Analysis Of Reliability From Time Response Of Structure And System

The reliability from time response of the structure and system were studied in thedegree paper. The model of the structural random reliability from time response, themodel of the structural interval reliability from time response, the model of thestructural fuzzy reliability from time response, the model of the reparable k-out-of-nsystem reliability from time response, the model of the multi-state reparable k-out-of-nsystem reliability from time response are established, respectively. The dynamicreliability of the structure and system are computed, predicted, analyzed. The maincontents are as follows.1. The structural random reliability from time response.Stochastic loads are classified three types: dynamic load accumulation, amplitudeand obey the Poisson distribution whose parameter is t, load changing with time andnot subject to any distribution. As these conditions, their reliability from time responsemodels are established under structural strength constant and structural strengthdegenerating by using stress-strength interference theory and stochastic process theory;it shows that the structural reliability is gradually reduced with time, but not unchanged.The models are simple and easy computing, the change regular of the structuralreliability from time response can be obtained. The probability density evolutionmethod of the structural reliability from the time response prediction models underseveral times random loads are researched. Firstly, the probability density of severaltimes stochastic loads can be obtained according to the probability density of a timestochastic load. The prediction models of the structural reliability from the timeresponse under several times stochastic loads with the strength degeneration andwithout degeneration over time are established by using the stress-strength interferencetheory and probability density evolution method. The differential equation in the modelscan be solved by using the forward differential method. The probability densityfunctions of the structural strength redundancy in any time can be obtained. Thestructural prediction reliability from time response can be obtained by using integralmethod. For the structural reliability is only considered a load for structural influence incurrently research, the4types common loads that act on the structure have beencombined3different combinations by Turkstra method, the loads of the threecombinations were believed as the structural stress. The models of the structuralreliability from time response without structural strength degeneration and with degeneration over time have been established by using the stress-strength interferencetheory. The minimum reliability index from time response of the three reliabilityindexes from time response which was obtained in the models is determined thestructural reliability index from time response. It is shown that models are practicable,feasible by using example.2. The structural interval reliability from time response.The structural non-probabilistic reliability from time response under the intervalvariable of loads changing over time and the interval variable of structural strengthdegrading over time is researched. The formulas for the change interval of structuralstrength degradation and its mean value and deviation are shown. According to thestress-strength interference theory and the interval theory, the structural reliability fromtime response prediction models are established under the structural strengthdegradation over time while the loads of the structure bearing are classified three casesloads: ladder type, constant amplitude alternating type and random changing over timetype. For the hybrid model of several times interval loads and structural stochasticstrength with degradation and without degradation over time are established. Firstly,several times interval loads are substituted by the equivalent interval load. Secondly, theequivalent interval load is thought as the random variable who obeys the uniformdistributed. The random variables of the uniform distribution and structural randomstrength are done with the equivalent normal method. Then the structuralinterval-random hybrid reliability from time response under several times interval loadsand structural random strength degeneration and without degeneration over time iscomputed by using the first secondly order moment method according to thestress-strength interference theory. It is shown that the models are reasonable andpracticable by using examples.3. The structural fuzzy reliability from time response.For the several times fuzzy loads and fuzzy structural strength in the practiceengineer, the fuzzy loads and the fuzzy strength are analyzed. The predictionfuzzy-fuzzy models of the structural fuzzy reliability from time response are establishedby using the stress-strength interference theory when the several times fuzzy loadschanges over time and the structural strength changes without degeneration and withdegeneration. For the several times random loads and fuzzy structural strength in thepractice engineer, the loads and the fuzzy strength are analyzed. The predictionrandom-fuzzy hybrid models of the structural fuzzy reliability from time response areestablished by using the stress-strength interference theory when the several times random loads changes over time and the structural strength changes withoutdegeneration and with degeneration. Finally, it is shown that the models are feasible andreasonable by examples. Further it is pointed out that the reliability of probability is aspecial case of fuzzy reliability.4. The reparable k-out-of-n system reliability from time response.The model of unit reliability from time response of repairable k/n (G) system withunit strength degradation under repeated random shocks has been developed accordingto the stress-strength interference theory. The unit failure number is obtained based onthe unit failure probability which can be computed from the unit reliability from timeresponse. Then, the transfer probability function of the repairable k/n (G) system isgiven by its Markov property. Once the transfer probability function has been obtained,the probability density matrix and the steady-state probabilities of the system can beretrieved. Finally, the reliability from time response of the repairable k/n (G) system isobtained by solving the differential equations. Anovel reliability-based model of k/n (G)system has been developed. Unit failure probability is first calculated based on theapplied load and strength distributions according to the stress-strength interferencetheory. Then, a reliability prediction model from time response for the whole repairablek/n (G) system is established using the probabilistic differential equations. Finally, theresulting differential equations are solved and the value of k can be determined precisely.It is illustrated that the proposed methods are practicable, feasible and gives reasonableprediction which conforms to the engineering practice.5. The reparable multi-state k-out-of-n system reliability from time response.For the complexity of multi-state repairable k-out-of-n system, firstly, the diversityof the components of the system are analyzed by using discrete time Markov chains andsemi-Markov chain, the probability distribution computing formula of the change ofstate and the sojourn time in the state are obtained. Secondly, the first order transitionprobability matrix of the change of state and lifetime in the state areobtained. Finally,the reliability and availability prediction model of the system are obtained according tothe analysis of the components. For the multi-state engine system, Firstly, the enginesystem is discrete and quantization processed, the output power of the engine is becomea state discrete time continue Markov random process; Secondly, the multi-state Markovmodel is established, according to the observed data, the algorithm of transitionintensities is obtained; Finally, the proposed method is used to calculate the forcedoutage rate and the expected engine capacity deficiency of the engine changing overtime. For forecasting and monitoring the reliability from time response of the engine to work properly is supplied a new method. It is shown that the methods are practical,effective by using the engineering numerical examples.