| In the production system,there are various disturbance factors inside and out,which seriously affect the normal dynamic performance of the system.A perturbation factor may cause vulnerability propagation,and all equipment in upstream and downstream of the production line will be shut down.The vulnerability effect is not conducive to releasing capacity and guaranteeing delivery of production line,which will seriously affect the production plan of enterprises and even cause huge losses.Quantitative analysis and evaluation of vulnerability can effectively improve the stability of production line.At the same time,vulnerability can be used as an evaluation index of production system configuration and design,and it is also the basic work of performance control.Therefore,vulnerability quantization is more valuable than the mainstream qualitative analysis,and new quantitative analysis methods should be developed to understand the characteristics of vulnerability effect.However,due to the dynamic nature of the vulnerability effect,it is difficult to establish an accurate mathematical model.In this paper,a method of transient and steady-state vulnerability analysis considering time and space properties is proposed for series random system with finite buffer.Firstly,elastic production system can be regarded as a spatial-temporal dynamic system,the evolution of system state has obvious space-time property in the process of vulnerability.Based on different analysis perspectives,vulnerability quantization can be divided into two parts: the vulnerability effect of the end machine and the vulnerability effect of the bottleneck machine.Thus,Terminal Time Delay(TTD),Terminal Time Window(TTW),Bottleneck Time Delay(TTD)and Bottleneck Time Window(TTW),are difined to expound temporal and spatial attributes of disruptive events.Secondly,the vulnerability is further evaluated and quantified by using precise solution.For the series random production system with finite buffer,a series open queuing network model is established,the recursive representation of state transition matrix is obtained,and the influence of machine reliability is considered as well.Based on the state space probability,the mathematical model of the four vulnerability indexes defined in this paper is derived.And an example is given to verify the evaluation model,which shows the effectiveness of the method.What is more,considering the limitation of the precise solution method for large-scale manufacturing systems,based on the precise solution method of this paper,the extended approximation method is used to solve and establish an quantitative mathematical model for the vulnerability of same type manufacturing systems.For the series production system of this paper,the single node is taken as unit to be decomposed,and the coupling relationship between nodes is considered for analysis,so as to solve the steady-state distribution index of each queue.The steady-state vulnerability and transient vulnerability of the end machine and the bottleneck machine were evaluated and quantified based on the characteristics of series manufacturing system.An example is given to verify the evaluation model,which shows the effectiveness of the method.Finally,the Digital Twinning System(DTS)is designed and developed,which has the functions of near physical simulation,multi-view synchronization and performance analysis and control.The system includes a numerical solver for vulnerability analysis,which supports the testing of vulnerability and other properties.The research results of this paper are transformed into a software tool that can solve the problem of vulnerability evaluation and quantification of production system. |
