This paper presents a polynomial dimensional decomposition (PDD) method for global sensitivity analysis of stochastic systems subject to independent random input following arbitrary probability distributions. The method involves Fourier-polynomial expansions of lower-variate component functions of a stochastic response by measure-consistent orthonormal polynomial bases, analytical formulae for calculating the global sensitivity indices in terms of the expansion coefficients, and dimension-reduction integration for estimating the expansion coefficients. Due to identical dimensional structures of PDD and analysis-of-variance decomposition, the proposed method facilitates simple and direct calculation of the global sensitivity indices. Numerical results of the global sensitivity indices computed for smooth systems reveal significantly higher convergence rates of the PDD approximation than those from existing methods, including polynomial chaos expansion, random balance design, state-dependent parameter, improved Sobol’s method, and sampling-based methods. However, for non-smooth functions, the convergence properties of the PDD solution deteriorate to a great extent, warranting further improvements. The computational complexity of the PDD method is polynomial, as opposed to exponential, thereby alleviating the curse of dimensionality to some extent. Mathematical modeling of complex systems often requires sensitivity analysis to determine how an output variable of interest is influenced by individual or subsets of input variables. A traditional local sensitivity analysis entails gradients or derivatives, often invoked in design optimization, describing changes in the model response due to the local variation of input. Depending on the model output, obtaining gradients or derivatives, if they exist, can be simple or difficult. In contrast, a global sensitivity analysis (GSA), increasingly becoming mainstream, characterizes how the global variation of input, due to its uncertainty, impacts the overall uncertain behavior of the model. In other words, GSA constitutes the study of how the output uncertainty from a mathematical model is divvied up, qualitatively or quantitatively, to distinct sources of input variation in the model [1].

Reliability Engineering and System Safety

Applications of machine learning to machine fault diagnosis: A review and roadmap

This paper surveys expert systems (ES) development using a literature review and classification of articles from 1995 to 2004 with a keyword index and article abstract in order to explore how ES methodologies and applications have developed during this period. Based on the scope of 166 articles from 78 academic journals (retrieved from five online database) of ES applications, this paper surveys and classifies ES methodologies using the following eleven categories: rule-based systems, knowledge-based systems, neural networks, fuzzy ESs, object-oriented methodology, case-based reasoning, system architecture, intelligent agent systems, database methodology, modeling, and ontology together with their applications for different research and problem domains. Discussion is presented, indicating the followings future development directions for ES methodologies and applications: (1) ES methodologies are tending to develop towards expertise orientation and ES applications development is a problem-oriented domain. (2) It is suggested that different social science methodologies, such as psychology, cognitive science, and human behavior could implement ES as another kind of methodology. (3) The ability to continually change and obtain new understanding is the driving power of ES methodologies, and should be the ES application of future works.

http://www.sci.brooklyn.cuny.edu/~kopec/cis718/fall_2005/sdarticle5.pdf

Expert system methodologies and applications—a decade review from 1995 to 2004

Microgrids have been proposed as a way of integrating large numbers of distributed renewable energy sources with distribution systems. One problem with microgrid implementation is designing a proper protection scheme. It has been shown that traditional protection schemes will not work successfully. In this paper a protection scheme using digital relays with a communication network is proposed for the protection of the microgrid system. The increased reliability of adding an additional line to form a loop structure is explored. Also a novel method for modeling high impedance faults is demonstrated to show how the protection scheme can protect against them. This protection scheme is simulated on a realistic distribution system containing a high penetration of inverter connected Distributed Generation (DG) sources operating as a microgrid. In all possible cases of operation the primary and secondary relays performed their intended functions including the detection of high impedance faults. This system is simulated using Matlab Simulink's SimPowerSystems toolbox to establish the claims made in this paper.

Microgrid Protection Using Communication-Assisted Digital Relays

This paper presents an artificial neural network (ANN) and support vector machine (SVM) approach for locating faults in radial distribution systems. Different from the traditional Fault Section Estimation methods, the proposed approach uses measurements available at the substation, circuit breaker and relay statuses. The data is analyzed using the principal component analysis (PCA) technique and the faults are classified according to the reactances of their path using a combination of support vector classifiers (SVCs) and feedforward neural networks (FFNNs). A practical 52 bus distribution system with loads is considered for studies, and the results presented show that the proposed approach of fault location gives accurate results in terms of the estimated fault location. Practical situations in distribution systems, such as protective devices placed only at the substation, all types of faults, and a wide range of varying short circuit levels, are considered for studies. The results demonstrate the feasibility of applying the proposed method in practical distribution system fault diagnosis.

/pdf/artificial-neural-network-and-support-vector-machine-3qxm6rnabi.pdf

Artificial neural network and support vector Machine approach for locating faults in radial distribution systems

An integrated fuzzy expert system is presented to diagnose various faults that may occur in a regional transmission network and substations. Fuzzy reasoning method is applied, and it is discussed in detail. Discrimination of false operations or nonoperations of protective devices as well as the fault identification scheme are also analyzed, together with the fuzzy inference process. The proposed system is designed to improve efficiency, generality, and reliability of the solution. The system will replace a fault diagnosis system that had been tested as a part of an intelligent support system on a local control center in Korea.

A fuzzy expert system for the integrated fault diagnosis

Assessment of customer power supply reliability is an important part of distribution system operation and planning. Monte Carlo simulations can be used to find the statistical distribution of the reliability indices, along with their mean and standard deviation. The standard deviation of the reliability indices provides distribution engineers with information on the expected range of the annual values. However, the Monte Carlo simulation usually is a time-consuming computation. In this paper, an efficient Monte Carlo simulation method for distribution system reliability assessment is presented. Analysis of outage data from a practical distribution system is performed to determine the failure and repair models appropriate for use in the Monte Carlo simulation. The sensitivity of the reliability indices to the choice of model is presented. Finally, the impact of protection devices on the statistical distribution of System Average Interruption Frequency Index (SAIFI) for a practical distribution feeder is presented.

Modeling and analysis of distribution reliability indices

Lightning is a significant cause of faults and outages in many electric power systems and is one of the major causes of poor system reliability. Predictive assessment of distribution reliability indices can be used to identify areas that have poor reliability so that appropriate changes in system design can be implemented. The assessment of distribution system performance under lightning conditions requires modeling of storm characteristics and system response. In this paper, a Monte Carlo simulation for evaluating distribution system reliability under lightning storm conditions is presented. The results from a practical distribution system show the importance of detailed modeling of storm characteristics and simulation of the system response in assessing distribution system reliability during lightning storms.

Distribution system reliability assessment due to lightning storms

Typically, the modeling of highly varying, nonlinear loads such as electric arc furnaces has involved stochastic techniques. This paper presents the use of chaotic dynamics to describe the operation of nonlinear loads. Included is a discussion of the Lyapunov exponents, a measure of chaotic behavior. The alternate approach is applied to electric arc furnaces. A tuning mode is described to develop the parameters of a chaotic model. This model is trained to have time and frequency responses that are tuned to match the current from the arc furnace under study. The simulated data are compared to actual arc furnace data to validate the model. This model is used to assess the impact of various highly varying nonlinear loads that exhibit chaos in power systems.

Nonlinear deterministic modeling of highly varying loads

In order to ensure that the changing utility environment does not adversely affect the reliability of electric power supplied to customers, several state regulatory agencies have started to prescribe reliability standards-minimum reliability levels-to be maintained by electric power distribution companies. The standards are based on reliability indexes computed from historical outage data. The reliability indexes vary from year to year because of the statistical variation in the number of customer interruptions and the duration of such interruptions. To be effective, the reliability standards adopted must identify feeders that consistently perform poorly, while being insensitive to those that occasionally have poor reliability. This paper employs a duration based Monte Carlo simulation to explore the predicted impact of various reliability standards on a large practical distribution system. The sensitivity of different standards to differences in system size and component failure rate is also explored.

S.S. Venkata

Papers

A fuzzy expert system for the integrated fault diagnosis

Modeling and analysis of distribution reliability indices

Distribution system reliability assessment due to lightning storms

Nonlinear deterministic modeling of highly varying loads

Predicting distribution system performance against regulatory reliability standards