Research On The Method Of Bayesian Reliability Modeling For The CNC Machine Tools Based On The Information Entropy Theory

CNC machine tools is the pillar of the equipment manufacturing industry,especially the high-grade CNC machine tools technology is the tip of the fiercecompetition in the international market. However, the domestic CNC industry keeps alow market share, and the high-grade products almost come from imports. One of themost important reasons leading to this kind of unhealthy situation is the poorreliability and the frequently failures of our CNC machine tools. In order to examinethe reliability of the domestic CNC machine tools, discussed the small-samplereliability modeling and comprehensive evaluation on CNC machine tools werediscussed systematically, to provide some advice on improving the reliability ofdomestic CNC machine tools with the purpose of expanding market share and revivingthe national industry eventually.CNC machine tools especially the high-grade has a complicated structure, a longexperiment period and an expensive experiment cost, which leads to difficulties ofreliability evaluation and prediction. Assisted by information entropy theory, theproblems of CNC machine tools small-sample reliability modeling was solved byBayesian method, and the comprehensive evaluation of CNC machine tools based onthe combination weighting method was carried on, after full research of the domesticand foreign research status.The Bayesian small-sample reliability estimation of CNC machine tools wasstudied, including pre-processing of prior information, representation of priordistribution, estimation of posteriori and comprehensive estimation of multiple indexes.Firstly, multi-source prior information of CNC machine tools has been classified inorder to collect, and then discussed conversion methods and test means ofmulti-source prior information according to its different nature and characteristics.What was innovational, information entropy theory was applied to reliability dataconversion of life-type sophisticated system. The prior information of CNC machinetools was converted from subsystem level into system level based on entropy theory,and the method was proved to be more credible than the conservative original methodby the example of a certain type CNC lathe subsystem’s small-sample reliability data conversion. Secondly, the paper used the extremum property of information entropy tocarry through the prior distribution representation and multi-source information fusion.Maximum entropy theory was introduced into conjugate method, Bootstrap methodand Bayesian Bootstrap method, in order to speed up the solving process and reduceartificial uncertainty factors of priori distribution, and this kind of methods has beenproved to be efficient and feasible by the example of prior distribution solution of acertain type CNC lathe subsystem. Thirdly, Bayesian posteriori estimation methodsand qualitative&quantitative robustness analysis methods were introduced. How toapply the asymmetric entropy loss function to Weibull posteriori estimates was mainlydiscussed, and described the cause of the error by an example. Finally, the relativeentropy method of multi-index comprehensive evaluation on CNC machine tools’reliability was presented, to avoid the arbitrary decision of single index evaluation.According to some reliability information of two type CNC machine tools, the twosimilar systems’ reliability were examined based on the relative entropy method ofmulti-index comprehensive evaluation.In the process of applying Bayesian method to discuss the small-samplereliability estimation on CNC machine tools, the information entropy theory wasapplied to conversion of prior information, representation and fusion of priordistribution, estimation of posteriori and comprehensive estimation of multiple indexesand etc. By increasing the using range of priori information, fusing multi-sourceinformation and reducing artificial factor of small-sample evaluation process, theBayesian solving process was speed up to be more suitable for engineering application,and at the same time, the risk of posteriori estimation was reduced to increase thecredibility of the small-sample evaluation. Proved by the small-sample reliability data,information entropy method on Bayesian reliability estimation for CNC machine toolsand other large-scale complex electromechanical liquid equipments are practical andeffective.