower than the preset error threshold. Step S55: Model output. When the preset convergence condition is met, the iteration stops, and the candidate formula with the best prediction accuracy evaluation result in the current generation is output as a nonlinear damping ratio prediction model.

[0008] In one embodiment, the physical relationship expression for the damping ratio in step S4 is characterized by the following formula:

[0009] in, For the damping ratio, The elastic modulus of the material. For a unit volume of material at stress amplitude Damping energy dissipation under the following conditions The total volume of the component. This represents the maximum normal stress amplitude of the component's cross-section. Among them, the damping energy dissipation The following power-law constitutive relations are satisfied:

[0010] in, These are material parameters related to the type of material and the level of application.

[0011] In one embodiment, the mean square error in step S5 is calculated using the following formula:

[0012] in, Indicates mean square error; This represents the predicted value of each candidate formula on the training dataset. This indicates the actual damping ratio. The total number of samples for the composite component.

[0013] In a preferred embodiment, the nonlinear damping ratio prediction model is characterized by the following formula:

[0014] in, This represents the predicted damping ratio. Indicates the type of concrete. Indicates the layup angle of the composite material layer. For hollow rate, The cross-sectional shape of the sample composite component; The degree of damage is indicated, which is related to the seawater erosion cycle, the salt solution concentration, and the stress level. , These are real-valued parameters obtained by the genetic programming algorithm on the training dataset.

[0015] In one embodiment, step S6 is followed by a dynamic iterative update step: Step S71: Use the predicted damping ratio output in step S6 as the initial damping ratio, and use it as the current damping ratio in the current iteration round t; Step S72: Based on the current damping ratio, perform structural dynamic response analysis on the target composite component, and calculate the stress-strain parameters, deformation parameters, and damage parameters of the target composite component under the current iteration round t; Step S73: Update the damage degree of the target composite component based on at least one of the calculated stress-strain parameters, deformation parameters, and damage parameters; Step S74: Input the updated damage degree, the environmental conditions and the load in step S1, along with the material properties and geometric parameters of the target composite component, into the nonlinear damping ratio prediction model to obtain the updated damping ratio prediction value. Step S75: Use the updated predicted damping ratio as the current damping ratio for the next iteration t+1, and return to step S72 to achieve continuous recursive updating of the damping ratio as component damage evolves.

[0016] In one embodiment, the finite element model in step S3 is established using ABAQUS to simulate the composite material layer, concrete layer, and steel pipe respectively and define the interaction relationships of each interface; the parametric analysis includes changing at least one parameter among the number of composite material layers, the winding angle of the composite material, the strength of the concrete, and the thickness of the steel pipe.

[0017] The technical advantages of the first aspect of this application are as follows: First, the test dataset of the sample composite component under different environmental conditions and loads is obtained and preprocessed; then, a finite element model is established and calibrated to generate numerical simulation data, which is merged with the test data to form a training dataset; a physical relationship expression for the damping ratio is established based on the principle of energy dissipation; a genetic programming algorithm is used to perform symbolic regression with the training dataset as the target and the physical relationship expression as the basis function, and iterative optimization is performed to generate a nonlinear damping ratio prediction model that integrates physical constraints; finally, the parameters of the target composite component are input into the model to output the predicted damping ratio value, which can effectively solve the problem of insufficient prediction accuracy of the damping ratio of composite components under multi-factor coupling and damage evolution, and improve the reliability of structural dynamic performance evaluation.

[0018] In a second aspect, this application provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the method for predicting the nonlinear damping ratio of composite components under multi-factor coupling as described in the first aspect above.

[0019] Thirdly, this application provides a computer program product that stores a computer program, which, when executed by a computer device, implements the nonlinear damping ratio prediction method for composite components under multi-factor coupling as described in the first aspect above.

[0020] It is understood that the beneficial effects of the second and third aspects mentioned above can be found in the relevant descriptions in the first aspect above, and will not be repeated here. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 This paper illustrates the main process of a method for predicting the nonlinear damping ratio of a composite component under multi-factor coupling, as provided in an embodiment of this application. Figure 2 A schematic diagram of an embodiment of the present application relating to the generation of a nonlinear damping ratio prediction model incorporating physical constraints is shown. Figure 3 The illustration shows a schematic diagram of an embodiment of the present application involving the generation of data preprocessing of the experimental dataset to construct a standardized small sample dataset; Figure 4A schematic flowchart of an embodiment of the dynamic iterative update scheme involved in this application is shown; Figure 5 A schematic diagram of the structure of a computer device provided in an embodiment of this application is shown. Detailed Implementation

[0023] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0024] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0025] It should also be understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0026] As used in this application specification and the appended claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrase "if determined" or "if detected [the described condition or event]" may be interpreted, depending on the context, as meaning "once determined," "in response to determination," "once detected [the described condition or event]," or "in response to detection [the described condition or event]."

[0027] Furthermore, in the description of this application and the appended claims, the terms "first," "second," "third," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0028] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0029] In the description of the embodiments of this application, the term "multiple" refers to two or more (including two), unless otherwise expressly and specifically defined.

[0030] Understandably, when users are using small acoustic devices such as cochlear implants and hearing aids, complex ambient noise can significantly reduce speech intelligibility and device performance. Traditional speech enhancement algorithms are prone to producing musical noise or speech distortion in non-stationary noise scenarios, especially under low signal-to-noise ratio conditions where their effectiveness is limited. Furthermore, existing algorithms often rely on fixed parameters or single feature discrimination, making it difficult to adapt to dynamically changing noise environments.

[0031] The applicant has found that the prior art most closely related to this application mainly falls into the following categories: In existing technologies, the damping ratio of composite material-concrete-steel composite components is typically estimated based on empirical values. The large variations in damping ratio values ​​lead to errors in dynamic response prediction. Current methods do not consider environmental factors such as long-term seawater erosion and damage evolution under load, and their time-varying effects on the damping ratio, resulting in a lack of effective prediction models. Particularly in marine engineering environments, material degradation and interfacial debonding cause the damping ratio to exhibit nonlinear and time-varying characteristics, making traditional linear superposition or single-parameter estimation methods unable to accurately reflect the actual situation.

[0032] To address the technical problems of insufficient damping ratio prediction accuracy and lack of physical mechanism support in existing technologies when facing multi-factor coupling and damage evolution, please refer to Figure 1. This application provides a nonlinear damping ratio prediction method for composite components under multi-factor coupling. The execution subject of this method is a computer device, which can be a desktop computer, laptop computer, or smartphone, etc. The computer device stores the algorithm program related to the nonlinear damping ratio prediction method for composite components under multi-factor coupling. When the program is executed by the computer device, it implements the following... Figure 1 The method steps shown include: Step S1: Obtain the test dataset. The test dataset is obtained by measuring the damping characteristics of the sample composite component under different environmental conditions and loads. The sample composite component consists of a composite material layer, a concrete layer, and a steel pipe. The environmental conditions include the seawater erosion cycle and the salt solution concentration. The loads include normal loads. The damping characteristic measurement includes measuring the damping ratio of the component at different damage stages by using the free decay method and / or hysteresis test method. The sample composite component can be a combined structure formed by fiber-reinforced polymer (FRP), a concrete core, and external steel pipe constraints. The seawater erosion cycle in the environmental conditions can be the duration of the component's immersion in simulated seawater, for example, set to multiple gradients such as 30 days, 90 days, 180 days, 270 days, and 360 days; the salt solution concentration can simulate the content of salts such as sodium chloride in seawater, used to characterize the severity of the corrosive environment. The normal load in the load application can be the pressure or tension applied along the component's axial direction, used to simulate the stress state under actual working conditions. Damping characteristic determination is the process of obtaining the component's dynamic response parameters through physical experiments, specifically including the free decay method, which records the free vibration decay curve of the component after giving it an initial displacement and calculates the damping ratio using the logarithmic decay rate; and the hysteresis test method, which records the force-displacement hysteresis curve under cyclic loading and calculates the energy dissipation capacity using the equivalent viscous damping ratio formula. This step aims to construct a high-fidelity original database covering material degradation, environmental erosion, and load coupling effects, solving the problems of traditional methods having a single data source and lacking damage evolution information.

[0033] Step S2: Preprocess the experimental dataset to construct a standardized small sample dataset; Data preprocessing involves cleaning, filtering, and format conversion of the raw experimental data to eliminate dimensional differences and extract key features. A standardized small-sample dataset is a processed dataset with uniform dimensions, removed redundant information, and suitable for input to machine learning algorithms. Specifically, firstly, Pearson correlation coefficient analysis is used to analyze the linear correlation between each input variable and the damping ratio, filtering out key features with correlation coefficients higher than a preset threshold (e.g., 0.5) and eliminating irrelevant variables. Secondly, Z-score standardization is performed on the selected numerical features (e.g., load magnitude, erosion time) to convert them into a distribution with a mean of 0 and a standard deviation of 1, thus unifying the dimensions. Finally, one-hot encoding is performed on categorical features (e.g., concrete type, cross-sectional shape) to convert them into binary vector form, for example, encoding rectangular cross-sections as [1, 0] and circular cross-sections as [0, 1]. This processing effectively reduces noise interference and improves the convergence speed of model training, ensuring that parameters with different physical meanings are calculated on the same scale. This step provides high-quality, low-dimensional input data for subsequent symbolic regression, effectively mitigating the risk of overfitting under small sample conditions.

[0034] Step S3: Establish and calibrate the finite element model of the sample composite component, calibrate the finite element model by comparing the experimental results, and perform parametric analysis based on the calibrated model to generate numerical simulation data under different working conditions. The finite element model (FEM) can be a digital model built in a computer to simulate the mechanical behavior of composite components. It is typically created using software such as ABAQUS and includes three-dimensional solid elements of FRP layers, concrete layers, and steel pipes, defining the contact relationships and constitutive models between the interfaces. Model calibration involves adjusting material parameters, interfacial friction coefficients, and damage evolution rules in the model to ensure that the load-displacement curves and failure modes obtained from the numerical simulation are consistent with the experimental results. Parametric analysis, based on the calibrated model, involves systematically changing parameters such as the FRP ply angle, concrete strength grade, steel pipe thickness, and damage degree to simulate numerous working conditions not covered in experiments. Numerical simulation data can be an extended dataset obtained through finite element calculations, containing stress distribution, strain energy, and equivalent damping ratio under the corresponding working conditions. By introducing numerical simulation data, the quantity and diversity of training samples can be significantly expanded, compensating for the sample scarcity problem caused by the high cost and long cycle of physical experiments. This step achieves complementary fusion of virtual and real data, laying a solid data foundation for building a high-precision prediction model.

[0035] Step S4: Merge the standardized small sample dataset with the numerical simulation data into a training dataset, calculate the energy consumption per unit volume of the component based on the hysteresis curve in the training dataset, and establish a physical relationship expression for the damping ratio with stress, material parameters and damage degree as independent variables according to the principle of energy dissipation. The training dataset is the union of the standardized small sample dataset and the numerical simulation data mentioned above, ensuring broad data coverage. Energy consumption per unit volume can be the energy consumed by a component within a unit volume due to internal material friction, interface slippage, and microcrack propagation, specifically obtained by dividing the area enclosed by the hysteresis curve by the total volume of the component.

[0036] As an example, the physical relationship of the damping ratio is characterized by the following formula:

[0037] in, For the damping ratio, The elastic modulus of the material. For a unit volume of material at stress amplitude Damping energy dissipation under the following conditions The total volume of the component. This represents the maximum normal stress amplitude of the component's cross-section. Among them, the damping energy dissipation The following power-law constitutive relations are satisfied:

[0038] in, These are material parameters related to the type of material and the application level. For example, for FRP materials, n The value is typically greater than 2 to reflect its nonlinear energy dissipation characteristics. By embedding the physical mechanism into the mathematical expression, this step establishes the basic architecture of the model, ensuring that the final generated prediction model conforms to the basic principles of mechanics and avoiding the physical inconsistencies that may occur in purely data-driven models.

[0039] Step S5: Using the genetic programming algorithm, with the training dataset as the target data and the physical relationship expression of the damping ratio as the basis function, a symbolic regression is performed to iteratively optimize and generate a nonlinear damping ratio prediction model that incorporates physical constraints. Among them, genetic programming is an intelligent optimization algorithm that simulates the biological evolution process, used to automatically search for the optimal mathematical expression structure. Symbolic regression can discover the mathematical patterns behind data through evolutionary operations without pre-fixing the function form. The nonlinear damping ratio prediction model that incorporates physical constraints can be an explicit analytical model that conforms to both experimental and simulated data distributions and satisfies physical laws such as energy conservation.

[0040] As a specific implementation method, participate Figure 2 In step S5 of this application embodiment, the use of a genetic programming algorithm for symbolic regression to generate a nonlinear damping ratio prediction model specifically includes: Step S51 (Initialization): Randomly generate several candidate formulas to form an initial formula group. Each candidate formula is composed of predefined construction units, which include at least variables, operators, constants and functions. The initial formula population can be a set of multiple random mathematical expressions generated by the first generation of the algorithm. The building blocks are the basic elements that construct the formulas; variables include the previously determined stress, damage degree, and material parameters; operators include addition, subtraction, multiplication, and division; constants include randomly generated real numbers; and functions include nonlinear operators such as exponential, logarithmic, and trigonometric functions. For example, the initial population may generate simple formulas or more complex nested structures. Through random initialization, the algorithm can explore a broad solution space, avoiding getting trapped in local optima. This step provides a diverse starting population for subsequent evolutionary optimization.

[0041] Step S52 (Fitness Evaluation): Using the mean squared error as the fitness function, calculate the error between the predicted value and the actual damping ratio of each candidate formula on the training dataset, and use the calculated error value as the prediction accuracy evaluation result of the candidate formula. The fitness function is used to evaluate the quality of candidate formulas; here, mean squared error (MSE) is used to quantify the deviation between predicted and true values. As an example, the mean squared error in step S5 can be calculated using the following formula:

[0042] in, Indicates mean square error; This represents the predicted value of each candidate formula on the training dataset. This indicates the actual damping ratio. This represents the total number of samples in the composite component dataset. A smaller error value indicates higher fitness and a closer approximation to the true physical laws of the candidate formula. By traversing all samples in the training dataset, the generalization ability of the formula can be comprehensively evaluated. This step provides an objective quantitative basis for the selection operation, driving the algorithm towards higher accuracy.

[0043] Step S53 (Selection and Evolution): Based on the prediction accuracy evaluation results, select one or more candidate formulas with the smallest prediction error as excellent individuals; perform crossover operations on excellent individuals to exchange some of their structures, and / or perform mutation operations to randomly change their operators or functions, thereby generating a new generation of candidate formula population. In this process, "superior individuals" can be candidate formulas with high fitness rankings. Crossover can involve exchanging partial subtree structures of two superior individuals; for example, swapping the logarithmic term in formula A with the exponential term in formula B to generate a new formula that combines characteristics of both. Mutation can randomly change a node in the formula, such as changing a plus sign to a multiplication sign, or modifying variables... D Replace with variable A This approach introduces new genetic diversity. By selecting and retaining superior genes, cross-recombining advantageous structures, and using mutations to prevent premature convergence, the synergistic effect of these three factors allows the formula population to continuously optimize during iteration. This step simulates the survival-of-the-fittest mechanism of natural selection, gradually approaching the global optimum.

[0044] Step S54 (Iteration and Convergence Judgment): Repeat steps S52 and S53, and monitor in real time whether the preset convergence conditions are met; the preset convergence conditions include any of the following: the number of iterations reaches the preset maximum number of iterations, or the error value calculated by the fitness function is lower than the preset error threshold. The iteration can be a process of repeatedly performing evaluation, selection, crossover, and mutation. The convergence condition is the criterion for stopping the algorithm. A preset maximum number of generations is set, for example, to 100 or 500 generations to prevent infinite loops; a preset error threshold is set, for example, to... When the mean squared error is below this value, the model is considered sufficiently accurate. A real-time monitoring mechanism ensures timely termination when accuracy requirements are met or computational resources are exhausted, balancing computational efficiency and model accuracy. This step guarantees that the algorithm outputs stable and reliable results within a finite timeframe.

[0045] Step S55 (Model Output): When the preset convergence condition is met, stop the iteration and output the candidate formula with the best prediction accuracy evaluation result in the current generation as a nonlinear damping ratio prediction model. Among them, the nonlinear damping ratio prediction model is the best mathematical expression for the final output of the algorithm, which has a clear physical meaning and extremely high prediction accuracy. As a preferred example, the nonlinear damping ratio prediction model is characterized by the following formula:

[0046] It should be noted that the above formula is a preferred example formula selected by the genetic programming algorithm. That is, the formula is only a preferred formula of the nonlinear damping ratio prediction model, not the only formula. The nonlinear damping ratio prediction model can also be characterized by other formulas, which will not be elaborated here in the embodiments of this application. In the above preferred example formula, This represents the predicted damping ratio. Indicates the type of concrete. Indicates the layup angle of the composite material layer. For hollow rate, The cross-sectional shape of the sample composite component; The degree of damage is indicated, which is related to the seawater erosion cycle, the salt solution concentration, and the stress level. , These are the real-valued parameters obtained by the genetic programming algorithm on the training dataset. It can be understood that the above formula characterizes the nonlinear accelerating effect of damage on damping through the exponential term, reflects the marginal effect of concrete type through the logarithmic term, and captures the complex coupling mechanism between geometric parameters and material properties through power functions and trigonometric functions.

[0047] This step ultimately generates a white-box model that is highly interpretable and generalizable, directly serving engineering applications.

[0048] Step S6: Input the material properties, geometric parameters, environmental conditions and load conditions of the target composite component into the nonlinear damping ratio prediction model, and output the predicted damping ratio value of the target composite component under the current damage state; wherein, the target composite component and the sample composite component have the same material composition and structural form.

[0049] The target composite component can be the actual engineering structure to be evaluated, with material composition (FRP, concrete, steel pipe) and structural form consistent with the training samples. Input parameters include specific material properties (such as elastic modulus), geometric parameters (such as ply angle and void ratio), environmental conditions (such as erosion cycle corresponding to the service life), and load conditions (such as current stress level). After receiving these inputs, the model directly substitutes them into the generated analytical formulas to perform calculations and instantly outputs the corresponding predicted damping ratio value. This step realizes the transformation from theoretical model to engineering application, providing accurate parameter support for dynamic response analysis and seismic assessment of structures such as offshore platforms and cross-sea bridges, significantly improving the reliability of structural safety assessment.

[0050] This application achieves high-precision prediction of the nonlinear damping ratio of composite components under multi-factor coupling through the synergistic effect of the aforementioned technical features. The embodiments of this application pre-construct a high-quality hybrid dataset integrating physical experiments and numerical simulations, effectively solving the problem of training complex models with small sample data. Furthermore, the finite element model is calibrated using physical experiments, ensuring the authenticity and coverage of the data. Based on this, the embodiments introduce physical relationship expressions based on the principle of energy dissipation, providing solid physical constraints for subsequent symbolic regression and avoiding the phenomenon of violating mechanical common sense that may occur with purely data-driven models. Moreover, the embodiments utilize a genetic programming algorithm to intelligently optimize using the physical expressions as basis functions, automatically mining the complex nonlinear mapping relationships between damage degree, stress, material parameters, and geometric features, ultimately outputting an explicit analytical model containing various nonlinear operators such as exponential, logarithmic, and trigonometric functions. This model not only possesses the high precision of a black-box model but also the interpretability of a white-box model, clearly revealing the contribution mechanism of each factor to the damping ratio. Finally, the model was applied to a real-world engineering scenario, enabling rapid and accurate prediction of the damping ratio of the target component under its current damage state. This significantly improves the scientific rigor and accuracy of the dynamic performance evaluation of composite structures in marine environments.

[0051] Furthermore, in some embodiments, after performing the composite component nonlinear damping ratio prediction method of steps S1 to S6 above, a model verification step is also included: The nonlinear damping ratio prediction model is validated using a validation dataset different from the training dataset in step S4 above. The validation dataset includes finite element simulation data and / or existing literature data. The prediction accuracy of the model is evaluated by mean square error and mean absolute error.

[0052] Furthermore, in another optional embodiment, step S2 in the aforementioned embodiment method further includes a specific step of data preprocessing of the experimental dataset to address the problems of redundant features, inconsistent dimensions, and the inability to directly calculate categorical variables in the original data. (Refer to...) Figure 3 Step S2 specifically includes: Step S21: Using the Pearson correlation coefficient, key features with a correlation higher than a preset threshold with the damping ratio are selected from the experimental dataset; The Pearson correlation coefficient is a statistic used to measure the degree of linear correlation between two variables. Its value ranges from -1 to 1, with a value closer to 1 indicating a stronger linear correlation. In this step, the system first reads the original test dataset obtained in step S1, which includes material properties, environmental conditions, geometric parameters, and load conditions. It then calculates the Pearson correlation coefficient between each feature variable and the target variable (i.e., damping ratio). By setting a preset threshold, such as 0.6 or 0.7, the system retains only those features with absolute correlation coefficients higher than this threshold as key features, while discarding redundant variables with weak correlations. For example, if the correlation coefficient between seawater erosion cycle and damping ratio is found to be 0.85, and the correlation coefficient between salt solution concentration and damping ratio is 0.72, while the correlation coefficient between a certain minor geometric dimension parameter and damping ratio is only 0.15, then the former two are retained, and the latter is discarded. This feature selection mechanism based on statistical significance can effectively reduce the dimensionality of input data, reduce noise interference, and prevent overfitting caused by the introduction of irrelevant variables in the subsequent modeling process, thereby improving the model's generalization ability and robustness under small sample conditions.

[0053] Step S22: Perform Z-score standardization on the numerical features among the selected key features to unify the units of measurement; Numerical features refer to variables in the dataset that have continuous numerical meaning, such as normal load (unit: kN), erosion time (unit: days), and stress amplitude (unit: MPa). Because different physical quantities have vastly different dimensions and orders of magnitude, directly inputting them into the model can lead to features with larger numerical values ​​dominating the loss function calculation, affecting algorithm convergence. Z-score standardization transforms the original data into standard normally distributed data with a mean of 0 and a standard deviation of 1 by subtracting the mean of the feature and dividing by its standard deviation. Specifically, for any numerical feature... x The formula for calculating its standardized value z is: ,in μ This is the average value of the feature across the dataset. The standard deviation is denoted as .

[0054] For example, if the mean of the normal load is 500 kN and the standard deviation is 100 kN, when a sample load is 600 kN, it is converted to a standard value of 1.0 after processing. Similarly, if the mean of the erosion time is 180 days and the standard deviation is 90 days, when a sample time is 270 days, it is also converted to a standard value of 1.0. After this processing, all numerical features are on the same order of magnitude, eliminating the influence of dimensions. This allows the subsequent genetic programming algorithm to treat each variable fairly when searching for the optimal formula structure, significantly accelerating the iteration convergence speed and improving prediction accuracy.

[0055] Step S23: Perform one-hot encoding on the categorical features among the selected key features to convert them into numerical form in order to construct a standardized small sample dataset.

[0056] Categorical features can refer to non-numerical variables representing discrete states or types in the dataset, such as the type of concrete (C30, C40, etc.), the cross-sectional shape of composite components (circular, rectangular, etc.), and the layup method of composite material layers. These features cannot be directly involved in mathematical operations, and simply assigning integer numbers (e.g., circle = 1, rectangle = 2) will incorrectly introduce a size order, misleading the model into believing that rectangle is superior to circle. One-hot encoding solves this problem by mapping each category to an independent binary vector. Specifically, if the concrete type has... k Seed, then generate k A new binary feature column is generated. For a given sample, the column corresponding to its concrete type is marked as 1, and the other columns are marked as 0. For example, if the cross-sectional shape includes three types—circular, rectangular, and square—then three feature bits are generated after encoding: circular samples are represented as [1, 0, 0], and rectangular samples are represented as [0, 1, 0]. Through this encoding method, discrete category information is transformed into a numerical vector that the model can recognize. This preserves the independence between categories and avoids artificially imposed ordinal relationships, ensuring that the final nonlinear damping ratio prediction model can accurately capture the nonlinear influence of different material types and structural forms on damping characteristics.

[0057] This embodiment constructs a high-quality standardized small-sample dataset through the synergistic effect of the aforementioned data preprocessing steps. First, Pearson correlation coefficients are used to screen key features, eliminating noisy data unrelated to the damping ratio evolution law at the source, thus reducing model complexity. Based on this, Z-score normalization eliminates the dimensional barriers between multi-physics coupling factors (such as load, time, and stress), allowing parameters under different physical mechanisms to be balanced and calculated within the same mathematical space. Simultaneously, one-hot encoding technology transforms discrete engineering classification information into computable numerical vectors, bridging the gap between qualitative description and quantitative calculation. Steps S21, S22, and S23 collectively address the technical problems of complex data sources and inconsistent formats under multi-factor coupling, providing a structurally clear, semantically explicit, and numerically stable input foundation for the subsequent symbolic regression based on the genetic programming algorithm. This ensures that the final nonlinear damping ratio prediction model not only reflects the physical mechanism but also possesses extremely high prediction accuracy and generalization ability.

[0058] Furthermore, in practical engineering applications, the environmental erosion and cyclic loads experienced by composite components during long-term service are continuously changing, and the evolution of the damage state over time leads to dynamic changes in the damping ratio. If only the damping ratio predicted in a single instance is used for full-life dynamic response analysis, the coupling feedback mechanism between the damping ratio and damage evolution will be ignored, resulting in significant errors. Therefore, based on step S6, this application further provides a dynamic iterative update method to achieve the co-evolution calculation of the damping ratio and the time-varying damage state.

[0059] In one specific embodiment, reference Figure 4 The step S6 is followed by a dynamic iterative update step: Step S71: Use the predicted damping ratio output in step S6 as the initial damping ratio, and use it as the current damping ratio in the current iteration round t; Step S72: Based on the current damping ratio, perform structural dynamic response analysis on the target composite component, and calculate the stress-strain parameters, deformation parameters, and damage parameters of the target composite component under the current iteration round t; Specifically, a dynamic analysis model of the target composite component can be established using the finite element method (such as ABAQUS), with the current damping ratio input into the Rayleigh damping coefficient or modal damping ratio settings of the model. Under specified environmental conditions and loads (i.e., the seawater erosion cycle, salt solution concentration, and normal load in step S1), time history analysis or frequency response analysis is performed to calculate the stress-strain parameters (such as maximum normal stress amplitude), deformation parameters (such as deflection and interlayer displacement angle), and damage parameters (such as the proportion of interface debonding area, microcrack density, and damage degree) of the target composite component under the current damping ratio. (Updated value).

[0060] Step S73: Update the damage degree of the target composite component based on at least one of the calculated stress-strain parameters, deformation parameters, and damage parameters; Specifically, degree of damage The damage degree D can be recalibrated based on the combined effects of erosion time, salt solution concentration, and stress level, or calculated according to the cumulative damage law in damage mechanics (such as linear cumulative damage theory). For example, if the calculation finds that new interface debonding or concrete microcrack propagation has occurred in the component under the current stress level, the value of damage degree D should be increased accordingly.

[0061] Step S74: Input the updated damage degree, the environmental conditions and the load in step S1, along with the material properties and geometric parameters of the target composite component, into the nonlinear damping ratio prediction model to obtain the updated damping ratio prediction value. For example, the updated damage level, along with the environmental conditions and loads (i.e., seawater erosion cycle, salt solution concentration, normal load, etc.) in step S1, can be input into the nonlinear damping ratio prediction model along with the material properties (such as elastic modulus, concrete type) and geometric parameters (such as ply angle, void ratio, cross-sectional shape) of the target composite component. The model calculates the updated predicted damping ratio based on the latest damage state and environmental load conditions.

[0062] Step S75: Use the updated predicted damping ratio as the current damping ratio for the next iteration t+1, and return to step S72 to achieve continuous recursive updating of the damping ratio as component damage evolves. The dynamic iterative updating scheme of this embodiment is suitable for marine engineering structures subjected to long-term alternating loads and environmental erosion, and helps improve the accuracy of dynamic response time history analysis throughout the entire life cycle.

[0063] Secondly, this application also proposes a computer device, please refer to... Figure 5 , Figure 5 This is a schematic diagram of the structure of an embodiment of the computer device provided in this application. The computer device may be a desktop computer, a laptop computer, or a smartphone device, etc. This embodiment does not limit it.

[0064] like Figure 5 As shown, the computer device 1 of this embodiment includes: at least one processor 10, a memory 11, and a computer program 12 stored in the memory 11 and executable on the at least one processor 10. When the processor 10 executes the computer program 12, it implements the steps in the embodiment of the nonlinear damping ratio prediction method for composite components under multi-factor coupling described in this application.

[0065] Figure 5 The computer device shown may include, but is not limited to, processor 10 and memory 11. Those skilled in the art will understand that... Figure 5 The examples of computer devices are merely examples and do not constitute a limitation on computer devices. They may include more or fewer components than shown in the illustration, or combinations of certain components, or different components. For example, they may also include input / output devices, network access devices, etc.

[0066] The processor 10 may be a central processing unit (CPU), or it may be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0067] In some embodiments, the memory 11 may be an internal storage unit of the computer device, such as a hard drive or memory. In other embodiments, the memory 11 may be an external storage device of the computer device, such as a plug-in hard drive, Smart Media Card (SMC), Secure Digital (SD) card, or Flash Card. Furthermore, the memory 11 may include both internal and external storage units of the computer device. The memory 11 is used to store the operating system, applications, bootloader, data, and other programs, such as the program code of the editing program for the presentation file. The memory 11 can also be used to temporarily store data that has been output or will be output.

[0068] This application also provides a computer-readable storage medium including an editing program for a presentation file, which, when run on a computer, causes the computer to execute the method provided in the above-described embodiments of the method for predicting the nonlinear damping ratio of composite components under multi-factor coupling.

[0069] This application also provides a computer program product containing instructions that, when run on a computer, cause the computer to execute the method provided in the above-described embodiment of the method for predicting the nonlinear damping ratio of composite components under multi-factor coupling.

[0070] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for predicting the nonlinear damping ratio of a composite component under multi-factor coupling, characterized in that, The method is executed by a computer and includes the following steps: Step S1: Obtain the test dataset, which is obtained by measuring the damping characteristics of the sample composite component under different environmental conditions and loads; wherein, the sample composite component is composed of a composite material layer, a concrete layer and a steel pipe, the environmental conditions include seawater erosion cycle and salt solution concentration, the loads include normal loads, and the damping characteristic measurement includes measuring the damping ratio of the component at different damage stages by using the free decay method and / or hysteresis test method; Step S2: Perform data preprocessing on the experimental dataset to construct a standardized small sample dataset; Step S3: Establish and calibrate the finite element model of the sample composite component, calibrate the finite element model by comparing the experimental results, and perform parametric analysis based on the calibrated model to generate numerical simulation data under different working conditions. Step S4: Merge the standardized small sample dataset with the numerical simulation data into a training dataset, calculate the energy consumption per unit volume of the component based on the hysteresis curve in the training dataset, and establish a physical relationship expression for the damping ratio with stress, material parameters and damage degree as independent variables according to the principle of energy dissipation. Step S5: Using the genetic programming algorithm, with the training dataset as the target data and the physical relationship expression of the damping ratio as the basis function, a symbolic regression is performed to iteratively optimize and generate a nonlinear damping ratio prediction model that integrates physical constraints; Step S6: Input the material properties, geometric parameters, environmental conditions, and load conditions of the target composite component into the nonlinear damping ratio prediction model, and output the predicted damping ratio value of the target composite component under the current damage state; wherein, the target composite component has the same material composition and structural form as the sample composite component; The physical relationship expression for the damping ratio in step S4 is characterized by the following formula: in, For the damping ratio, The elastic modulus of the material. For a unit volume of material at stress amplitude Damping energy dissipation under the following conditions The total volume of the component. This represents the maximum normal stress amplitude of the component's cross-section. Among them, the damping energy dissipation The following power-law constitutive relations are satisfied: in, These are material parameters related to the type of material and the level of application.

2. The method as described in claim 1, characterized in that, Step S2 involves preprocessing the experimental dataset to construct a standardized small sample dataset, including: Using the Pearson correlation coefficient, key features with a correlation higher than a preset threshold with the damping ratio were selected from the experimental dataset; Z-score standardization is performed on the numerical features among the selected key features to unify the units of measurement; One-hot encoding is performed on the categorical features among the selected key features to convert them into numerical form in order to construct a standardized small sample dataset.

3. The method as described in claim 1, characterized in that, Step S5, which involves using a genetic programming algorithm to perform symbolic regression to generate a nonlinear damping ratio prediction model, specifically includes: Step S51: Randomly generate several candidate formulas to form an initial formula group. Each candidate formula is composed of predefined construction units, which include at least variables, operators, constants and functions. Step S52: Using the mean square error as the fitness function, calculate the error between the predicted value and the actual damping ratio of each candidate formula on the training dataset, and use the calculated error value as the prediction accuracy evaluation result of the candidate formula. Step S53: Based on the prediction accuracy evaluation results, select one or more candidate formulas with the smallest prediction error as excellent individuals; perform crossover operation on the excellent individuals to exchange some of their structures, and / or perform mutation operation to randomly change their operators or functions, thereby generating a new generation of candidate formula population; Step S54: Repeat steps S52 and S53, and monitor in real time whether the preset convergence condition is met; the preset convergence condition includes any one of the following: the number of iterations reaches the preset maximum number of iterations, or the error value calculated by the fitness function is lower than the preset error threshold. Step S55: When the preset convergence condition is met, stop the iteration and output the candidate formula with the best prediction accuracy evaluation result in the current generation as a nonlinear damping ratio prediction model.

4. The method as described in claim 3, characterized in that, The mean square error in step S5 is calculated using the following formula: in, Indicates mean square error; This represents the predicted value of each candidate formula on the training dataset. This indicates the actual damping ratio. The total number of samples for the composite component.

5. The method as described in claim 3, characterized in that, The nonlinear damping ratio prediction model is characterized by the following formula: in, This represents the predicted damping ratio. Indicates the type of concrete. Indicates the layup angle of the composite material layer. For hollow rate, The cross-sectional shape of the sample composite component; The degree of damage is indicated, and the degree of damage is related to the seawater erosion cycle, the salt solution concentration, and the stress level. , These are real-valued parameters obtained by the genetic programming algorithm on the training dataset.

6. The method according to any one of claims 1 to 5, characterized in that, Step S6 is followed by a dynamic iterative update step: Step S71: Use the predicted damping ratio output in step S6 as the initial damping ratio, and use it as the current damping ratio in the current iteration round t; Step S72: Based on the current damping ratio, perform structural dynamic response analysis on the target composite component, and calculate the stress-strain parameters, deformation parameters, and damage parameters of the target composite component under the current iteration round t; Step S73: Update the damage degree of the target composite component based on at least one of the calculated stress-strain parameters, deformation parameters, and damage parameters; Step S74: Input the updated damage degree, the environmental conditions and the load in step S1, along with the material properties and geometric parameters of the target composite component, into the nonlinear damping ratio prediction model to obtain the updated damping ratio prediction value. Step S75: Use the updated damping ratio prediction value as the current damping ratio for the next iteration t+1, and return to execute step S72.

7. The method according to any one of claims 1 to 5, characterized in that, In step S3, the finite element model is established using ABAQUS to simulate the composite material layer, the concrete layer, and the steel pipe, and to define the interaction relationship between the three. The parametric analysis includes changing at least one parameter among the number of composite material layers, the winding angle of the composite material, the strength of the concrete, and the thickness of the steel pipe.

8. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the nonlinear damping ratio prediction method for composite components under multi-factor coupling as described in any one of claims 1 to 7.

9. A computer program product, said computer program product storing a computer program, characterized in that, When the computer program is executed by a computer device, it implements the nonlinear damping ratio prediction method for composite components under multi-factor coupling as described in any one of claims 1 to 7.

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