Science and Technology of Nuclear Installations

Volume 2014, Article ID 286826, 9 pages

http://dx.doi.org/10.1155/2014/286826

## PSO Based Optimization of Testing and Maintenance Cost in NPPs

^{1}Software Development Center, State Nuclear Power Technology Corporation, Beijing 102209, China^{2}School of Nuclear Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

Received 11 July 2014; Revised 13 November 2014; Accepted 13 November 2014; Published 9 December 2014

Academic Editor: Alejandro Clausse

Copyright © 2014 Qiang Chou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Testing and maintenance activities of safety equipment have drawn much attention in Nuclear Power Plant (NPP) to risk and cost control. The testing and maintenance activities are often implemented in compliance with the technical specification and maintenance requirements. Technical specification and maintenance-related parameters, that is, allowed outage time (AOT), maintenance period and duration, and so forth, in NPP are associated with controlling risk level and operating cost which need to be minimized. The above problems can be formulated by a constrained multiobjective optimization model, which is widely used in many other engineering problems. Particle swarm optimizations (PSOs) have proved their capability to solve these kinds of problems. In this paper, we adopt PSO as an optimizer to optimize the multiobjective optimization problem by iteratively trying to improve a candidate solution with regard to a given measure of quality. Numerical results have demonstrated the efficiency of our proposed algorithm.

#### 1. Introduction

Improvement of the availability performance for safety-related systems has drawn much attention in Nuclear Power Plant (NPP) nowadays. One way to increase availability of these systems is to improve availability of the equipment that constitutes them. In this way, people often pay attention to the more efficient testing and maintenance activities. NPPs often pursue more efficient testing and maintenance activities to control risk and cost. Actually, safety-critical equipment is normally on standby till occurrence of an accident situation which requires safety-related systems to prevent or mitigate the accident process. In order to keep safe-related systems at a high level of availability or safety, regular testing and maintenance activities are implemented. Efficient regular testing and maintenance strategy can improve the availability performance of the systems, and meanwhile it will lead to great expenditure cost. Therefore, both risk controlling and expenditure effectiveness have drawn much attention in NPP [1, 2].

Technical specifications define the limits and conditions for operating NPPs which can be seen as a set of safety rules and criteria required as a part of safety analysis report of each NPP. Both technical specifications and maintenance activities are associated with controlling risk and then with availability of safety-related systems. The resource related to risk controlling rules and criteria formally enter into optimization problems. Using a limited expenditure resource to keep safety-critical equipment at a high level of availability or safety actually is a constrained multiobjective optimization problem where the cost or the burden, that is, number of tests conducted, duration, incurred cost, and so forth, is to be minimized while the unavailability or the performance of the safety-critical equipment is constrained at a given level.

By now, some researchers have made great achievements in nuclear technology area. References [3, 4] presented a constrained multiobjective optimization model to solve this problem using genetic algorithm (GA); reference [5] first presented PSA-based techniques to solve risk-cost maintenance and testing model of an NPP using GA; reference [6] puts forward using a multiobjective approach to regulate Nuclear Power Plant (NPP); reference [7] presents using fuzzy-genetic approach to optimize the test interval of safety systems at NPP considering parameters uncertainty. In this paper, we put forward using PSO to solve the constrained multiobjective optimization problem which simulates the testing and maintenance activities. The PSO method is firstly used to solve the multiobjective optimization problem described by testing and maintenance activities in NPPs. It is a heuristic algorithm and can offer the solution by iteratively trying to improve a candidate solution with regard to a given measure of quality. Numerical results have demonstrated the reasonability of PSO method.

The plan of this paper is the following: Section 2 presents the unavailability and cost models of critical systems/components of NPP; Section 3 gives the multiobjective problem model; Section 4 reviews PSO method; Section 5 presents a case study; finally, Section 6 draws a short conclusion.

#### 2. System Risk and Cost Function

##### 2.1. System Unavailability Model

As to nuclear facilities, the system unavailability is classified into three types: component’s unavailability, common failure, and human errors. In this paper, we just consider the component’s unavailability which is caused by random failure and test and maintenance activities which are the functions of the optimization variables such as test interval, test duration, maintenance period, allowed outage time, and so on. The system unavailability is often modeled by fault tree using rare-event approximation as follows [4]: where is the decision variable vector; the sum in refers to the number of minimal cut sets generated from the considered system structure function and the product in represents the number of the basic events belonging to the corresponding MCS. The represents the unavailability of the basic event contained in minimal cut sequence (MCS) .

The unavailability expressions of basic events caused by random failure are written as [4]:

Equation (2) is the time-dependent unavailability evaluated at , where denotes per-demand failure probability and represents the failure rate. Equation (3) is the average time-dependent over a given time span .

To reflect the effect of age, preventive maintenance, and working conditions, an averaged standby failure rate is developed [8, 9]:

Note that (4) is applicable for proportional age setback (PAS) mode, and (5) is used for proportional age reduction PAR. The meanings of the parameters involved in (4) and (5) are listed in Table 1.