Saideep Nannapaneni

Reliability analysis under epistemic uncertainty

This paper proposes a probabilistic framework to include both aleatory and epistemic uncertainty within model-based reliability estimation of engineering systems for individual limit states. Epistemic uncertainty is considered due to both data and model sources. Sparse point and/or interval data regarding the input random variables leads to uncertainty regarding their distribution types, distribution parameters, and correlations; this statistical uncertainty is included in the reliability analysis through a combination of likelihood-based representation, Bayesian hypothesis testing, and Bayesian model averaging techniques. Model errors, which include numerical solution errors and model form errors, are quantified through Gaussian process models and included in the reliability analysis. The probability integral transform is used to develop an auxiliary variable approach that facilitates a single-level representation of both aleatory and epistemic uncertainty. This strategy results in an efficient single-loop implementation of Monte Carlo simulation (MCS) and FORM/SORM techniques for reliability estimation under both aleatory and epistemic uncertainty. Two engineering examples are used to demonstrate the proposed methodology.

Towards Reliability-Based Decision Making in Cyber-Physical Systems

Cyber-physical systems (CPS) are systems with a tight integration between the computational (also referred to as software or cyber) and physical (hardware) components. While the reliability evaluation of physical systems is well-understood and well-studied, reliability evaluation of CPS is difficult because software systems do not degrade and follow a well-defined failure model like physical systems. In this paper, we propose a framework for formulating the CPS reliability evaluation as a dependence problem derived from the software component dependences, functional requirements and physical system dependences. We also consider sensor failures, and propose a method for estimating software failures in terms of associated hardware and software inputs. This framework is codified in a domain-specific modeling language, where every system-level function is mapped to a set of required components using functional decomposition and function-component association; this provides details about operational constraints and dependences. We also illustrate how the encoded information can be used to make reconfiguration decisions at runtime. The proposed methodology is demonstrated using a smart parking system, which provides localization and guidance for parking within indoor environments.

Uncertainty quantification in performance evaluation of manufacturing processes

This paper proposes a systematic framework using Bayesian networks to integrate all the available information for uncertainty quantification (UQ) in the performance evaluation of a manufacturing process. Energy consumption, one of the key metrics of sustainability, is used to illustrate the proposed methodology. The evaluation of energy consumption is not straight-forward due to the presence of uncertainties in different variables in the process and occurring at different stages in the process. Both aleatory and epistemic sources of uncertainty are considered in the UQ methodology. A dimension reduction approach through variance-based global sensitivity analysis is proposed to reduce the number of variables in the system and facilitate scalability to high-dimensional problems. The proposed methodologies for uncertainty quantification and dimension reduction are demonstrated using two examples - an injection molding process and a welding process.

Efficient Kriging surrogate modeling approach for system reliability analysis

Abstract Current limit state surrogate modeling methods for system reliability analysis usually build surrogate models for failure modes individually or build composite limit states. In practical engineering applications, multiple system responses may be obtained from a single setting of inputs. In such cases, building surrogate models individually will ignore the correlation between different system responses and building composite limit states may be computationally expensive because the nonlinearity of composite limit state is usually higher than individual limit states. This paper proposes a new efficient Kriging surrogate modeling approach for system reliability analysis by constructing composite Kriging surrogates through selection of Kriging surrogates constructed individually and Kriging surrogates built based on singular value decomposition. The resulting composite surrogate model will combine the advantages of both types of Kriging surrogate models and thus reduce the number of required training points. A new stopping criterion and a new surrogate model refinement strategy are proposed to further improve the efficiency of this approach. The surrogate models are refined adaptively with high accuracy near the active failure boundary until the proposed new stopping criterion is satisfied. Three numerical examples including a series, a parallel, and a combined system are used to demonstrate the effectiveness of the proposed method.

Model and Data Uncertainty Effects on Reliability Estimation

This paper proposes a probabilistic framework to include both aleatory and epistemic uncertainty within model-based reliability estimation of engineering systems. Epistemic uncertainty is considered due to both data and model sources. Sparse point and/or interval data regarding the input random variables leads to uncertainty regarding their distribution types, distribution parameters, and correlations; this statistical uncertainty is included in the reliability analysis through a combination of likelihood-based representation, Bayesian hypothesis testing and Bayesian model averaging techniques. Model errors, which include numerical solution errors and model form errors, are quantified through Gaussian process models and included in the reliability analysis. The probability integral transform helps to implement an auxiliary variable approach that facilitates a single-level representation of both aleatory and epistemic uncertainty. This strategy results in an efficient single-loop implementation of Monte Carlo simulation (MCS) and FORM/SORM techniques for reliability estimation under aleatory and epistemic uncertainty. An aeroelasticity example is used to demonstrate the proposed methodology.

Automated uncertainty quantification analysis using a system model and data

Understanding the sources of, and quantifying the magnitude of, uncertainty can improve decision-making and, thereby, make manufacturing systems more efficient. Achieving this goal requires knowledge in two separate domains: data science and manufacturing. In this paper, we focus on quantifying uncertainty, usually called uncertainty quantification (UQ). More specifically, we propose a methodology to perform UQ automatically using Bayesian networks (BN) constructed from three types of sources: a descriptive system model, physics-based mathematical models, and data. The system model is a high-level model describing the system and its parameters; we develop this model using the Generic Modeling Environment (GME) platform. Physics-based models, which are usually in the form of equations, are assumed to be in a text format. The data is also assumed to be available in a text format. The proposed methodology involves creating a meta-model for the Bayesian network using GME and a syntax representation for the conditional probability tables/ distributions. The actual Bayesian network is an instance model of the Bayesian network meta-model. We describe algorithms for automated BN construction and UQ analysis, which are implemented programmatically using the GME platform. We finally demonstrate the proposed techniques for quantifying the uncertainty in two example systems.