- International Symposium on NDT Contribution to the Infrastructure Safety Systems, 1999 NOV 22-26 Torres, published by UFSM, Santa Maria, RS, Brazil

TABLE OF CONTENTS

Abstract Introduction The Optimization Model Conclusion References

Abstract

Application of optimal complex of nondestructive testing (NDT) methods can contribute significantly to the extension of life expectation, reliability and, finally, safety, especially for very complex systems like nuclear power plants, ground rocket complexes, etc.
The NPP is a complex system and its safety is related to the safety of each of the system elements. Safety of power supply systems occupies one of the most important roles in the NPP safety, because cables are potential source of fire.
This article deals with the task of complex optimization of NDT methods and contains the idea to detect the set of possible and dangerous defects for NPP power system cables taking into account the criteria of defect detection and efficiency level. The application of multilevel one-criterion task of discrete programming is presented and discussed. Efficiency of complex application of NDT methods depends on scheme of testing organization, planning, data acquisition and processing and personnel qualification.

Keywords: NDT methods; discrete optimization model; safety; power systems; cables

Introduction

The economical efficiency of complicate technical systems, such as power and space systems, military objects, etc. depends entirely on reliability and long lasting during all the time of operation. It is well known the cost of accidents happened at the NPPs all over the world. Among them inflammation of cables plays not the last role.
The Ukrainian and foreign practices confirm that appearance of accidental conditions at cable communications leads to fires at NPP units [1, 2]. The most well-known of them - Browns Ferry fire [3], fires at the Armenian NPP, Unit 1, in October, 1982; Zaporizhzhya NPP, Unit 1, January, 1984, etc. Annual hazard estimated resulting from fires had some times ago order of billions US$.
In spite of the requirements to the NPPs cables are very high, long operation and limited set of means to keep safety of cable communications at Ukrainian NPPs can not provide sufficient confidence with respect to absence of new fires.
When considering the safety enhancement of cable communications for NPPs, one of the most actual problem is to reveal defects of different nature reliably in various elements of power systems: cables, insulation, etc. and to provide the preventive measures to controlling the defects development taking into account ageing processes as well as modeling of degradation mechanisms.
One of the most effective ways to avert the possible consequences caused by operation of devices with defects is using the NDT methods.
The Ukrainian practice to control the current state of cables at NPPs includes the filling of cable journals with information concerning each separate cable. It means that only visual testing is available to fix possible defect. But some defects becoming apparent while operation and can not be identified by visual testing only.
One of the main parameters to describe the cable condition is the insulation temperature. It is world experience to use some special doughs and coatings to cover the cables to improving the fire safety. But, in the same way, as a result the insulation temperature may arise. To avoid such the dangerous situation, the power (current) of cables has to be decreased at 3 ¸ 7%.
Existing level of safety control assurance for electric power equipment does not meet the requirements for modern NPPs operation conditions, but enhanced international demands to NPP operation safety put the task of creation of new monitoring ideology for control of power cables communication safety level. There is necessity to develop the computerized control system being able to solve task of maintenance and service planning to detect defects by means of NDT under conditions of limited resources and also to develop new theoretical approaches for development of continuos monitoring system.
Applying of NDT for detection of different nature defects in systems allows to detect in time and to remove damages, and, thus, to extend the life cycle of expensive and safety important equipment. However, separate defects remain undetected and become the cause of emergencies and catastrophes. Objective analyses of different NDT application for defects detection in complex systems led to the idea to develop complex of NDT methods. These testing complexes use methods of different physical nature and labor efforts. System analyses allows eliminating shortages for one method, to supplement one methods by others and, consequently to realize the "superfluity" principle for reliable control.
While forming the NDT complex there the problem arises to optimize its structure relying upon various effectiveness criteria. Each NDT method can be characterized by different economical parameters, labor efforts, sensitivity, application conditions, reliability, etc. But, in the same way, the application of the most sensitive methods does not guarantee that the reliability of testing will always be the highest. Moreover the technical output can be in contradiction with economical criteria (labor-efforts, cost, time of control, etc.) and, finally, the NDT complex proposed cannot be considered as optimal and effective.

The Optimization Model

Let's carry out formalization of a task of formation of NDT complex for detection of set of dangerous defects in power system of NPP, as the discrete optimization-programming problem.
Let's assume, that the final set of possible defects d_lÎ D, is given, and defects can be present at cables of power system, where - set of different types of defects, and L - set of indexes for various types of defects. The defects d_l Î D, are being characterized by parameters, for example, parameters of potential danger of defect, geometrical parameters (such as extent of defect or cracks) etc.
Let's assume, that for detection of defects d_l Î D some NDT methods are used. Let's suggest, that - NDT method set of a j -type, which can be used for detection of defect d_l, where j Î J_l = {1,2,...n_l} - set of NDT types indexes, and m_jk - K modification of j - NDT method, where K_j = {1,2,...,k^*_j} - set of indexes of modification type j -NDT method.
Let's designate p_j ( m_jk, d_l) - probability of detection of defect d_l, and g_il ( m_jk, d_l), i Î I- efforts to conduct testing by method m_jk (time necessary for realization the control by the group of experts, cost of the control), I = {1,...,m^*} - set of indexes of effort parameters.
To detect set of defects D it's necessary to construct the NDT complex (set of devices and order of employment of using for each of them), which would be most effective for the NPP power system. Under formation and choosing of a NDT complex, we consider, that the strategy, or order of application the methods from a NDT complex is fixed.
Let's designate S₁={s₁ = {j₁,j₂,...,j_l^*}| j₁,j₂,...,j_l^* Î J_l} - set of combination s_l indexes of NDT method types, which are used for diagnostics of defect . A combination s_l would be interpreted as technology of application of separate NDT methods in a complex, where the specificity of devices as well as specificity of specimen to be tested is taken into account.
For each combination s_l we shall define a complex of various NDT methods, which can be used for detection of defect d_l Î D . Let's assume that the sequence of methods application is fixed (keeping in mind the existing experience in various NDT applications obtained after research of various types of cables and power system elements) by the order of indexes in combination s_l .
The following sets may be defined: - set of complexes of methods, which determine possible realization of technology s_l ; -set of all possible complexes, which can be used for detection of defect d_l. The multitude of complexes for detection of all set of defects d_l Î D is defined as follows:
. Here Ä is Dekart product of the sets.
Probability of defects detection by NDT complex can be defined through the probability of defects detection parameters of separate NDT methods, which are included in technology s_l .
To increase the reliability of control for cables technical condition it is expedient to use a principle of redundancy of the control, i.e. to control the same defect by applying a complex of NDT methods, based on different physical nature. The using of multitude of various methods and ways of their application can contribute to increasing the probability of defect detection. Then the expression for probability of defect detection d_l , by a complex can be defined as follows:


(1)

The formula (1) gives lower estimation for probability of defect detection with a complex of methods .
To using of NDT complex, as well as examination procedure are directed at formation of the valid conditions, increasing of reliable operation and decreasing of risk. Let's consider formal optimization tasks.
Problem 1. All defects have to be detected.
Given condition could be interpreted as follows. The set of defects D could be considered, as a complex system, which consists of l^* elements (in this case elements are - defects). Then a parameter of probability for reliable operation of consistent system (when the fault even in one of subsystems could lead to fault of all the system as a whole [4,5]) may be considered as a parameter of probability of detection of defect set by the complex and may be defined as follows:
where - is given by expression (1).
Problem 2. Some unimportant defects are considered not to be detected.
Defects in set D could have various importance and therefore it is possible to speak about inadmissibility, possibility of detection or not detection of dangerous and other defects, and these defects cannot result in considerable consequences. By other worlds the probable cost of element fault is insignificant for availability of power system as a whole.
This task could be interpreted in the terms of reliability of systems with complex (coherent) structure [4,5]. In a common case for such tasks, the fault of separate elements could not always result in occurrence of an emergency or fault of system as a whole.
Let's x_l, l Î L - Boolean variable, such as

Then x = (x₁,....,x_l,...,x_l^*) - is a vector of possible combinations of defect detection. X- set of all possible combinations x Î X and j (x) is structure functions. [4,5].
It is necessary to form such NDT complex n , which has a maximum to detect the defects for given restrictions on resources available b_i,i Î I.
The mathematical model for this problem is: to maximize


(2)

Under constraints

	(3)
	(4)

Parameters of resource efforts G_i( n), i Î I for using method with a complex of methods n are defined, for example, by total inspection cost for methods from NDT complex; by cost of auxiliary activities necessary to conduct the examination, by cost of expense deal with the charge for energy and routing of premises, etc. Thus G_i( n) is additive function: and the parameters of resource efforts for a vector could be determined in the following way: [5].
In general case the form of technological and economic parameters depends on technology of NDT complex using. The task (2)-(4) could be considered also as a multi criterion optimization problem. The problem (2)-(4) represents two-level of discrete monotonous programming problem and for its solution the algorithm based on a method of the consecutive analysis of variants was used [5].

Conclusion

Some optimization models of NDT complexes are presented in this article and have been used in pilot projects to forming the NDT complexes for defect detection in units, electric equipment and launching rocket complexes. As a result of implemented efforts the lifetime of rocket complex was prolonged and allowed to save about $500,000 USD. For effective application of presented approach at Ukrainian NPPs it is necessary to take into account specific features of cables and their design parameters and their operation conditions as well.

References

1. Joglar F., Mowrer F., Modarres M., Azarm A. Probabilistic-Deterministic Fire Risk Analysis// 3-d International Conference "Fire & Safety". Frankfurt. -1999. 8p.
2. Joglar F., Mowrer F., Modarres M., Azarm A. Description of a Fire Hazard Screening Methodology // 3-d International Conference "Fire & Safety". Frankfurt. -1999. 6p.
3. F.E.Haskin, A.L.Camp. Perspectives on Reactor Safety, NUREG/CR-6042, 1993.
4. Barlow R., Proschan F. Statistical theory of reliability and life testing probability.- Holt, Rinehard and Winston, Inc,1975.
5. Volkovich V.L., Voloshin A.F., Zaslavskii V.A., Ushakov I.A. Models and techniques for reliability optimization of complex systems.-Kiev: Naukova Dumka, 1993.-312 p. (in Russian).

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