Gregory Levitin

Redundancy optimization for series-parallel multi-state systems

This paper generalizes a redundancy optimization problem to multi-state systems, where the system and its components have a range of performance levels-from perfect functioning to complete failure. The components are: (1) chosen from a list of products available in the market; and (2) characterized by their nominal performance level, availability and cost. System availability is represented by a multi-state availability function, which extends the binary-state availability. To satisfy the required multi-state system availability, the redundancy for each component can be used. A procedure which determines the minimal-cost series-parallel system structure subject to a multi-state availability constraint is proposed. A fast procedure is developed, based on a universal generating function, to evaluate the multi-state system availability. Two important types of systems are considered and special operators for the universal generating function determination are introduced. A genetic algorithm is used as an optimization technique. Examples are given.

Optimization of imperfect preventive maintenance for multi-state systems

Abstract The paper generalizes a preventive maintenance optimization problem to multi-state systems, which have a range of performance levels. Multi-state system reliability is defined as the ability to satisfy given demand. The reliability of system elements is characterized by their hazard functions. The possible preventive maintenance actions are characterized by their ability to affect the effective age of equipment. An algorithm is developed which obtains the sequence of maintenance actions providing system functioning with the desired level of reliability during its lifetime by minimum maintenance cost. To evaluate multi-state system reliability, a universal generating function technique is applied. A genetic algorithm (GA) is used as an optimization technique. Basic GA procedures adapted to the given problem are presented. Examples of the determination of optimal preventive maintenance plans are demonstrated.

Optimal capacitor allocation in distribution systems using a genetic algorithm and a fast energy loss computation technique

This paper presents a new approach to shunt capacitor placement in distribution systems having customers with different load patterns. The allocation of capacitors is considered in a system comprising a network of feeders fed from an upstream equivalent transmission system through a substation transformer. The benefits of capacitor placement, such as the system capacity release and reduction of overall power and energy losses, are considered. The fast method of total energy loss calculation based on the computation of the moments of normalized daily load curves is used to calculate the annual energy loss reduction. An example of optimal capacitor allocation in a distribution system is presented in which customers with commercial, urban residential, rural and light industrial load patterns are considered.

Joint redundancy and maintenance optimization for multistate series–parallel systems

Abstract This paper formulates the joint redundancy and replacement schedule optimization problem generalized to multistate system, where the system and its components have a range of performance levels. Multistate system reliability is defined as the ability to maintain a specified performance level. The system elements are chosen from a list of available products on the market and the number of such elements is determined for each system component. Each element is characterized by its capacity, reliability and cost. The reliability of a system element is characterized by its lifetime distribution with the hazard rate, which increases with time. It is specified as the expected number of failures during different time intervals. The optimal system structure and the number of element replacements during the study period are defined as those which provide the desired level of system reliability with minimal sum of costs of capital investments, maintenance and unsupplied demand caused by failures. A universal generating function technique is applied to evaluate the multistate system reliability. A genetic algorithm is used as an optimization technique. Examples of determination of the optimal system structure and replacement schedule are provided.

Power system structure optimization subject to reliability constraints

Abstract The problem of the optimization of the structure of a power system where redundant elements are included in order to provide a desired level of reliability is considered. A procedure which determines the minimal cost series-parallel system configuration is proposed. In this procedure, system elements are chosen from a list of products available on the market and the number of such elements is determined for each system component. The elements are characterized by their capacity, availability and cost. System reliability is defined as the ability to satisfy consumer demand which is represented as a piecewise cumulative load curve. To evaluate system reliability, a fast procedure is developed which is based on a universal generating function. A genetic algorithm is used as an optimization technique. An example of the redundancy optimization of a power station coal feeding system is presented.

Structure optimization of power system with different redundant elements

Abstract The problem of optimization of the structure of a power system where redundant elements are included in order to provide a desired level of reliability is considered. The elements of the system are characterized by their capacity, availability and cost. A procedure which determines the minimal cost series-parallel system configuration is proposed which allows elements with different parameters to be allocated in parallel. In this procedure, system elements are chosen from a list of products available on the market. System reliability is defined as the ability to satisfy consumer demand which is represented as a piecewise cumulative load curve. To evaluate system reliability, a universal generating function technique is applied. A genetic algorithm (GA) is used as an optimization technique. Basic GA procedures adapted to the given problem are presented, and different versions of the GA are compared to determine the most effective one. An example of the optimal structure determination and optimal extension of a power station coal transportation system are presented.

A universal generating function approach for the analysis of multi-state systems with dependent elements

Abstract The paper extends the universal generating function technique used for the analysis of multi-state systems to the case when the performance distributions of some elements depend on states of another element or group of elements.

Importance and sensitivity analysis of multi-state systems using the universal generating function method

Abstract A method for the evaluation of element reliability importance in a multi-state system is proposed. The method is based on the universal generating function technique. It provides an effective importance analysis tool for complex series–parallel multi-state systems with a different physical nature of performance and takes into account a required performance (demand). The method is also extended for the sensitivity analysis of important multi-state system output performance measures: mean system performance and mean unsupplied demand during operating period. Numerical examples are given.

Robust recurrent neural network modeling for software fault detection and correction prediction

Software fault detection and correction processes are related although different, and they should be studied together. A practical approach is to apply software reliability growth models to model fault detection, and fault correction process is assumed to be a delayed process. On the other hand, the artificial neural networks model, as a data-driven approach, tries to model these two processes together with no assumptions. Specifically, feedforward backpropagation networks have shown their advantages over analytical models in fault number predictions. In this paper, the following approach is explored. First, recurrent neural networks are applied to model these two processes together. Within this framework, a systematic networks configuration approach is developed with genetic algorithm according to the prediction performance. In order to provide robust predictions, an extra factor characterizing the dispersion of prediction repetitions is incorporated into the performance function. Comparisons with feedforward neural networks and analytical models are developed with respect to a real data set.

Optimal Defense Strategy Against Intentional Attacks

This paper presents a generalized model of damage caused to a complex multi-state series-parallel system by intentional attack. The model takes into account the defense strategy that presumes separation and protection of system elements. The defense strategy optimization methodology is suggested, based on the assumption that the attacker tries to maximize the expected damage of an attack. An optimization algorithm is presented that uses a universal generating function technique for evaluating the losses caused by system performance reduction, and a genetic algorithm for determining the optimal defense strategy. Illustrative examples of defense strategy optimization are presented