VI Workshop on Computational Data Analysis and Numerical Methods: Book of Abstracts

The VI Workshop on Computational Data Analysis and Numerical Methods (WCDANM) is going to be held on June 27-29, 2019, in the Department of Mathematics of the University of Beira Interior (UBI), Covilhã, Portugal and it is a unique opportunity to disseminate scientific research related to the areas of Mathematics in general, with particular relevance to the areas of Computational Data Analysis and Numerical Methods in theoretical and/or practical field, using new techniques, giving especial emphasis to applications in Medicine, Biology, Biotechnology, Engineering, Industry, Environmental Sciences, Finance, Insurance, Management and Administration. The meeting will provide a forum for discussion and debate of ideas with interest to the scientific community in general. With this meeting new scientific collaborations among colleagues, namely new collaborations in Masters and PhD projects are expected. The event is open to the entire scientific community (with or without communication/poster)

Maintenance optimisation for systems with multi-dimensional degradation and imperfect inspections

In this paper, we develop a maintenance model for systems subjected to multiple correlated degradation processes, where a multivariate stochastic process is used to model the degradation processes, and the covariance matrix is employed to describe the interactions among the processes. The system is considered failed when any of its degradation features hits the pre-specified threshold. Due to the dormancy of degradation-based failures, inspection is implemented to detect the hidden failures. The failed systems are replaced upon inspection. We assume an imperfect inspection, in such a way that a failure can only be detected with a specific probability. Based on the degradation processes, system reliability is evaluated to serve as the foundation, followed by a maintenance model to reduce the economic losses. We provide theoretical boundaries of the cost-optimal inspection intervals, which are then integrated into the optimisation algorithm to relieve the computational burden. Finally, a fatigue crack propagation process is employed as an example to illustrate the effectiveness and robustness of the developed maintenance policy. Numerical results imply that the inspection inaccuracy contributes significantly to the operating cost and it is suggested that more effort should be paid to improve the inspection accuracy

A Generic Prognostic Framework for Remaining Useful Life Prediction of Complex Engineering Systems

Prognostics and Health Management (PHM) is a general term that encompasses methods used to evaluate system health, predict the onset of failure, and mitigate the risks associated with the degraded behavior. Multitudes of health monitoring techniques facilitating the detection and classification of the onset of failure have been developed for commercial and military applications. PHM system designers are currently focused on developing prognostic techniques and integrating diagnostic/prognostic approaches at the system level. This dissertation introduces a prognostic framework, which integrates several methodologies that are necessary for the general application of PHM to a variety of systems. A method is developed to represent the multidimensional system health status in the form of a scalar quantity called a health indicator. This method is able to indicate the effectiveness of the health indicator in terms of how well or how poorly the health indicator can distinguish healthy and faulty system exemplars. A usefulness criterion was developed which allows the practitioner to evaluate the practicability of using a particular prognostic model along with observed degradation evidence data. The criterion of usefulness is based on comparing the model uncertainty imposed primarily by imperfectness of degradation evidence data against the uncertainty associated with the time-to-failure prediction based on average reliability characteristics of the system. This dissertation identifies the major contributors to prognostic uncertainty and analyzes their effects. Further study of two important contributions resulted in the development of uncertainty management techniques to improve PHM performance. An analysis of uncertainty effects attributed to the random nature of the critical degradation threshold, , was performed. An analysis of uncertainty effects attributed to the presence of unobservable failure mechanisms affecting the system degradation process along with observable failure mechanisms was performed. A method was developed to reduce the effects of uncertainty on a prognostic model. This dissertation provides a method to incorporate prognostic information into optimization techniques aimed at finding an optimal control policy for equipment performing in an uncertain environment

Operations and Maintenance Optimization of Stochastic Systems: Three Essays

This dissertation presents three essays on topics related to optimally operating and maintaining systems that evolve randomly over time. Two primary areas are considered: (i) joint staffing and pricing strategies for call centers that use co-sourcing to improve service operations and reduce costs; and (ii) optimally maintaining stochastically degrading systems when either multiple systems are associated via a common environment, or when a single-unit system is maintained using a population of heterogeneous spare parts. First we present a queueing and stochastic programming framework for optimally staffing a call center utilizing co-sourced service capacity. The interplay between the call center and external service provider is modeled as a leader-follower game in which the call center, acting as the follower, solves a two-stage stochastic integer program. The problem is reformulated as a quadratically-constrained linear program to obtain the optimal contract prices and the optimal staffing problem yields a closed-form solution. Numerically we demonstrate that significant cost reductions can be achieved, even in the presence of imperfect and asymmetric information. Second the problem of optimally replacing multiple stochastically degrading systems using condition-based maintenance is considered. Properties of the optimal value function and policy motivate a tractable, approximate model with state- and action-space transformations and a basis-function approximation of the action-value function. It is demonstrated that near optimal policies are attainable and significantly outperform heuristics. Finally, we consider the problem of optimally maintaining a stochastically degrading system using spares of varying quality. Conditions are provided under which the optimal value function exhibits monotonicity and the optimal policy is characterized. Numerically we demonstrate the utility of our proposed framework, and provide insights into the optimal policy as an exploration-exploitation type policy

A Stochastic Approach to Measurement-Driven Damage Detection And Prognosis in Structural Health Monitoring

Damage detection and prognosis are integral to asset management of critical mechanical and civil engineering infrastructure. In practice, these two aspects are often decoupled, where the former is carried out independently using sensor data (e.g., vibrations), while the latter is undertaken based on reliability principles using life time failure data of the system or the component of interest. Only in a few studies damage detection results are extended to remaining useful life estimation, which is achieved by modeling the underlying degradation process using a surrogate measure of degradation. However, an integrated framework which undertakes damage detection, prognosis, and maintenance planning in a systematic way is lacking in the literature. Furthermore, the parameters of degradation model which are utilized for prognosis are often solely estimated using the degradation data obtained from the monitored unit, which represents the degradation of a specific unit, but ignores the general population trend. The main objectives of this thesis are three-fold: first, a mathematical framework using surrogate measure of degradation is developed to undertake the damage detection and prognosis in a single framework; next, the prior knowledge obtained from the historical failed units are integrated in model parameter estimation and residual useful life (RUL) updating of a monitored unit using a Bayesian approach; finally, the proposed degradation modeling framework is applied for maintenance planning of civil and industrial systems, specifically, for reinforced concrete beams and rolling element bearings. The initiation of a fault in these applications is often followed by a sudden change in the degradation path. The location of a change-point can be associated with a sudden loss of stiffness in the case of structural members, or fault initiation in the case of bearings. Hence, in this thesis, the task of change point location identification is thought of as being synonymous with damage or fault detection in the context of structural health monitoring. Furthermore, the change point results are used for two-phase degradation modeling, future degradation level prediction and subsequent RUL estimation. The model parameters are updated using a Bayesian approach, which systematically integrates the prior knowledge obtained from historical failure-time data with monitored data obtained from an in-situ unit. Once such a model is established, it is projected to a failure threshold, thereby allowing for RUL estimation and maintenance planning. Results from the numerical as well as actual field data shows that the proposed degradation modeling framework is good in performing these two tasks. It was also found that as more degradation data is utilized from the monitoring unit, the progressing fault is detected in a timely manner and the model parameters estimates and the end life predictions become more accurate

Optimal Replacement Strategies for Wind Energy Systems

Motivated by rising energy prices, global climate change, escalating demand for electricity and global energy supply uncertainties, the U.S. government has established an ambitious goal of generating 80% of its electricity supply from clean, renewable sources by 2035. Wind energy is poised to play a prominent role in achieving this goal as it is estimated that 20% of the total domestic electricity supply can be reliably generated by land-based and offshore wind turbines by 2030. However, the cost of producing wind energy remains a significant barrier with operating and maintenance (O&M) costs contributing 20 to 47.5% of the total cost of energy. Given the urgent need for clean, renewable energy sources, and the widespread appeal of wind energy as a viable alternative, it is imperative to develop effective techniques to reduce the O&M costs of wind energy. This dissertation presents a framework within which real-time, condition-based data can be exploited to optimally time the replacement of critical wind turbine components. First, hybrid analytical-statistical tools are developed to estimate the current health of the component and approximate the expected time at which it will fail by observing a surrogate signal of degradation. The signal is assumed to evolve as a switching diffusion process, and its parameters are estimated via a novel Markov chain Monte Carlo procedure. Next, the problem of optimally replacing a critical component that resides in a partially-observable environment is addressed. Two models are formulated using a partially-observed Markov decision process (POMDP) framework. The first model ignores the cost of turbine downtime, while the second includes this cost explicitly. For both models, it is shown that a threshold replacement policy is optimal with respect to the cumulative level of component degradation. A third model is presented that considers cases in which the environment is partially observed and degradation measurements are uncertain. A threshold policy is shown to be optimal for a special case of this model. Several numerical examples will illustrate the main results and the value of including environmental observations in the wind energy setting

Development of Probabilistic Corrosion Growth Models with Applications in Integrity Management of Pipelines

Metal-loss corrosion is a major threat to the structural integrity and safe operation of underground oil and gas pipelines worldwide. The reliability-based corrosion management program has been increasingly used in the pipeline industry, which typically includes three tasks, namely periodic high-resolution inline inspections (ILIs) to detect and size corrosion defects on a given pipeline, engineering critical assessment of the corrosion defects reported by the inspection tool and mitigation of defects. This study addresses the core involved in the reliability-based corrosion management program. First, the stochastic process in conjunction with the hierarchical Bayesian methodology is used to characterize the growth of defect depth using imperfect ILI data. The biases, random scattering errors as well as the correlations between the random scattering errors associated with the ILI tools are accounted for in the Bayesian inference. The Markov Chain Monte Carlo (MCMC) simulation techniques are employed to carry out the Bayesian updating and numerically evaluate the posterior distributions of the parameters in the growth model. Second, a simulation-based methodology is presented to evaluate the time-dependent system reliability of pressurized energy pipelines containing multiple active metal-loss corrosion defects using the developed growth models. Lastly, a probabilistic investigation is carried out to determine the optimal inspection interval for the newly-built onshore underground natural gas pipelines with respect to external metal-loss corrosion by considering the generation of corrosion defects over time and time-dependent growth of individual defects. The proposed methodology will facilitate the reliability-based corrosion management for corroding pipelines