تجزیه و تحلیل حساسیت مبتنی بر واریانس و تجزیه از طریق شبکه های عصبی

Sensitivity analysis is a tool which may be used to study the behavior of a model and to ascertain how much the outputs of a given model depend on each or some of its input parameters [1]. In this respect it constitutes an aide for risk-based design and management of hazardous plants, such as the nuclear and chemical ones, in that it can help in retrieving information on components and systems’ criticality. Several approaches have been developed for performing sensitivity studies, ranging from differential to Monte Carlo analysis, response surface methodology, and Fourier amplitude sensitivity test (FAST). These approaches are based on Taylor series expansion, random sampling, response surface construction, and Fourier series, respectively [1], [2], [3] and [4]. Typically, these approaches entail to compute the model output (a reliability or risk measure in our case of interest) several times for different input values sampled from appropriate ranges. Often, the computation times required by the numerical solution of the model render these analyses prohibitively costly, so that one has to resort to simplified but fast models or empirical response surfaces. The objective of this work is to devise a method for performing a multiparametric uncertainty and sensitivity analysis of the reliability model of a properly selected system. The technique used to quantify the uncertainty contribution of a component is based on the variance decomposition method [5]. It consists in considering several evaluations of the system unreliability/unavailability characteristics in correspondence of different values of the uncertain parameters (e.g. component failure rates) and computing an index of importance that measures how much a set of parameters influences the uncertainty in the system unreliability and unavailability. When the model of the system is realistically complicated, its analytical evaluation is at least impractical and one has to resort to Monte Carlo simulation which, however, could be computationally burdensome [6] and [7]. Therefore, since the variance decomposition method requires a large number of system evaluations, each one to be performed by Monte Carlo simulation, the need arises for substituting the Monte Carlo simulation model with a fast, approximated, algorithm. In our work, we employ an empirical model built by training artificial neural networks (ANN) on the results of the Monte Carlo simulation [8] and [9]. The type of neural network employed here is the classical multi-layered, feed-forward one trained by the error back-propagation method [10]. The networks used have been generated with a user-friendly software Neural Simulation Tool (NEST) developed at the Department of Nuclear Engineering of the Polytechnic of Milan (http://www.cesnef.polimi.it/ricerca/sicura/pagweb/lasar/nest.htm). The training patterns for the ANNs have been generated using a user-friendly Monte Carlo simulation code, Monte Carlo Availability Reliability Analysis (MARA), also developed at the same Department of the Polytechnic of Milan (http://www.cesnef.polimi.it/ricerca/sicura/pagweb/lasar/mara.htm). The work presented here was supported with JRC contract No. 14546-1998-11 F1 ED ISPIT.

Sensitivity analysis is a tool which may be used to study the behavior of a model and to ascertain how much the outputs of a given model depend on each or some of its input parameters [1]. In this respect it constitutes an aide for risk-based design and management of hazardous plants, such as the nuclear and chemical ones, in that it can help in retrieving information on components and systems’ criticality. Several approaches have been developed for performing sensitivity studies, ranging from differential to Monte Carlo analysis, response surface methodology, and Fourier amplitude sensitivity test (FAST). These approaches are based on Taylor series expansion, random sampling, response surface construction, and Fourier series, respectively [1], [2], [3] and [4]. Typically, these approaches entail to compute the model output (a reliability or risk measure in our case of interest) several times for different input values sampled from appropriate ranges. Often, the computation times required by the numerical solution of the model render these analyses prohibitively costly, so that one has to resort to simplified but fast models or empirical response surfaces. The objective of this work is to devise a method for performing a multiparametric uncertainty and sensitivity analysis of the reliability model of a properly selected system. The technique used to quantify the uncertainty contribution of a component is based on the variance decomposition method [5]. It consists in considering several evaluations of the system unreliability/unavailability characteristics in correspondence of different values of the uncertain parameters (e.g. component failure rates) and computing an index of importance that measures how much a set of parameters influences the uncertainty in the system unreliability and unavailability. When the model of the system is realistically complicated, its analytical evaluation is at least impractical and one has to resort to Monte Carlo simulation which, however, could be computationally burdensome [6] and [7]. Therefore, since the variance decomposition method requires a large number of system evaluations, each one to be performed by Monte Carlo simulation, the need arises for substituting the Monte Carlo simulation model with a fast, approximated, algorithm. In our work, we employ an empirical model built by training artificial neural networks (ANN) on the results of the Monte Carlo simulation [8] and [9]. The type of neural network employed here is the classical multi-layered, feed-forward one trained by the error back-propagation method [10]. The networks used have been generated with a user-friendly software Neural Simulation Tool (NEST) developed at the Department of Nuclear Engineering of the Polytechnic of Milan (http://www.cesnef.polimi.it/ricerca/sicura/pagweb/lasar/nest.htm). The training patterns for the ANNs have been generated using a user-friendly Monte Carlo simulation code, Monte Carlo Availability Reliability Analysis (MARA), also developed at the same Department of the Polytechnic of Milan (http://www.cesnef.polimi.it/ricerca/sicura/pagweb/lasar/mara.htm). The work presented here was supported with JRC contract No. 14546-1998-11 F1 ED ISPIT.

This paper has presented a methodological study concerning the feasibility of using neural networks to build empirical models for use in variance decomposition-based sensitivity analysis. The idea behind the approach stands on the possibility of exploiting the speed of neural computing in the numerous model evaluations typically required to perform a thorough sensitivity analysis. A reliability/unavailability model was chosen for the analysis. Being a methodological feasibility study, the investigation was carried out on a suitable reference plant model, structured so as to easily show the influence of the different parameters involved. On the contrary, consideration of realistic aspects such as aging, stand-by, maintenance, imperfect repair, has rendered impractical an analytical evaluation so that we resorted to Monte Carlo simulation. In order to perform the many model evaluations required by the variance decomposition sensitivity analysis, we substituted the Monte Carlo simulation model with appropriately trained neural networks capable of providing model solutions in much shorter computer times. The approach followed has led to satisfactory results in both the training of neural networks to provide reasonably accurate model outputs and in the savings of computing time. Thus, we conclude that it is feasible to employ the approximate mapping provided by neural networks for the repetitive model evaluations required by thorough multiparametric sensitivity analysis.