Research On Degradation Failure Modelling Theories Based On Stochastic Process

For highly reliable products in a ammunition system,accelerated life tests are used for lifetime and reliability assessment.However,with the increasing of our country's manufacturing level and the application of new technologies,new materials on ammunition system,it is not an easy task to obtain their life information by using traditional life tests because failures are not likely to occur in a certain period of time,even by censoring life test or accelerated life test.In such a case,degradation data are widely used in the field of life prediction due to the following reasons,easy to obtain,low cost,short test period and informative data.Wiener process with good statistic property is one of the stochastic processes and is suitable for both linear degradation data and nonlinear degradation data.Therefore,this thesis focus on reliability and life assessment of ammunitions based on accelerated degradation data and degradation data from the nature storage environment.The main research and innovation results in this dissertation are as follows.(1)The concept of the accelerated factor in the transformed time scale is proposed in modeling nonlinear Wiener model with a time scale transformation of ammunitions.The quantitative functional relationship between the drift parameter and stress variables is derived based on the invariance principle of failure mechanism and Nelson assumption,so as the connection between the diffusion parameter and accelerated stress.To test if the failure mechanism has changed under two accelerated stresses,a t statistic is constructed.Moreover,constant stress accelerated degradation process and step-stress accelerated degradation process of ammunitions with random effects are modeled.The unknown parameters in the established model are estimated based on the property of degradation by the maximum likelihood estimation approach and expectation maximization algorithm.Finally,a case study of the capacitor in acoustic interference shrapnel is conducted to demonstrate the benefits of our model in practical engineering.(2)The temperature is varying rather than constant with climate and the seasons in nature storage environment of ammunitions.Then,a generalized equivalent temperature model is proposed based on the equal principle of average degradation value.Compared with the empirical equivalent temperature and the average equivalent temperature,the proposed equivalent temperature model extends the applicable field for its applicability on both nonlinear degradation data and linear degradation data.Besides,the sensitivity of each parameter on the equivalent temperature is analyzed by taking the first partial derivative with respect to the parameter.The model is applied to a case study of nitrile rubber O-rings used in the rocket.There is humidity which could influence the degradation of products in nature storage environment beside temperature.The load spectrums of humidity and temperature are set up based on nature environmental data monitoring,separately,based on which the stochastic distributions are adopted to describe the stochastic characteristic of environmental stresses.Then the reliability and the lifetime prediction model is constructed.Moreover,the expectation and variance of the degradation in stochastic stress environment are derived based on the property of Brownian motion,Taylor expansion and It(?) formula.Since they are both the linear function of transformed time function,the degradation process is approximated by introducing a new nonlinear Wiener process.The work could promote the exploration of the degradation process of ammunitions in stochastic stresses.(3)The theory of remaining useful life prediction is researched by fusing accelerated degradation data and degradation data from nature storage environment of ammunitions.There are degradation data from different sources where some are from accelerated degradation test and others are from the collection and measurement in nature storage environment and more degradation information can be acquired by fusing them together.However,in the nature storage environment,there could be some other stresses,which cannot be accelerated but still have an impact on degradation.Therefore,to model the influence of these stresses,a calibration factor is introduced to calibrate the difference between the normal environment and nature storage environment.In addition,the unit-to-unit variability in the fusion model is also considered by conjugate prior distribution assumption.Then the relations between distribution parameters of degradation and acceleration factor is derived.It is proved that the invariance principle of failure mechanism is still satisfied with random effects at the scale of mean value.The unknown parameters are estimated from data fusing converted degradation data in the normal environment and degradation data in the nature storage environment by means of maximum likelihood estimation and expectation maximization algorithm.The remaining useful life for the individual sample is predicted by updating the degradation parameters through Bayes theory.Finally,the validity of the proposed model is demonstrated through several groups of simulation data and a case study of nitrile rubber O-rings used in the rocket.(4)A new accelerated degradation model of ammunitions based on generalized nonlinear Wiener process is proposed.The diffusion coefficients are often assumed irrelevant to accelerated stress level in the Wiener process.However,it can be proved by reduction to absurdity that the diffusion coefficients under different accelerated stress level are diverse in accelerated degradation test where higher accelerated stress could lead to bigger diffusion.Therefore,distinctive from the existing models in which the diffusion coefficients are assumed to be constants or irrelevant to stress level,we allow both the drift coefficients and the diffusion coefficients being defined as the function of accelerated stresses.The validity of the proposed model is demonstrated through two case study.Furthermore,the consequence of model misspecification where the proposed model is wrongly fitted by its special case is analyzed based on Kullback-Leibler distance.At the same time,the influence of each degradation parameter on the relative bias and the relative variation of the mean time to failure and 100 p th percentage of first hinting life is analyzed by the simulation method.(5)Uncertain measurements widely exist in the acquisition of degradation data of ammunitions which could have influences on remaining useful life estimation.An accelerated degradation model based on the generalized nonlinear Wiener process is proposed here and the measurement error is described by following the normal distribution.Besides,the variability of samples is also included in the model.To predict the remaining useful life of individual sample with measurement error,Bayes method and Kalman filtering technique are both applied to update the distribution parameters of drift coefficient.Moreover,the Kalman filtering technique can also update the estimates of degradation by constructing a state-space model.The analytical form of remaining useful life distribution is derived for each method.A simulation example is used to verify the model and compare different methods.In conclusion,the degradation model and lifetime prediction theory proposed in this dissertation could provide theoretical support for health condition prediction and remaining useful life assessment of ammunitions who have degradation characteristics.The research on them is valuable in both theory and engineering application.