Linear Multi-step Quantized State System Solution Method And Application In Safety Valve Of Hatch Door

Ordinary Differential Equation(ODE)system are widely used in mechanical,electronic,control,aerospace and other engineering fields.It’s accurate and efficient solution is one of the important research directions in fields like modeling and simulation,numerical computation and high performance computing.the traditional simulation solution usually adopts the “leapfrog type”numerical solution method based on time axis discretization,such as Euler,Runger-Kutta,etc.However,when solving complex system models with the characteristics of stiffness,nonlinearity and strong coupling,this kind of methods always expose some limitations,such as poor stability,low convergence efficiency and slow solving speed.Quantized State System(QSS)method is a brand new numerical integration method.Compared with the traditional methods.QSS still cannot be free from the low stability in terms of solving stiff problems despite some advantages in solving process.To solve these problems,this paper proposes a Linear Multi-step Quantization State System solution algorithm(LMSQSS):1)It discretizes the state variables and expresses the implicit algorithm in explicit expression by estimating the value of quantitative variables,therefore,not only avoiding iterative solution but also effectively improving the solution efficiency.2)It confirms the transition condition of the state variables according to the coupling multiple variables.3)At the same time,the obtain results can be used to correct the solution results at the next moment,so as to further improve the solution accuracy.The feasibility of LMSQSS method is proved by simulating the three classical stiff examples.The performance comparison of LMSQSS method,the traditional time axis discrete numerical integration method,QSS1 method and LIQSS1 method in solution accuracy and efficiency shows that LMSQSS algorithm enjoys a better performance than that of traditional method and QSS family methods.And the simulation accuracy can be improved by appropriately increasing the algorithm order or reducing the quantum sizeIn order to further verify the effectiveness of this paper the propose algorithm and the practical applicability in engineering.This paper sets a safety valve motion process with characteristics of nonlinearity,strong stiffness,and strong coupling as a dynamic model,and applies a simulation solution to it.First,the mathematical model of the safety valve is established by adopting the power bonding graph method;then the obtained mathematical model is processed to obtain the ordinary differential equation;finally,the traditional methods(ODE45,ODE15 s,ODE23s),QSS1 method,LIQSS1 method and LMSQSSS method are used to conduct a simulation solution,and the results will be compared.The results show that,when solving the safety valve dynamics problem,the algorithm proposed in this paper shows superiority in both the effiency and the accuracy of simulation.