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Research On Precision Assessment And Reliability Growth Evaluation Based On Bayesian Inference On Dynamic Population

Posted on:2009-08-12Degree:DoctorType:Dissertation
Country:ChinaCandidate:X X LiFull Text:PDF
GTID:1102360278956699Subject:Control Science and Engineering
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The assessment and evaluation of weapon systems'tactical and technical indices is an important work. Especially for dynamic population and small sample conditions, it is a problem emergent to be handled with in engineering practice that how to use helpful multi-source information correctly and offer accurate evaluation for weapons'performance and quality. The theory and methods on Bayesian dynamic population statistics are the main thread of the thesis, and the precision assessment of WCMD(Wind Corrected Munition Dispenser, a kind of aeronautic cluster warhead) and the evaluation of RGT (Reliability Growth Test) are selected as the application backgrounds. Faced with the difficulty of dynamic population and small sample, a series of technical problems on the precision assessment and RGT evaluation are studied, and WCMD precision assessment scheme and several kinds of RGT evaluation schemes applicable to different conditions are put forward, which offer relatively sufficient theoretical preparation for practice application. The leading contents are as follows:(1) The guidance precision assessment of WCMD. Unlike the conventional holistic warhead, the cluster warhead assessment theory and practice are relatively weak, and the relationship between the points of fall, the air dispense points, the damage tactical index and the guidance technical index still need to be studied and verified. Firstly, based on WCMD test throwing conditions and damage mechanism, the thesis studies the relationship between the weapon damage efficiency tactical index and guidance precision technical index, and presents the conversion method of both indices. Secondly, on the condition of small sample, the Bayesian theory and methods are used to put forward the assessment scheme of guidance precision and dispense equality for WCMD. Among the assessment, the dispense equality is a new index coming forth with the cluster warhead, whose measurement is still in dispute. The dispense equality measurement and the assessment scheme presented here are reasonable and feasible. Besides, the assessment scheme improved the Bayesian SPRT method by modifying the decision threshold values, which further reduces the test times that decision needs. Analysis and simulation suggests that this assessment scheme can be used for similar weapons assessment, and possesses certain characteristic of general use. RGT evaluation is the main research concern of the thesis. According to different ways of failure fix, RGT test can be classified into the following 3 modes: instant fix mode, delayed fix mode and the both-combined fix mode. The main concerns are the Bayesian evaluations of the latter two fix modes. Because the reliability level grows stepwise at the new stage beginning, it is not proper to directly use the Bayesian"successive law"to convert the previous stage posterior to next stage prior. Therefore, the key of Bayesian evaluation lies on the transfer and expression of the prior information.(2) The evaluation of RGT with delayed fix modes. Firstly, the multi-stage RGT Bayesian model is established, which serves as the research basis of the following chapters. Secondly, on the precondition of knowing the distribution parameters'priors, the Bayesian analysis methods of inner-stage RGT are studied, including the posteriors acquisition and point estimations and interval estimations of the system reliability parameters such as the failure rate, reliability degree, and MTBF. This research emphasizes on the determination of distribution parameters'priors, the essence of which is the transfer of diverse test stages'prior information, i.e. the improvement of Bayesian"successive law". The above concludes: use conversion factor to realize the test data conversion between test stages, and use growth factor to realize the information transfer between stages and the determination of current stage's prior. The randomized computation of conversion factor is studied. Then diverse computations of growth factor are researched, where the way of ML-II to determine the growth factor is appreciated. But the available references have some shortages, which are discovered and conquered here, and a new improved ML-II method is presented to compute the growth factor and the prior, which shows sound effectiveness. Based on the theoretical work, two ways of Bayesian evaluation flow for RGT with delayed fix modes are put forward, which have engineering practicability.Before the current test stage, besides the field data of the previous stage, there still exists multi-source and multi-form prior information on system reliability. For this condition, the thesis also studies the fusion method based on the belief weights, and deduce the fusion posterior. Based on the fusion prior and fusion posterior, the Bayesian evaluation and hypothesis test scheme for exponential life model reliability parameters is studied and offered.(3) Bayesian evaluation of single equipment RGT with instant & delayed fix modes. Firstly the inner-stage reliability Bayesian evaluation is discussed. Secondly, the model equivalence and conversion method is discussed, which is commonly used in engineering practice. By this method we can convert the AMSAA model data to exponential life model data. As to the data after conversion, the reliability growth process of instant & delayed fix modes is equivalent to the reliability growth process with delayed fix mode. The growth factor method presented above is ready to be used in Bayesian evaluation.Emphasis is placed on the problem of information transfer through stages based on AMSAA model. The way of using growth factor to relate adjacent stages scale parameter a is put forward to realize the prior information transfer. Then it is not the adjacent stages failure rate that the growth factor relates but the adjacent stages scale parameter a in AMSAA model. By this method, we can also synthesize multi-stage information to carry out reliability evaluation. The application effects of both methods for RGT with instant & delayed fix modes are compared by simulating examples.In this thesis, Bayesian evaluation based on ranking relationship is also researched. By introducing such loose restriction, the posterior marginal distribution density of failure rate in the last stage can be directly gotten and the calculation turns simpler. Without the growth factor involved, we obtain another approach of Bayesian evaluation on reliability parameters such as failure rate.(4) Bayesian evaluation of multi-equipment RGT with instant & delayed fix modes. For the inner stage evaluation, the available methods commonly start from the parameters ( a , b ) in the AMSAA model. Differently in the thesis, a new parameter group ( SÏ„, b) is chosen as the starting point of Bayesian evaluation. Assuming the priors with the Gamma distribution form, the posteriors are deduced accordingly. By further research, we notice that the posteriors are also Gamma distributions and are conjugate with the priors. This concise form simplifies the computation.With SÏ„as the relation object, the rationality of the variance equation restriction of the growth factor is attached much emphasis, and this restriction is amended rationally. Based on the above, we deduce the evaluation steps such as prior distribution conversion, Gamma distribution approximation, time alignment and growth factor transfer. Then an integral Bayesian evaluation scheme is present, which can be conveniently used in the cases with moderate precision requirement such as the development phase evaluation. The simulating example shows the same results.(5) The robustness analysis of Bayesian method. Firstly, the basic methods about robustness are studied. Among others, the prior marginal density likelihood and the posterior lost expectation are two important indices, on which the methods discussed here are mainly concerned.In the determination of the growth factor by F distribution quantile, the significance level can affect the growth factor. By analyzing the prior and posterior robustness of Bayesian evaluation, we determine the significance level that shows better robustness, which help get more precise prior of current stage. Some examples are also given to suggest.As to the Bayesian evaluation of multi-stage RGT with instant & delayed fix modes, posterior robustness is also analyzed, including robustness analysis of approximate computation and growth factor, which is followed by corresponding examples. We also discuss the problems that need to be noticed in robustness analysis. The consistency between prior information and field data is the decisive factor in Bayesian robustness.
Keywords/Search Tags:Bayesian method, precision assessment, reliability growth, reliability evaluation, robustness analysis
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