Mahesh D. Pandey

Differential quadrature method in the buckling analysis of beams and composite plates

Abstract This paper discusses the accuracy and convergence of the method of differential quadrature for solving a variety of differential equations with variable coefficients associated with plate and beam instability problems. The detailed solutions for buckling of rectangular, orthotropic and anisotropic, symmetric, angle-ply composite laminates under linearly varying uniaxial compression, uniaxial buckling of rectangular, isotropic plates with variable longitudinal thickness and lateral-torsional beam buckling under moment gradient are presented which highlight various computational aspects and, hopefully, contribute to a better understanding and judicious application of the method.

Gamma processes and peaks-over-threshold distributions for time-dependent reliability

In the evaluation of structural reliability, a failure is defined as the event in which stress exceeds a resistance that is liable to deterioration. This paper presents a method to combine the two stochastic processes of deteriorating resistance and fluctuating load for computing the time-dependent reliability of a structural component. The deterioration process is modelled as a gamma process, which is a stochastic process with independent non-negative increments having a gamma distribution with identical scale parameter. The stochastic process of loads is generated by a Poisson process. The variability of the random loads is modelled by a peaks-over-threshold distribution (such as the generalised Pareto distribution). These stochastic processes of deterioration and load are combined to evaluate the time-dependent reliability.

The influence of temporal uncertainty of deterioration on life-cycle management of structures

In the life-cycle management of infrastructure systems, the decisions regarding the time and frequency of inspection, maintenance and replacement are confounded by sampling and temporal uncertainties associated with deterioration of the structural resistance. To account for these uncertainties, probabilistic models of deterioration have been developed under two broad categories, namely the random variable model and the stochastic process model. This paper presents a conceptual exposition of these two models and highlights their profound implications on age-based and condition-based preventive maintenance policies. The stochastic gamma process model of deterioration proposed here is more versatile than the random rate model commonly used in structural reliability literature.

An effective approximation to evaluate multinormal integrals

In structural system reliability theory, the evaluation of multivariate normal distributions is an important problem. Numerical integration of multinormal distributions with high accuracy and efficiency is known to be impractical when the number of distribution dimensions is large, typically greater than five. The paper presents a practical and effective approach to approximate a multinormal integral by a product of one-dimensional normal integrals, which are easy to evaluate. Examples considered in the paper illustrate a remarkable accuracy of the approximation in comparison with exact integration. Unlike a first-order multinormal approximation widely used in the literature, this method does not involve any iterative linearization, minimization or integration. Computational simplicity with high accuracy is the major advantage of the proposed method, which also highlights its potential for estimating reliability of structural systems.

Probabilistic models for condition assessment of oil and gas pipelines

Abstract The paper is primarily concerned with the interpretation of in-line inspection data collected using magnetic flux leakage tools to characterize the actual condition of pipelines vulnerable to metal loss corrosion. The paper presents a probabilistic analysis framework to estimate the pipeline reliability incorporating the impact of inspection and repair activities planned over the service life. The framework is applied to determine the optimal inspection interval and the repair strategy that would satisfy a target reliability requirement. To update the pipeline failure probability after maintenance, a practical approximation is developed and validated using Monte Carlo simulation results.

PROBABILISTIC NEURAL NETWORK FOR RELIABILITY ASSESSMENT OF OIL AND GAS PIPELINES

A fuzzy artificial neural network (ANN)-based approach is proposed for reliability assessment of oil and gas pipelines. The proposed ANN model is trained with field observation data collected using magnetic flux leakage (MFL) tools to characterize the actual condition of aging pipelines vulnerable to metal loss corrosion. The objective of this paper is to develop a simulation-based probabilistic neural network model to estimate the probability of failure of aging pipelines vulnerable to corrosion. The approach is to transform a simulation-based probabilistic analysis framework to estimate the pipeline reliability into an adaptable connectionist representation, using supervised training to initialize the weights so that the adaptable neural network predicts the probability of failure for oil and gas pipelines. This ANN model uses eight pipe parameters as input variables. The output variable is the probability of failure. The proposed method is generic, and it can be applied to several decision problems related with the maintenance of aging engineering systems.

The estimation of extreme quantiles of wind velocity using L-moments in the peaks-over-threshold approach

Abstract The paper evaluates the effectiveness of the method of L-moments for estimating parameters of the Pareto distribution model of peaks over a sufficiently high threshold, and compares its performance against a widely used method of de Haan (de Haan L. Extreme value statistics. In: Galambos J, Lechner J, Simin E, editor. Extreme value theory and applications, vol. 1. 1994. p. 93–122). Monte Carlo simulations and actual wind speed data collected at various stations in the United States have been utilized in this study. In the de Haan method, the first two moments of peaks of log-transformed data are used for the parameter estimation, whereas the L-moment method utilizes linear combinations of expectations of order statistics of peaks in the original data. Despite the procedural differences, the paper shows that the de Haan and two L-moments based estimates of the tail shape parameter are in fairly close agreement in simulated data as well as in the US wind speed data. Furthermore, higher order estimates of the shape parameter are obtained using the L-skewness of peaks data. Such estimates appear to provide a more stable upper bound, which can be useful in identifying meaningful values of design quantiles.

Discounted cost model for condition-based maintenance optimization

This paper presents methods to evaluate the reliability and optimize the maintenance of engineering systems that are damaged by shocks or transients arriving randomly in time and overall degradation is modeled as a cumulative stochastic point process. The paper presents a conceptually clear and comprehensive derivation of formulas for computing the discounted cost associated with a maintenance policy combining both condition-based and age-based criteria for preventive maintenance. The proposed discounted cost model provides a more realistic basis for optimizing the maintenance policies than those based on the asymptotic, non-discounted cost rate criterion.

A nonlinear mixed-effects model for degradation data obtained from in-service inspections

Monitoring of degradation and predicting its progression using periodic inspection data are important to ensure safety and reliability of engineering systems. Traditional regression models are inadequate in modeling the periodic inspection data, as it ignores units specific random effects and potential correlation among repeated measurements. This paper presents an advanced nonlinear mixed-effects (NLME) model, generally adopted in bio-statistical literature, for modeling and predicting degradation in nuclear piping system. The proposed model offers considerable improvement by reducing the variance associated with degradation of a specific unit, which leads to more realistic estimates of risk.

Modified Cross-Correlation Method for the Blind Identification of Structures

Recently, blind source separation (BSS) methods have gained significant attention in the area of signal processing. Independent component analysis (ICA) and second-order blind identification (SOBI) are two popular BSS methods that have been applied to modal identification of mechanical and structural systems. Published results by several researchers have shown that ICA performs satisfactorily for systems with very low levels of structural damping, for example, for damping ratios of the order of 1% critical. For practical structural applications with higher levels of damping, methods based on SOBI have shown significant improvement over ICA methods. However, traditional SOBI methods suffer when nonstationary sources are present, such as those that occur during earthquakes and other transient excitations. In this paper, a new technique based on SOBI, called the modified cross-correlation method, is proposed to address these shortcomings. The conditions in which the problem of structural system identification can be posed as a BSS problem is also discussed. The results of simulation described in terms of identified natural frequencies, mode shapes, and damping ratios are presented for the cases of synthetic wind and recorded earthquake excitations. The results of identification show that the proposed method achieves better performance over traditional ICA and SOBI methods. Both experimental and large-scale structural simulation results are included to demonstrate the applicability of the newly proposed method to structural identification problems.