Research On Uncertain Game Optimization For The Large Caliber Artillery

Information warfare is characterized by long-range precision strikes and digital warfare,in which combat targets are highly mobile,the battlefield is rapidly changing,and war opportunities are fleeting.This places higher requirements on the remoteness,precision and mobility of artillery weapon systems.The future army combat model must evolve from traditional firepower attrition warfare to "surgical" intelligent long-range precision strikes.High muzzle velocity is an important initiative for artillery long-range,but the increase in muzzle velocity directly leads to a significant increase in muzzle kinetic energy and muzzle momentum,which will make the forces and laws of motion of the artillery firing process more complex and lead to a more acute contradiction between artillery power and maneuverability.The difficulty in resolving this prominent contradiction using existing design theory has severely constrained the development of high-performance artillery weapons for two fundamental reasons.On the one hand,the existing design theory generally treats the artillery as a deterministic system and uses the deterministic theory to establish the dynamics model of the artillery firing process,while the firing process is essentially an uncertain process influenced by multiple sources of uncertainties such as structural uncertainty,load uncertainty and model uncertainty.With the increasing muzzle velocity,the influence of uncertainty factors becomes more and more prominent,and it is difficult to reveal the influence law of the uncertainty of the artillery and ammunition system on the key performance of the artillery by directly using the existing deterministic design theory.On the other hand,the performance indexes of artillery firing accuracy and maneuverability are often contradictory,full of conflicts and constrained by each other,and it is difficult for the existing artillery optimization methods to deal with such contradictions effectively.With this background,this dissertation uses the interval model to characterize the uncertain parameters in the artillery and ammunition system,and carries out an in-depth and systematic study of the artillery uncertain optimization problem using noncooperative game theory.The main research contents include.(1)The theory of interval uncertain optimization and game theory are analyzed.Starting from the use of interval number to describe parameter uncertainty,interval arithmetic and interval analysis theory based on interval arithmetic are given,which leads to the interval function expansion problem.Two methods to suppress the interval expansion problem are discussed: interval analysis based on interval regression method and interval analysis method based on global optimization algorithm.The interval uncertain optimization problem is discussed,and a double-loop nested interval uncertain optimization algorithm is given.Further,the basic principles of the game theory are described,from the perspectives of both the composition and classification of the game.(2)The interval uncertain optimization of the design parameters of large-caliber artillery is carried out.To address the low computational efficiency caused by double-loop nested optimiztaion,an interval optimization method based on affine arithmetic and Chebyshev surrogate model is proposed.To overcome the interval expansion problem caused by interval arithmetic,the interval numbers are rewritten as affine form and the interval analysis is completed by the affine arithmetic.The results of two numerical examples verify the accuracy,efficiency and feasibility of the proposed method.By using the affine arithmetic to carry out interval analysis,the intervals of the uncertain objective function and constraint function can be directly obtained,thus converting the double-loop nested optimization problem into a single-loop deterministic optimization problem.The results of numerical example show that the method can significantly improve the computational efficiency.The affine arithmetic can only deal with problems have explicit expressions.To apply the affine arithmetic to artillery structural optimization,the uncertainty objective function is converted into a polynomial approximation model using Chebyshev polynomial expansion.The proposed method is utilized to solve the interior ballistics uncertain optimization problem where the muzzle velocity and interval economics index are set as objective,besides,the maximum chamber pressure,muzzle pressure,and maximum pressure wave are set as constraints.The optimization results demonstrate the effectiveness of the method in the field of artillery design parameters optimization.(3)Research on Robust Nash game strategy for design parameters of large caliber artillery is carried out.First,a Nash game optimization method based on Chebyshev polynomial expansion and the fuzzy cluster is proposed to address the contradiction between different optimization objectives.In order to convert the multi-objective optimization problem into a Nash game problem,a splitting method of the design variables set based on sensitivity analysis and Fuzzy C-mean clustering analysis is first proposed.The sensitivity results of each design variable to the objective function is used as the basis for partitioning,and the fuzzy clustering method is used to partition the set of design variables into several subsets.Then the optimization objectives and objective functions are set as players and cost functions,respectively,and the subsets of design variables are divided into each player by combining the sensitivity data.Chebyshev polynomial expansion is employed to construct surrogate models for the cost functions of computationally intensive engineering problems.To avoid the problem of dimensional catastrophe associated with Chebyshev tensor product sampling,a truncated form of Chebyshev polynomial expansion is used.The sample points are generated by the OLHD method and the polynomial coefficients are calculated by the collocation method.The proposed method is successfully applied to the structural optimization of large-caliber artillery eddy current brakes,which opens up a new optimization idea for artillery system optimization.Furthermroe,considering the presence of incomplete information in the game,a Robust Nash game approach based on the affine arithmetic and Chebyshev polynomial expansion in truncated form is proposed.Traditional matrix game cannot be applied to complex engineering optimization problems and the nested problem caused by the worst-case analysis method,to end these,the Chebyshev polynomial expansion is used to convert the cost function into polynomial form,and then the "worst case scenario" of the uncertain cost function is obtained directly by the affine arithmetic,thus directly converting the incomplete information game into a complete but imperfect information game.Numerical example shows that the proposed method can obtain Robust Nash equilibrium almost identical to the nested strategy,but the computation time is significantly reduced.A Robust Nash game model for a large caliber artillery eddy current brake is established and solved simultaneously using the proposed method and the nested strategy,and it is found that the convergence process of the two methods is almost the same,which proves the feasibility,accuracy,and high efficiency of the proposed method in the field of artillery system optimization.(4)Based on the Robust Nash game study,the Robust Stackelberg game study of the artillery firing dynamics problem is carried out from the perspective of incomplete information and the hierarchy between the game players.A multi-flexible system dynamics model for a large-caliber artillery at angle of maximum range is established.The design variables are assigned to players as strategy sets using sensitivity analysis and cluster analysis.A multi-leader-single-follower Robust Stackelberg game model is established.Robust Stackelberg equilibrium is obtained using the Chebyshev interval affine Robust Stackelberg game strategy,and the optimization results show that all the performance indexes are improved.The proposed method is generally applicable to any optimization problem of artillery systems containing interval parameters and has a broad application prospect.