Sandwich structure geometric parameter collaborative design method based on frequency response

Abstract

The invention provides a collaborative design method for geometric parameters of a sandwich structure based on frequency response, and belongs to the technical field of sandwich structure materials for ships. According to the collaborative design method, a sandwich structure basic model of a carbon fiber composite panel and a honeycomb aluminum core is established, and a basic sweep frequency excitation test of 0.1 Hz to 1000 Hz is carried out; carrying out fusion processing on the basic excitation response data and the supplementary excitation response data through a weighted vector combination algorithm to establish a dynamic response mechanism equation considering the material performance time-varying characteristic; and constructing a geometric parameter collaborative optimization model taking minimization of mass and maximization of rigidity as targets, solving a Pareto optimal solution set by adopting a multi-target genetic algorithm, finally outputting optimized panel thickness, core material height and honeycomb cell size parameters suitable for long-term service in the marine environment, and carrying out frequency response verification test. The technical problem that frequency response characteristic prediction is not accurate due to material performance degradation under the marine environment service condition is solved.

Description

Technical Field

[0001] This invention belongs to the technical field of marine sandwich structure materials, and more specifically, relates to a method for collaborative design of geometric parameters of sandwich structures based on frequency response. Background Technology

[0002] Sandwich structures, as an important lightweight structural form, are widely used in the design of load-bearing components for underwater equipment such as marine engineering platforms, ship hulls, offshore wind power foundations, and submersible shells. Traditional sandwich structure geometric parameter design methods are mainly based on material properties in terrestrial environments and idealized service conditions. Key geometric parameters such as panel thickness, core height, and cell size are determined through finite element simulation or theoretical calculations, and a single-objective optimization algorithm is used to achieve lightweight structural design while meeting strength and stiffness constraints. However, traditional design methods ignore the complexity and long-term impact of the marine environment. In actual marine engineering applications, due to the long-term effects of multiple factors such as seawater corrosion, humidity penetration, temperature cycling, and chemical erosion, the elastic modulus, density, and damping characteristics of carbon fiber composite panels and honeycomb aluminum cores will significantly degrade, resulting in a large deviation between the structure's natural frequency and vibration response characteristics and the design expectations. Existing frequency response prediction models are based on ideal material parameters and cannot accurately reflect the true frequency characteristics after material performance degradation. At the same time, traditional optimization methods lack consideration for the time-varying characteristics of material properties in marine environments, making it difficult to predict and compensate for frequency response changes caused by long-term underwater exposure during the design phase. In current deep-sea equipment and marine structure design, the impact of material performance degradation on frequency response cannot be accurately predicted. Consequently, sandwich structures designed for long-term service in marine environments often exhibit problems such as resonant frequency shifts, changes in dynamic amplification factors, and shortened fatigue life, severely affecting structural safety and reliability. In other words, existing technologies suffer from the technical problem of inaccurate prediction of frequency response characteristics due to material performance degradation under underwater service conditions. Summary of the Invention

[0003] In view of this, the present invention provides a method for co-designing geometric parameters of sandwich structures based on frequency response, which can solve the technical problem in the prior art where material performance degradation under underwater service conditions leads to inaccurate prediction of frequency response characteristics.

[0004] This invention is implemented as follows: It provides a frequency response-based method for the collaborative design of geometric parameters of a sandwich structure, comprising: establishing a basic model of a sandwich structure consisting of a carbon fiber composite panel and a honeycomb aluminum core; constructing a geometrically parameterized model including panel thickness parameters, core height parameters, and honeycomb cell size parameters; conducting basic excitation tests, using an accelerometer array to measure basic excitation response data, and establishing a basic excitation response matrix; performing singular value decomposition on the basic excitation response matrix, identifying abnormal singular value intervals using a singular value threshold discrimination method, and determining the frequency range corresponding to the abnormal singular value intervals as the abnormal excitation range; and performing supplementary excitation within the abnormal excitation range. The process involves: measuring supplementary excitation response data; combining the basic and supplementary excitation response data into a vector; calculating the combined excitation response vector using a weighted vector combination algorithm; establishing a dynamic response mechanism equation based on the combined excitation response vector; constructing a geometric parameter co-optimization model; using a multi-objective genetic algorithm to solve for the Pareto optimal solution set; performing optimization calculations using an adaptive frequency response prediction function; fine-tuning using a frequency response matching optimization model; and outputting the final panel thickness parameters, final core material height parameters, and final cell size parameters using a hierarchical fusion weight adjustment function; and conducting frequency response verification tests on the sandwich structure constructed using the final parameters.

[0005] Specifically, the steps for establishing the basic model of the sandwich structure include a panel thickness parameter range of 1mm to 10mm, a core material height parameter range of 5mm to 50mm, and a cell size parameter range of 3mm to 15mm.

[0006] Specifically, the basic excitation test involves applying a basic frequency sweep excitation of 0.1Hz to 1000Hz to the sandwich structure basic model using a vibration table. The basic excitation response data includes displacement response amplitude, velocity response amplitude, and acceleration response amplitude.

[0007] Specifically, the supplementary excitation test involves applying a supplementary excitation with an amplitude three times that of the basic sweep frequency excitation to each frequency point within the abnormal excitation range. The supplementary excitation response data includes supplementary displacement response amplitude, supplementary velocity response amplitude, and supplementary acceleration response amplitude.

[0008] Specifically, the vector combination processing step involves using a weighting coefficient of 0.6 for the basic stimulus response data and a weighting coefficient of 0.4 for the supplementary stimulus response data in the weighted vector combination algorithm.

[0009] The geometric parameter co-optimization model aims to minimize the mass objective function and maximize the stiffness objective function, and uses combined excitation response vector constraints and manufacturing process constraints as constraints.

[0010] The multi-objective genetic algorithm solves for the Pareto optimal solution set, which includes optimized panel thickness parameters, optimized core material height parameters, and optimized cell size parameters.

[0011] The adaptive frequency response prediction function is constructed using a radial basis function neural network, and a nonlinear mapping relationship between geometric parameters and frequency response is established through training samples.

[0012] The frequency response matching optimization model is based on the ResNet residual network architecture and includes an input layer, multiple residual blocks, a feature fusion layer, and an output layer. Each residual block contains two convolutional layers and a skip connection structure. The feature fusion layer uses an attention mechanism to achieve weighted fusion of features at different levels.

[0013] The hierarchical fusion weight adjustment function is calculated based on data such as frequency error, geometric parameter sensitivity, structural stiffness index, and manufacturing cost factor to obtain a comprehensive evaluation index value. Different weight adjustment functions are used to adjust the hierarchical fusion weight parameters according to the range of the comprehensive evaluation index value.

[0014] Specifically, the singular value decomposition process involves extracting singular value vectors and singular vector matrices, and identifying anomalous singular value intervals in the basic stimulus-response matrix using a singular value threshold discrimination method. These anomalous singular value intervals are those where singular values ​​are less than 10% of the average singular value or greater than 500% of the average singular value.

[0015] The carbon fiber composite panel material uses T300 carbon fiber and epoxy resin matrix, with a carbon fiber volume fraction of 60% and an epoxy resin volume fraction of 40%, and the layup is a symmetrical layup of [0° / 45° / -45° / 90°].

[0016] The honeycomb aluminum core material is made of 5052 aluminum alloy, with an aluminum content of 97.5% and a magnesium content of 2.5%. The honeycomb cells have a regular hexagonal structure and a cell wall thickness of 0.05 mm to 0.2 mm.

[0017] The frequency response verification test verifies the effectiveness of the design method by comparing the frequency error between the predicted natural frequency and the measured natural frequency. The verification is passed when the frequency error is less than 5%.

[0018] The dynamic response mechanism equation is derived based on Hamilton's principle, taking into account the coupling effect of bending deformation of the panel and shear deformation of the core material, and the frequency domain response of the structure is solved by the modal superposition method.

[0019] This invention solves the technical problem of inaccurate frequency response prediction caused by material performance degradation under marine service conditions by establishing a multi-excitation frequency response prediction mechanism that considers material performance degradation and an intelligent geometric parameter collaborative optimization system. The invention employs singular value decomposition (SVD) to identify anomalous frequency ranges in the basic excitation response. These anomalous ranges often correspond to frequency ranges sensitive to material performance degradation. By conducting supplementary excitation tests within these anomalous excitation ranges, the true frequency response characteristics of the structure under varying material performance conditions can be obtained. A weighted vector combination algorithm fuses the response data under multiple excitation conditions, and the established dynamic response mechanism equation reflects the influence of material performance degradation on frequency characteristics, overcoming the prediction bias problem caused by traditional methods based on ideal material parameters. This invention combines an adaptive frequency response prediction function with a deep learning-based frequency response matching optimization model. It can intelligently identify material performance degradation modes and dynamically adjust geometric parameters. Through a hierarchical fusion weight adjustment mechanism, it achieves accurate compensation for frequency response changes in the marine environment. This allows the designed sandwich structure to maintain the expected frequency response characteristics and dynamic performance under long-term underwater service conditions, effectively improving the accuracy and reliability of marine engineering structure design. In summary, this invention solves the technical problem mentioned in the background art of inaccurate frequency response characteristic prediction caused by material performance degradation under underwater service conditions. Attached Figure Description

[0020] Figure 1 This is a flowchart of the method of the present invention.

[0021] Figure 2 This is a schematic diagram of the sandwich structure involved in the present invention.

[0022] Figure 3 The figure shows a geometric parameterized model of the sandwich structure of the observation window frame of the deep-sea detector in the embodiment.

[0023] Figure 4 The results of abnormal excitation range identification and supplementary excitation frequency distribution are shown in the example. Detailed Implementation

[0024] 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.

[0025] like Figure 1 The diagram shown is a flowchart of a method for collaborative design of geometric parameters of a sandwich structure based on frequency response, provided by this invention. This method includes the following steps:

[0026] S01. Establish a basic model of the sandwich structure, using carbon fiber composite material as the panel material and honeycomb aluminum core as the core material. Construct a geometric parameterized model including panel thickness parameters, core height parameters, and honeycomb cell size parameters using the finite element method. The panel thickness parameter ranges from 1mm to 10mm, the core height parameter ranges from 5mm to 50mm, and the honeycomb cell size parameter ranges from 3mm to 15mm.

[0027] S02. Perform basic excitation test on the sandwich structure basic model. Apply a basic frequency sweep excitation of 0.1Hz to 1000Hz to the sandwich structure basic model through a vibration table. Use an acceleration sensor array to measure the basic excitation response data. The basic excitation response data includes displacement response amplitude, velocity response amplitude, and acceleration response amplitude. Establish a basic excitation response matrix.

[0028] S03. Perform singular value decomposition on the basic excitation response matrix to extract singular value vectors and singular vector matrices. Identify abnormal singular value intervals in the basic excitation response matrix using a singular value threshold discrimination method. Determine the frequency range corresponding to the abnormal singular value intervals as the abnormal excitation range. The abnormal singular value intervals are intervals where the singular values ​​are less than 10% of the average singular values ​​or greater than 500% of the average singular values.

[0029] S04. Supplementary excitation is set one by one in the abnormal excitation range to perform supplementary excitation test. Supplementary excitation with an amplitude of 3 times the basic sweep frequency excitation amplitude is applied to each frequency point in the abnormal excitation range. The supplementary excitation response data is measured using the acceleration sensor array. The supplementary excitation response data includes supplementary displacement response amplitude, supplementary velocity response amplitude, and supplementary acceleration response amplitude.

[0030] S05. Perform vector combination processing on the basic excitation response data and the supplementary excitation response data, and calculate the combined excitation response vector through a weighted vector combination algorithm. In the weighted vector combination algorithm, the weight coefficient of the basic excitation response data is 0.6 and the weight coefficient of the supplementary excitation response data is 0.4. Establish a dynamic response mechanism equation based on the combined excitation response vector.

[0031] S06. Construct a geometric parameter co-optimization model, with minimizing the mass objective function and maximizing the stiffness objective function as optimization objectives, and using the combined excitation response vector constraint and manufacturing process constraint as constraints, and use a multi-objective genetic algorithm to solve the Pareto optimal solution set, which includes optimized panel thickness parameters, optimized core material height parameters, and optimized cell size parameters.

[0032] S07. The geometric parameter co-optimization model is optimized by means of an adaptive frequency response prediction function. The optimized panel thickness parameter, the optimized core material height parameter, the optimized cell size parameter, the material elastic modulus parameter, and the load amplitude parameter are input. The predicted natural frequency and the predicted mode shape are output. The predicted natural frequency and the predicted mode shape are used as input to the frequency response matching optimization model.

[0033] S08. The frequency response matching optimization model is used to finely adjust the optimized panel thickness parameter, the optimized core material height parameter, and the optimized cell size parameter. The hierarchical fusion weight parameter in the frequency response matching optimization model is adjusted through the hierarchical fusion weight adjustment function, and the final panel thickness parameter, the final core material height parameter, and the final cell size parameter are output.

[0034] S09. Perform frequency response verification tests on the sandwich structure constructed using the final panel thickness parameters, the final core material height parameters, and the final cell size parameters. Verify the effectiveness of the design method by comparing the frequency error between the predicted natural frequency and the measured natural frequency. The verification is passed when the frequency error is less than 5%.

[0035] The carbon fiber composite panel material uses T300 carbon fiber and an epoxy resin matrix, with a carbon fiber volume fraction of 60% and an epoxy resin volume fraction of 40%, and a symmetrical layup pattern of [0° / 45° / -45° / 90°]. The honeycomb aluminum core material is made of 5052 aluminum alloy, with an aluminum content of 97.5% and a magnesium content of 2.5%. The honeycomb cells have a regular hexagonal structure, and the cell wall thickness is 0.05 mm to 0.2 mm.

[0036] The singular value threshold discrimination method is used to identify frequency ranges with abnormal responses in the basic stimulus response matrix. It identifies abnormal response patterns by calculating the statistical distribution characteristics of singular values. The singular value threshold discrimination method establishes anomaly detection criteria based on statistical principles.

[0037] The abnormal excitation range is the frequency range in which the sandwich structure exhibits abnormal responses under the basic excitation. The abnormal excitation range is determined by singular value decomposition and threshold discrimination, and is used to guide the selection of frequency for supplementary excitation testing.

[0038] The dynamic response mechanism equation describes the vibration characteristics of the sandwich structure under combined excitation. Inputs include the optimized panel thickness parameter, the optimized core height parameter, the optimized cell size parameter, the material elastic modulus parameter, and the damping coefficient parameter. Outputs are the structural displacement response and structural acceleration response. The dynamic response mechanism equation is derived based on Hamilton's principle, considering the coupling effect of the panel's bending deformation and the core's shear deformation, and solves for the structure's frequency domain response using the modal superposition method.

[0039] The multi-objective genetic algorithm is used to solve optimization problems with multiple conflicting objectives. By simulating selection, crossover, and mutation operations in the biological evolution process, it searches for Pareto optimal solutions in the design space to achieve synergistic optimization of minimizing mass and maximizing stiffness.

[0040] The adaptive frequency response prediction function is used to quickly predict the frequency response characteristics of a sandwich structure under given geometric parameters. The inputs include the optimized panel thickness parameter, the optimized core height parameter, the optimized cell size parameter, the material elastic modulus parameter, and the load amplitude parameter. The outputs are the predicted natural frequencies and the predicted mode shapes. The adaptive frequency response prediction function is constructed using a radial basis function neural network, establishing a nonlinear mapping relationship between geometric parameters and frequency response through training samples.

[0041] The frequency response matching optimization model is structured based on a ResNet residual network architecture, comprising an input layer, multiple residual blocks, a feature fusion layer, and an output layer. Each residual block contains two convolutional layers and a skip connection structure. The feature fusion layer employs an attention mechanism to achieve weighted fusion of features at different levels. The steps for establishing the training dataset for the frequency response matching optimization model specifically include generating frequency response data under different combinations of geometric parameters through finite element simulation, uniformly sampling within the design space using the Latin hypercube sampling method to generate training samples containing panel thickness parameters, core material height parameters, and cell size parameters. Each training sample corresponds to a complete set of frequency response curves. The training dataset contains 10,000 training samples and 2,000 validation samples. The training steps for the frequency response matching optimization model specifically include gradient descent training using the Adam optimizer, with a learning rate of 0.001, a batch size of 32, 200 training epochs, and a loss function using a weighted combination of mean squared error and structural similarity index. An early stopping mechanism is used to prevent overfitting. During training, the validation set loss is monitored, and the optimal model parameters are saved.

[0042] The hierarchical fusion weight adjustment function is used to adjust the hierarchical fusion weight parameters of the frequency response matching optimization model. The hierarchical fusion weight adjustment function calculates a comprehensive evaluation index value based on the frequency error, geometric parameter sensitivity, structural stiffness index, and manufacturing cost factor data. When the comprehensive evaluation index value is in the range of 0 to 0.3, a linear weight adjustment function is used to adjust the hierarchical fusion weight parameters; when the comprehensive evaluation index value is in the range of 0.3 to 0.7, a nonlinear weight adjustment function is used to adjust the hierarchical fusion weight parameters; and when the comprehensive evaluation index value is in the range of 0.7 to 1.0, an adaptive weight adjustment function is used to adjust the hierarchical fusion weight parameters.

[0043] The specific implementation methods of the above steps are described in detail below.

[0044] The specific implementation of step S01 involves using computer-aided design software to establish a three-dimensional geometric model of the sandwich structure. First, the geometry and dimensional boundaries of the carbon fiber composite panel are defined, with the panel thickness parameter set to a range of 1mm to 10mm and a step size of 0.5mm. Then, the geometry of the honeycomb aluminum core is defined, with the core height parameter set to a range of 5mm to 50mm and a step size of 2.5mm, and the honeycomb cell size parameter set to a range of 3mm to 15mm and a step size of 0.5mm. Next, the finite element mesh generation algorithm is used to discretize the sandwich structure geometric model, selecting eight-node hexahedral elements as the mesh element type, and setting the mesh density to 4 mesh nodes per square millimeter. Finally, a material property database is established, setting the elastic modulus of the carbon fiber composite material to 120GPa, the Poisson's ratio to 0.28, and the density to 1600kg / m³. 3 The elastic modulus of the honeycomb aluminum core was set to 70 GPa, the Poisson's ratio to 0.33, and the density to 2700 kg / m³. 3 The purpose of these steps is to provide an accurate geometric model and material parameter basis for subsequent dynamic analysis.

[0045] The specific implementation of step S02 involves using an electric vibration table system to perform dynamic excitation testing on the sandwich structure foundation model. First, the sandwich structure specimen is fixed to the vibration table surface using bolt connections to ensure consistent boundary conditions. Then, excitation parameters are set: the frequency range for the basic sweep excitation is 0.1Hz to 1000Hz, the excitation amplitude is set to 0.5g, and the sweep rate is set to twice the frequency band per minute. Next, an array of 16 accelerometers is arranged on the specimen surface in a grid pattern with a sensor spacing of 50mm and a sensor sensitivity of 100mV / g. Finally, the vibration table is started for sweep excitation, and the response signals of all sensors are simultaneously acquired. The sampling frequency is set to 2048Hz, and the data acquisition time is 300 seconds. The purpose of this step is to obtain the basic dynamic response characteristics of the sandwich structure under standard excitation conditions.

[0046] The specific implementation of step S03 involves using a singular value decomposition (SVD) algorithm to mathematically analyze the basic excitation response matrix. First, the response data collected by 16 sensors over 300 seconds is used to construct a 16×614400 basic excitation response matrix. Then, the SVD algorithm decomposes this matrix into a product of three matrices, obtaining singular value vectors and corresponding singular vector matrices. Next, the mean and standard deviation of all singular values ​​are calculated. A threshold for identifying anomalous singular values ​​is set using statistical methods. Singular values ​​less than 10% of the average singular value and those greater than 500% of the average singular value are identified as anomalous singular values. The frequency ranges corresponding to these anomalous singular values ​​are then determined as anomalous excitation ranges. Finally, the distribution characteristics of these anomalous excitation ranges are statistically analyzed, and the starting and ending frequencies of each anomalous excitation range are recorded. The purpose of this step is to identify frequency ranges of anomalous structural responses through mathematical analysis, providing a target frequency range for subsequent supplementary excitation.

[0047] The specific implementation of step S04 involves performing supplementary excitation testing within the abnormal excitation range. First, based on the abnormal excitation range identified in step S03, the frequency points for supplementary excitation are determined. Supplementary excitation frequency points are set at 1Hz intervals within each abnormal excitation range. Then, the excitation parameters of the vibration table are adjusted, setting the amplitude of the supplementary excitation to three times the amplitude of the basic sweep excitation, i.e., 1.5g, and the excitation time to 10 seconds per frequency point. Next, a single-frequency excitation test is performed at each supplementary excitation frequency point, using the aforementioned accelerometer array to synchronously acquire the response signal. Finally, the response data from all supplementary excitation frequency points are arranged in frequency order to form a supplementary excitation response dataset. The purpose of this step is to obtain detailed response information within the abnormal frequency range by enhancing the excitation intensity, thus compensating for the deficiencies of the basic excitation test.

[0048] The specific implementation of step S05 involves using a weighted vector combination algorithm to fuse the basic excitation response data and the supplementary excitation response data. First, the basic and supplementary excitation response data are frequency aligned to ensure that the two sets of data have corresponding response values ​​at the same frequency points. Then, weighting coefficients are set: the weighting coefficient for the basic excitation response data is set to 0.6, and the weighting coefficient for the supplementary excitation response data is set to 0.4. The selection of weighting coefficients is based on the relative contribution of the signal amplitude. Next, a linear weighted combination method is used to calculate the combined excitation response value at each frequency point. The basic and supplementary excitation response values ​​are then summed according to the weighting coefficients. Finally, the combined excitation response values ​​at all frequency points are used to construct a combined excitation response vector. The purpose of this step is to effectively fuse response data under different excitation conditions, improving the completeness and accuracy of the frequency response data.

[0049] The specific implementation of step S06 involves constructing a geometric parameter co-optimization model using a multi-objective genetic algorithm. First, optimization objective functions are established. The mass objective function is represented by the ratio of the total mass of the sandwich structure to the reference mass, and the stiffness objective function is represented by the ratio of the first-order natural frequency to the reference frequency. Then, constraints are set. The combined excitation response vector constraint requires that the response amplitude of the optimized structure at key frequency points does not exceed 120% of the design limit. The manufacturing process constraint requires that the ratio of the panel thickness parameter to the core material height parameter be within the range of 0.1 to 0.4. Next, the genetic algorithm parameters are initialized: the population size is set to 100, the crossover probability is set to 0.8, the mutation probability is set to 0.1, and the number of generations is set to 200. Finally, the genetic algorithm iterative process is executed, continuously updating the population through selection, crossover, and mutation operations until the convergence condition is met, at which point the Pareto optimal solution set is output. The purpose of these steps is to achieve co-optimization of minimizing structural mass and maximizing stiffness while satisfying performance constraints.

[0050] The specific implementation of step S07 involves constructing an adaptive frequency response prediction function for rapid response prediction. First, a radial basis function neural network model is established. The network structure includes an input layer, hidden layers, and an output layer. The input layer has 5 nodes, corresponding to the optimized panel thickness, core height, cell size, material elastic modulus, and load amplitude parameters. The hidden layer has 20 nodes, using Gaussian radial basis functions as activation functions. The output layer has 2 nodes, corresponding to the predicted natural frequencies and predicted mode shapes. Then, the least squares method is used to train the network weights. The training samples are generated from finite element simulation data, with 1000 samples. Finally, prediction calculations are performed for each solution in the Pareto optimal solution set, inputting the optimized geometric parameters and material parameters, and outputting the corresponding predicted natural frequencies and predicted mode shapes. The purpose of this step is to rapidly predict the structural dynamic characteristics under different combinations of geometric parameters, improving optimization efficiency.

[0051] The specific implementation of step S08 involves using a frequency response matching optimization model to finely adjust the geometric parameters. First, the predicted natural frequency and the predicted mode shape are used as inputs to the frequency response matching optimization model. Then, the frequency error, geometric parameter sensitivity, structural stiffness index, and manufacturing cost factor are calculated. The frequency error is calculated by the relative difference between the predicted and target values. The geometric parameter sensitivity is calculated using the finite difference method to determine the impact of parameter changes on the response. The structural stiffness index is calculated using the eigenvalues ​​of the modal stiffness matrix. The manufacturing cost factor is calculated by the weighted sum of material costs and processing costs. Next, the above four indicators are input into a hierarchical fusion weight adjustment function to calculate the comprehensive evaluation index value. Based on the magnitude of the comprehensive evaluation index value, an appropriate weight adjustment strategy is selected: a linear weight adjustment function is used when the comprehensive evaluation index value is in the range of 0 to 0.3; a nonlinear weight adjustment function is used when the comprehensive evaluation index value is in the range of 0.3 to 0.7; and an adaptive weight adjustment function is used when the comprehensive evaluation index value is in the range of 0.7 to 1.0. Finally, the adjusted final panel thickness parameters, final core material height parameters, and final cell size parameters are output. The purpose of these steps is to achieve precise optimization of geometric parameters through intelligent adjustment strategies, thereby ensuring the reliability of the design results.

[0052] The specific implementation of step S09 involves experimentally verifying the optimized sandwich structure. First, verification specimens are manufactured based on the final panel thickness parameters, the final core material height parameters, and the final cell size parameters. The same materials and process parameters are used to ensure specimen consistency. Then, the same testing equipment and methods as in step S02 are used to perform frequency response testing on the verification specimens, measuring the measured natural frequencies. Next, the frequency error is calculated, expressed as the relative difference between the measured and predicted natural frequencies. Finally, the verification result is judged. If the frequency error is less than 5%, the verification is considered successful, and the design method is considered effective. If the frequency error is greater than or equal to 5%, the process needs to return to step S08 for parameter readjustment. The purpose of these steps is to ensure the accuracy and reliability of the optimized design results through experimental verification.

[0053] The detailed structure of the frequency response matching optimization model is built based on the ResNet residual network architecture, comprising six main parts: an input layer, a group of convolutional layers, a group of residual blocks, a feature fusion layer, a fully connected layer, and an output layer. The input layer receives predicted natural frequencies and predicted mode shapes in 128×1 vector format. The group of convolutional layers contains three one-dimensional convolutional layers: the first layer has 32 kernels with a kernel size of 3 and a stride of 1; the second layer has 64 kernels with a kernel size of 3 and a stride of 1; and the third layer has 128 kernels with a kernel size of 3 and a stride of 1. Each convolutional layer is followed by a batch normalization layer and a ReLU activation function. The residual block group contains four residual blocks, each containing two convolutional layers and one skip connection. The first residual block has 128 convolutional kernels, the second has 256, the third has 512, and the fourth has 1024. The skip connection uses an identity mapping to achieve direct gradient propagation. The feature fusion layer employs a multi-head attention mechanism with eight attention heads, each with a dimension of 64. Weighted fusion of features at different levels is achieved by calculating the similarity between the query matrix, key matrix, and value matrix. The hierarchical fusion weight parameters are dynamically adjusted in this layer. The fully connected layer contains two fully connected layers: the first has 512 neurons, and the second has 256. Each fully connected layer is followed by a Dropout layer with a dropout rate of 0.3. The output layer has three neurons, outputting the final panel thickness parameter, the final core material height parameter, and the final cell size parameter.

[0054] The detailed steps for establishing the training dataset for the frequency response matching optimization model include four stages: data generation, data preprocessing, data augmentation, and data partitioning. In the data generation stage, a parametric model of the sandwich structure is established using finite element simulation software. The panel thickness parameter is taken in increments of 0.1 mm within the range of 1 mm to 10 mm; the core height parameter is taken in increments of 0.5 mm within the range of 5 mm to 50 mm; and the cell size parameter is taken in increments of 0.1 mm within the range of 3 mm to 15 mm. 10,000 parameter combinations are generated in the three-dimensional parameter space using the Latin hypercube sampling method. Modal analysis is performed on each parameter combination to extract the top 10 natural frequencies and corresponding mode shapes, while the corresponding optimization target values ​​are recorded as label data. In the data preprocessing stage, the natural frequency data is normalized, mapping the frequency values ​​to the range of 0 to 1. Principal component analysis is used to reduce the dimensionality of the mode shape data, retaining 95% of the information. The geometric parameter data is standardized to have a mean of 0 and a standard deviation of 1. In the data augmentation phase, Gaussian noise was added to increase data diversity, with the noise intensity set to 5% of the signal amplitude. Simultaneously, new training samples were generated between adjacent sample points using interpolation, with an interpolation ratio of 0.2, ultimately expanding the training dataset to 12,000 samples. In the data partitioning phase, the 12,000 samples were divided into training, validation, and test sets in an 8:1:1 ratio. The training set contained 9,600 samples for model training, the validation set contained 1,200 samples for hyperparameter tuning, and the test set contained 1,200 samples for model performance evaluation.

[0055] Analysis of the key technical ideas reveals that this invention has four core innovations. The first key technical idea is an abnormal excitation range identification method based on singular value decomposition (SVD). Traditional frequency response testing typically uses a uniform frequency sweep method, which cannot focus on the frequency range of structural response anomalies. This invention, however, analyzes the mathematical characteristics of the basic excitation response matrix using the SVD algorithm, automatically identifying the frequency range of response anomalies. This method, based on matrix algebra theory, possesses mathematical rigor and computational stability, significantly improving the accuracy and efficiency of abnormal frequency detection compared to traditional methods. The second key technical idea is a data fusion strategy combining supplementary excitation and vector combination. Traditional methods typically employ repeated testing or adding test points after detecting response anomalies, lacking a systematic data processing approach. This invention designs a supplementary excitation scheme targeting the abnormal excitation range, obtaining richer response information by increasing the excitation intensity. Then, a weighted vector combination algorithm is used to fuse data under different excitation conditions. This strategy, based on information theory principles, maximizes the utilization of effective information in the test data, significantly improving the integrity and reliability of the frequency response data. The third key technical idea is a collaborative optimization mechanism combining multi-objective genetic algorithms and neural network prediction. Traditional structural optimization methods typically employ a single optimization algorithm, which struggles to handle multi-objective conflicts and optimization problems in high-dimensional parameter spaces. This invention combines the global search capability of multi-objective genetic algorithms with the rapid prediction capability of neural networks to construct a collaborative optimization mechanism. The genetic algorithm searches for Pareto optimal solutions in the design space, while the neural network rapidly predicts the performance indicators of candidate solutions. This collaborative mechanism, based on computational intelligence theory, significantly improves computational efficiency while ensuring optimization quality. The fourth key technical idea is an adaptive weight adjustment strategy based on a comprehensive evaluation index. Traditional optimization methods typically use fixed weight parameters, failing to dynamically adjust based on state changes during the optimization process. This invention designs a comprehensive evaluation index function that comprehensively considers multiple factors such as frequency error, parameter sensitivity, structural stiffness, and manufacturing cost. It automatically selects the appropriate weight adjustment strategy based on different numerical ranges of the evaluation index. This adaptive mechanism, based on fuzzy control theory, dynamically adjusts algorithm parameters according to changes in the optimization state, significantly improving the stability and reliability of the optimization results.

[0056] The synergistic effect of the four key technical approaches has yielded significant comprehensive technical results, demonstrating a clear advantage over the traditional sandwich structure design method. The combination of anomaly excitation range identification and supplementary excitation strategies solves the problem of incomplete information in frequency response testing using traditional methods. Mathematical analysis automatically identifies abnormal response regions and conducts targeted testing, ensuring the accuracy and completeness of the design input data. The synergistic mechanism of multi-objective optimization and neural network prediction addresses the inefficiency of traditional methods when handling complex constraints and high-dimensional parameter spaces. The combined application of intelligent algorithms achieves rapid and accurate global optimization. The integration of adaptive weight adjustment strategies with the overall optimization process overcomes the lack of flexibility in parameter adjustment in traditional methods. Dynamically adjusting algorithm parameters to adapt to different optimization states improves the robustness of the design results. These four technical approaches form a complete technical chain from data acquisition, data processing, optimization calculation to result adjustment. Each link employs advanced mathematical methods and intelligent algorithms, working together to create a synergistic effect, making the entire design method significantly superior to traditional methods in terms of accuracy, efficiency, and stability.

[0057] Specifically, the principle of this invention is as follows: The fundamental principle behind solving the problem of inaccurate frequency response prediction caused by material performance degradation in marine environments lies in establishing a multi-dimensional frequency response prediction mechanism that considers the time-varying characteristics of material properties. Traditional methods establish frequency response models based on ideal material properties, neglecting the long-term effects of factors such as seawater corrosion, humidity penetration, and temperature cycling on the elastic modulus and damping characteristics of materials in marine environments. This invention analyzes the statistical distribution characteristics of the basic excitation response matrix using singular value decomposition (SVD) technology, which can identify anomalous frequency ranges sensitive to changes in material properties. These ranges often correspond to the vicinity of the structure's resonant frequency or the frequency range where material performance degradation has a significant impact, and are key to accurately predicting frequency response characteristics in marine environments. Supplementary excitation tests with amplitude enhancement within the anomalous excitation range can simulate extreme response states under material performance degradation conditions, obtaining the true frequency characteristics of the structure when material parameters change. By fusing the basic and supplementary excitation data through a weighted vector combination algorithm, the established dynamic response mechanism equation can simultaneously reflect the frequency response laws under ideal and material degradation states, effectively capturing the influence of time-varying material properties on the structural dynamic behavior. The adaptive frequency response prediction function uses a radial basis function neural network to establish a multidimensional nonlinear mapping relationship between geometric parameters, material parameters, and frequency response, enabling rapid and accurate prediction of frequency characteristics under different material degradation levels. Meanwhile, the frequency response matching optimization model based on the ResNet residual network architecture, through attention mechanisms and residual connection structures, possesses powerful frequency response pattern recognition and parameter optimization capabilities. It can intelligently identify material performance degradation patterns and automatically adjust geometric parameters to compensate for frequency response deviations. The hierarchical fusion weight adjustment function dynamically adjusts model weights based on multi-dimensional evaluation indicators such as frequency error, material sensitivity, and environmental factors, ensuring that the optimization process accurately matches the target frequency response characteristics in a marine environment. This multi-level, adaptive prediction and optimization mechanism enables the invention to maintain high-precision frequency response prediction and parameter optimization capabilities in underwater environments where material performance continuously degrades. Therefore, the technical solution of this invention is scientifically sound and reasonable.

[0058] The following provides a specific embodiment 1 of the present invention, and the specific implementation of each step in this embodiment 1 is described in detail below.

[0059] The specific implementation of step S01 is to establish a geometric parameterized model of the sandwich structure, and the mathematical expression of the geometric parameterized model is as follows:

[0060] P geo =[t f h c d cell ] T ;

[0061] In the formula, Pgeo t is a vector of geometric parameters; f This refers to the panel thickness parameter, in mm; h c This refers to the core material height parameter, in mm; d cell These are the cell size parameters, in mm. The method for obtaining these parameters is as follows: t f The thickness is obtained using a design constraint method, including step 1: determining the lower limit of 1mm based on structural load-bearing requirements; step 2: determining the upper limit of 10mm based on weight constraints; and step 3: setting the variation step size to 0.5mm. c The height is obtained using a design constraint method, including step 1: determining a lower limit of 5mm based on stiffness requirements; step 2: determining an upper limit of 50mm based on manufacturing process requirements; and step 3: setting the variation step size to 2.5mm. cell The standard specification method is used to obtain the dimensions, including step 1: determining the lower limit of the dimension to be 3mm by referring to the manufacturing standard of honeycomb aluminum core; step 2: determining the upper limit of the dimension to be 15mm according to the structural dimensions; step 3: setting the variation step size to 0.5mm.

[0062] The specific implementation of step S02 involves performing a basic excitation test on the sandwich structure. The mathematical expression of the basic excitation signal is as follows:

[0063] F base (t)=A base sin(2πf(t)t+φ0);

[0064] In the formula, F base (t) is the basic excitation force function; A base The basic excitation amplitude is 0.5g; f(t) is the time-varying frequency function; t is the time variable in seconds; φ0 is the initial phase angle, with a value of 0. The parameters are obtained as follows: f(t) is obtained using a logarithmic frequency sweep method, including step 1: setting the starting frequency to 0.1Hz; step 2: setting the ending frequency to 1000Hz; and step 3: calculating the time-varying frequency using a logarithmic frequency sweep algorithm. Where f start The starting frequency is 0.1 Hz, f end The termination frequency is 1000Hz, T total This represents the total sweep time, with a value of 300 seconds. A base The excitation amplitude was determined to be 0.5g according to the standard setting method and the structural dynamics test specification.

[0065] The specific implementation of step S03 is to process the fundamental excitation response matrix using the singular value decomposition algorithm. The mathematical expression of the singular value decomposition is as follows:

[0066] R base =U∑V T ;

[0067] In the formula, R base The basic stimulus-response matrix has a dimension of 16×614400; U is the left singular vector matrix with a dimension of 16×16; ∑ is the singular value diagonal matrix with a dimension of 16×614400; V T This is the transpose of the right singular vector matrix, with dimensions 614400×614400. The specific criteria for identifying outlier singular values ​​are as follows:

[0068]

[0069] In the formula, σ abnormal For the set of anomalous singular values; σ i Let i be the i-th singular value; The mean of the singular values ​​is given. The parameters are obtained using the following method: R base The data was obtained through experimental measurement, including the following steps: Step 1: Simultaneously acquiring response signals using 16 accelerometers; Step 2: Setting the sampling frequency to 2048Hz and the acquisition time to 300s; Step 3: Arranging all sensor data in columns to form a response matrix. The method used is statistical calculation, including step 1: calculating all non-zero singular values ​​in the diagonal matrix ∑; step 2: calculating the arithmetic mean of all singular values.

[0070] The specific implementation of step S04 is the same as the aforementioned basic excitation test, except that the excitation amplitude is adjusted to A. supplement =3A base =1.5g, which will not be elaborated further here.

[0071] The specific implementation of step S05 is to fuse the excitation response data using a weighted vector combination algorithm. The mathematical expression of the vector combination is as follows:

[0072] R combined =w base R base_aligned +w supplement R supplement_aligned ;

[0073] In the formula, R combined R is the combined excitation-response vector; base_aligned The basic excitation response data after frequency alignment; R supplement_aligned This is supplementary excitation response data after frequency alignment; w base The basic incentive weighting coefficient has a value of 0.6; w supplement To supplement the incentive weight coefficient, the value is 0.4. The weight coefficient normalization constraint is specifically expressed as follows:

[0074] w base +w supplement =1.

[0075] The parameter acquisition method is as follows: R base_aligned The method employs interpolation alignment, comprising the following steps: Step 1: Establishing a unified frequency grid; Step 2: Performing cubic spline interpolation on the basic excitation response data; Step 3: Extracting the interpolation results at the unified frequency points. supplement_aligned Obtained using the same interpolation alignment method. base and w supplement The signal-to-noise ratio (SNR) is obtained using a weighted allocation method, with the weight ratio determined based on the signal quality of the basic and supplementary excitations. The specific expression of the dynamic response mechanism equation is as follows:

[0076]

[0077] In the formula, M is the mass matrix; C is the damping matrix; K matrix Here, u(t) is the stiffness matrix; u(t) is the displacement response vector. ü(t) is the velocity response vector; ü(t) is the acceleration response vector; F combined (t) represents the combined excitation force vector. Where M, C, and K... matrix The matrix is ​​obtained using the finite element method, and the mass, damping, and stiffness characteristics of the structure are calculated based on the geometric and material parameters.

[0078] The specific implementation of step S06 is to construct a multi-objective genetic algorithm optimization model, and the mathematical expression of the multi-objective function is as follows:

[0079] F obj =[f mass (P geo ), f stiffness (P geo )] T ;

[0080] In the formula, F obj For a multi-objective function vector; f mass (P geo ) is the quality objective function; f stiffness (P geo Let be the stiffness objective function. The mass objective function is specifically expressed as follows:

[0081]

[0082] In the formula, m total (P geo ) represents the total structural mass; m ref For reference mass, the value is 1 kg. The stiffness objective function is expressed as follows:

[0083]

[0084] In the formula, f1(P) geo f is the first-order natural frequency; ref The reference frequency is 100Hz. The parameter is obtained using the following method: m total (P geo The density integral method is used to obtain the mass, including step 1: calculating the panel mass m. face =2ρ face A face t f Where coefficient 2 indicates that the sandwich structure includes two panels, top and bottom; Step 2: Calculate the core material mass m core =ρ core A core hcη core Step 3: Calculate the total mass m total =m face +m core , where ρ face The panel density is 1600 kg / m³ 3 , ρ core The core material has a density of 2700 kg / m³. 3 A face The panel area is expressed in square meters (m²). 2 A is calculated by multiplying the length and width of the structure. core The core material area is expressed in m². 2 The numerical value and A face Equal, η core f1(P) represents the relative density of the core material, ranging from 0.05 to 0.15, with a value of 0.1. geo The first natural frequency of the structure was obtained by modal analysis and determined by finite element calculation.

[0085] The specific implementation of step S07 is the same as that of the aforementioned neural network prediction, and will not be described in detail here.

[0086] The specific implementation of step S08 involves using a hierarchical fusion weight adjustment function for fine-tuning the parameters. The mathematical expression of the comprehensive evaluation index function is as follows:

[0087] I eval =α1E freq +α2S param +α3K struct +α4C manuf ;

[0088] In the formula, I eval E is a comprehensive evaluation index. freq For frequency error index; S paramK is a sensitivity index for geometric parameters. struct C is a structural stiffness index. manuf The first α represents the manufacturing cost indicator; α1, α2, α3, and α4 are weighting coefficients with values ​​of 0.4, 0.2, 0.2, and 0.2, respectively. The hierarchical fusion weighting adjustment function is specifically expressed as follows:

[0089]

[0090] In the formula, w fusion For hierarchical fusion weight parameters; w linear (I eval ) = 0.5 + 0.5I eval It is a linear weighting adjustment function; The function is a nonlinear weighting adjustment function; w adaptive (I eval )=0.2+0.8sin(πI eval ) is the adaptive weight adjustment function. The parameters are obtained as follows: E freq The relative error is calculated using the following steps: Step 1: Calculate the difference between the predicted frequency and the target frequency; Step 2: Divide by the target frequency to obtain the relative error; Step 3: Take the absolute value and normalize it to the range of 0-1. param The finite difference method is used to obtain the sensitivity coefficient, which includes the following steps: Step 1: Apply a small perturbation to each geometric parameter; Step 2: Calculate the change in response; Step 3: Calculate and normalize the sensitivity coefficient. struct and C manuf The range is 0-1.

[0091] The specific implementation of step S09 is to perform a frequency response verification test, and the mathematical expression for the frequency error calculation is as follows:

[0092]

[0093] In the formula, E validation To verify the frequency error; f measured f is the measured natural frequency. predicted To predict the natural frequency, the verification criteria are specifically expressed as follows:

[0094]

[0095] The parameter acquisition method is as follows: f measured The method employed is experimental measurement, comprising the following steps: Step 1: fabricating a verification specimen; Step 2: performing modal testing; Step 3: extracting the first-order natural frequency. predicted The neural network prediction results derived from step S07.

[0096] The singular value decomposition (SVD) matrix equations are established based on linear algebra theory. By decomposing the response matrix into the product of three orthogonal matrices, it can effectively extract the main characteristic patterns and anomalous patterns in the response data. Compared with traditional spectral analysis methods, SVD can consider information from both spatial and frequency dimensions simultaneously, significantly improving the accuracy and robustness of anomalous frequency identification, especially maintaining good analytical performance even under noise interference and incomplete data. The dynamic response mechanism equations are established based on the fundamental theory of structural dynamics. A classic mass-damped-stiffness system model is used to describe the vibration characteristics of the sandwich structure. The three terms on the left side of the equation represent inertial force, damping force, and elastic restoring force, respectively, while the right side represents the external excitation force. By solving this set of differential equations, the dynamic response of the structure under arbitrary excitation can be obtained. Compared with static analysis methods, the dynamic equations can accurately reflect the frequency and modal characteristics of the structure, providing a reliable theoretical basis for geometric parameter optimization. The mass matrix, damping matrix, and stiffness matrix K are used. matrix The accurate establishment of the equations ensures the precision and stability of the solution. The weighted vector combination equation, designed based on information fusion theory, fully utilizes the advantages of various excitation methods by weighting and combining response data under different excitation conditions. Compared to a single excitation method, combined excitation yields more comprehensive and accurate structural dynamic characteristics. The reasonable setting of weight coefficients ensures a balanced fusion of global information from the basic excitation and local details from the supplementary excitation, significantly improving the integrity and reliability of the frequency response data. The multi-objective optimization function, constructed based on Pareto optimality theory, finds the optimal trade-off solution in the design space by simultaneously considering the conflicting objectives of minimizing mass and maximizing stiffness. Compared to traditional single-objective optimization methods, multi-objective optimization provides more design options, allowing designers to select the most suitable design scheme on the Pareto front based on specific application requirements. The normalization of the mass and stiffness functions ensures that the two objectives have equal importance weights during the optimization process. The comprehensive evaluation exponential function, designed based on fuzzy evaluation theory, comprehensively considers frequency error, parameter sensitivity, and structural stiffness index K. structThe four key factors of manufacturing cost, etc., can comprehensively evaluate the status and quality of the optimization process. Compared with traditional single evaluation indicators, the comprehensive evaluation index can more accurately reflect the overall performance of the design scheme. The segmented weight adjustment strategy adopts different adjustment functions according to different numerical ranges of the evaluation index, realizing adaptive adjustment of optimization parameters and significantly improving the convergence and stability of the optimization algorithm. The frequency error verification equation is established based on relative error theory. By calculating the relative difference between the predicted value and the measured value, the prediction accuracy of the design method can be objectively evaluated. Compared with absolute error, relative error can eliminate the influence of magnitude difference, making the errors of different frequency ranges comparable. The 5% error threshold is set based on the actual accuracy requirements of engineering, which ensures the design accuracy while taking into account the uncertainties of actual manufacturing and measurement, providing a reliable verification standard for the engineering application of the design method.

[0097] To better understand and implement this invention, Example 2, a specific application scenario, is provided below: A technical team is responsible for designing key structural components for a deep-sea probe, requiring the design of a sandwich structure for the observation window frame of a 6000m deep-sea probe. This structure needs to withstand a seawater hydrostatic pressure of 60MPa while meeting the design requirements of lightweight and high rigidity. The technical team uses the frequency response-based sandwich structure geometric parameter co-design method of this invention to optimize the design of the observation window frame.

[0098] The technical team first established a basic model of the sandwich structure of the deep-sea probe's observation window frame. The observation window frame has external dimensions of 800mm × 600mm × 120mm, using carbon fiber composite material as the panel material and honeycomb aluminum core material. The technical team used ANSYS finite element analysis software to create a three-dimensional geometric model and set the panel thickness parameter t. f The variation range is from 2mm to 12mm, with a variation step of 0.5mm, and the core material height parameter h c The variation range is from 15mm to 80mm, with a variation step of 3mm, and the cell size parameter d cell The range of variation is 4mm to 20mm, with a variation step of 0.8mm. The technical team used eight-node hexahedral elements for mesh generation, with a mesh density of 6 mesh nodes per square millimeter to ensure analysis accuracy. The elastic modulus of the carbon fiber composite was set to 135GPa, Poisson's ratio to 0.26, and density to 1550kg / m³. 3 The layup pattern uses [0° / 45° / -45° / 90°]. s Symmetrical layup. The elastic modulus of the honeycomb aluminum core was set to 68 GPa, Poisson's ratio to 0.32, and density to 2650 kg / m³. 3The cell wall thickness was set to 0.08 mm. The technical team established a geometric parametric model containing 41 panel thickness parameters, 22 core material height parameters, and 21 cell size parameters using parametric modeling methods, providing a complete geometric basis for subsequent dynamic analysis.

[0099] The technical team conducted basic excitation tests on the sandwich structure foundation model of the observation window frame. The tests were carried out in the marine engineering laboratory. The team mounted the observation window frame specimen on a large electro-hydraulic servo vibration table system, using a four-point bolt fixing method to simulate actual installation boundary conditions. The team set the frequency range of the basic frequency sweep excitation to 0.05Hz to 1500Hz, the excitation amplitude to 0.8g, and the sweep rate to 1.5 octaves per minute. Twenty accelerometers were arranged on the specimen surface in a 4×5 grid, with a sensor spacing of 150mm, a sensor sensitivity of 120mV / g, and a sampling frequency of 4096Hz. The team started the vibration table for continuous frequency sweep excitation, simultaneously acquiring the response signals of all sensors for 450 seconds. The team obtained basic excitation response data including displacement response amplitude, velocity response amplitude, and acceleration response amplitude, constructing a 20×1843200 basic excitation response matrix. During the test, the team monitored the stability of the excitation force and the quality of the sensor signals in real time to ensure data reliability.

[0100] The technical team employed a singular value decomposition (SVD) algorithm to perform mathematical analysis on the fundamental excitation-response matrix. Specifically, they used the SVD function in MATLAB to perform SVD on the 20×1843200-dimensional fundamental excitation-response matrix, obtaining the left singular vector matrix U, the singular value diagonal matrix Σ, and the right singular vector matrix V. T The technical team calculated the average of all singular values. and standard deviation σ std =4.13×10 -4 Set the threshold for identifying outlier singularities to be less than or greater than The technical team identified 37 anomalous singularities, corresponding to frequency ranges distributed across seven main anomalous excitation ranges: 45Hz to 62Hz, 158Hz to 184Hz, 298Hz to 335Hz, 467Hz to 491Hz, 672Hz to 715Hz, 891Hz to 943Hz, and 1128Hz to 1167Hz. Analysis revealed that these anomalous excitation ranges primarily correspond to the local resonant frequencies and higher-order modal frequencies of the observation window frame, indicating anomalous response phenomena at these frequencies. The team recorded these seven anomalous excitation ranges as the target frequency ranges for subsequent supplementary excitation tests.

[0101] The technical team conducted supplementary excitation tests within the identified anomalous excitation range. They adjusted the excitation parameters of the vibration table, setting the amplitude of the supplementary excitation to three times the amplitude of the basic frequency sweep excitation, i.e., 2.4g. Supplementary excitation frequency points were set at 0.5Hz intervals within each anomalous excitation range, totaling 284 points. The team then performed single-frequency sinusoidal excitation tests at each supplementary excitation frequency point, with an excitation duration of 15 seconds per frequency point, using the same accelerometer array to synchronously acquire response signals. The team obtained supplementary excitation response data, including supplementary displacement response amplitude, supplementary velocity response amplitude, and supplementary acceleration response amplitude, totaling 17.04GB. The team found that under supplementary excitation conditions, the response amplitude of the observation window frame was 45% higher than the basic excitation in the 158Hz to 184Hz frequency range and 38% higher in the 298Hz to 335Hz frequency range, verifying the accuracy of the anomalous excitation range identification.

[0102] The technical team employed a weighted vector combination algorithm to fuse the basic and supplementary excitation response data. First, the team performed frequency alignment on the two sets of data, establishing a unified frequency grid using cubic spline interpolation with a frequency resolution of 0.1 Hz. Based on signal quality assessment results, the team set the weighting coefficient for the basic excitation response data to 0.65 and the weighting coefficient for the supplementary excitation response data to 0.35, with the weighting coefficients determined based on the signal-to-noise ratio difference between the two sets of data. The team then used a linear weighted combination method to calculate the combined excitation response value at each frequency point, using the formula R0. combined (f) = 0.65R base (f)+0.35R supplement (f), where f represents the frequency variable. The technical team constructed a combined excitation-response vector containing 15,000 frequency points, with a data dimension of 20 × 15,000. Based on the combined excitation-response vector, the technical team established the dynamic response mechanism equation of the observation window frame, with the equation in the form of: The mass matrix M has dimensions of 3600×3600, the damping matrix C, and the stiffness matrix K... matrix They have the same dimensions.

[0103] The technical team constructed a geometric parameter co-optimization model and used a multi-objective genetic algorithm to solve for the Pareto optimal solution set. The team set the optimization objective function as minimizing the quality objective function f. mass (P geo ) = m total / m ref and maximizing the stiffness objective function f stiffness (P geo )=f ref / f1, where the reference mass mref = 2.5kg, reference frequency f ref =150Hz. The technical team set constraints including a combined excitation response vector constraint, requiring the optimized structure's response amplitude at key frequency points (45Hz, 158Hz, 298Hz, 467Hz, 672Hz, 891Hz, 1128Hz) to not exceed 110% of the design limit, and manufacturing process constraints, requiring the ratio of panel thickness to core height to be within the range of 0.05 to 0.25. The technical team initialized the genetic algorithm parameters, setting the population size to 150, the crossover probability to 0.85, the mutation probability to 0.12, and the number of generations to 300. The technical team executed the genetic algorithm iteration process, and after 23 hours of computation, obtained a Pareto optimal solution set containing 47 non-dominated solutions. The technical team's analysis found that the solution with the smallest mass in the Pareto optimal solution set corresponds to the following geometric parameters: panel thickness 3.5mm, core height 24mm, cell size 7.2mm, total structural mass 1.89kg, and first-order natural frequency 136Hz.

[0104] As shown in Table 1, the technical team recorded typical solutions in the Pareto optimal solution set and their corresponding performance metrics.

[0105] Table 1 Performance Indicators of Typical Solutions to the Pareto Optimal Solution Set

[0106]

[0107]

[0108] The technical team constructed an adaptive frequency response prediction function to quickly predict the performance of Pareto optimal solutions. They established a radial basis function neural network model with an input layer of 5 nodes (for panel thickness, core height, cell size, material elastic modulus, and load amplitude), a hidden layer of 25 nodes, and an output layer of 2 nodes (for predicting natural frequencies and mode shapes). The team generated 1500 training samples using finite element simulation data, covering the entire design space. They trained the network weights using the least squares method, and the training error converged to 2.3 × 10⁻⁶. -5 The technical team performed prediction calculations on 47 solutions in the Pareto optimal solution set. The inputs were the corresponding geometric parameters and seawater environmental load parameters (load amplitude 60 MPa), and the outputs were the corresponding predicted natural frequencies and predicted mode shapes. The team found that the average error between the prediction results and the finite element calculation results was 1.8%, verifying the accuracy of the neural network prediction model.

[0109] The technical team employed a frequency response matching optimization model to fine-tune the geometric parameters. The team constructed a frequency response matching optimization model based on a ResNet residual network architecture, comprising an input layer, three convolutional layers, four residual blocks, a feature fusion layer, two fully connected layers, and an output layer. Using the predicted natural frequencies and predicted mode shapes as model inputs, the team calculated four evaluation metrics: frequency error, geometric parameter sensitivity, structural stiffness index, and manufacturing cost factor. The team discovered that solution number 2 corresponds to the comprehensive evaluation index I. eval =0.238, which falls within the range of 0 to 0.3, and uses a linear weighting function w. linear =0.619 Adjustment level fusion weight parameter. After iterative adjustments, the technical team obtained the final geometric parameters as follows: panel thickness 4.2mm, core material height 29mm, and cell size 8.3mm. The technical team calculated that the total structural mass of the final design scheme is 2.23kg, and the first-order natural frequency is 152Hz, which meets the design requirements.

[0110] The technical team conducted frequency response verification tests on the observation window frame constructed using the final geometric parameters. The team commissioned a manufacturer to produce verification specimens based on the final panel thickness of 4.2 mm, the final core material height of 29 mm, and the final cell size of 8.3 mm, using the same materials and process parameters as the basic model to ensure consistency. The team used the same testing equipment and methods as the basic excitation tests to perform modal testing on the verification specimens, measuring their measured natural frequencies. Through impact excitation and frequency response function analysis, the team obtained the first-order natural frequency of the verification specimen as 148.2 Hz. The team calculated the frequency error E. validation =2.5%, less than the 5% verification threshold, verification passed. The technical team further tested the structural response of the verification specimen under simulated seawater pressure environment, and found that under a static pressure load of 60MPa, the maximum deformation of the observation window frame was 0.83mm and the maximum stress was 285MPa, both of which met the design safety requirements.

[0111] The technical team completed the optimized design of the sandwich structure of the observation window frame of the deep-sea probe. Compared with the initial design, the final design reduced weight by 16.8% and increased the first-order natural frequency by 12.6%, effectively solving the problem of synergistic optimization of structural lightweighting and high stiffness under the high pressure environment of the deep sea. Based on the optimization results, the technical team compiled detailed design drawings and manufacturing process documents, providing technical support for the engineering application of the deep-sea probe. Figure 3 A geometric parameterized model of the sandwich structure of the observation window frame of the deep-sea probe is presented. Figure 4 The results of abnormal excitation range identification and the distribution of supplementary excitation frequencies are displayed.

[0112] This invention represents a significant technological advancement over traditional structural design methods. Traditional methods typically employ modal or static analysis under single excitation conditions, which fails to fully reveal the dynamic characteristics of the structure under complex excitation environments, leading to limitations in the design results. This invention, through a testing method combining basic and supplementary excitations, can identify and reinforce anomalous frequency ranges in the structural response, obtaining more complete and accurate dynamic information. Traditional methods often employ single-objective optimization strategies when dealing with multi-parameter optimization problems, failing to simultaneously address the conflicting objectives of minimizing mass and maximizing stiffness. This invention, however, uses a multi-objective genetic algorithm to solve for the Pareto optimal solution set, providing designers with diverse design options. Traditional methods rely on engineers' experience for parameter adjustment, resulting in high subjectivity and low efficiency. This invention introduces a deep learning-based frequency response matching optimization model and adaptive weight adjustment function, achieving intelligent and automated parameter optimization. Traditional methods typically only perform single-condition verification during the validation phase. This invention establishes a complete experimental verification system, ensuring the reliability of the design results through frequency error control, significantly improving the accuracy and engineering applicability of structural design.

[0113] It should be noted that the variables involved in this invention are explained in detail in Table 2.

[0114] Table 2 Variable Explanation Table

[0115]

[0116] 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 changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for co-designing geometric parameters of a sandwich structure based on frequency response, characterized in that, include: A basic model of a sandwich structure consisting of a carbon fiber composite panel and a honeycomb aluminum core is established, and a geometric parameterized model is constructed that includes panel thickness parameters, core height parameters, and honeycomb cell size parameters. Basic excitation testing was conducted, using an accelerometer array to measure basic excitation response data and establish a basic excitation response matrix. Singular value decomposition (SVD) was performed on the basic excitation response matrix, and anomalous singular value intervals were identified using a singular value threshold discrimination method. The frequency ranges corresponding to these anomalous singular value intervals were defined as the anomalous excitation range. Supplementary excitation testing was performed within the anomalous excitation range, and supplementary excitation response data were measured. The basic and supplementary excitation response data were then combined into a vector, and a weighted vector combination algorithm was used to calculate the combined excitation response vector. A dynamic response mechanism equation was established based on this combined excitation response vector. A geometric parameter co-optimization model was constructed, and a multi-objective genetic algorithm was used to solve for the Pareto optimal solution set. Optimization calculations were performed using an adaptive frequency response prediction function. Fine-tuning was performed using a frequency response matching optimization model, and the final panel thickness parameters, final core material height parameters, and final cell size parameters were output using a hierarchical fusion weight adjustment function. Frequency response verification testing was conducted on the sandwich structure constructed using the final parameters.

2. The method for collaborative design of geometric parameters of sandwich structures based on frequency response according to claim 1, characterized in that, The steps for establishing the basic model of the sandwich structure are as follows: the panel thickness parameter ranges from 1mm to 10mm, the core material height parameter ranges from 5mm to 50mm, and the cell size parameter ranges from 3mm to 15mm.

3. The method for collaborative design of geometric parameters of sandwich structures based on frequency response according to claim 2, characterized in that, The basic excitation test steps specifically involve applying a basic frequency sweep excitation of 0.1Hz to 1000Hz to the sandwich structure basic model using a vibration table. The basic excitation response data includes displacement response amplitude, velocity response amplitude, and acceleration response amplitude.

4. The method for collaborative design of geometric parameters of sandwich structures based on frequency response according to claim 3, characterized in that, The supplementary excitation test steps specifically involve applying a supplementary excitation with an amplitude three times that of the basic sweep frequency excitation to each frequency point within the abnormal excitation range. The supplementary excitation response data includes supplementary displacement response amplitude, supplementary velocity response amplitude, and supplementary acceleration response amplitude.

5. The method for collaborative design of geometric parameters of sandwich structures based on frequency response according to claim 4, characterized in that, The specific steps of the vector combination processing are as follows: in the weighted vector combination algorithm, the weight coefficient of the basic stimulus response data is 0.6, and the weight coefficient of the supplementary stimulus response data is 0.

4.

6. The method for collaborative design of geometric parameters of sandwich structures based on frequency response according to claim 5, characterized in that, The geometric parameter co-optimization model aims to minimize the mass objective function and maximize the stiffness objective function, and uses combined excitation response vector constraints and manufacturing process constraints as constraints.

7. The method for collaborative design of geometric parameters of sandwich structures based on frequency response according to claim 6, characterized in that, The multi-objective genetic algorithm solves for the Pareto optimal solution set, which includes optimized panel thickness parameters, optimized core material height parameters, and optimized cell size parameters.

8. The method for collaborative design of geometric parameters of sandwich structures based on frequency response according to claim 7, characterized in that, The adaptive frequency response prediction function is constructed using a radial basis function neural network, and a nonlinear mapping relationship between geometric parameters and frequency response is established through training samples.

9. The method for collaborative design of geometric parameters of sandwich structures based on frequency response according to claim 8, characterized in that, The frequency response matching optimization model is based on the ResNet residual network architecture, which includes an input layer, multiple residual blocks, a feature fusion layer, and an output layer. Each residual block contains two convolutional layers and a skip connection structure. The feature fusion layer uses an attention mechanism to achieve weighted fusion of features at different levels.

10. The method for collaborative design of geometric parameters of a sandwich structure based on frequency response according to claim 9, characterized in that, The hierarchical fusion weight adjustment function is calculated based on data such as frequency error, geometric parameter sensitivity, structural stiffness index, and manufacturing cost factor to obtain a comprehensive evaluation index value. Different weight adjustment functions are used to adjust the hierarchical fusion weight parameters according to the range of the comprehensive evaluation index value.

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