CN116956498A - Rapid robustness design technology for weapon multi-body system - Google Patents
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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
Technical field:
the invention relates to the field of weapon multi-body system robustness design, in particular to weapon multi-body system vibration reduction robustness design considering influence of accidental uncertainty factors.
The background technology is as follows:
most mechanical systems in the field of weaponry can be seen as multi-body systems consisting of "body units" and "hinge units" in a certain connection. The accuracy and the efficiency of dynamic (vibration) characteristic analysis of the multi-body mechanical system are ensured, and efficient and reasonable vibration reduction design is carried out according to the vibration characteristics of the system, so that the method is very important for improving the performance of weaponry. The multi-body system dynamics method and the finite element method are main methods for weapon multi-body system dynamics research. However, all these methods require the establishment of a system overall dynamics equation, involving a system matrix order proportional to the system degrees of freedom. With the increase of the matrix order of the system, the calculation speed of the dynamics of the multi-body system is reduced exponentially, and the calculation speed is low because the overall dynamics equation of the complex weapon system relates to the high matrix order, so that the rapid calculation requirement of the dynamics design of the complex weapon system cannot be met.
There are some uncertainty factors, such as randomness of the mechanical properties of the materials, errors in geometry, dispersion of external loads, which are unavoidable during design, manufacture and use. These uncertainty factors often further affect the performance and safety of weapon multi-body systems, which becomes a great impediment to the performance improvement of current weaponry. Therefore, the development of the high-efficiency rapid robustness design method of the uncertain weapon multi-body system has important theoretical and practical significance for improving the performance of weapon equipment, guaranteeing the safety of the equipment, saving the cost of the equipment, guaranteeing the fight force of the equipment and the like.
The dynamics of a multi-body system is one of the current mechanical research hot spots, and is an important foundation for designing and testing dynamic performance of a large number of industrial products such as weapons, ships, aviation, spaceflight, vehicles, general machinery and the like. However, the following features are common in various multi-body system dynamics methods which are rapidly developed in the last 50 years: (1) the system overall dynamics equation must be established; (2) Once the topology of the system is changed, the overall dynamic equation of the system needs to be deduced again; (3) Complex system global dynamics equations involve high matrix orders (typically not less than the number of degrees of freedom of the system), with computation speeds significantly slowing down as the system scale increases. The multi-body system transfer matrix method can realize the rapid calculation of multi-rigid body system dynamics, multi-rigid-flexible body system dynamics, controlled multi-body system dynamics, especially complex emission system dynamics without a system overall dynamics equation and with the system matrix order far lower than the system freedom degree.
For uncertainty multi-body dynamics, the related research work at home and abroad is less, the multi-source uncertainty of accidental and cognitive mixing in a multi-body system is processed by adopting an interval method, and the related research work for a weapon multi-body system is more spent. The interval method has the advantages that only the upper and lower bounds of the random parameters need to be determined, the prior statistical information is less, but the interval method has the disadvantages of poor precision and easy overestimation of the influence of randomness on the dynamics response of the multi-body system. Thus, this type of approach is not suitable for weapon multisystem vibration analysis problems that take into account multisource uncertainties.
On the basis of the dynamic analysis research of the uncertainty multi-body system, the research work aiming at the robustness design of the multi-body system also basically processes multi-source uncertainty parameters by an interval method, solves the problem of robustness design optimization by adopting a double-circulation method, and no related research work aiming at the robustness design of the uncertainty weapon multi-body system exists at present. It should be noted that: robustness is designed into double loops nested inside and outside, multi-body system uncertainty propagation analysis considering multi-source uncertainty random input is needed to be carried out inside (meanwhile, accuracy and efficiency of multi-body system dynamics analysis are needed to be considered), and optimization solution is needed to be carried out outside. Therefore, multi-body system robustness design considering multi-source uncertainty currently faces the problems of low accuracy and efficiency of multi-source uncertainty dynamics modeling and analysis, low solving efficiency of the robustness design and the like. This is especially true in the field of weaponry that includes typical multi-body systems, which severely restricts the rapid improvement of the performance of weaponry in our country at present.
The invention comprises the following steps:
the technical solution of the invention is as follows: the invention aims to improve the calculation efficiency of the vibration reduction robustness design of the uncertain weapon multi-body system by integrating the current research situation at home and abroad, and realizes the dynamics modeling of the weapon multi-body system based on a transfer matrix method by constructing a self-adaptive rigid-flexible coupling dynamics analysis model of the weapon multi-body system. Meanwhile, the invention provides a weapon multi-body system vibration reduction robustness design high-efficiency solving method integrating a self-adaptive mixed agent model, a multi-target subset simulation optimizing method, a weighted single-target optimizing method and a single-cycle solving strategy, and the efficiency of the whole weapon multi-body system vibration reduction robustness design process is improved.
The technical solution of the invention is as follows: a rapid robustness design technology for a weapon multi-body system comprises three steps: firstly, rapidly solving vibration response of a weapon multi-body system; then, obtaining an optimal agent model; finally, based on an optimal proxy model, the robustness design problem of the weapon multi-body system is solved efficiently; the whole rapid analysis and design method comprises three 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 high-efficiency modeling and analyzing module for the multi-body dynamics comprises: and solving rigid-flexible coupling dynamic models of the rigid barrel and the flexible barrel, and deriving a transfer matrix equation by using a large-motion small-deformation flexible straight beam dynamic equation.
Establishing a solution model of the dynamic response of the warship by a linear multi-body system transfer matrix method, such as
Fig. 1 shows that element 1 is a cradle, element 3 is a revolution body, element 5 is a pitching body, element 7 is a gun tail, element 8 is a barrel, element 6 is a sliding hinge, elements 2 and 4 are elastic hinges, elements 3, 5 and 7 are rigid bodies, element 8 is an elastic body, and the angle of pitching body 5 is θ.
(1) Rigid barrel
The input and output state vectors of each element of the model are:
each element transfer equation is
Z O ＝UZ I (2)
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, and the form is shown as formula (4)
(2) Large-motion small-deformation flexible straight beam
Taking a single-end input single-end output space motion straight beam i as an example shown in fig. 2, for a small deformation space motion straight beam i, the whole node displacement array delta is formed i The available mode superposition form is expressed as
in the formula
For the j-th order mode shape of the flexible beam i, < >>And M is the number of the selected mode vibration modes for the j-th order deformation generalized coordinates corresponding to the mode vibration modes.
1) Equation of straight beam kinematics
The position vector of the spatial motion straight beam inode k in the global inertial coordinate system accounting for the axial shortening effect can be expressed as
in the formula Is the mode shape, l, of the flexible beam i node k linear displacement deformation p For the initial length of the spatially moving straight beam i unit p, v and w are the beam units, respectivelyThe point on the neutral axis is deformed along the y-axis and z-axis of the floating coordinate system. H 1 ＝[1 0 0] T Is a constant matrix.
The last term in equation (8) can be rewritten as using a matrix of unit-shaped functions
in the formula
δ ip For the node deformation displacement array of the flexible beam i unit p, N v(x) and Nw (x) A matrix of shape functions corresponding to v and w, N' · (x) Representational function matrix N · (x) The first derivative of the ordinate x of the compliant beam. It is easy to find from formula (10)Is a symmetric matrix.
Substituting formula (5) into formula (9), and further finishing to obtain
in the formula
Substituting formula (11) into formula (8)
The first derivative over time of equation (13) may be the absolute velocity vector of spatial motion straight beam inode k in the global inertial coordinate system, i.e.
in the formula The projection of the absolute angular velocity vector of the floating coordinate system for the compliant beams i in the global inertial coordinate system. From the angular velocity superposition theorem the node coordinate system +.>Angular velocity vector relative to global inertial coordinate system is
in the formula The mode shape is the mode shape of the flexible beam i node k angular displacement deformation.
Formulas (14) and (15) may be integrated into
in the formula
The Ruodan variant of the formula (18) is
Taking the first derivative of equation (19) over time may be used to determine the absolute acceleration (including angular acceleration) of the spatial motion straight beam inode k, i.e
in the formula The specific expression of (2) is
2) Straight beam dynamics equation
The virtual power equation of the space motion straight beam i written by using the Ruondan variation principle column is as follows
in the formula For the node mass matrix of the flexible beam inode k represented in the floating coordinate system +.>Node moment of inertia matrix for representation in floating coordinate system, +.> and />Projection of node external force and node external moment on flexible beam i node k in global inertial coordinate system> and />The mass matrix and the rigidity matrix are respectively a flexible beam i generalized deformation mass matrix and a generalized deformation rigidity matrix, and alpha and beta are generalized deformation damping coefficients. /> and Ωi，I ，/> and Ωi，O The absolute speed and the absolute angular speed of the input and output ends of the single-ended input and single-ended output space motion flexible straight beam i are respectively; q i，I and mi，I ，q i，O and mi，O The internal force and the internal moment of the input end and the output end respectively. q i，I Positive direction along coordinate axis, m i，I Along the coordinate axis, reverse direction is positive, q i，O and mi，O Positive direction and q of (2) i，I and mi，I On the contrary.
Substituting the formulas (19) and (20) into the formula (23) to obtain the final product
in the formula Mi Generalized mass matrix for flexible beam i, Q i，I and Qi，O Is a force array in the input and output ends of the flexible beam i,the device is a generalized force array consisting of centrifugal inertial force, ke's inertial force, generalized external force and generalized elastic force of a flexible beam i. The specific form of each matrix is +.>
Wherein the specific expression of each blocking matrix is
M rr ＝I 1
M FF ＝I 6
in the formula
Representing the projection of the absolute angular velocity vector of the flexible body i floating coordinate system relative to the global inertial coordinate system in the floating coordinate system.
The 23 constant matrices in the partitioned 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)
The dynamic equation of the spatial motion straight beam i can be obtained by the virtual power equation (24) of the spatial motion straight beam i, namely
3) Straight beam transfer equation
Similar to the space motion rigid body, in the new version of the multi-body system transfer matrix method, the corresponding element transfer equation can be derived only by rewriting the form of the dynamics and kinematics equation of the space motion straight beam, and the specific derivation process is as follows.
The examination object of the kinematic equation (20) of the space motion flexible straight beam i is respectively set as the input end and the output end, so that the acceleration array of the input end and the output end of the space motion flexible straight beam i can be obtained, namely
From the kinetic equation (57) of the spatial movement straight beam i
By substituting the formula (60) into the formulas (58) and (59), respectively
Formulas (61) and (62) may be organized into
in the formula
Defining the state vector of the single-end input single-end output space motion flexible straight beam input/output end>(/>Can be in the form of input end I or output end O) and is
I.e. the
Then equation (63) may be rewritten as a form of transfer equation, i.e
z i，O ＝U i z i，I (67)
in the formula Ui Namely a single-end input single-end output space motion flexible straight beam i, which is in the specific form of
It can be seen from (67) that the state vector of the single-ended input single-ended output spatial motion straight beam is exactly the same as the state vector form of the single-ended input single-ended output rigid body. In the process of assembling the total transfer equation of the system by utilizing the topological structure of the system, the transfer matrix of the single-end input single-end output space motion straight beam can be simply operated like a rigid body with the transfer matrix of other elements. The unknown state variables in the state vector of the boundary point of the system can be obtained by using the total transfer equation of the system and the boundary conditions of the system, and then the state vector of each connecting end in the system is obtained by using the transfer equation of each element again. The state vector of the single-end input single-end output space motion straight beam does not contain the flexible deformation generalized accelerationTherefore, the state vector z of the single-ended input and single-ended output space motion straight beam input and output end is obtained i，j and zi，O Then the generalized acceleration of its flexible deformation is determined by means of equation (60)>
An adaptive hybrid proxy module:
(1) Response surface method
In the model, a Chebyshev (Chebyshev) polynomial in a high-order response surface method is replaced by a Hermite (Hermite) polynomial, and a new sampling method, a polynomial highest order of the high-order response surface method and a method for determining cross terms are designed. The response surface method can improve the accuracy of identifying the highest order of each random variable in the high-order polynomial, effectively reduce unnecessary additional sample points and further improve the calculation efficiency of the high-order response surface method.
(2) Self-adaptive Kriging model
1) Basic principle of Kriging model
The Kriging proxy model technique is a spatial interpolation technique based on known sample point information, and the predicted value can be expressed as the sum of a regression model F (β, x) and a random process Z (x). The mathematical expression is as follows:
G(x)＝F(β，x)+Z(x)＝h(x) T β+Z(x) (69)
wherein F (beta, x) is a regression function of the Kriging proxy model, h (x) T The form of the base function of the Kriging proxy model determines the regression form of the Kriging proxy model, and mainly comprises constants, linear functions and quadratic function models, wherein constant terms are selected as the regression form of the proxy model. The correlation coefficient beta is a regression parameter. Z (x) is a random process with a mean of 0, and the covariance matrix between the predictions 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)
wherein ,xi and xj Representing the test sample point, sigma Z 2 For process variance, R (x i ，x j θ) is x i and xj The correlation function between the two is mainly formed by: gaussian, exponential, cubic, etc., and gaussian is chosen herein as the correlation function between the different sample points:
where n is the dimension of the random variable, x i k ，x j k and θk Is x i ，x j And a k-dimensional component of θ. The parameter theta can be obtained by a maximum likelihood estimation method:
where m is the number of test sample points. When θ is determined, 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)
the mean and variance of the Kriging proxy model at the set of predicted points can be defined as:
wherein ,u＝FT 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 prediction sample point set and the training sample point set. In summary, the prediction value of the prediction sample point set x using the Kriging proxy model obeys the gaussian distribution:
2) Adaptive scheme
The self-adaptive process is to automatically adjust and supplement model processing parameters and processing methods thereof according to the data characteristics of known sample points when exploring unknown region model characteristics, so that the model processing parameters are consistent with the statistical distribution characteristics or the structural characteristics of the required processing target data; and (3) fully utilizing the information of the known sample points to continuously approach the required target, and obtaining the process of the best effect. Compared to traditional single-step modeling methods, the adaptive modeling method can obtain relatively more accurate results with fewer test schemes. Has important research value in the field of small sample reliability analysis. The flow of the adaptation process is as follows
Shown in fig. 3.
3) U-H mixed dotting criterion
And updating the proxy model by using a sample with the highest misjudgment probability of the identification symbol of the U learning function, and refining the model by using a sample with the largest prediction uncertainty selected by the H learning function. Therefore, the module updating strategy combines the U learning function and the H learning function, and improves the accuracy and updating efficiency of the agent model.
4) Self-adaptive Kriging model based on U-H mixed dotting criterion
Based on the self-adaptive scheme and the U-H mixed dotting criterion, the algorithm flow of the self-adaptive Kriging model is as follows:
(1) parameter setting. The initial number of samples N is set to build an initial Kriging model.
(2) Discretizing the random process. The time interval is [0, t f ]First discretized into s=t f Time node is t i I=1, 2..s the time step is Δt. The random process Y (t) is converted into a function of the standard normal variable Z using the EOLE method.
(3) Generating an initial training sample set. A sample cell D is generated. Then, N samples W are selected from D and the transient response G of the corresponding performance function is evaluated n ＝g(W，t i ) I=1, 2,..s. And is composed of W andconstructing an initial training sample set
(4) Constructing a Kriging model. The T-based Kriging model was built by using MATLAB toolbox UQLAB. Here a gaussian correlation function is used.
(5) Judging the correctness of the sample symbol. Checking whether the predicted signs of the samples in D are all acceptable based on the stopping criteria of the U-learning function expressed in the equationLetter (23). If equation (23) is satisfied, go to step 6. Otherwise, the sample satisfying equation (23) in sample D is composed into the sample cellAnd then goes to step 9.
(6) The best sample is identified by H-learning criteria. Searching for the best sample in D based on H-learning criteria
(7) H-stopping criteria for learning functions. It is checked whether the stopping criterion of the H-learning function is fulfilled. If not, go to step 8, otherwise go to step 12.
(8) The true transient response on the best sample is evaluated. In the sampleComputing true transient response of performance functionAdd-> and />To training set W and->Respectively expressed as-> and />Then, the process returns to step 3.
(9) Two best samples were identified by the U-learning criteria and the H-learning criteria. Finding two best samples based on U-learning criteria and H-learning criteriaNotably, the->Found in D, < >>At D 1 Is found.
Proposed stopping criteria. It is checked whether the proposed stopping criterion is fulfilled. If not, go to step 11, otherwise go to step 12.
The true transient response on the two best samples is evaluated. In the sample-> and />True transient response of the computational performance function>Will-> and />Added to the initial set W and +.>Respectively, denoted as and />And then returns to step 3.
And (5) completing the Kriging model construction.
(3) PCE-Kriging (PCK) proxy model based on U-H mixed dotting criterion
The module also combines the improved proxy modeling technology of the respective advantages of the Polynomial Chaotic Expansion (PCE) and the Kriging model to provide a PCE-Kriging (PCK) proxy model. The PCE has the advantages that the global behavior of the vibration quality calculation model of the weapon multi-body system can be better captured, the Kriging model has the advantages that the Kriging model is subjected to normal distribution, the mean value and the mean square error of the calculation prediction point can be calculated at the same time, and the model is utilized for updating. The PCK model combines the PCE with the original Kriging regression basis function to improve the global approximation accuracy, and the approximation of the local variability is still provided by the original Kriging random process. Thus, the PCK model expression is
The PCK model inherits the characteristics that the original Kriging model can provide a predicted value and a mean square error thereof, and enhances the capability of global approximation, so that the PCK model has more practical application value in the project.
The calculation flow of the PCE-Kriging model of the weapon multisystem dynamics response root mean square based on the U-H mixed dotting criterion is consistent with that of a corresponding self-adaptive Kriging model, and only the model construction part is needed to be replaced. And inputs the highest order P required by the PCE in a first step.
(4) Adaptive hybrid proxy model
Based on three proxy model methods: response surface method, self-adaptive Kriging method and self-adaptive PCE-Kriging method, forming self-adaptive mixed agent model library facing vibration response of weapon multi-body system, such as
As shown in fig. 4, the complex weapon multi-body system structural analysis model, i.e. the resulting multi-body system dynamics equation in module one, is then replaced with a proxy model of simple construction. Aiming at different problems, the fitting precision and efficiency of the weapon multi-body system dynamic response are comprehensively compared, an optimal agent model is selected, and a specific analysis process is shown in a later specific embodiment.
And a robustness design solving strategy module: based on the optimal agent model obtained by the second module, the optimal design is carried out on the robustness of the weapon multi-body system by adopting a decision model and an optimization method strategy, wherein the decision model and the optimization method strategy are as follows.
(1) Robust design optimization decision model under accidental uncertainty condition
According to the traditional deterministic optimization model, based on an optimal proxy model, a robust design optimization decision model under the condition of considering accidental uncertainty is as follows: :
wherein ,for the sum of squares arithmetic square root mean of the two norms over time of the amplitudes in the x and y directions based on the optimal proxy model described above +.>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.
(2) Weighted single-objective optimization method
The optimized design of vibration reduction robustness of the weapon multi-body system is a multi-objective multi-parameter problem, and a multi-objective mathematical model is as follows:
where x (t) and y (t) are the amplitudes in the x-direction and y-direction described above. n is the number of design variables d. The weapon multi-body system is a double-target optimization problem, and can adopt multi-target subset simulation optimization solution, wherein the solution flow is as follows
Shown in fig. 5.
The optimal solution for directly solving the multi-objective problem has higher difficulty. Therefore, based on a certain engineering experience, a proper weight coefficient can be selected, the multi-objective problem is converted into a single-objective problem by a weighting method, and the following weapon multi-body system deterministic vibration reduction optimization model can be constructed according to the determined design variables.
in the formula ω1 and ω2 The weight coefficients of the overall effects of the amplitudes in the x-direction and the y-direction are respectively, considering that the amplitudes in the x-direction and the y-direction are effectively suppressed, ω is selected here 1 ＝ω 2 =0.5. As can be seen from the above: the original double objective problem can be converted into a single objective problem solution.
In order to further reduce the number of objective functions, the problem that the number of objective functions is too large to add extra calculation burden to the robustness design problem is avoided; meanwhile, considering that the design target is the minimum vibration response, the mean square sum of two norms of the amplitudes in the x and y directions on the time history can be calculated, namely: the total effect of the displacement is used as an optimization target. Thus, equation (80) can be rewritten as:
(3) Single cycle solution strategy
For robustness (robustness) optimization design problems, its solving process is as follows
Shown in fig. 6. It can be seen that: during the iteration of each step of design point, uncertainty propagation analysis of a physical model (simulation or experiment, the project is an optimal proxy model of the multi-body dynamics response of the carrier-based artillery) is required. Specifically, a large number of model call analysis is required, and feature quantities such as mean and variance required by the robust design are obtained through statistical analysis. Thus, the problem is effectively a two-cycle solution. The outer loop is an optimization process, the inner loop is uncertainty propagation analysis, namely thousands of times of statistical calculation, and the double-loop problem is often huge in calculation amount.
Aiming at the multi-objective optimization problem and the double-cycle solving problem, the module integrates a weighted single-objective optimization method, a multi-objective subset simulation optimization method and a single-cycle robustness solving strategy to carry out vibration reduction robustness design.
The specific flow is as shown in FIG. 7: firstly, initializing design variables, optimizing by using a weighted single-target optimization method and a multi-target subset simulation optimization method, calculating Euclidean distances among obtained sample points, finding a point x closest to any sample distance, and obtaining a sample point set (x 1 ，...，x k ) Obtaining seed sample matrixes, carrying out robustness optimization design on the seed sample matrixes, taking a sample point with the largest response value as a threshold sample according to F=F (x), and taking the corresponding response value as F (x) k )。
Then, a new sample point x is calculated k+1 And a corresponding response value F (x k+1 ) If F (x) k+1 )≤F(x k ) Then update its neighborhood (x 1 ，...，x k ，x k+1 ) Updating seed sample matrix and sampling point x k+1 An information matrix is added.
Finally, if the termination criterion is met or the calculated number of samples reaches the maximum acceptable value, the current value is stopped and output. Otherwise, the sample is continuously updated.
Compared with the prior art, the invention has the advantages that:
(1) A novel transfer matrix method is adopted to construct a rigid-flexible coupled dynamic model of the weapon multi-body system, and under the condition that the output result meets the precision requirement, the simulation efficiency is greatly improved
(2) Aiming at the multi-fidelity requirement of rapid robust vibration response of an uncertain weapon multi-body system, a response surface method, an adaptive Kriging method and an adaptive PCE-Kriging method are integrated to form an adaptive mixed agent model library aiming at different multi-body systems, the precision and efficiency of an agent model are comprehensively considered, and an optimal agent model scheme is used.
(3) The method has the advantages that the robustness design optimization decision model under the condition of considering accidental uncertainty is constructed, the weighted single-target solving strategy, the single-cycle solving strategy and the multi-target subset simulation optimization method are adopted, the rapid robustness design method for the uncertain weapon multi-body system is formed, and the efficiency of the robustness design of the weapon multi-body system is greatly improved.
Description of the drawings:
FIG. 1 is a schematic diagram of a calculation model of the dynamic response of a cannon system;
FIG. 2 is a schematic diagram of a single-ended input single-ended output spatial motion straight beam;
FIG. 3 is a flow chart of an adaptation process;
FIG. 4 is a schematic diagram of a hybrid proxy model;
FIG. 5 is a flow chart of a multi-objective subset simulation optimization;
FIG. 6 is a flow chart of a dual loop robustness design;
FIG. 7 is a single loop robustness design flow diagram;
FIG. 8 multi-target subset simulation contingent uncertainty optimized pareto front;
FIG. 9 weighted single target subset simulation contingent uncertainty optimization iterative process
Fig. 10 multi-target subset simulated contingent uncertainty optimized pareto front
The specific embodiment is as follows:
the invention is further described below with reference to the drawings and examples. Taking a certain ship vibration reduction robustness analysis process as an example.
(1) Multi-body system model building
Modeling of the solution of the dynamic response of a vessel by the linear multi-body system transfer matrix method (MSTMM), e.g.
Fig. 1 shows that element 1 is a cradle, element 3 is a revolution body, element 5 is a pitching body, element 7 is a gun tail, element 8 is a barrel, element 6 is a sliding hinge, elements 2 and 4 are elastic hinges, elements 3, 5 and 7 are rigid bodies, element 8 is an elastic body, and the angle of pitching body 5 is θ.
The dynamic response calculation needs to use a new-version multi-body system transfer matrix method, and the input and output state vectors of each element are:
each element transfer equation is
Z O ＝UZ I (84)
In NVMSTMM, the elastic hinge is cut off and divided into two subsystems, and the elastic hinge is added as external force and external moment into the rigid body transmission matrix. The total transfer matrix is:
if the element 8 is considered to be a rigid beam, U 3 ，U 5 ，U 7 ，U 8 All are one-end input and one-section output rigid body transmission matrix, U 6 For a slip hinge transfer matrix, the relevant transfer matrix is detailed in appendix two.
All boundaries of the two transfer equations are free boundary conditions, and the form is shown as formula (4)
On the basis of a rigid barrel and vessel multi-body dynamics topological structure, the rigid barrel is considered to be a flexible structure, and a transfer equation modeling of a large-motion small-deformation flexible straight beam is adopted to obtain a relative vibration response in the X, Y direction at the muzzle.
After the deterministic multi-body dynamics analysis, the vibration response and y (t) of the muzzle in the x and y directions in time history can be obtained. To comprehensively evaluate the vibration characteristics of the muzzle, the comprehensive vibration quality was quantified by the root mean square of the relative vibration response as follows
(2) Optimal proxy model
Three types of agent model methods are adopted by the self-adaptive mixed agent model library, namely: the high-order response surface method, the self-adaptive Kriging model and the self-adaptive PCK mixed proxy model are comprehensively compared for fitting precision and efficiency of weapon multi-body system dynamics response, an optimal proxy model selection scheme of vibration quality of a certain ship multi-body system can be provided, the optimal proxy model selection scheme is used as mathematical model input for subsequent robust design optimization, and comparison results are shown in the following table.
Table 1 three proxy model comparisons
Under the current limited cost model relationship, the maximum error of the three proxy models is compared to find the self-adaptive PCK model, the relative error is the lowest, the number of times of calling the original simulation model is the lowest, the performance is the best, and the method is used for subsequent robust design optimization research.
(3) Weapon multi-body system robustness design
Based on an optimal agent model, multi-target subset simulation optimization is adopted to respectively give out calculation results of a muzzle vibration accidental uncertainty robust decision model and a weighted multi-target accidental uncertainty robust decision model of a certain ship-based artillery multi-body system under single-cycle and double-cycle robust design strategies.
1) Dual-cycle robustness design method
The robustness design problem is solved by adopting a double-circulation method. Firstly solving a double-target optimization problem, and simulating N (population number) =100 and p of each layer of samples by using a multi-target subset 0 Taking 0.2, iterating (population number) for 20 times, adopting 1700 samples for the outer layer, solving vibration quality mean value and variance corresponding to each sample point for the inner layer by Monte Carlo method, and taking 100 samples each time, wherein 1700 times 100=170000 times of analysis of original structural system, and the obtained pareto front and result are as follows
Fig. 8 shows the same.
All "≡" in the figure constitute a feasible solution set under the dual objective of considering the mean and variance of the vibration quality, where the mean of the vibration quality is at least 0.4148. For convenience of optimization comparison with the single target weighted later, a group (11 th group) of solution set corresponding design values with the vibration quality mean value of 0.4427 and the standard deviation of 0.0999 are selected as the compromise:
table 2 multi-objective subset simulation contingent uncertainty optimization design
Then solving a weighted-transformed single-objective optimization problem, wherein the subset simulates each layer of samples N (population) =100, p 0 Taking 0.2, iterating for 10 times, adopting 820 samples for the outer layer, solving vibration quality mean value and variance corresponding to each sample point for the inner layer by Monte Carlo method, taking 100 samples each time, and taking 820 times for 100=82000 times of original structural system analysis to obtain the minimum vibration quality 0.3966, wherein the iteration process is as follows
As shown in fig. 9, the resulting optimal design is:
table 3 weighted single objective occasional uncertainty optimized optimal design
Comparing the two optimization results, it can be seen that: for occasional uncertainty vibration reduction robustness design, obtaining almost minimum vibration quality mean (0.4148 for multiple targets and 0.3966 for single target), 170000 times of original structural system analysis are needed for multiple targets, 82000 times are needed for weighting single targets, and for the double-target problem, efficiency is doubled by adopting a single-target weighting method.
2) Single-cycle robustness design method
Solving the above problems by single cycle method, analyzing 8720 times (samples) only by using secondary structure, and obtaining pareto front and results such as
Shown in fig. 10.
All "≡" in the figure constitute a feasible solution set under the dual objective of considering the mean and variance of the vibration quality, where the mean of the vibration quality is at least 0.3027. For convenience of optimization comparison with a single target weighted later, a group (13 th group) of solution sets with the standard deviation of 0.0960 and the vibration quality mean value of 0.3642 is selected as a compromise, wherein the corresponding design values are as follows:
table 4 multi-objective subset simulated contingent uncertainty optimal design
It can further be found that: if the single-cycle method is adopted to solve the multi-objective problem, compared with the original double-cycle method, the vibration reduction robustness design problem of accidental uncertainty is considered, and the calculation efficiency is further improved by about 17 times.
The foregoing is only illustrative of the present invention and the present invention is not limited to the above embodiments, but is capable of modification and improvement without departing from the spirit and principles of the present invention.
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.
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