Bayesian Reliability Evaluation Of NC Turret Based On Hamilton Monte Carlo Algorithm

As the key functional component of CNC machine tool,the reliability level of CNC turret is closely related to the availability of the whole machine.Therefore,it is of great significance to study the reliability of NC turret for improving the reliability level of domestic CNC machine tools and reducing the gap with foreign advanced level.According to the failure data of NC turret in the actual test process,it is necessary to carry out the reliability modeling evaluation.However,under the background of new era and special machine tool,in the face of high reliability,small batch production of NC turret,in the process of reliability test,there is a situation of small sample of fault data.The classical statistical methods dealing with large sample data are no longer suitable to solve such problems.How to solve the evaluation problem of small sample data becomes more and more important.It has important academic significance and engineering application value to carry out the comprehensive research on the reliability of domestic NC turret.In this paper,the research object is the domestic SLT** NC turret.Based on Bayesian framework,this paper studies how to solve the problem of small sample reliability evaluation of NC turret.1.The small sample reliability evaluation model of NC turret is established.Two parameter weibull distribution is used as the small sample evaluation model of NC turret.The posterior distribution of model parameters is derived based on the Bayesian theoretical framework.Two key points to solve the small sample evaluation are pointed out: the establishment of prior distribution and the solution of posterior distribution.The mean time between failures(MTBF)is used as the reliability evaluation index.The theoretical derivation is based on the parametric model.2.The prior distribution of model parameters is established.The NC turret which is close to the research object and has large sample data is selected as the reference system,and the reliability level comparison is given by the expert scoring;the weight of expert judgment is calculated based on the AHP by establishing the evaluation index system of expert ranking;the final result is obtained by comparing the time function value and reliability level of the reference turret at the selected quantile,through the method of expert scoring,the process of extracting expert judgment information and transforming the expert judgment result into parameter prior distribution is established.3.To solve the problem that there is no analytic solution for the parameters of posterior distribution,this paper starts from two aspects: M-H algorithm and traditional Bayesian software Win BUGS.The basic algorithm of MCMC algorithm family: metropolis Hastings algorithm is developed.Combined with the sample model of the research object,the recommendation distribution,acceptance probability and iteration steps of the algorithm are studied.The algorithm is programmed in MATLAB,and the reliability index result is calculated.Based on the traditional Bayesian analysis software Win BUGS,the bugs model of weibull parameters is established,and the simulation process of parameters is introduced.From six aspects,the convergence of parameters under different iteration times is compared comprehensively.Finally,the simulation estimation of parameters under convergence state is obtained,and the calculation of reliability index is completed.4.Aiming at the problems of low iteration efficiency,slow convergence speed of traditional MCMC algorithm and Win BUGS software stop updating,a new Bayesian analysis tool Stan based on HMC algorithm is used to solve the problem of parameter non analytic solution more efficiently.Combined with the research of small sample reliability model,the Stan probability model of weibull parameters is established,and the sampling program of HMC algorithm is written on the platform of Rstudio.The convergence of parameters is judged from six angles,and the simulation estimation of parameters is obtained with fewer iterations,and the calculation of reliability index is completed.5.Based on the convergence rate of Markov chain,the results of traditional MCMC,Win BUGS and HMC algorithms are compared;Based on the perspective of generality,the results of Stan are compared with grid approximation method;As a new Bayesian analysis tool,Stan has the advantages of high iterative efficiency and wide generality,and has good generality for other complex Bayesian statistical models.