Three-loop Monte Carlo simulation approach to Multi-State Physics Modeling for system reliability assessment

Multi-State Physics Modeling (MSPM) provides a physics-based semi-Markov modeling framework for a more detailed reliability assessment. In this work, a three-loop Monte Carlo (MC) simulation scheme is proposed to operationalize the MSPM approach, quantifying and controlling the uncertainty affecting the system reliability model. The proposed MC simulation scheme involves three steps: (i) the identification of the system components that deserve MSPM, (ii) the quantification of the uncertainties in the MSPM component models and their propagation onto the system-level model, and (iii) the selection of the most suitable modeling alternative that balances the computational demand for the system model solution and the robustness of the system reliability estimates. A Reactor Protection System (RPS) of a Nuclear Power Plant (NPP) is considered as case study for numerical evaluation

Parametric Sensitivity Analysis for Importance Measure on Failure Probability and Its Efficient Kriging Solution

The moment-independent importance measure (IM) on the failure probability is important in system reliability engineering, and it is always influenced by the distribution parameters of inputs. For the purpose of identifying the influential distribution parameters, the parametric sensitivity of IM on the failure probability based on local and global sensitivity analysis technology is proposed. Then the definitions of the parametric sensitivities of IM on the failure probability are given, and their computational formulae are derived. The parametric sensitivity finds out how the IM can be changed by varying the distribution parameters, which provides an important reference to improve or modify the reliability properties. When the sensitivity indicator is larger, the basic distribution parameter becomes more important to the IM. Meanwhile, for the issue that the computational effort of the IM and its parametric sensitivity is usually too expensive, an active learning Kriging (ALK) solution is established in this study. Two numerical examples and two engineering examples are examined to demonstrate the significance of the proposed parametric sensitivity index, as well as the efficiency and precision of the calculation method

The Bhattacharyya distance: Enriching the P-box in stochastic sensitivity analysis

© 2019 Elsevier Ltd The tendency of uncertainty analysis has promoted the transformation of sensitivity analysis from the deterministic sense to the stochastic sense. This work proposes a stochastic sensitivity analysis framework using the Bhattacharyya distance as a novel uncertainty quantification metric. The Bhattacharyya distance is utilised to provide a quantitative description of the P-box in a two-level procedure for both aleatory and epistemic uncertainties. In the first level, the aleatory uncertainty is quantified by a Monte Carlo process within the probability space of the cumulative distribution function. For each sample of the Monte Carlo simulation, the second level is performed to propagate the epistemic uncertainty by solving an optimisation problem. Subsequently, three sensitivity indices are defined based on the Bhattacharyya distance, making it possible to rank the significance of the parameters according to the reduction and dispersion of the uncertainty space of the system outputs. A tutorial case study is provided in the first part of the example to give a clear understanding of the principle of the approach with reproducible results. The second case study is the NASA Langley challenge problem, which demonstrates the feasibility of the proposed approach, as well as the Bhattacharyya distance metric, in solving such a large-scale, strong-nonlinear, and complex problem

Advanced Bayesian networks for reliability and risk analysis in geotechnical engineering

The stability and deformation problems of soil have been a research topic of great concern since the past decades. The potential catastrophic events are induced by various complex factors, such as uncertain geotechnical conditions, external environment, and anthropogenic influence, etc. To prevent the occurrence of disasters in geotechnical engineering, the main purpose of this study is to enhance the Bayesian networks (BNs) model for quantifying the uncertainty and predicting the risk level in solving the geotechnical problems. The advanced BNs model is effective for analyzing the geotechnical problems in the poor data environment. The advanced BNs approach proposed in this study is applied to solve the stability of soil slopes problem associated with the specific-site data. When probabilistic models for soil properties are adopted, enhanced BNs approach was adopted to cope with continuous input parameters. On the other hand, Credal networks (CNs), developed on the basis of BNs, are specially used for incomplete input information. In addition, the probabilities of slope failure are also investigated for different evidences. A discretization approach for the enhanced BNs is applied in the case of evidence entering into the continuous nodes. Two examples implemented are to demonstrate the feasibility and predictive effectiveness of the BNs model. The results indicate the enhanced BNs show a precisely low risk for the slope studied. Unlike the BNs, the results of CNs are presented with bounds. The comparison of three different input information reveals the more imprecision in input, the more uncertainty in output. Both of them can provide the useful disaster-induced information for decision-makers. According to the information updating in the models, the position of the water table shows a significant role in the slope failure, which is controlled by the drainage states. Also, it discusses how the different types of BNs contribute to assessing the reliability and risk of real slopes, and how new information could be introduced in the analysis. The proposed models in this study illustrate the advanced BN model is a good diagnosis tool for estimating the risk level of the slope failure. In a follow-up study, the BNs model is developed based on its potential capability for the information updating and importance measure. To reduce the influence of uncertainty, with the proposed BN model, the soil parameters are updated accurately during the excavation process, and besides, the contribution of epistemic uncertainty from geotechnical parameters to the potential disaster can be characterized based on the developed BN model. The results of this study indicate the BNs model is an effective and flexible tool for risk analysis and decision making support in geotechnical engineering

Sensitivitätsanalyse und robustes Prozessdesign pharmazeutischer Herstellungsprozesse

The existence of parameter uncertainties(PU) limits model-based process design techniques. It also hinders the modernization of pharmaceutical manufacturing processes, which is necessitated for intensified market competition and Quality by Design (QbD) principles. Thus, in this thesis, proper approaches are proposed for efficient and effective sensitivity analysis and robust design of pharmaceutical processes. Moreover, the point estimate method (PEM) and polynomial chaos expansion (PCE) are further implemented for uncertainty propagation and quantification (UQ) in the proposed approaches. Global sensitivity analysis (GSA) provides quantitative measures on the influence of PU on process outputs over the entire parameter domain. Two GSA techniques are presented in detail and computed with the PCE. The results from case studies show that GSA is able to quantify the heterogeneity of the information in PU and model structure and parameter dependencies affects significantly the final GSA result as well as output variation. Frameworks for robust process design are introduced to alleviate the adverse effect of PU on process performance. The first robust design framework is developed based on the PEM. The proposed approach has high computational efficiency and is able to take parameter dependencies into account. Then, a novel approach, in which the Gaussian mixture distribution (GMD) concept is combined with PEM, is proposed to handle non-Gaussian distribution. The resulting GMD-PEM concept provides a better trade-off between process efficiency and probability of constraint violations than other approaches. The second robust design framework is based on the iterative back-off strategy and PCE. It provides designs with the desired robustness, while the associated computational expense is independent from the optimization problem. The decoupling of optimization and UQ provides the possibility of implementing robust process design to more complex pharmaceutical manufacturing processes with large number of PU. In this thesis, the case studies include unit operations for (bio)chemical synthesis, separation (crystallization) and formulation (freeze-drying), which cover the complete production chain of pharmaceutical manufacturing. Results from the case studies reveal the significant impact of PU on process design. Also they show the efficiency and effectiveness of the proposed frameworks regarding process performance and robustness in the context of QbD.Die pharmazeutische Industrie muss sowohl den gestiegenen Wettbewerbsdruck standhalten als auch die von Regulierungsbehörden geforderte QbD-Initiative (Quality by Design) umsetzen. Modellgestützte Verfahren können einen signifikanten Beitrag leisten, aber Parameterunsicherheiten (PU) erschweren jedoch eine zuverlässige modellgestützte Prozessauslegung. Das Ziel dieser Arbeit ist daher die Erforschung von effizienten Approaches zur Sensitivitätsanalyse und robusten Prozessdesign der pharmazeutische Industrie. Methoden, Point Estimate Method (PEM) und Polynomial Chaos Expansion (PCE), wurde implementiert, um effizient Unsicherheitenquantifizierung (UQ) zu erlauben. Der globalen Sensitivitätsanalyse (GSA) ist eine systematische Quantifizierung von Parameterschwankungen auf die Simulationsergebnisse. Zwei GSA Techniken werden im Detail vorgestellt und an Beispielen demonstriert. Die Ergebnisse zeigen sowohl den Mehrwert der GSA im Kontext des robusten Prozessdesigns als auch die Relevanz zur korrekten Berücksichtigung von Parameterkorrelationen bei der GSA. Um den schädlichen Einfluss von PU auf die modellgestützte Prozessauslegung zusätzlich zu minimieren, wurden weitere Konzepte aus der robusten Optimierung untersucht. Zunächst wurde das erste Konzept basierend auf der PEM entwickelt. Das erste Konzept zeigt einen deutlich reduzierte Rechenaufwand und kann auch die Parameterkorrelationen entsprechend in der robusten Prozessauslegung berücksichtigen. In einem zweiten Schritt wurde ein neuer Ansatz, der die Gauß-Mischverteilung mit der PEM kombiniert, hierzu für nicht normalverteilte PU erfolgreich implementiert. Weiterhin wurde eine iterative Back-off-Strategie erforscht, die auch die PU entsprechend berücksichtigt aber leichte Rechenaufwand zeigt. Durch die Entkoppelung von UQ und Optimierung können wesentlich komplexere pharmazeutische Herstellungsprozesse mit einer hohen Anzahl an PU implementiert werden. Die in dieser Arbeit untersuchten verfahrenstechnische Grundoperationen decken somit einen Großteil der gesamten Produktionskette der pharmazeutischen Herstellung ab. Die Ergebnisse der untersuchten Beispiele zeigen deutlich den Einfluss von PU auf das modellgestützte Prozessdesign auf. Mithilfe der vorgeschlagenen Approaches können die PU effektiv und effizient bei einer optimalen Balance von Rechenaufwand und der geforderten Zuverlässigkeit ganz im QbD-Sinne berücksichtigt werden