Functioning of a technical system with an instantly replenished time reserve, taking into account preventive maintenance

В работе рассматривается функционирование технической системы с мгновенно пополняемым резервом времени с учетом профилактики. Приводится описание функционирования такой системы. При использовании аппарата полумарковских исследований производится построение аналитической модели системы с мгновенно пополняемым резервом времени при учете влияния профилактики на ее производительность. При построении полумарковской модели принимается ограничение на количество профилактик за время восстановления рабочего элемента. Описываются полумарковские состояния исследуемой системы, и приводится граф состояний. Определяются времена пребывания в состояниях системы, вероятности переходов и стационарное распределение вложенной цепи Маркова. Для определения функции распределения времени пребывания системы в подмножестве работоспособных состояний с использованием метода траекторий находятся все траектории переходов системы из этого подмножества в подмножество неработоспособных состояний и вероятности их реализации. Определяются времена пребывания системы в найденных траекториях. На основании теоремы полной вероятности определяются функции распределения времен пребывания системы в подмножествах работоспособных и неработоспособных состояний и коэффициент готовности системы. Приводится пример моделирования исследуемой системы. Проводится сравнение полученных результатов с результатами использования теоремы о среднестационарном времени пребывания системы в подмножестве состояний. The work examines the functioning of a technical system with an instantly replenished reserve of time, taking into account prevention. The description of the functioning of such a system is given. When using the apparatus of semi-Markov studies, an analytical model of the system is constructed with an instantly replenished reserve of time, taking into account the effect of prevention on its performance. When constructing a semi-Markov model, a limitation on the number of preventive measures during the restoration of a working element is adopted. The semi-Markov states of the system under study are described, and the state graph is given. The sojourn times in the states of the system, the transition probabilities, and the stationary distribution of the embedded Markov chain are determined. To determine the distribution function of the time spent by the system in a subset of operable states using the trajectory method, all trajectories of the system's transitions from this subset to the subset of inoperable states and the probability of their realization are found. The residence times of the system in the found trajectories are determined. On the basis of the total probability theorem, the distribution functions of the sojourn times of the system in subsets of the healthy and inoperable states and the system availability factor are determined. The modeling example of th system under study is given. The results obtained are compared with the results of using the theorem on the average stationary sojourn time of the system in a subset of states.

Hazard characterization for alternative intensity measures using the total probability theorem

Since their inception in the 1980s, simplified procedures for the analysis of liquefaction hazards have typically characterized seismic loading using a combination of peak ground acceleration and earthquake magnitude. However, more recent studies suggest that certain evolutionary intensity measures (IMs) such as Arias intensity or cumulative absolute velocity may be more efficient and sufficient predictors of liquefaction triggering and its consequences. Despite this advantage, widespread hazard characterizations for evolutionary IMs are not yet feasible due to a relatively incomplete representation of the ground motion models (GMMs) needed for probabilistic seismic hazard analysis (PSHA). Without widely available hazard curves for evolutionary IMs, current design codes often rely on spectral targets for ground motion selection and scaling, which are shown in this study to indirectly result in low precision of evolutionary IMs often associated with liquefaction hazards. This study presents a method to calculate hazard curves for arbitrary intensity measures, such as evolutionary IMs for liquefaction hazard analyses, without requiring an existing GMM. The method involves the conversion of a known IM hazard curve into an alternative IM hazard curve using the total probability theorem. The effectiveness of the method is illustrated by comparing hazard curves calculated using the total probability theorem to the results of a PSHA to demonstrate that the proposed method does not result in additional uncertainty under idealized conditions and provides a range of possible hazard values under most practical conditions. The total probability theorem method can be utilized by practitioners and researchers to select ground motion time series that target alternative IMs for liquefaction hazard analyses or other geotechnical applications. This method also allows researchers to investigate the efficiency, sufficiency, and predictability of new, alternative IMs without necessarily requiring GMMs.

A Framework for Simulation-Based Internal Flooding Risk Assessment

Internal flooding due to pipe breaks can interfere with a plant's ability to safely shut down or maintain the decay heat removal. Flooding simulation tools require information on location of pipe breaks and the degree of damage at each location as input for assessing the flooding risk. This can be especially challenging as the number of potential leakage locations are quite large and the state-of-the-art simulation tools cannot determine the degree of damage at a location. This paper presents a novel simulation-based framework that can be used to determine seismically induced flooding scenarios including the potential locations of leakage and the degree of leakage at each location. The proposed framework builds upon a few recent experimental and simulation-based studies on piping fragilities. This research identifies that a direct use of piping fragility information by flooding simulation tools is not appropriate. This paper presents a new approach that creates mutually exclusive and collectively exhaustive events to characterize the complete sample space at each location and employs the total probability theorem to characterize the probabilities for each event in this space. This paper also identifies the importance of including the temporal effects in the piping fragilities in order to allow a more realistic simulation of internal flooding scenarios.

Time-Dependent Reliability Analysis of Vibratory Systems With Random Parameters

The field of random vibrations of large-scale systems with millions of degrees-of-freedom (DOF) is of significant importance in many engineering disciplines. In this paper, we propose a method to calculate the time-dependent reliability of linear vibratory systems with random parameters excited by nonstationary Gaussian processes. The approach combines principles of random vibrations, the total probability theorem, and recent advances in time-dependent reliability using an integral equation involving the upcrossing and joint upcrossing rates. A space-filling design, such as optimal symmetric Latin hypercube (OSLH) sampling, is first used to sample the input parameter space. For each design point, the corresponding conditional time-dependent probability of failure is calculated efficiently using random vibrations principles to obtain the statistics of the output process and an efficient numerical estimation of the upcrossing and joint upcrossing rates. A time-dependent metamodel is then created between the input parameters and the output conditional probabilities allowing us to estimate the conditional probabilities for any set of input parameters. The total probability theorem is finally applied to calculate the time-dependent probability of failure. The proposed method is demonstrated using a vibratory beam example.

A Random Process Metamodel Approach for Time-Dependent Reliability

A new metamodeling approach is proposed to characterize the output (response) random process of a dynamic system with random variables, excited by input random processes. The metamodel is then used to efficiently estimate the time-dependent reliability. The input random processes are decomposed using principal components, and a few simulations are used to estimate the distributions of the decomposition coefficients. A similar decomposition is performed on the output random process. A Kriging model is then built between the input and output decomposition coefficients and is used subsequently to quantify the output random process. The innovation of our approach is that the system input is not deterministic but random. We establish, therefore, a surrogate model between the input and output random processes. To achieve this goal, we use an integral expression of the total probability theorem to estimate the marginal distribution of the output decomposition coefficients. The integral is efficiently estimated using a Monte Carlo (MC) approach which simulates from a mixture of sampling distributions with equal mixing probabilities. The quantified output random process is finally used to estimate the time-dependent probability of failure. The proposed method is illustrated with a corroding beam example.