Optimizing the Managerial Decision in Energetic Industry

Making a decision is a complex process which must be based upon a method that is able to establish the optimum criteria in choosing an alternative, in evaluating the main effects of implementing the decision which was taken and in estimating the risks involved. The optimizing methods and techniques fall into several groups. Thus, judging by the number of criteria that was taken into consideration when making decisions, the optimization methods and techniques can be identified as uni-criterial decisions and multi-criterial decisions; considering the objective condition state which affects the problem that needs decisional solution, there can be decisional methods and techniques used in optimizing decisions in conditions of certainty, decisional methods and techniques used in optimizing decisions in conditions of uncertainty and decisional methods and techniques used in optimizing decisions in risky conditions. The continuous improvement of the decisional subsystem - an important component of the firm’s management - represents a necessity under the circumstances that the latest decades reveal a development of the decisional elements, both in the theoretic-methodological field and in the application field. The decisional methods and techniques must be found in the managers’ decisional processes at different hierarchical levels (individual managers or group managers), so that a high scientific materialization level of the methods should be ensured.decision; variant; optimizing methods and techniques; decisional tree; certainty; uncertainty; risk

Probabilistic engineering analysis and design under time-dependent uncertainty

Time-dependent uncertainties, such as time-variant stochastic loadings and random deterioration of material properties, are inherent in engineering applications. Not considering these uncertainties in the design process may result in catastrophic failures after the designed products are put into operation. Although significant progress has been made in probabilistic engineering design, quantifying and mitigating the effects of time-dependent uncertainty is still challenging. This dissertation aims to help build high reliability into products under time-dependent uncertainty by addressing two research issues. The first one is to efficiently and accurately predict the time-dependent reliability while the second one is to effectively design the time-dependent reliability into the product. For the first research issue, new time-dependent reliability analysis methodologies are developed, including the joint upcrossing rate method, the surrogate model method, the global efficient optimization, and the random field approach. For the second research issue, a time-dependent sequential optimization and reliability analysis method is proposed. The developed approaches are applied to the reliability analysis of designing a hydrokinetic turbine blade subjected to stochastic river flow loading. Extension of the proposed methods to the reliability analysis with mixture of random and interval variables is also a contribution of this dissertation. The engineering examples tested in in this work demonstrate that the proposed time-dependent reliability methods can improve the efficiency and accuracy more than 100% and that high reliability can be successfully built into products with the proposed method. The research results can benefit a wide range of areas, such as life cycle cost optimization and decision making --Abstract, page iv

HETEROGENEOUS UNCERTAINTY QUANTIFICATION FOR RELIABILITY-BASED DESIGN OPTIMIZATION

Uncertainty is inherent to real-world engineering systems, and reliability analysis aims at quantitatively measuring the probability that engineering systems successfully perform the intended functionalities under various sources of uncertainties. In this dissertation, heterogeneous uncertainties including input variation, data uncertainty, simulation model uncertainty, and time-dependent uncertainty have been taken into account in reliability analysis and reliability-based design optimization (RBDO). The input variation inherently exists in practical engineering system and can be characterized by statistical modeling methods. Data uncertainty occurs when surrogate models are constructed to replace the simulations or experiments based on a set of training data, while simulation model uncertainty is introduced when high-fidelity simulation models are built through idealizations and simplifications of real physical processes or systems. Time-dependent uncertainty is involved when considering system or component aging and deterioration. Ensuring a high level of system reliability is one of the critical targets for engineering design, and this dissertation studies effective reliability analysis and reliability-based design optimization (RBDO) techniques to address the challenges of heterogeneous uncertainties. First of all, a novel reliability analysis method is proposed to deal with input randomness and time-dependent uncertainty. An ensemble learning framework is designed by integrating the Long short-term memory (LSTM) and feedforward neural network. Time-series data is utilized to construct a surrogate model for capturing the time-dependent responses with respect to input variables and stochastic processes. Moreover, a RBDO framework with Kriging technique is presented to address the time-dependent uncertainty in design optimization. Limit state functions are transformed into time-independent domain by converting the stochastic processes and time parameter to random variables, and Kriging surrogate models are then built and enhanced by a design-driven adaptive sampling scheme to accurately identify potential instantaneous failure events. Secondly, an equivalent reliability index (ERI) method is proposed for handling both input variations and surrogate model uncertainty in RBDO. To account for the surrogate model uncertainty, a Gaussian mixture model is constructed based on Gaussian process model predictions. To propagate both input variations and surrogate model uncertainty into reliability analysis, the statistical moments of the GMM is utilized for calculating an equivalent reliability index. The sensitivity of ERI with respect to design variables is analytically derived to facilitate the surrogate model-based product design process, lead to reliable optimum solutions. Thirdly, different effective methods are developed to handle the simulation model uncertainty as well as the surrogate model uncertainty. An active resource allocation framework is proposed for accurate reliability analysis using both simulation and experimental data, where a two-phase updating strategy is developed for reducing the computational costs. The framework is further extended for RBDO problems, where multi-fidelity design algorithm is presented to ensure accurate optimum designs while minimizing the computational costs. To account for both the bias terms and unknown parameters in the simulation model, Bayesian inference method is adopted for building a validated surrogate model, and a Bayesian-based mixture modeling method is developed to ensure reliable system designs with the consideration of heterogeneous uncertainties

Time-dependent reliability methodologies with saddlepoint approximation

Engineers always encounter time-dependent uncertainties that ubiquitously exist, such as the random deterioration of material properties and time-variant loads. Therefore the reliability of engineering systems becomes time-dependent. It is crucial to predict the time-dependent reliability in the design stage, given possible catastrophic consequences of a failure. Although extensive research has been conducted on reliability analysis, estimating the reliability accurately and efficiently is still challenging. The objective of this work is to develop accurate and efficient reliability methodologies for engineering design. The basic idea is the integration of traditional reliability methods with saddlepoint approximation (SPA), which can accurately approximate the tail distribution of a random variable. Four methods are proposed in this work. The first three methods deal with time-independent reliability while the last one estimates the time-dependent reliability. The first method combines SPA with first-order approximation and achieves higher accuracy over the traditional first-order reliability method when bimodal distributions are involved. The second method further improves the accuracy of reliability estimation by integrating SPA with the second-order approximation. The third method extends the second method into the reliability-based design for higher accuracy, and the high efficiency is maintained by an efficient algorithm for searching for an equivalent reliability index. The fourth method uses sequential efficient global optimization to convert a time-dependent problem into a time-independent counterpart. Then the second method is utilized to estimate the time-independent reliability after the conversion. The accuracy and effectiveness of the above methods are demonstrated by both numerical examples and engineering applications --Abstract, page iv

Time- and space-dependent uncertainty analysis and its application in lunar plasma environment modeling

”During an engineering system design, engineers usually encounter uncertainties that ubiquitously exist, such as material properties, dimensions of components, and random loads. Some of these parameters do not change with time or space and hence are time- and space-independent. However, in many engineering applications, the more general time- and space-dependent uncertainty is frequently encountered. Consequently, the system exhibits random time- and space-dependent behaviors, which may result in a higher probability of failure, lower average lifetime, and/or worse robustness. Therefore, it is critical to quantify uncertainty and predict how the system behaves under time- and space- dependent uncertainty. The objective of this study is to develop accurate and efficient methods for uncertainty analysis. This study contains five works. In the first work, an accurate method based on the series expansion, Gauss-Hermite quadrature, and saddle point approximation is developed to calculate high-dimensional normal probabilities. Then the method is applied to estimate time-dependent reliability. In the second work, we develop an adaptive Kriging method to estimate product average lifetime. In the third work, a time- and space-dependent reliability analysis method based on the first-order and second-order methods is proposed. In the fourth work, we extend the existing robustness analysis to time- and space-dependent problems and develop an adaptive Kriging method to evaluate the time- and space-dependent robustness. In the fifth work, we develop an adaptive Kriging method to efficiently estimate the lower and upper bounds of the electric potentials of the photoelectron sheaths near the lunar surface”--Abstract, page iv