CN116956498A - Rapid robustness design technology for weapon multi-body system - Google Patents

Abstract

The invention discloses a rapid robustness design technology of a weapon multi-body system, which comprises three main modules, namely: the system comprises a multi-body dynamics efficient modeling and analyzing module, a self-adaptive mixed agent module and a robustness design solving strategy module. The technology highlights the characteristics of quick and accurate modeling of a multi-body system transmission matrix method, a self-adaptive mixed agent model and a single-cycle robustness design strategy in the vibration reduction robustness optimization design process of the uncertain weapon multi-body system. The high-efficiency and accurate robust design solving process provides a new reference for the robust design of the uncertain weapon multi-body system.

Description

A rapid and robust design technology for weapon multi-body systems

Technical areas:

The present invention relates to the field of robust design of multi-body weapons systems, and in particular to the robust design of vibration reduction of multi-body weapons systems that takes into account the influence of accidental uncertainty factors.

Background technique:

Most mechanical systems in the field of weapons and equipment can be regarded as multi-body systems composed of "body units" and "hinge units" connected in a certain way. Ensuring the accuracy and efficiency of dynamic (vibration) characteristics analysis of multi-body mechanical systems and conducting efficient and reasonable vibration reduction designs based on system vibration characteristics are crucial to improving the performance of weapons and equipment. The multi-body system dynamics method and the finite element method are the main methods for studying the dynamics of weapon multi-body systems. However, all these methods need to establish the overall dynamics equation of the system, and the order of the system matrix involved is proportional to the number of degrees of freedom of the system. As the order of the system matrix increases, the calculation speed of multi-body system dynamics decreases exponentially. Because the overall dynamics equation of the complex weapon system involves a high matrix order, the calculation speed is slow and cannot meet the dynamic design of complex weapon system dynamics. Fast calculations are needed.

Because there are inevitably some uncertainties in the design, manufacturing and use processes, such as the randomness of material mechanical properties, geometric size errors, and the dispersion of external loads. These uncertain factors often further affect the performance and safety of multi-body weapons systems, becoming a great obstacle to improving the performance of weapons and equipment at this stage. Therefore, developing an efficient and fast robust design method for uncertain weapon multi-body systems has important theoretical and practical significance for improving the performance of weapons and equipment, ensuring equipment safety, saving equipment costs, and ensuring its combat effectiveness at this stage. .

Multi-body system dynamics is one of the hot topics in mechanical research today and is an important basis for the dynamic performance design and testing of a large number of industrial products such as weapons, ships, aviation, aerospace, vehicles, and general machinery. However, various multi-body system dynamics methods that have developed rapidly in the past 50 years generally have the following characteristics: (1) the overall dynamics equation of the system must be established; (2) once the system topology changes, the overall dynamics equation of the system needs to be re-derived; (3) The overall dynamics equation of a complex system involves a high matrix order (usually not less than the number of degrees of freedom of the system), and the calculation speed slows down significantly as the system scale increases. The multi-body system transfer matrix method does not require the overall system dynamics equation and makes the system matrix order much lower than the system degrees of freedom. It can realize multi-rigid body system dynamics, multi-rigid and flexible body system dynamics, controlled multi-body system dynamics, special It is a fast calculation of the dynamics of complex launch systems.

Regarding uncertain multi-body dynamics, there are currently few related research works at home and abroad. Interval methods are mostly used to deal with the multi-source uncertainties mixed by chance and cognition in multi-body systems. However, for the correlation of multi-body weapons systems, Research work is even more lackluster. The advantage of the interval method is that it only needs to determine the upper and lower bounds of the random parameters and requires less prior statistical information. However, the disadvantage is that the accuracy is poor and it is easy to "overestimate" the impact of randomness on the dynamic response of the multi-body system. Therefore, this type of method is not suitable for vibration analysis problems of weapon multi-body systems that consider multi-source uncertainties.

Based on the dynamic analysis and research of uncertain multi-body systems, the research work on the robust design of multi-body systems also basically uses the interval method to deal with multi-source uncertainty parameters, and uses the double-loop method to solve the robust design optimization problem, and there is currently no relevant research work on the robust design of uncertain weapon multi-body systems. It should be pointed out that the robustness design is a double loop nested inside and outside, and the multi-body system uncertainty propagation analysis that considers the random input of multi-source uncertainties needs to be carried out internally (it also needs to consider the accuracy and accuracy of the multi-body system dynamics analysis itself). efficiency), external optimization solution is required. Therefore, the robust design of multi-body systems that considers multi-source uncertainties currently faces problems such as low accuracy and efficiency of multi-source uncertainty dynamics modeling and analysis, and low efficiency of robust design solutions. This is especially true in the field of weapons and equipment containing typical multi-body systems, which seriously restricts the rapid improvement of the performance of my country's weapons and equipment at this stage.

Contents of the invention:

The technical problem solved by this invention: Based on the current research status at home and abroad, this invention aims to improve the calculation efficiency of the vibration reduction robustness design of the uncertain weapon multi-body system, by constructing adaptive rigid-soft coupling dynamics analysis of the weapon multi-body system model to implement dynamic modeling of weapon multi-body systems based on the transfer matrix method. At the same time, the present invention proposes an efficient solution method for the vibration reduction robustness design of a multi-body weapon system that integrates an adaptive hybrid agent model, a multi-objective subset simulation optimization method, a weighted single-objective optimization method and a single-loop solution strategy, thereby improving the overall multi-body weapon system. Efficiency of system vibration damping robustness design process.

The technical solution of the present invention: a rapid robustness design technology for a multi-body weapon system. The analysis process can be divided into three steps: first, quickly solve the vibration response of the multi-body weapon system; then, obtain the optimal surrogate model; Finally, based on the optimal agent model, the robustness design problem of the weapon multi-body system is efficiently solved; the entire rapid analysis and design method includes three modules, namely: multi-body dynamics efficient modeling and analysis module, adaptive hybrid agent module, Robust design solution strategy module.

Multi-body dynamics efficient modeling and analysis module: solve the rigid-flexible coupling dynamic model of rigid body tube and flexible body tube, and derive the transfer matrix equation based on the dynamic equation of flexible straight beam with large motion and small deformation.

The naval gun dynamic response solution model is established by the linear multi-body system transfer matrix method, such as

As shown in Figure 1, element 1 is the gun base, element 3 is the rotating body, element 5 is the pitching body, element 7 is the breech, element 8 is the barrel, element 6 is the sliding hinge, and elements 2 and 4 are elastic hinges. , where elements 3, 5 and 7 are rigid bodies, element 8 is an elastic body, and the angle of incidence of the pitching body 5 is θ.

(1) Rigid body tube

The input and output state vectors of each component of the model are:

The transfer equation for each element is

Z _O =UZ _I (2)

In the new version of the multi-body system transfer matrix method, the elastic hinges are cut off and divided into two subsystems. The elastic hinges will be added to the rigid body transfer matrix as external forces and external moments. The total transfer matrix is:

All boundaries of the two transfer equations are free boundary conditions, in the form of formula (4)

(2) Flexible straight beam with large movement and small deformation

Taking a single-end input single-end output space motion straight beam i shown in Figure 2 as an example, for a small deformation space motion straight beam i, its overall node displacement array δ ⁱ can be expressed in the form of modal superposition as

in the formula

is the jth-order mode shape of flexible beam i,/> is the corresponding generalized coordinate of the j-th order deformation, and M is the number of selected mode shapes.

1)Kinematic equation of straight beam

Taking into account the axial shortening effect, the position vector of the spatially moving straight beam i node k in the global inertial coordinate system can be expressed as

in the formula is the displacement deformation mode shape of the flexible beam i node k line, l _p is the initial length of the space motion straight beam i unit p, v and w are the points on the neutral axis of the beam unit along the y and z axes of the floating coordinate system respectively. of deformation. H ₁ =[1 0 0] ^T is a constant matrix.

Using the unit shape function matrix, the last term in equation (8) can be rewritten as

in the formula

δ ^ip is the node deformation displacement array of unit p of flexible beam i, N _v (x) and N _w (x) are the shape function matrices corresponding to v and w respectively, N′ _· (x) represents the shape function matrix N _· (x) The first derivative with respect to the ordinate x of the flexible beam. It is not difficult to find from equation (10) is a symmetric matrix.

Substitute equation (5) into equation (9) and further organize it to get

in the formula

Substituting equation (11) into equation (8), we can get

Calculating the first derivative of equation (13) with respect to time can obtain the absolute velocity vector of node k of the spatially moving straight beam i in the global inertial coordinate system, that is

in the formula is the projection of the absolute angular velocity vector of the floating coordinate system of flexible beam i in the global inertial coordinate system. The node coordinate system can be obtained from the angular velocity superposition theorem/> The angular velocity vector relative to the global inertial coordinate system is

in the formula is the angular displacement deformation mode shape of node k of the flexible beam.

Equations (14) and (15) can be integrated into

in the formula

The Jordan variation form of equation (18) is

Calculating the first derivative of equation (19) with respect to time can obtain the absolute acceleration (including angular acceleration) of node k of the straight beam i in space, that is

in the formula The specific expression of

2) Straight beam dynamic equation

The virtual power equation of the space moving straight beam i written using the Rodin variation principle is:

in the formula is the node mass matrix of node k of flexible beam i represented in the floating coordinate system, /> is the node moment of inertia matrix represented in the floating coordinate system,/> and/> are respectively the projection of the nodal external force and the nodal external moment on the global inertial coordinate system of the flexible beam i and node k,/> and/> are the generalized deformation mass matrix and generalized deformation stiffness matrix of the flexible beam i, respectively, α and β are the generalized deformation damping coefficients. /> andΩi _,I ,/> and Ω _{i, O} are respectively the absolute velocity and absolute angular velocity of the input and output ends of the single-end input single-end output space motion flexible straight beam i; q _{i, I} and m _{i, I} , q _{i, O} and m _{i, O} are the inputs respectively. Internal force and internal moment at the output end. q _{i, I} is positive along the forward direction of the coordinate axis, m _{i, I} is positive along the reverse coordinate axis, and the positive directions of q _{i, O} and m _{i, O} are opposite to q _{i, I} and m _{i, I.}

Substituting equations (19) and (20) into equation (23), we can get

In the formula, M _i is the generalized mass matrix of flexible beam i, Q _{i, I} and Q _{i, O} is the internal force array at the input and output ends of flexible beam i, It is a generalized force array composed of centrifugal inertial force, Coriolis inertial force, generalized external force and generalized elastic force of the flexible beam i. The specific forms of each matrix are/>

The specific expression of each block matrix is

M _rr =I ¹

M _FF =I ⁶

in the formula

Represents the projection of the absolute angular velocity vector of the floating coordinate system of the flexible body i relative to the global inertial coordinate system in the floating coordinate system.

The 23 constant matrices in the block matrix expression are respectively

in the formula

H ₁ ＝ [1 0 0] ^T , H ₂ ＝ [0 1 0] ^T , H ₃ ＝ [0 0 1] ^T (56)

From the virtual power equation (24) of the space-moving straight beam i, the dynamic equation of the space-moving straight beam i can be obtained, that is

3) Straight beam transfer equation

Similar to the rigid body moving in space, in the new version of the multi-body system transfer matrix method, the corresponding component transfer equation can be derived simply by rewriting the dynamics and kinematic equations of the straight beam moving in space. The specific derivation process is as follows.

By setting the test objects of the kinematics equation (20) of the flexible straight beam i in space as its input and output terminals respectively, the acceleration array of the input and output terminals of the flexible straight beam i in space can be obtained, that is

From the dynamic equation (57) of the space moving straight beam i, we can get

Substituting equation (60) into equation (58) and equation (59) respectively, we can get

Equations (61) and (62) can be organized as

in the formula

Define the state vector of the input and output ends of the single-end input single-end output spatial motion flexible straight beam/> (/> It can be the input terminal I or the output terminal O). The form is

That is to say

Then equation (63) can be rewritten in the form of a transfer equation, that is

z _{i, O} = U _i z _{i, I} (67)

In the formula, U _i is the transfer matrix of the single-end input single-end output spatial motion flexible straight beam i. The specific form is:

It can be seen from Equation (67) that the state vector of a single-end input single-end output space motion straight beam is exactly the same as the state vector form of a single-end input single-end output rigid body. In the process of assembling the total transfer equation of the system using the system topology, the transfer matrix of the single-end input single-end output spatial motion straight beam can be simply calculated with the transfer matrices of other components like a rigid body. The unknown state variables in the system boundary point state vector can be obtained by using the total transfer equation of the system and the system boundary conditions, and then the state vectors of each connection end of the system can be obtained by using the transfer equation of each component. Since the state vector of the single-end input single-end output spatial motion straight beam does not include its flexible deformation generalized acceleration Therefore, after obtaining the single-end input single-end output spatial motion straight beam input and output end state vectors z _{i, j} and z _{i, O,} it is necessary to use equation (60) to obtain its flexible deformation generalized acceleration/>

Adaptive hybrid agent module:

(1) Response surface method

In this model, the Chebyshev polynomials in the high-order response surface method are replaced by Hermite polynomials, and a new sampling method is designed to determine the highest polynomial order and cross terms of the high-order response surface method. method. This response surface method can improve the accuracy of identifying the highest order of each random variable in a high-order polynomial, and effectively reduce unnecessary additional sample points to improve the computational efficiency of the high-order response surface method.

(2)Adaptive Kriging model

1) Basic principles of Kriging model

Kriging surrogate model technology is a spatial interpolation technology based on known sample point information. The predicted value can be expressed as the sum of the regression model F (β, x) and the random process Z (x). Its mathematical expression is:

G(x)＝F(β,x)+Z(x)＝h(x) ^T β+Z(x) (69)

Among them, F (β, x) is the regression function of the Kriging surrogate model, h (x) ^T is the basis function of the Kriging surrogate model, and its form determines the regression form of the Kriging surrogate model, which mainly includes constants, linear functions and quadratic functions. Model, in this article, the constant term is selected as the regression form of the proxy model. The correlation coefficient β is the regression parameter. Z(x) is a random process with a mean value of 0. The covariance matrix between the predicted values of different sample points can be defined as:

COV(Z(x _i ), Z(x _j ))=σ _Z ² R(x _i , x _j , θ) (70)

Among them, x _i and x _j represent test sample points, σ _Z ² is the process variance, R( _xi , x _j , θ) is the correlation function between x _i and x _j . Its main forms include: Gaussian function , exponential function and Cubic function, etc. In this article, a Gaussian function is selected as the correlation function between different sample points:

Among them, n is the dimension of the random variable, x _i ^k , x _j ^k and θ ^k are the k-dimensional components of x _i , x _j and θ. Its parameter θ can be obtained through the maximum likelihood estimation method:

Among them, m is the number of test sample points. When θ is determined, the regression parameter β and process variance σ _Z ² can be expressed as:

β ^* =(F ^T R ^-1 F) ^-1 F ^T R ^-1 Y (73)

Then the mean and variance of the Kriging surrogate model in the prediction point set can be defined as:

Among them, u=F ^T R ^-1 r(x)-f(x), Y is the true response set of the training sample point set, and r is the correlation coefficient matrix between the predicted sample point set and the training sample point set. To sum up, the predicted value of the predicted sample point set x using the Kriging surrogate model obeys the Gaussian distribution:

2) Adaptive solution

The adaptive process is to automatically adjust and supplement the model processing parameters and processing methods according to the data characteristics of known sample points when exploring the model characteristics of unknown areas, so that they are consistent with the statistical distribution characteristics or structural characteristics of the target data to be processed. Consistent; the process of making full use of known sample point information to continuously approach the required target and achieve the best results. Compared with the traditional single-step modeling method, the adaptive modeling method can use fewer test plans to obtain relatively more accurate results. It has important research value in the field of small sample reliability analysis. The flow of the adaptive process is as follows:

As shown in Figure 3.

3) U-H mixed point addition criteria

The U learning function identifies samples with the highest probability of symbol misjudgment to update the surrogate model, and the H learning function selects samples with the highest prediction uncertainty to refine the model. Therefore, the update strategy of this module will combine the U learning function and the H learning function to improve the accuracy and update efficiency of the agent model.

4) Adaptive Kriging model based on U-H mixed point addition criterion

Based on the adaptive scheme and the U-H mixed point addition criterion, the algorithm flow of the adaptive Kriging model is as follows:

①.Parameter setting. Set the initial number of samples N to build the initial Kriging model.

②. Discretization of random processes. The time interval is [0, t _f ], and the first discretization is s=t _f /Δt+1. The time node is t _i , i=1, 2...s, and its time step is Δt. Use the EOLE method to transform the random process Y(t) into a function of the standard normal variable Z.

③.Generate initial training sample set. Generate sample pool D. Then, select N samples W from D and evaluate the instantaneous responses of their corresponding performance functions G _n =g (W, _ti ), i = 1, 2, ..., s. And by W and Constitute the initial training sample set

④.Construct the Kriging model. Create a T-based Kriging model by using the MATLAB toolbox UQLAB. Gaussian correlation function is used here.

⑤. Determine the correctness of the sample symbols. According to the stopping criterion of the U-learning function expressed in Eq., check whether the predicted symbols of the samples in D are all credible (23). If equation (23) is satisfied, go to step 6. Otherwise, the samples in sample D that satisfy equation (23) are composed into the sample pool Then go to step 9.

⑥.Identify the best samples through the H-learning criterion. Find the best sample in D based on H-learning criterion

⑦.H-stop criterion of learning function. Check whether the stopping criterion of the H-learning function is satisfied. If not, you will go to step 8, otherwise go to step 12.

⑧.Evaluate the true instantaneous response on the best sample. in sample Calculate the true instantaneous response of the performance function Add/> and/> to the training set W and/> Respectively expressed as/> and/> Then, return to step 3.

⑨.Identify the two best samples through U-learning criteria and H-learning criteria. Find the two best samples based on U-learning criterion and H-learning criterion It is worth noting that/> Found in D,/> Found in D ₁ .

⑩. Proposed stopping criteria. Check whether the proposed stopping criteria are met. If not satisfied, go to step 11, otherwise go to step 12.

Evaluate the true instantaneous response on the two best samples. In sample/> and/> Calculate the true instantaneous response of the performance function/> Will/> and/> Add to initial set W and /> respectively, expressed as and/> Then return to step 3.

Complete the Kriging model construction.

(3) PCE-Kriging (PCK) agent model based on U-H mixed point addition criterion

This module also combines the improved agent modeling technology with the respective advantages of polynomial chaos expansion (PCE) and Kriging model, and proposes the PCE-Kriging (PCK) agent model. The advantage of PCE is that it can better capture the global behavior of the vibration quality calculation model of the weapon multi-body system. The advantage of the Kriging model is that it obeys the normal distribution and can simultaneously calculate the mean and mean square errors of the calculation prediction points, making use of model updates. In the PCK model, the combination of the two is that PCE replaces the regression basis function part of the original Kriging to improve the global approximation accuracy, while the approximation of local variability is still provided by the stochastic process of the original Kriging. Therefore, the PCK model expression is

The PCK model inherits the original Kriging model's ability to provide predicted values and its mean square error characteristics, and at the same time enhances its global approximation capabilities, so it has more practical application value in this project.

The PCE-Kriging model calculation process for the root mean square of the dynamic response of the weapon multi-body system based on the U-H mixed point criterion is consistent with the corresponding adaptive Kriging model, and only the model construction part is replaced. And enter the highest order P required by PCE in the first step.

(4)Adaptive hybrid agent model

Based on three surrogate model methods: response surface method, adaptive Kriging method and adaptive PCE-Kriging method, an adaptive hybrid surrogate model library for the vibration response of weapon multi-body systems is formed, such as

As shown in Figure 4, a simple surrogate model is then used to replace the complex weapon multi-body system structural analysis model, that is, the multi-body system dynamics equation obtained in module one. For different problems, the optimal surrogate model is selected through a comprehensive comparison of the fitting accuracy and efficiency of the dynamic response of the weapon multi-body system. The specific analysis process will be shown in the specific implementation methods later.

Robust design solution strategy module: Based on the optimal agent model obtained in module two, this module uses decision-making models and optimization methods and strategies to optimize the robustness of the weapon multi-body system. The decision-making model and optimization methods and strategies are as follows.

(1) Robust design optimization decision-making model considering accidental uncertainty

According to the traditional deterministic optimization model, based on the optimal agent model, the robust design optimization decision-making model considering accidental uncertainty is as follows::

in, is the square and arithmetic square root mean of the two norms of the amplitudes in the x and y directions on the time history based on the optimal surrogate model mentioned above,/> is the corresponding standard deviation. The optimization goal is to minimize the mean square sum of the amplitude mean and variance in the two directions over time. x is the random variable vector corresponding to the design variable vector d.

(2) Weighted single objective optimization method

The optimization design of vibration reduction robustness of a multi-body weapon system is a multi-objective and multi-parameter problem. Its multi-objective mathematical model is as follows:

Among them, x(t) and y(t) are the amplitudes in the x-direction and y-direction mentioned above. n is the number of design variables d. This weapon multi-body system is a dual-objective optimization problem, which can be solved using multi-objective subset simulation optimization. The solution process is as follows

As shown in Figure 5.

It is difficult to directly solve the optimal solution of multi-objective problems. Therefore, based on certain engineering experience, appropriate weight coefficients can be selected, and the multi-objective problem can be converted into a single-objective problem through the weighting method. Based on the above-identified design variables, the following deterministic vibration reduction optimization model of the weapon multi-body system can be constructed. .

In the formula, ω ₁ and ω ₂ are the weight coefficients of the overall effect of the amplitude in the x and y directions respectively. Considering that the amplitudes in both the x and y directions need to be effectively suppressed, ω ₁ =ω ₂ =0.5 is selected here. It can be seen from the above formula that the original dual-objective problem can be transformed into a single-objective problem to solve.

In order to further reduce the number of objective functions and prevent too many objective functions from adding additional computational burden to the robust design problem; at the same time, considering that the design goal is to minimize the vibration response, the amplitudes in the x and y directions can be calculated on the time history The mean square sum of the two norms, that is, the total displacement effect is used as the optimization objective. Therefore, formula (80) can be rewritten as:

(3)Single loop solution strategy

For robustness (robustness) optimization design problems, the solution process is as follows

As shown in Figure 6. It can be seen that at each iteration of the design point, uncertainty propagation analysis of the physical model (simulation or experiment, this project is the optimal proxy model for the multi-body dynamic response of the shipborne gun) is required. Specifically, a large number of model call analyzes are required, and statistical analysis is required to obtain feature quantities such as mean and variance required for robust design. Therefore, the problem is actually a double loop solution problem. The outer loop is an optimization process, and the inner loop is uncertainty propagation analysis, that is, tens of thousands of statistical calculations. This double-loop problem often requires a huge amount of calculations.

In view of the above-mentioned multi-objective optimization problems and double-loop solution problems, this module integrates the weighted single-objective optimization method, the multi-objective subset simulation optimization method and the single-loop robust solution strategy to conduct vibration reduction robustness design.

The specific process is shown in Figure 7: First, initialize the design variables, and use the weighted single-objective optimization method and the multi-objective subset simulation optimization method to optimize, then calculate the Euclidean distance between the obtained sample points, and find the point closest to any sample. x, obtain the seed sample matrix from the sample point set (x ¹ ,...,x ^k ) within the Euclidean distance T of its neighborhood, perform robust optimization design on them, and obtain the response according to F=F(x) The sample point with the largest value is used as the threshold sample, and the corresponding response value is F(x ^k ).

Then, calculate the new sample point x ^k+1 and obtain the corresponding response value F(x ^k+1 ). If F(x ^k+1 )≤F(x ^k ), update its neighborhood (x ¹ ,..., x ^k , x ^k+1 ), thereby updating the seed sample matrix, and adding the sample point x ^k+1 to the information matrix.

Finally, if the termination criterion is met or the calculated number of samples reaches the maximum tolerable value, stop and output the current value. Otherwise, continue updating the sample.

The advantages of the present invention compared with the prior art are:

(1) The new transfer matrix method is used to construct a rigid-flexible coupling dynamic model of the weapon multi-body system, which greatly improves the simulation efficiency while ensuring that the output results meet the accuracy requirements.

(2) In view of the multi-fidelity requirements for fast and robust vibration response of uncertain weapon multi-body systems, the response surface method, adaptive Kriging method and adaptive PCE-Kriging method are integrated to form an adaptive hybrid agent model for different multi-body systems. The library takes into account the accuracy and efficiency of the proxy model and uses the optimal proxy model solution.

(3) A robust design optimization decision-making model considering accidental uncertainty was constructed, using a weighted single-objective solution strategy, a single-loop solution strategy, and a multi-objective subset simulation optimization method to form a fast multi-body system for uncertain weapons. The robust design method greatly improves the efficiency of robust design of multi-body weapons systems.

Picture description:

Figure 1 Schematic diagram of the dynamic response calculation model of the naval gun system;

Figure 2 Schematic diagram of a single-end input single-end output spatial motion straight beam;

Figure 3 Adaptive process flow chart;

Figure 4 Schematic diagram of the hybrid agent model;

Figure 5 Multi-objective subset simulation optimization flow chart;

Figure 6 Dual-loop robustness design flow chart;

Figure 7 Single-cycle robustness design flow chart;

Figure 8 Multi-objective subset simulation of accidental uncertainty optimization Pareto front;

Figure 9 Weighted single-objective subset simulation of accidental uncertainty optimization iterative process

Figure 10 Multi-objective subset simulation of accidental uncertainty optimization Pareto front

Detailed ways:

The present invention will be further described below in conjunction with the accompanying drawings and examples. Take the vibration reduction robustness analysis process of a certain naval gun as an example.

(1) Establishment of multi-body system model

The naval gun dynamic response solution model is established by the linear multibody system transfer matrix method (MSTMM), such as

As shown in Figure 1, element 1 is the gun base, element 3 is the rotating body, element 5 is the pitching body, element 7 is the breech, element 8 is the barrel, element 6 is the sliding hinge, and elements 2 and 4 are elastic hinges. , where elements 3, 5 and 7 are rigid bodies, element 8 is an elastic body, and the angle of incidence of the pitching body 5 is θ.

The calculation of dynamic response requires the use of the new version of the multi-body system transfer matrix method. The input and output state vectors of each element are:

The transfer equation for each element is

Z _O =UZ _I (84)

In NVMSTMM, the elastic hinge is cut off and divided into two subsystems. The elastic hinge will be added to the rigid body transfer matrix as an external force and external moment. The total transfer matrix is:

If element 8 is considered to be a rigid beam, then U ₃ , U ₅ , U ₇ , and U ₈ are all one-end input and one output rigid body transfer matrices, and U ₆ is the slip hinge transfer matrix. The specific form of the relevant transfer matrix is shown in Appendix 2.

All boundaries of the two transfer equations are free boundary conditions, in the form of formula (4)

Based on the multi-body dynamic topology of a rigid barrel naval gun, the rigid barrel is considered as a flexible structure, and the transfer equation of a flexible straight beam with large motion and small deformation is used to model the relative vibration in the X and Y directions at the muzzle. response.

After the above deterministic multi-body dynamics analysis, the vibration responses of the muzzle in the x and y directions on the time history and y(t) can be obtained. In order to comprehensively evaluate the vibration characteristics of the muzzle, its comprehensive vibration quality is quantified according to the root mean square of the relative vibration response as follows:

(2) Optimal agent model

Using the adaptive hybrid surrogate model library, three types of surrogate model methods, namely: high-order response surface method, adaptive Kriging model and adaptive PCK hybrid surrogate model, are used to improve the fitting accuracy and efficiency of the dynamic response of the weapon multi-body system. Comprehensive comparison can provide the optimal surrogate model selection scheme for the vibration quality of a certain naval gun multi-body system, which can be used as the mathematical model input for subsequent robust design optimization. The comparison results are shown in the table below.

Table 1 Comparison of three agency models

Under the current limited cost model relationship, comparing the maximum errors of the three surrogate models, it was found that the adaptive PCK model has the lowest relative error and the least number of calls to the original simulation model, which performs best and can be used for subsequent robust design optimization research.

(3) Robust design of weapon multi-body system

On the basis of the optimal surrogate model, multi-objective subset simulation optimization is used to provide the robustness decisions for the accidental uncertainty of muzzle vibration of a certain shipborne artillery multi-body system under single-cycle and double-cycle robust design strategies. Model and computational results of a weighted multi-objective contingent uncertainty robust decision-making model.

1)Double cycle robust design method

A double-loop method is used to solve this robust design problem. First, solve the dual-objective optimization problem. The multi-objective subset simulates each layer with N (population number) = 100 samples. p ₀ is 0.2. A total of 20 iterations (population number) are performed. 1700 samples are used in the outer layer and Monte Carlo is used in the inner layer. The method is used to solve the vibration quality mean and variance corresponding to each sample point. Each time requires 100 samplings, and a total of 1700*100=170000 times of original structural system analysis is required. The resulting Pareto front and results are as follows

As shown in Figure 8.

All "○" in the figure constitute a feasible region solution set considering the dual objectives of vibration quality mean and variance, in which the minimum vibration quality mean is 0.4148. In order to facilitate comparison with the weighted single-objective optimization described later, a compromise was made to select a group (Group 11) with a vibration quality mean value of 0.4427 and a standard deviation of 0.0999. The corresponding design values of the solution set are:

Table 2 Multi-objective subset simulation optimal design for accidental uncertainty optimization

Then, solve the single-objective optimization problem after weighted transformation. The subset simulates each layer with N (population number) = 100 samples, p ₀ is 0.2, and a total of 10 iterations are performed. 820 samples are used in the outer layer, and the Monte Carlo method is used in the inner layer. To solve for the mean and variance of vibration quality corresponding to each sample point, 100 samplings are required each time. A total of 820*100=82000 times of original structural system analysis is required to obtain the minimum vibration quality of 0.3966. The iterative process is as follows

As shown in Figure 9, the optimal design obtained is:

Table 3 Weighted single-objective accidental uncertainty optimization optimal design

Comparing the two optimization results, it can be seen that for the accidental uncertainty vibration reduction robustness design, almost the minimum mean vibration quality is obtained (0.4148 for multi-objective and 0.3966 for single-objective). Multi-objective requires 170,000 times of original structural system analysis. , while the weighted single-objective method only needs 82,000 times. For this dual-objective problem, the efficiency has been more than doubled by using only the single-objective weighting method.

2) Single cycle robustness design method

Using the single cycle method to solve the above problem requires only 8720 times (samples) of secondary structure analysis. The resulting Pareto front and results are as follows

As shown in Figure 10.

All "○" in the figure constitute a feasible region solution set considering the dual objectives of vibration quality mean and variance, in which the minimum vibration quality mean is 0.3027. In order to facilitate comparison with the weighted single-objective optimization described later, a compromise was made to select a group (Group 13) with a vibration quality mean value of 0.3642 and a standard deviation of 0.0960. The corresponding design values of the solution set are:

Table 4 Multi-objective subset simulation optimal design for accidental uncertainty optimization

It can further be found that if the single-loop method is used to solve the above-mentioned multi-objective problem, compared with the original double-loop method, the calculation efficiency of the vibration damping robustness design problem considering accidental uncertainty is further improved by about 17 times.

The above are only preferred examples of the present invention. The present invention is not limited to the above examples. Any local changes, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention. Inside.

Claims (4)

1. The rapid robustness design technology of the weapon multi-body system is characterized by mainly comprising the following three modules:

module one: and the multi-body dynamics efficient modeling and analysis module is used for establishing a dynamics model of rigid-flexible coupling of the multi-body system by adopting a transfer matrix method in consideration of the rapid design requirements to be met by the rapid analysis and design method of the multi-body system.

The method comprises the steps of establishing a ship gun dynamics response solving model by a linear multi-body system transfer matrix method, wherein an element 1 is a gun holder, an element 3 is a revolving body, an element 5 is a pitching body, an element 7 is a gun tail, an element 8 is a barrel, an element 6 is a sliding hinge, elements 2 and 4 are elastic hinges, the elements 3, 5 and 7 are rigid bodies, the element 8 is an elastic body, and the angle of a pitching body 5 is theta.

(1) Rigid gun barrel

The input and output state vectors of each element of the model are:

each element transfer equation is

Z _O ＝UZ _I

In the new-version multi-body system transmission matrix method, the elastic hinge is cut off and divided into two subsystems, and the elastic hinge is added into the rigid body transmission matrix as external force and external force moment. The total transfer matrix is:

all boundaries of the two transfer equations are free boundary conditions, in the form of a formula

(2) Flexible gun barrel

The kinematic equation, the dynamic equation and the transmission matrix of the large-motion small-deformation flexible straight beam are respectively deduced under the rigid condition as follows

z _l，O ＝U _l z _i，I

And taking the rigid barrel into a flexible structure, and modeling by adopting a transfer equation of the large-motion small-deformation flexible straight beam to obtain a rigid-flexible coupling dynamics model of the multi-body system.

And a second module: the self-adaptive mixed agent module integrates a response surface method, a self-adaptive Kriging method and a self-adaptive PCE-Kriging method to form a self-adaptive mixed agent model for vibration response of a weapon multi-body system, the multi-body system model of a multi-body system structural analysis model obtained by a module I is replaced by a simply constructed agent model, data obtained by the three methods are analyzed, and efficiency and precision requirements are comprehensively considered to an optimal agent model scheme.

And a third module: and a robustness design solving strategy module: the robustness design optimization decision model under the accidental uncertainty condition is considered as follows

wherein ,for the square root mean of the sum of squares arithmetic of the two norms of the amplitudes in the x and y directions over time based on the module two optimal proxy model>Corresponding standard deviation. The optimization objective is that the mean and variance of the amplitudes in two directions are the least squares sum over time. And x is a random variable vector corresponding to the design variable vector d. Thus, for weapon multi-body systems, multi-body system damping robustness design that accounts for occasional uncertainties is typically a multi-objective optimization problem. Meanwhile, the robustness optimization design problem needs to carry out uncertainty propagation analysis of a physical model during iteration of each step of design point, so that the problem is also a double-loop solving problem.

Aiming at the multi-target double-circulation problem, a weighted single-target solving strategy, a single-circulation solving strategy and a multi-target subset simulation optimization method are adopted to form a rapid robustness design method for the uncertain weapon multi-body system, and the rate of vibration reduction robustness design of the weapon multi-body system is improved.

2. A weapon multi-body system rapid robustness design technique according to claim 1, characterized in that: and a dynamic model of rigid-flexible coupling of the weapon multi-body system is constructed based on a transfer matrix method in the second module.

3. A weapon multi-body system rapid robustness design technique according to claim 1, characterized in that: in a second module, aiming at the rapid robust vibration response multi-fidelity requirement of an uncertain weapon multi-body system, a response surface method, a self-adaptive Kriging method and a self-adaptive PCE-Kriging method are integrated to form a self-adaptive mixed agent model library aiming at different multi-body systems, the precision and efficiency of the agent model are comprehensively considered, and an optimal agent model scheme is provided.

4. A weapon multi-body system rapid robustness design technique according to claim 1, characterized in that: and a robust design optimization decision model under the condition of considering accidental uncertainty is constructed in the third module, and a weighted single-target solving strategy, a single-cycle solving strategy and a multi-target subset simulation optimization method are adopted to form a rapid robust design method for the uncertain weapon multi-body system.