Dynamic response modeling and parameter influence quantitative analysis method for high-energy absorption device

Abstract

In order to solve the problems that an existing high-energy absorption device dynamic response modeling method is difficult to consider efficiency and precision and only can qualitatively analyze influence of a single parameter, the invention provides a high-energy absorption device dynamic response modeling and parameter influence quantitative analysis method, which comprises the following steps: firstly, establishing a mathematical model of a high-energy absorption device; secondly, numerical simulation is conducted through the mathematical model, dynamic responses of the high-energy absorption device under various inputs are calculated, training data are obtained, a WOA-BPNN prediction model is trained based on the training data, the prediction model can efficiently and accurately predict the dynamic responses of the high-energy absorption device under various working conditions, and numerical simulation does not need to be conducted on specific working conditions. And finally, quantitatively analyzing the influence of each parameter on the dynamic response of the high-energy absorption device by adopting a Sobol global sensitivity analysis method, and solving key parameters influencing the dynamic response of the high-energy absorption device and the interaction degree among the input parameters.

Description

Technical Field

[0001] The invention relates to a dynamic response modeling and parameter influence quantitative analysis method for a high energy absorption device. Background Art

[0002] The high energy absorption device is a key device to ensure the safety of short-distance landing of aircraft. It is a complex electromechanical and hydraulic system. Figure 1 As shown in the figure, the high energy absorption device mainly consists of an arresting cable, a pulley cable, a main energy absorption device, a pulley buffer device, and a cable end buffer device. When the aircraft lands on the deck, the tail hook of the aircraft pulls out the arresting cable, and the kinetic energy of the aircraft is quickly absorbed by the high energy absorption device in a controlled manner to ensure a safe landing. Among them, the main energy absorption device is the main energy absorption component of the high energy absorption device. Its structural principle diagram is shown in the figure. Figure 3As shown, the system comprises a master hydraulic cylinder, accumulator, control valve, movable pulley, and fixed pulley. When the arresting cable is pulled, the movable pulley moves toward the fixed pulley, driving a piston to compress the fluid in the master hydraulic cylinder, causing it to flow through the control valve to the accumulator. The control valve can adjust the arresting force to suit different operating conditions, ensuring that any aircraft can be stopped within the appropriate distance under all operating conditions. Due to the extremely limited runway length and the high speed and heavy weight of the aircraft during landing, the entire arrested landing process typically takes only seconds. This places enormous impact loads on the HEA during operation and involves complex coupling effects across multiple disciplines, including mechanics, hydraulics, and materials. This unique operating environment places extremely high demands on the HEA's dynamic performance, which is directly related to the aircraft's landing safety and service life. Efficiently solving the HEA's dynamic response and quantifying the interactive effects of multiple parameters are crucial for improving its reliability and optimizing its structural design. The paper "H. Zhang, JQ Guo, JP Liu, GX Ren, An efficient multibody dynamic model of arresting cable systems based on ALE formulation, Mechanism and Machine Theory 151 (2020)103892." uses multibody dynamics modeling and the arbitrary Lagrange-Eulerian (ALE) formula to describe the sliding contact between the tail hook / pulley and the cable. A mathematical model of the hydraulic damper is established, and finally, the system dynamics equations are established to solve the dynamic response of the high-energy absorber. However, this research is primarily based on numerical simulation. To solve the dynamic response of the high-energy absorber under high-density gradient conditions, numerical simulations must be performed for each condition. This often makes it difficult to strike a balance between efficiency and accuracy when obtaining the dynamic characteristics of the high-energy absorber. Furthermore, due to the low efficiency of numerical simulations, current research has difficulty quantitatively studying the influence of various parameters on the dynamic response of the high-energy absorber. Consequently, existing research typically focuses on the influence of a single factor, such as the aircraft's speed and mass, and primarily conducts qualitative analysis. Because these studies have neglected the interactions between multiple parameters and lacked quantitative analysis of the effects of multi-parameter coupling, it is difficult to further reveal the combined impact of various factors on the performance of high-energy absorbers. Therefore, there is an urgent need for an efficient and accurate method for modeling the dynamic response of high-energy absorbers and a quantitative analysis method for their parameter effects. This will provide methodological and data support for the evaluation and optimization of high-energy absorber system performance under multi-parameter coupling, thereby improving the reliability and performance of high-energy absorbers. Summary of the Invention

[0003] In order to solve the technical problems that the existing high-energy absorption device dynamic response modeling method is difficult to strike a balance between efficiency and accuracy, and can only qualitatively analyze the influence of a single parameter, the present invention provides a high-energy absorption device dynamic response modeling and parameter influence quantitative analysis method. The motion and mechanical relationship of each component of the high-energy absorption device is accurately described through multi-body dynamic modeling, and the dynamic response of the high-energy absorption device under different conditions is predicted based on an intelligent algorithm. Global sensitivity analysis is used to quantify the degree of influence of each parameter on the high-energy absorption device, providing method and data support for the subsequent structural optimization design and reliability improvement of the high-energy absorption device.

[0004] The technical solution adopted by the present invention to solve its technical problem is:

[0005] The method for modeling the dynamic response of a high energy absorption device and quantitative analysis of its parameter influence is special in that it includes the following steps:

[0006] Step 1: Establish a mathematical model of the high energy absorption device based on multi-body dynamics theory and hydraulic system analysis methods;

[0007] Step 2: Establish and train a WOA-BPNN prediction model. The WOA-BPNN prediction model predicts the dynamic response of the high-energy absorber under different working conditions by fitting the relationship between the landing parameters of the aircraft and the dynamic response of the high-energy absorber.

[0008] Step 2.1: Construct training and test sets;

[0009] The landing parameters of the aircraft and the structural parameters of the high-energy absorption device are used as input parameters, and the value range of each parameter is determined; the input parameters are uniformly sampled, and the sampling results constitute an input set;

[0010] Substituting the data in the input set into the mathematical model of the high energy absorption device, obtaining the dynamic response results of the high energy absorption device through numerical simulation, and forming an output set;

[0011] The input set and output set constitute an input-output mapping database, process missing values ​​and outliers therein, and then divide them into a training set and a test set, and normalize the data in the training set and the test set;

[0012] Step 2.2: Build and train the WOA-BPNN prediction model;

[0013] Constructing a BP neural network structure, converting initial weights and biases of the BP neural network structure into position vectors of a WOA algorithm, optimizing the BP neural network structure using the WOA algorithm, and converting the optimal solution of the WOA algorithm into optimal weights and biases of the BP neural network structure;

[0014] Set the training parameters of the BP neural network structure, and train and test the BP neural network structure using the normalized training set and test set until the performance of the trained WOA-BPNN prediction model meets the requirements;

[0015] Step 3: Using the trained BP neural network prediction model as a function for calculating the sensitivity index, the Sobol global sensitivity analysis method is used to calculate the first-order sensitivity coefficient and the total sensitivity coefficient of each input parameter to the dynamics of the high energy absorption device.

[0016] Furthermore, the mathematical model of the high-energy absorption device established in step 1 includes a force model of the arresting cable and a mathematical model of the contact force between the arresting cable and the tail hook or pulley, a mathematical model of the main energy absorption device, a mathematical model of the pulley buffer device, and a mathematical model of the cable end buffer device;

[0017] The arresting cable is divided into multiple cylindrical rigid body units. Each cylindrical rigid body unit has 6 degrees of freedom. The force model of the arresting cable is:

[0018]

[0019] Where Q0 is the generalized preload acting on the cylindrical rigid body element; K and C are the stiffness coefficient matrix and damping coefficient matrix of the cylindrical rigid body element, respectively. K is calculated by the material mechanics equation, and C is obtained by experiment or finite element simulation. Q j is the generalized force vector on the j-th cylindrical rigid body element; q j is the generalized displacement vector of the mass center of the j-th cylindrical rigid body unit, q j =[q xj , q yj , q zj , q θxj , q θyj , q θzj ] T ;

[0020] The tail hook / pulley is considered as a cylindrical rigid body. The tail hook / pulley contacts multiple cylindrical rigid body units of the arresting cable. The mathematical model of the contact force between the tail hook / pulley and the arresting cable is:

[0021]

[0022]

[0023] Where, F cf and F cn are the tangential force and normal impact force between the tail hook / pulley and the single cylindrical rigid body unit respectively; k cnis the stiffness coefficient; δ is the penetration depth; e is the collision nonlinear index, which reflects the nonlinearity of the material; c m is the maximum damping coefficient; is the maximum penetration depth; is the damping ratio coefficient, defined as: ;

[0024] The mathematical model of the main energy absorption device is:

[0025]

[0026]

[0027]

[0028]

[0029]

[0030] Where p a , p a0 , V a0 and ΔV a are the pressure, initial pressure, initial gas volume and changing gas volume of the accumulator in the main energy absorption device respectively; A z and v z are the main hydraulic cylinder area and fluid flow rate in the main energy absorption device; C d is the flow coefficient; ρ is the density of the fluid; A zj is the valve hole area of ​​the control valve in the main energy absorption device; Δp z It is the pressure drop value when the fluid flows through the control valve in the main energy absorption device; is the half angle of the valve cone of the control valve in the main energy absorption device; d is the diameter of the control valve port; y represents the lifting distance of the valve cone of the control valve in the main energy absorption device; F z is the force acting on the piston in the main energy absorption device; x z and m z are the moving distance and mass of the piston of the main hydraulic cylinder in the main energy absorption device;

[0031] The mathematical model of the pulley buffer device is:

[0032]

[0033] Where, F h is the force acting on the piston in the pulley buffer device; p ah0 , V ah0 and ΔV ah are the initial pressure, initial gas volume and changing gas volume of the accumulator in the pulley buffer device respectively; Ah and v h are the hydraulic cylinder area and fluid flow rate in the pulley buffer device; A hj is the area of ​​the throttle valve hole in the pulley buffer device; x h is the travel distance of the hydraulic cylinder piston in the pulley buffer device, m h is the mass of the hydraulic cylinder piston in the pulley buffer device;

[0034] The mathematical model of the cable end buffer device is:

[0035]

[0036] Where, F g A is the force on the piston in the cable end buffer device; g is the area of ​​the hydraulic cylinder in the cable end buffer device; p a0 、V a0 and ΔV a are the initial pressure, initial gas volume and changing gas volume of the accumulator in the cable end buffer device respectively; x h is the travel distance of the hydraulic cylinder piston in the cable end buffer device, m g is the mass of the hydraulic cylinder piston in the cable end buffer.

[0037] Furthermore, the landing parameters of the aircraft in step 2.1 include the landing speed v, mass m, stopping distance s, eccentric distance x and yaw angle θ of the aircraft; the dynamic response result of the high energy absorption device described in step 2.1 is the maximum tension of the arresting cable.

[0038] Furthermore, in step 2.1, the Latin hypercube sampling method is used to uniformly sample the input parameters.

[0039] Furthermore, the BP neural network constructed in step 2.2 includes an input layer, a hidden layer, and an output layer. The number of nodes in the input layer is consistent with the number of parameters in the input set, the number of nodes in the output layer is consistent with the number of parameters in the output set, and the number of neuron nodes in the hidden layer is determined by the Kolmogorov theorem.

[0040] Furthermore, the method of using the WOA algorithm to optimize the BP neural network structure in step 2.2 is specifically as follows:

[0041] The initial weights and biases of the BP neural network structure are converted into position vectors of the WOA algorithm, and the population size and maximum number of iterations of the WOA algorithm are initialized. For each position component corresponding to the weight and bias, the whale movement range is set.

[0042] The improved WOA fitness function is used and the optimal whale position is updated accordingly; the expression of the improved WOA fitness function is: , where RMSE is the root mean square error of the input data in the training set;

[0043] Calculate the coefficient vector to generate a random number for decision-making, select a search strategy based on the random number, and update the whale position according to the selected search strategy. Each iteration updates the position of each whale and recalculates the individual fitness value using the improved WOA fitness function to update the optimal whale position.

[0044] When the WOA algorithm reaches the maximum number of iterations, the optimization is terminated; at this point, the optimal whale position is converted into the optimal weight and optimal bias of the BP neural network structure.

[0045] Furthermore, the method of selecting the search strategy according to the random number is: when the random number is less than 0.5, the search strategy adopts the shrinking and surrounding mechanism; when the random number is greater than or equal to 0.5, the search strategy adopts the spiral updating mechanism.

[0046] Furthermore, step 3 is specifically as follows:

[0047] Step 3.1: The constructed and trained WOA-BPNN prediction model is used as the function for calculating the sensitivity index, which is expressed as:

[0048]

[0049] Where Y represents the output response of the WOA-BPNN prediction model, X = (X1, X2, ... , X n ) is an n-dimensional input parameter, f(X) is a square integrable function, K n is the domain of X;

[0050] Step 3.2: Get the sampling matrix A, B and matrix ;

[0051] Use the Sobol sequence to perform quasi-Monte Carlo sampling in the input parameter space to generate two independent Sampling matrices A and B, with sampling matrix A as the main body, use the j-th column element of sampling matrix B to replace the j-th column element of sampling matrix A, and the remaining n-1 columns in sampling matrix A remain unchanged. ;

[0052] Step 3.3: Calculate the first-order sensitivity coefficient S i and the total sensitivity coefficient S Ti estimated value of;

[0053] The first-order sensitivity coefficient variance V in the Sobol method is calculated using the following formula: i , total sensitivity coefficient variance V Ti And the total variance V:

[0054]

[0055]

[0056]

[0057] Where a is the a-th row of the corresponding matrix.

[0058] The matrices A, B and Substitute each row of into the function constructed in step 3.1 to solve the corresponding response value, and then substitute the response value into the formula in step 3.3 to calculate V i , V Ti and V, and finally the first-order sensitivity coefficient S of each input parameter to the dynamic response of the high energy absorption device is calculated using the following formula i and the total sensitivity coefficient S Ti Estimated value of:

[0059]

[0060] .

[0061] The beneficial effects of the present invention are:

[0062] The present invention proposes a method for modeling the dynamic response of a high-energy absorber and quantitatively analyzing the influence of parameters. First, based on the multi-body dynamics theory and hydraulic system analysis method, the high-energy absorber is regarded as a multi-body system to establish a mathematical model of the high-energy absorber, and its accuracy is verified in combination with experimental data. Secondly, numerical simulation is performed on the established mathematical model of the high-energy absorber to calculate the dynamic response of the high-energy absorber under various inputs, obtain training data, and train the established BP neural network (WOA-BPNN) prediction model based on the improved whale optimization algorithm based on the obtained training data. This prediction model can efficiently and accurately predict the dynamic response of the high-energy absorber under various working conditions, eliminating the need for numerical simulation of specific working conditions, thereby overcoming the disadvantage of low efficiency of traditional numerical simulation solutions. Finally, the Sobol global sensitivity analysis method based on variance analysis is used to quantitatively analyze the influence of various parameters on the dynamic response of the high-energy absorber, and solve the key parameters affecting the dynamic response of the high-energy absorber and the degree of interaction between the input parameters, thereby solving the deficiency of the existing method in conducting quantitative analysis of the degree of parameter influence. The present invention can provide method and data support for the subsequent structural optimization design and reliability improvement of high-energy absorbers. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 It is a structural diagram of a high energy absorption device.

[0064] Figure 2 It is a schematic diagram of modeling of the arresting cable in the present invention.

[0065] Figure 3 It is a schematic diagram of the main energy absorbing device in the high energy absorbing device.

[0066] Figure 4 3 is a comparison of the tension on the tail hook of the numerical simulation and experimental data in the embodiment of the present invention.

[0067] Figure 5 This is a flow chart of the algorithm for establishing and training the WOA-BPNN prediction model in the present invention.

[0068] Figure 6 Schematic diagram of the BP neural network structure in the WOA-BPNN prediction model established by the present invention.

[0069] Figure 7 It is a performance comparison of different BP neural network structures.

[0070] Figure 8 is determined in the embodiment of the present invention for predicting F max BP neural network structure.

[0071] Figure 9 The F predicted by the trained WOA-BPNN prediction model max The F calculated based on the mathematical model of the high energy absorption device max The results of the comparison.

[0072] Figure 10 It is a linear regression graph of the total sample set in the embodiment of the present invention.

[0073] Figure 11 is the sampling matrix in the present invention Schematic diagram of the generation of .

[0074] Figure 12 It is the global sensitivity index result of the landing parameters in the embodiment of the present invention. DETAILED DESCRIPTION

[0075] The present invention is further described below in conjunction with the accompanying drawings and examples.

[0076] The method for modeling the dynamic response of a high-energy absorption device and quantitatively analyzing its parameter influence proposed in the present invention specifically includes the following steps:

[0077] Step 1: Construct a mathematical model of the high energy absorption device;

[0078] Step 1.1: Establish the force model of the arresting cable and the mathematical model of the contact force between the arresting cable and the tail hook or pulley;

[0079] like Figure 2 As shown in the figure, the arresting cable is divided into multiple cylindrical rigid body elements (RBE), each of which has 6 degrees of freedom, and its length and diameter are ΔL and D respectively; the generalized displacement vector of the center of mass of the j-th cylindrical rigid body element is defined as q j =[q xj , q yj , q zj , q θxj , q θyj , q θzj ] T , the generalized force vector acting on the cylindrical rigid body element is defined as Q j =[Q xj , Q yj , Q zj , Q Txj , Q Tyj , Q Tzj ] T , then the action on the j-th cylindrical rigid body element RBE j The generalized force vector Q on j Depends on its relative position to the j+1th cylindrical rigid body element RBE j+1 The generalized displacement and generalized velocity can be calculated by the following formula:

[0080]

[0081] Among them, Q0 is the generalized preload acting on all cylindrical rigid body elements; K and C are the stiffness coefficient matrix and damping coefficient matrix of the cylindrical rigid body element, respectively. K can be calculated by the material mechanics equation, and C can be obtained through experiments or finite element simulation.

[0082] The tail hook is regarded as a cylindrical rigid body, which contacts with multiple cylindrical rigid body units that constitute the arresting cable. The contact force between the tail hook and each cylindrical rigid body unit can be expressed as the normal impact force F cn and tangential force F cf express:

[0083] Tangential force , where μ f is the friction coefficient, which is related to the dynamic and static friction coefficients and critical speed between contacting objects;

[0084] Normal impact force F cn It can be represented by a spring-damper system, defined as

[0085]

[0086] Among them, k cnis the stiffness coefficient; δ is the penetration depth; e is the collision nonlinear index, which reflects the nonlinearity of the material; c m is the maximum damping coefficient; is the maximum penetration depth; is the damping ratio coefficient, defined as:

[0087]

[0088] Based on the above equations, the force model of the arresting cable and the mathematical model of the contact force between the arresting cable and the tail hook were established. The contact force mathematical model can also be used to describe the contact and collision between the arresting cable and the pulley.

[0089] Step 1.2: Establish a mathematical model of the main energy absorption device;

[0090] According to Boyle's law, the pressure of the accumulator in the main energy absorption device can be calculated by the following formula:

[0091]

[0092] Among them, p a , p a0 , V a0 and ΔV a are the accumulator pressure, initial pressure, initial gas volume and changed gas volume respectively.

[0093] When the fluid flows through the control valve in the main energy absorbing device, the pressure drops Δp z It can be expressed as

[0094]

[0095] Among them, A z and v z are the main hydraulic cylinder area and fluid flow rate in the main energy absorption device; C d is the flow coefficient; ρ is the density of the fluid; A zj is the area of ​​the control valve orifice in the main energy absorption device, which can be calculated by the following formula:

[0096]

[0097] in, is the half angle of the valve cone of the control valve; d is the diameter of the control valve port; y represents the lifting distance of the valve cone.

[0098] Force F acting on the piston in the main energy absorber z for:

[0099]

[0100] Where x zis the moving distance of the main hydraulic cylinder piston, m z is the mass of the piston.

[0101] The displacement of the piston acting in the main energy absorption device can be calculated by the following formula:

[0102]

[0103] Based on the above equations, the mathematical equation of the main energy absorption device was established.

[0104] Step 1.3: Following the modeling ideas and methods similar to those in step 1.2, establish the mathematical models of the pulley buffer device and the cable end buffer device respectively;

[0105] The mathematical model of the pulley buffer device is:

[0106]

[0107] Among them, F h is the force acting on the piston in the pulley buffer device; p ah0 , V ah0 and ΔV ah are the initial pressure, initial gas volume and changing gas volume of the accumulator in the pulley buffer device respectively; A h and v h are the hydraulic cylinder area and fluid flow rate in the pulley buffer device; A hj is the area of ​​the throttle valve hole in the pulley buffer device; x h is the travel distance of the hydraulic cylinder piston in the pulley buffer device, m h is the mass of the hydraulic cylinder piston in the pulley buffer device.

[0108] The mathematical model of the cable end buffer device is:

[0109]

[0110] Among them, F g A is the force on the piston in the cable end buffer device; g is the area of ​​the hydraulic cylinder in the cable end buffer; p a0 、V a0 and ΔV a are the initial pressure, initial gas volume and changing gas volume of the accumulator in the cable end buffer device respectively; x h is the travel distance of the hydraulic cylinder piston in the cable end buffer device, m g is the mass of the hydraulic cylinder piston in the cable end buffer.

[0111] The above-established force model of the arresting cable and the mathematical model of the contact force between it and the tail hook or pulley, the mathematical model of the main energy absorption device, the mathematical model of the pulley buffer device, and the mathematical model of the cable end buffer device together constitute a complete mathematical model of the high-energy absorption device.

[0112] Step 1.5: Under the same operating conditions, compare the numerical simulation results of the relationship between aircraft slip distance and tailhook tension in the HEA model (obtained in Step 4) with experimental data to verify the accuracy of the HEA model's arresting force output. If the average error in tailhook tension during the primary energy absorption phase exceeds 10%, this indicates that the HEA model's accuracy is insufficient. Further adjustments can be made to the model's parameters to achieve the desired values.

[0113] Step 2: Establish and train the BP neural network prediction model based on the improved whale optimization algorithm (WOA-BPNN);

[0114] Step 2.1: Construct training and test sets for training and testing the WOA-BPNN prediction model;

[0115] Step 2.1.1: Use parameters that affect the dynamic response of the HEA as input parameters for the WOA-BPNN prediction model. These parameters can be the aircraft's landing parameters or the HEA's structural parameters. For example, if you want to study the impact of the aircraft's landing parameters on the HEA's dynamic response, then the aircraft's landing parameters can be used as input parameters. If you want to study the impact of the HEA's structural parameters on the HEA's dynamic response, then the HEA's structural parameters can be used as input parameters. At the same time, clearly define the value ranges of these parameters.

[0116] Step 2.1.2: Uniformly sample the input parameters of step 2.1.1 to obtain n groups of data, which constitute the input set;

[0117] Step 2.1.3: Substitute the n sets of sampled data into the mathematical model of the high-energy absorber constructed in Step 1 to perform numerical simulation, thereby obtaining the corresponding dynamic response results of the high-energy absorber. The dynamic response results can be the dynamic response of any component in the high-energy absorber, such as the maximum tension of the arresting cable and the pressure of the main hydraulic cylinder. These dynamic response results constitute the output set;

[0118] Step 2.1.4: The input set and output set form an overall input / output mapping database, and missing values ​​and outliers in the input / output mapping database are processed to ensure data quality;

[0119] Step 2.1.5: Randomly divide the input and output mapping database processed in step 2.1.4 into a training set and a test set, where the training set accounts for 80% and the test set accounts for 20%. Both the training set and the test set include both input data and output data.

[0120] Step 2.1.6: To improve the performance of the WOA-BPNN prediction model, the input and output sets in the training and test sets are normalized so that the input set parameters are distributed between [-1, 1] and the output set parameters are distributed between [0, 1].

[0121] Step 2.2: Build the WOA-BPNN prediction model;

[0122] Step 2.2.1: Construct BP neural network structure (BPNN);

[0123] Constructing the BP neural network structure requires determining the input layer, hidden layer, and output layer, as well as the number of neuron nodes in each layer. The number of neuron nodes in the input layer and output layer is consistent with the number of input and output parameters, and the number of neuron nodes in the hidden layer is N. s This can be determined using Kolmogorov's theorem:

[0124]

[0125] Among them, p n is the number of neuron nodes in the input layer, o n is the number of neuron nodes in the output layer, M is a constant, and M∈[1,10], N s is an integer; typically, the number of hidden layers in a neural network is chosen between 1 and 3.

[0126] Step 2.2.2: Use the whale optimization algorithm (WOA) to optimize the weights and biases of the BP neural network (BPNN) constructed in step 2.2.1;

[0127] Step 2.2.2.1: Convert the initial weights and biases of the BP neural network structure into position vectors of the Whale Optimization Algorithm (WOA), and initialize its population size, number of iterations, and whale movement range;

[0128] Step 2.2.2.2: Use the improved WOA fitness function and update the optimal whale position accordingly. Its expression is,

[0129]

[0130] Where Fitness is the improved WOA fitness function, and RMSE is the root mean square error of the input data in the training set. This improved WOA fitness function can avoid excessively large or small errors, which can lead to slow algorithm convergence.

[0131] Step 2.2.2.3: Calculate the coefficient vector to generate random numbers for decision making, select a search strategy, and update the whale position;

[0132] Step 2.2.2.4: The WOA algorithm terminates after reaching the maximum number of iterations; at this point, the optimal solution is represented by the optimal whale position, which is then converted into the optimal weights and optimal bias of the BP neural network structure.

[0133] Step 2.2.3: Train the WOA-BPNN prediction model;

[0134] The training parameters of the BP neural network structure were set, and the performance of the BP neural network was tested based on the accuracy in the training set and the test set when the BP neural network structure adopted different numbers of hidden layer nodes. The actual performance of the WOA-BPNN prediction model after training was evaluated, and the WOA-BPNN prediction model under the optimal network structure was selected. At this time, the WOA-BPNN prediction model training was completed.

[0135] The WOA-BPNN prediction model constructed and trained through the above steps can fit the relationship between the input parameters and their output dynamic response parameters, and achieve high-precision and high-efficiency prediction of the dynamic response of the high-energy absorption device under different working conditions.

[0136] Step 3: Calculate the global sensitivity index of the dynamic response of the high energy absorption device;

[0137] Step 3.1: The WOA-BPNN prediction model constructed in step 2 is used as the function for calculating the sensitivity index, which is expressed as follows:

[0138]

[0139] Where Y represents the output response of the WOA-BPNN prediction model, X = (X1, X2, ... , X n ) is an n-dimensional input parameter, f(X) is a square integrable function, K n is the domain of X.

[0140] Step 3.2: Use the Sobol sequence to sample in the input parameter space so that the sampling points cover the entire input parameter space and obtain two independent Sampling matrices A and B, and defining matrices based on sampling matrices A and B ;

[0141] The Sobol sequence is a deterministic low-discrepancy sequence used in the quasi-Monte Carlo method. The sampling points are generated independently in each dimension, and the direction number function is used to avoid periodic overlap, making the distribution of the sampling points more uniform. Sampling matrices A and B, where k is the number of samples of each input quantity and n is the number of input quantities. Then, based on the sampling matrices A and B, we define the matrix , The matrix is ​​obtained by replacing the j-th column element of the sampling matrix A with the j-th column element of the sampling matrix B, while keeping the remaining n-1 columns in the sampling matrix A unchanged.

[0142] Step 3.3: Calculate the first-order sensitivity coefficient S i and the total sensitivity coefficient S Ti estimated value of;

[0143] The first-order sensitivity coefficient variance V in the Sobol method is i , total sensitivity coefficient variance V Ti and the total variance V are defined as:

[0144]

[0145]

[0146]

[0147] Where a is the a-th row of the corresponding matrix.

[0148] The first-order sensitivity coefficient S of each input parameter to the dynamic response of the high energy absorption device i and the total sensitivity coefficient S Ti The estimated values ​​of can be calculated by the following formula:

[0149]

[0150]

[0151] Calculate the first-order sensitivity coefficient S i and the total sensitivity coefficient S Ti After that, the influence of each input parameter on the dynamic response of the high energy absorption device can be quantitatively analyzed.

[0152] Example:

[0153] The high energy absorption device established in this embodiment is a Mark7Mod3 hydraulic buffer high energy absorption device. This embodiment studies the influence of aircraft landing parameters on the maximum tension of the arresting cable in the high energy absorption device. The aircraft landing parameters include the aircraft's centered landing speed v, mass m, stopping distance s (aircraft sliding distance s a maximum value), eccentric distance x and yaw angle θ.

[0154] Based on the method proposed by the present invention, this embodiment specifically includes the following steps:

[0155] Step 1: Construct a mathematical model of the high energy absorption device;

[0156] like Figure 2 As shown in the figure, the arresting cable is divided into a number of cylindrical rigid body elements (RBE). According to the actual design, the length of each cylindrical rigid body element is ΔL = 50 mm, the diameter is D = 36.5 mm, and it has 6 degrees of freedom. The generalized displacement vector of the center of mass of each cylindrical rigid body element is defined as q j =[q xj , q yj , q zj , q θxj , q θyj , q θzj ] T , the generalized force vector acting on the cylindrical rigid body element is defined as Q j =[Q xj , Q yj , Q zj , Q Txj , Q Tyj , Q Tzj ] T , then the action on the i-th cylindrical rigid body element RBE j The generalized force vector Q on j It can be calculated by the following formula

[0157] (1-1)

[0158] In the above formula, the generalized preload force Q0 acting on the cylindrical rigid body element is 100kN, and the stiffness coefficient K matrix of RBE can be obtained from the relevant knowledge of material mechanics:

[0159] (1-2)

[0160] The corresponding damping coefficient matrix C can be obtained through finite element simulation:

[0161] (1-3)

[0162] The tail hook is regarded as a cylindrical rigid body, which contacts multiple cylindrical rigid body units. The contact force between the tail hook and each cylindrical rigid body unit can be expressed as the normal impact force F. cn and tangential force F cf express:

[0163] Tangential force , friction coefficient μ f =0.25;

[0164] The normal impact force is represented by a spring-damper system and is defined as:

[0165] (1-4)

[0166] Where δ is the penetration depth; k cn is the stiffness coefficient, for the contact between the arresting cable and the tail hook =3.56×10 10 N / m, for contact between arresting cable and pulley =1.69×10 10 N / m; e is the collision nonlinearity index, e=1.5; c m is the maximum damping coefficient for the contact between the arresting cable and the tail hook =1.78×10 8 , for the contact between the arresting cable and the pulley =8.47×10 7 N / m;d m is the maximum penetration depth, d m =1×10 -4 m; is the damping ratio coefficient. The damping ratio coefficients of the arresting cable, tail hook and pulley are defined as:

[0167] (1-5)

[0168] (1-6)

[0169] Based on the above equations, the force model of the arresting cable and the mathematical model of the contact force between the arresting cable and the tail hook or pulley were established.

[0170] Step 1.2: Establish a mathematical model of the main energy absorption device;

[0171] According to Boyle's law, the pressure of the accumulator in the main energy absorption device can be calculated by the following formula:

[0172] (1-7)

[0173] Among them, p a and ΔV aare the pressure of the accumulator and the volume of the changing gas, respectively. The initial pressure p a0 =2.7MPa, initial gas volume V a0 =0.94m 2 .

[0174] When the fluid flows through the control valve, the pressure drops Δp z It can be expressed as:

[0175] (1-8)

[0176] Where, v z is the fluid flow rate of the master hydraulic cylinder; A z is the area of ​​the main hydraulic cylinder in the main energy absorption device, A z =0.20m 2 ; C d is the flow coefficient, C d =0.7; ρ is the fluid density, ρ=1130kg / m 3 ; A zj is the valve hole area of ​​the control valve in the main energy absorption device, which can be calculated by the following formula:

[0177] (1-9)

[0178] Where y represents the lifting distance of the valve cone, is the angle of the valve cone, =45°; d is the diameter of the control valve port, d=90mm.

[0179] Force F acting on the piston in the main energy absorber z for

[0180] (1-10)

[0181] The displacement x of the piston acting on the main energy absorption device z It can be calculated by the following formula:

[0182] (1-11)

[0183] The above equations establish the mathematical equation of the main energy absorption device.

[0184] Step 1.3: Following the modeling ideas and methods similar to those in step 1.2, mathematical models of the pulley buffer device and the cable end buffer device can be established respectively;

[0185] The mathematical model of the pulley buffer device is:

[0186] (1-12)

[0187] Among them, Fh is the force acting on the piston in the pulley buffer device; p ah0 , V ah0 and ΔV ah are the initial pressure, initial gas volume and changing gas volume of the accumulator in the pulley buffer device respectively; A h and v h are the hydraulic cylinder area and fluid flow rate in the pulley buffer device; A hj is the area of ​​the throttle valve hole in the pulley buffer device; x h is the travel distance of the hydraulic cylinder piston in the pulley buffer device, m h is the mass of the hydraulic cylinder piston in the pulley buffer device.

[0188] The mathematical model of the cable end buffer device is:

[0189] (1-13)

[0190] Among them, F g A is the force on the piston in the cable end buffer device; g is the area of ​​the hydraulic cylinder in the cable end buffer device; p a0 、V a0 and ΔV a are the initial pressure, initial gas volume and changing gas volume of the accumulator in the cable end buffer device respectively; x h is the travel distance of the hydraulic cylinder piston in the cable end buffer device, m g is the mass of the hydraulic cylinder piston in the cable end buffer.

[0191] The above-established force model of the arresting cable and the mathematical model of the contact force between it and the tail hook or pulley, the mathematical model of the main energy absorption device, the mathematical model of the pulley buffer device, and the mathematical model of the cable end buffer device together constitute a complete mathematical model of the high-energy absorption device.

[0192] Step 1.5: Based on the above method, calculate the aircraft slip distance s using the conditions of aircraft centered landing speed v = 260 km / h, mass m = 22.68 t, eccentric distance x = 0 m, and yaw angle θ = 0°. a The tension F on the tail hook of the aircraft a The relationship and corresponding test results are as follows Figure 4 Analysis shows that the maximum deviation in the tension on the aircraft's tail hook between simulation and experiment is 5.20%. During the primary energy absorption phase, the average deviation between simulation and experimental data is 3.48%. This comparison of simulation and experiment demonstrates the effectiveness of the established high-energy absorber model and can be used to analyze its dynamic response.

[0193] Step 2: Reference Figure 5 , establish and train the BP neural network prediction model based on the improved whale optimization algorithm (WOA-BPNN);

[0194] Step 2.1: Construct training and test sets for training and testing the WOA-BPNN prediction model;

[0195] Step 2.1.1: Use the aircraft's centered landing speed v, mass m, stopping distance s, eccentric distance x, and yaw angle θ as input parameters, with the value ranges shown in Table 1.

[0196] Table 1 Value ranges of landing parameters

[0197]

[0198] Step 2.1.2: Use the Latin hypercube sampling method to uniformly sample the input parameters and obtain 110 sets of data. These 110 sets of data constitute the input set.

[0199] Step 2.1.3: Substitute the 110 sets of data obtained in step 2.1.2 into the mathematical model of the high energy absorption device constructed in step 1 to carry out numerical simulation. By calculation, the maximum tension F of the arresting cable corresponding to each set of input data is obtained. max , and the maximum arresting cable tension F is obtained max Construct the output set;

[0200] Step 2.1.4: The input set and output set constitute an input / output mapping database, and missing values ​​and outliers in the input / output mapping database are processed to ensure data quality;

[0201] Step 2.1.5: Randomly divide the input and output mapping database processed in step 2.1.4 into a training set and a test set, where the training set contains 88 groups of data and the test set contains 22 groups of data;

[0202] Step 2.1.6: Normalize the input set and output set so that the parameters of the input set are distributed between [-1, 1] and the parameters of the output set are distributed between [0, 1].

[0203] Step 2.2: Construct a WOA-BPNN prediction model based on the improved BP neural network based on the whale optimization algorithm. The prediction model is constructed by fitting the landing parameters of the aircraft (aircraft speed v, mass m, stopping distance s, eccentricity distance x and yaw angle θ) with the maximum tension F of the arresting cable of the high energy absorption device. max to predict the maximum tension F of the arresting cable under different working conditions. max .

[0204] Step 2.2.1: Construct the neural network structure;

[0205] The constructed BP neural network structure includes input layer, hidden layer and output layer, such as Figure 6 As shown. According to the number of parameters in the input set and the output set, the number of neuron nodes in the input layer is 5, and the number of neuron nodes in the output layer is 1. The number of hidden layers is set to 2, and the number of neuron nodes in the hidden layer is N. s This can be determined using Kolmogorov's theorem:

[0206] (2-1)

[0207] Where M is a constant, and M∈[1, 10]; p n =5,o n =1; then the number of neuron nodes N in the hidden layer can be calculated using the above formula s is an integer from 3 to 13.

[0208] Step 2.2.2: Use the Whale Optimization Algorithm (WOA) to optimize the BP neural network structure constructed in step 2.2.1;

[0209] Step 2.2.2.1: Convert the initial weights and biases of the BP neural network structure into position vectors for the Whale Optimization Algorithm (WOA). Initialize the population size of the Whale Optimization Algorithm to 20 and the maximum number of iterations to 50. For each position component corresponding to the weight and bias, set the whale movement range to [-1, 1].

[0210] Step 2.2.2.2: Use the improved WOA fitness function and update the optimal whale position accordingly. The improved WOA fitness function expression is:

[0211] (2-2)

[0212] Among them, Fitness is the improved WOA fitness function, and RMSE is the root mean square error of the input data in the training set.

[0213] Step 2.2.2.3: Calculate the coefficient vector to generate a random number for decision-making. When the random number is less than 0.5, the search strategy adopts a shrinking and surrounding mechanism. When the random number is greater than or equal to 0.5, the search strategy adopts a spiral update mechanism. Update the whale positions according to the selected search strategy. Each iteration updates the position of each whale and uses the improved WOA fitness function to recalculate the individual fitness value, thereby updating the optimal whale position.

[0214] Step 2.2.2.4: The WOA algorithm terminates when it reaches the maximum number of iterations, 50; at this point, the optimal whale position is converted into the optimal weight and optimal bias of the BP neural network structure.

[0215] Step 2.2.3: Train the WOA-BPNN prediction model;

[0216] The BP neural network structure in the WOA-BPNN prediction model was trained using the LM (Levenberg-Marquardt) algorithm to continuously adjust the weights and biases of the BP neural network so that the target loss function gradually decreased. The LM algorithm combines the advantages of the gradient descent method and the Gauss-Newton method and can efficiently solve nonlinear problems. During the training process, different numbers of hidden layer nodes were selected for network testing, and the accuracy of the BP neural network structure on the training set and test set was monitored in real time. The maximum number of iterations of the BP neural network structure was set to 1000, the learning rate was 0.01, and the target minimum error was 1×10 -6 , the test results are shown in Table 2:

[0217] Table 2 Network performance with different numbers of hidden layer nodes

[0218]

[0219] The average error and maximum error of the training set and test set of different BP neural network structures are as follows Figure 7 As shown in Table 2 and Figure 7 It can be obtained that when the BP neural network structure is as follows Figure 8 When the (5-7-5-1) structure is used, the best performance is achieved in terms of average error and maximum error for both the training and test sets. The average error and maximum error for the training set are 1.16% and 4.75% respectively; the average error for the test set is 1.93% and the maximum error is 4.41%.

[0220] The F predicted by the trained WOA-BPNN prediction model max The F calculated based on the mathematical model of the high energy absorption device max For comparison, the results are as follows Figure 9 As shown in Figure 2, it shows that the WOA-BPNN model prediction has good generalization ability. Figure 10 It can be seen from the linear regression diagram of the total sample set that the data set is evenly distributed along the line Y=0.98T+0.01, and its determination coefficient R 2 > 0.99 indicates that the WOA-BPNN prediction model has a high accuracy.

[0221] Based on the above analysis, it can be concluded that the BP neural network structure (5-7-5-1) in the WOA-BPNN prediction model can efficiently and accurately predict F max , which shows that the established and trained WOA-BPNN prediction model has good performance and can be used for further analysis.

[0222] Step 3: Calculate the global sensitivity index of the dynamic response of the high energy absorption device;

[0223] Step 3.1: The WOA-BPNN prediction model constructed and trained in step 2 is used as the function to calculate the sensitivity index (first-order sensitivity coefficient and total sensitivity coefficient), which can be expressed as:

[0224] (3-1)

[0225] Step 3.2: Use the Sobol sequence to sample in the input parameter space so that the sampling points cover the entire input parameter space and obtain two independent Sampling matrices A and B, and defining matrices based on sampling matrices A and B ;

[0226] Use the Sobol sequence to perform a 2×10 4 Quasi-Monte Carlo sampling generates two independent 10 4 ×5 sampling matrices A and B; then, based on the sampling matrices A and B, define the matrix , The matrix is ​​obtained by taking the sampling matrix A as the main body and replacing the j-th column element of the sampling matrix A with the j-th column element of the sampling matrix B, while the remaining n-1 columns in the sampling matrix A remain unchanged, as shown in Figure 11 As shown. Since the matrix Most of the sample structure of the sampling matrix A is retained, and the value of the i-th variable is replaced by the value of the sampling matrix B, so that the influence of the i-th variable can be separated.

[0227] Step 3.3: Calculate the first-order sensitivity coefficient S i and the total sensitivity coefficient S Ti estimated value of;

[0228] The first-order sensitivity coefficient variance V in the Sobol method is calculated using the following formula: i , total sensitivity coefficient variance V Ti And the total variance V:

[0229] (3-2)

[0230] (3-3)

[0231] (3-4)

[0232] Where a is the a-th row of the corresponding matrix.

[0233] The first-order sensitivity coefficient S of each input parameter to the dynamic response of the high energy absorption devicei and the total sensitivity coefficient S Ti The estimated values ​​of can be calculated by the following formula:

[0234] (3-5)

[0235] (3-6)

[0236] The matrices A, B and Each row is substituted into the function Solve the corresponding response value, and then calculate the first-order sensitivity coefficient S according to formulas (3-2) to (3-6). i and the total sensitivity coefficient S Ti , the result is as follows Figure 12 The first-order sensitivity coefficient S of parameters v and m is shown. i They are 0.5844 and 0.2526 respectively. Figure 12 It can be seen that within the parameter range given in Table 1, the landing speed v and the landing mass m are the factors that affect the maximum tension F of the arresting cable. max The most important factors; the first-order sensitivity coefficient S of the stopping distance s, the eccentric distance x and the yaw angle θ i The values ​​are all less than 0.1, which means that within the parameter range given in Table 1, the stopping distance s, eccentric distance x and yaw angle θ have a great influence on the maximum tension F of the arresting cable. max The impact is small. Figure 12 As shown, the first-order sensitivity coefficient S of each landing parameter i The values ​​are all less than the corresponding total sensitivity coefficient S Ti This indicates that the impact of these landing parameters has an interactive effect. The first-order sensitivity coefficient S of a single landing parameter i and the total sensitivity coefficient S Ti The greater the difference between them, the stronger the interaction between these parameters.

Claims

1. A method for modeling the dynamic response of a high energy absorption device and quantitative analysis of its parameter impact, characterized in that: Including steps: Step 1: Establish a mathematical model of the high energy absorption device based on multi-body dynamics theory and hydraulic system analysis methods; Step 2: Establish and train a WOA-BPNN prediction model. The WOA-BPNN prediction model predicts the dynamic response of the high-energy absorber under different working conditions by fitting the relationship between the landing parameters of the aircraft and the dynamic response of the high-energy absorber. Step 2.1: Construct training and test sets; The landing parameters of the aircraft and the structural parameters of the high-energy absorption device are used as input parameters, and the value range of each parameter is determined; the input parameters are uniformly sampled, and the sampling results constitute an input set; Substituting the data in the input set into the mathematical model of the high energy absorption device, obtaining the dynamic response results of the high energy absorption device through numerical simulation, and forming an output set; The input set and output set constitute an input-output mapping database, process missing values ​​and outliers therein, and then divide them into a training set and a test set, and normalize the data in the training set and the test set; Step 2.2: Build and train the WOA-BPNN prediction model; Constructing a BP neural network structure, converting initial weights and biases of the BP neural network structure into position vectors of a WOA algorithm, optimizing the BP neural network structure using the WOA algorithm, and converting the optimal solution of the WOA algorithm into optimal weights and biases of the BP neural network structure; Set the training parameters of the BP neural network structure, and train and test the BP neural network structure using the normalized training set and test set until the performance of the trained WOA-BPNN prediction model meets the requirements; Step 3: Using the trained BP neural network prediction model as a function for calculating the sensitivity index, the Sobol global sensitivity analysis method is used to calculate the first-order sensitivity coefficient and the total sensitivity coefficient of each input parameter to the dynamics of the high energy absorption device.

2. The method for modeling the dynamic response of a high energy absorption device and quantitative analysis of its parameter influence according to claim 1 is characterized in that: The mathematical model of the high-energy absorption device established in step 1 includes the force model of the arresting cable and the mathematical model of the contact force between the arresting cable and the tail hook or pulley, the mathematical model of the main energy absorption device, the mathematical model of the pulley buffer device, and the mathematical model of the cable end buffer device; The arresting cable is divided into multiple cylindrical rigid body units. Each cylindrical rigid body unit has 6 degrees of freedom. The force model of the arresting cable is: Where Q0 is the generalized preload acting on the cylindrical rigid body element; K and C are the stiffness coefficient matrix and damping coefficient matrix of the cylindrical rigid body element, respectively. K is calculated by the material mechanics equation, and C is obtained by experiment or finite element simulation. Q j is the generalized force vector on the j-th cylindrical rigid body element; q j is the generalized displacement vector of the mass center of the j-th cylindrical rigid body unit, q j =[q xj , q yj , q zj , q θxj , q θyj , q θzj ] T ; The tail hook / pulley is considered as a cylindrical rigid body. The tail hook / pulley contacts multiple cylindrical rigid body units of the arresting cable. The mathematical model of the contact force between the tail hook / pulley and the arresting cable is: Where, F cf and F cn are the tangential force and normal impact force between the tail hook / pulley and the single cylindrical rigid body unit respectively; k cn is the stiffness coefficient; δ is the penetration depth; e is the collision nonlinear index, which reflects the nonlinearity of the material; c m is the maximum damping coefficient; is the maximum penetration depth; is the damping ratio coefficient, defined as: ； The mathematical model of the main energy absorption device is: Where p a , p a0 , V a0 and ΔV a are the pressure, initial pressure, initial gas volume and changing gas volume of the accumulator in the main energy absorption device respectively; A z and v z are the main hydraulic cylinder area and fluid flow rate in the main energy absorption device; C d is the flow coefficient; ρ is the density of the fluid; A zj is the valve hole area of ​​the control valve in the main energy absorption device; Δp z It is the pressure drop value when the fluid flows through the control valve in the main energy absorption device; is the half angle of the valve cone of the control valve in the main energy absorption device; d is the diameter of the control valve port; y represents the lifting distance of the valve cone of the control valve in the main energy absorption device; F z is the force acting on the piston in the main energy absorption device; x z and m z are the moving distance and mass of the piston of the main hydraulic cylinder in the main energy absorption device; The mathematical model of the pulley buffer device is: Where, F h is the force acting on the piston in the pulley buffer device; p ah0 , V ah0 and ΔV ah are the initial pressure, initial gas volume and changing gas volume of the accumulator in the pulley buffer device respectively; A h and v h are the hydraulic cylinder area and fluid flow rate in the pulley buffer device; A hj is the area of ​​the throttle valve hole in the pulley buffer device; x h is the travel distance of the hydraulic cylinder piston in the pulley buffer device, m h is the mass of the hydraulic cylinder piston in the pulley buffer device; The mathematical model of the cable end buffer device is: Where, F g A is the force on the piston in the cable end buffer device; g is the area of ​​the hydraulic cylinder in the cable end buffer device; p a0 、V a0 and ΔV a are the initial pressure, initial gas volume and changing gas volume of the accumulator in the cable end buffer device respectively; x h is the travel distance of the hydraulic cylinder piston in the cable end buffer device, m g is the mass of the hydraulic cylinder piston in the cable end buffer.

3. The method for modeling the dynamic response of a high energy absorption device and quantitative analysis of its parameter influence according to claim 2 is characterized in that: The landing parameters of the aircraft in step 2.1 include the landing speed v, mass m, stopping distance s, eccentric distance x and yaw angle θ of the aircraft; the dynamic response result of the high energy absorption device described in step 2.1 is the maximum tension of the arresting cable.

4. The method for modeling the dynamic response of a high energy absorption device and quantitative analysis of its parameter impact according to claim 3 is characterized in that: In step 2.1, the Latin hypercube sampling method is used to uniformly sample the input parameters.

5. The method for dynamic response modeling and parameter influence quantitative analysis of a high energy absorption device according to any one of claims 1 to 3, characterized in that: The BP neural network constructed in step 2.2 includes an input layer, a hidden layer, and an output layer. The number of nodes in the input layer is consistent with the number of parameters in the input set, the number of nodes in the output layer is consistent with the number of parameters in the output set, and the number of neuron nodes in the hidden layer is determined by the Kolmogorov theorem.

6. The method for modeling the dynamic response of a high energy absorption device and quantitative analysis of its parameter influence according to claim 5 is characterized in that: The specific method of using the WOA algorithm to optimize the BP neural network structure in step 2.2 is: The initial weights and biases of the BP neural network structure are converted into position vectors of the WOA algorithm, and the population size and maximum number of iterations of the WOA algorithm are initialized. For each position component corresponding to the weight and bias, the whale movement range is set. The improved WOA fitness function is used and the optimal whale position is updated accordingly; the expression of the improved WOA fitness function is: , where RMSE is the root mean square error of the input data in the training set; Calculate the coefficient vector to generate a random number for decision-making, select a search strategy based on the random number, and update the whale position according to the selected search strategy. Each iteration updates the position of each whale and recalculates the individual fitness value using the improved WOA fitness function to update the optimal whale position. When the WOA algorithm reaches the maximum number of iterations, the optimization is terminated; at this point, the optimal whale position is converted into the optimal weight and optimal bias of the BP neural network structure.

7. The method for modeling the dynamic response of a high energy absorption device and quantitative analysis of its parameter influence according to claim 6 is characterized in that: The method of selecting the search strategy according to the random number is: when the random number is less than 0.5, the search strategy adopts the shrinking and surrounding mechanism; when the random number is greater than or equal to 0.5, the search strategy adopts the spiral updating mechanism.

8. The method for modeling the dynamic response of a high energy absorption device and quantitative analysis of its parameter influence according to claim 7 is characterized in that: Step 3 is as follows: Step 3.1: The constructed and trained WOA-BPNN prediction model is used as the function for calculating the sensitivity index, which is expressed as: Where Y represents the output response of the WOA-BPNN prediction model, X = (X1, X2, ... , X n ) is an n-dimensional input parameter, f(X) is a square integrable function, K n is the domain of X; Step 3.2: Get the sampling matrix A, B and matrix ; Use the Sobol sequence to perform quasi-Monte Carlo sampling in the input parameter space to generate two independent Sampling matrices A and B, with sampling matrix A as the main body, use the j-th column element of sampling matrix B to replace the j-th column element of sampling matrix A, and the remaining n-1 columns in sampling matrix A remain unchanged. ; Step 3.3: Calculate the first-order sensitivity coefficient S i and the total sensitivity coefficient S Ti estimated value of; The first-order sensitivity coefficient variance V in the Sobol method is calculated using the following formula: i , total sensitivity coefficient variance V Ti And the total variance V: Where a is the a-th row of the corresponding matrix; The matrices A, B and Substitute each row of into the function constructed in step 3.1 to solve the corresponding response value, and then substitute the response value into the formula in step 3.3 to calculate V i , V Ti and V, and finally the first-order sensitivity coefficient S of each input parameter to the dynamic response of the high energy absorption device is calculated using the following formula i and the total sensitivity coefficient S Ti Estimated value of: 。

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