ADVANCES IN SYSTEM RELIABILITY-BASED DESIGN AND PROGNOSTICS AND HEALTH MANAGEMENT (PHM) FOR SYSTEM RESILIENCE ANALYSIS AND DESIGN

Failures of engineered systems can lead to significant economic and societal losses. Despite tremendous efforts (e.g., $200 billion annually) denoted to reliability and maintenance, unexpected catastrophic failures still occurs. To minimize the losses, reliability of engineered systems must be ensured throughout their life-cycle amidst uncertain operational condition and manufacturing variability. In most engineered systems, the required system reliability level under adverse events is achieved by adding system redundancies and/or conducting system reliability-based design optimization (RBDO). However, a high level of system redundancy increases a system's life-cycle cost (LCC) and system RBDO cannot ensure the system reliability when unexpected loading/environmental conditions are applied and unexpected system failures are developed. In contrast, a new design paradigm, referred to as resilience-driven system design, can ensure highly reliable system designs under any loading/environmental conditions and system failures while considerably reducing systems' LCC. In order to facilitate the development of formal methodologies for this design paradigm, this research aims at advancing two essential and co-related research areas: Research Thrust 1 - system RBDO and Research Thrust 2 - system prognostics and health management (PHM). In Research Thrust 1, reliability analyses under uncertainty will be carried out in both component and system levels against critical failure mechanisms. In Research Thrust 2, highly accurate and robust PHM systems will be designed for engineered systems with a single or multiple time-scale(s). To demonstrate the effectiveness of the proposed system RBDO and PHM techniques, multiple engineering case studies will be presented and discussed. Following the development of Research Thrusts 1 and 2, Research Thrust 3 - resilience-driven system design will establish a theoretical basis and design framework of engineering resilience in a mathematical and statistical context, where engineering resilience will be formulated in terms of system reliability and restoration and the proposed design framework will be demonstrated with a simplified aircraft control actuator design problem

Reliability-based design of offshore structures for oil and gas applications

Offshore structures are complex in their structural and functional form and operate in a harsh and uncertain environment with complex interactions between ocean variables. Consequently, the ocean environment presents a high risk to these structures hence the need to develop an efficient and reliable design. Therefore, the need for a design that effectively: captures complex ocean parameter interactions, reduces the computational burden in structural response determination, quantifies the structure's ability to bounce back when faced with disruptive events, and minimizes cost under uncertainty at the desired safety levels of the asset is critical. A robust offshore structural design under uncertainty is essential for the safety of life, asset, and the environment during oil and gas exploration and production activities. This thesis presents improved methods for the effective reliability-based design of offshore structures. First, a framework is developed to capture the dependency of multivariate environmental ocean variables using vine copula and its impact on the reliability assessment of offshore structural systems. The model was tested using a cantilever beam and applied to an offshore jacket structure. The comparative results from the jacket structure and cantilever problem reveals that failure probability considering dependence between ocean variables is closer to the reference value than when variables are independent or modeled with a Gaussian copula. The outcome shows the importance of capturing nonlinearity and tail dependence between ocean variables in reliability evaluation. Secondly, the effectiveness of a hybrid metamodel, which is a combination of two commonly and independently used methods, Kriging and Polynomial Chaos Expansions (PCE), is investigated for offshore structural response determination and reliability studies. The hybrid metamodel herein, called (APCKKm-MCS) is constructed from an adaptive process with multiple enrichment of Experimental Design (ED). The hybrid approach was tested on simple non-linear functions, a truss bar, and an offshore deepwater Steel Catenary Riser (SCR). The study's outcome revealed that APCKKm-MCS produced a high predictive response capacity, reduced model evaluation, and shorter computing time during reliability evaluation than the single enrichment case (APCK-MCS) and the adaptive ordinary Kriging case (AK-MCS) considered. In addition, a novel framework is developed for the resilience quantification of offshore structures in terms of their time-varying reliability, adaptability, and maintainability. The developed framework was demonstrated using an internally corroded pipeline segment subject to disruptive events of leak, burst, and rupture. The framework captured the resilience index of the natural gas pipeline for its design life, and its sensitivity analysis revealed the influence of the pipe wall thickness and corrosion depth growth rate on the resilience of the pipeline. The framework provides a quantitative approach to determine the resilience of offshore structures and ascertain their critical influencing parameters for effective decision-making. Finally, a methodology for optimal structural design under uncertainty considering the dependency of environmental variables with the implementation of a hybrid metamodel in the inner loop of a nested optimization problem is presented and demonstrated on a steel column function and a segmented SCR. The study showed different decision outcomes for various vine tree configurations in the dependence modeling for the steel column function noting the importance of choosing the appropriate variable order in the vine tree for optimal design under uncertainty. Also, the research reveals the suitability of adaptive PCK for the inner loop reliability phase for a double-loop structural optimization due to its high predictive capacity and observed relatively low cross-validation error. The method shows the importance of effective dependence modeling of environmental ocean variables in structural cost minimization and selecting optimal structural design variables under uncertainty. From the research outcomes, considering multivariate dependence between ocean variables using vine copula and utilizing multiple enrichment hybrid metamodels in response evaluation for reliability and optimal design assessment of offshore structures could better predict their failure probability and enhance a safer structural design. In addition, the resilience quantification framework developed provides a vital decision-making tool for offshore structural systems' design and integrity management. The research into high dimensional dependence modeling of offshore structures using vine copula, comparative study of sampling strategies required for the hybrid (Kriging and PCE) metamodel construction, dependence-based structural resilience quantification, and multiobjective dependence-based structural optimization under uncertainty are among areas proposed for future investigation

Surrogate-Assisted Unified Optimization Framework for Investigating Marine Structural Design Under Information Uncertainty.

Structural decisions made in the early stages of marine systems design can have a large impact on future acquisition, maintenance and life-cycle costs. However, owing to the unique nature of early stage marine system design, these critical structure decisions are often made on the basis of incomplete information or knowledge about the design. When coupled with design optimization analysis, the complex, uncertain early stage design environment makes it very difficult to deliver a quantified trade-off analysis for decision making. This work presents a novel decision support method that integrates design optimization, high-fidelity analysis, and modeling of information uncertainty for early stage design and analysis. To support this method this dissertation improves the design optimization methods for marine structures by proposing several novel surrogate modeling techniques and strategies. The proposed work treats the uncertainties that are sourced from limited information in a non-statistical interval uncertainty form. This interval uncertainty is treated as an objective function in an optimization framework in order to explore the impact of information uncertainty on structural design performance. In this examination, the potential structural weight penalty regarding information uncertainty can be quickly identified in early stage, avoiding costly redesign later in the design. This dissertation then continues to explore a balanced computational structure between fidelity and efficiency. A proposed novel variable fidelity approach can be applied to wisely allocate expensive high-fidelity computational simulations. In achieving the proposed capabilities for design optimization, several surrogate modeling methods are developed concerning worst-case estimation, clustered multiple meta-modeling, and mixed variable modeling techniques. These surrogate methods have been demonstrated to significantly improve the efficiency of optimizer in dealing with the challenges of early stage marine structure design.PhDNaval Architecture and Marine EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133365/1/yanliuch_1.pd

Probabilistic optimization of engineering system with prescribed target design in a reduced parameter space

A novel probabilistic robust design optimization framework is presented here using a Bayesian inference framework. The objective of the proposed study is to obtain probabilistic descriptors of the system parameters conditioned on the user-prescribed target probability distributions of the output quantities of interest or figures of merit of a system. A criterion-based identification of a reduced important parameter space is performed from the typically high number of parameters modelling the stochastically parametrized physical system. The criterion can be based on sensitivity indices, design constraints or expert opinion or a combination of these. The posterior probabilities on the reduced or important parameters conditioned on prescribed target distributions of the output quantities of interest is derived using the Bayesian inference framework. The probabilistic optimal design proposed here offers the distinct advantage of prescribing probability bounds of the system performance functions around the optimal design points such that robust operation is ensured. The proposed method has been demonstrated with two numerical examples including the optimal design of a structural dynamic system based on user-prescribed target distribution for the resonance frequency of the system

Probabilistic optimization of engineering system with prescribed target design in a reduced parameter space

A novel probabilistic robust design optimization framework is presented here using a Bayesian inference framework. The objective of the proposed study is to obtain probabilistic descriptors of the system parameters conditioned on the user-prescribed target probability distributions of the output quantities of interest or figures of merit of a system. A criterion-based identification of a reduced important parameter space is performed from the typically high number of parameters modelling the stochastically parametrized physical system. The criterion can be based on sensitivity indices, design constraints or expert opinion or a combination of these. The posterior probabilities on the reduced or important parameters conditioned on prescribed target distributions of the output quantities of interest is derived using the Bayesian inference framework. The probabilistic optimal design proposed here offers the distinct advantage of prescribing probability bounds of the system performance functions around the optimal design points such that robust operation is ensured. The proposed method has been demonstrated with two numerical examples including the optimal design of a structural dynamic system based on user-prescribed target distribution for the resonance frequency of the system

The use of geometric uncertainty data in aero engine structural analysis and design

A gas turbine disc has three critical regions for which lifing calculations are essential: the assembly holes or weld areas, the hub region, and the blade-disc attachment area. Typically, a firtree joint is used to attach the blades to the turbine disc instead of a dove-tail joint, which is commonly used for compressor discs. A firtree joint involves contact between two surfaces at more than one location which makes the joint more difficult to design. Large loads generated due to the centrifugal action of the disc and associated blades are distributed over multiple areas of contact within the joint. All of the contacts in a firtree joint are required to be engaged simultaneously when the blades are loaded. However, slight variations in the manufacture of these components can have an impact on this loading. It is observed that small changes in the geometric entities representing contact between the two bodies can result in variations in the stress distribution near contact edges and the notch regions. Even though manufacturing processes have advanced considerably in the last few decades, the variations in geometry due to these processes cannot be completely eliminated. Hence, it is necessary to design such components in the presence of uncertainties in order to minimise the variation observed in their performance. In this work, the variations in geometry due to the manufacturing processes used to produce firtree joints between a gas turbine blade and the disc are evaluated. These variations are represented in two different ways using measurement data of firtree joints obtained from a coordinate measuring machine (CMM): (i) the variation for the pressure angle in the firtree joint is extracted from a simple curve fit and (ii) using the same measurement data, the unevenness of the pressure surfaces is represented using a Fourier series after filtering noise components. A parametric computer aided design (CAD) model which represents the manufacturing variability is implemented using Siemens NX. Non-smooth surfaces are also numerically generated by assuming the surface profile to be a random process. Two- and three-dimensional elastic stress analysis is carried out on the firtree joint using the finite element code, Abaqus and the variations observed in the notch stresses with changing pressure angle are extracted. A surrogate assisted multiobjective optimisation is performed on the firtree joint based on the robustness principles. Kriging based models are used to build a surrogate for notch stresses and the non-dominated sorting genetic algorithm-II (NSGA-II) is implemented to perform a multiobjective optimisation in order to minimise the mean and standard deviation of the notch stresses. An iterative search algorithm that updates the Kriging models with equally spaced infill points from the predicted Pareto front is adopted. Finally, a new design of the firtree joint is obtained which has better performance with respect to the variation in the notch stresses due to manufacturing uncertainties

Managing computational complexity through using partitioning, approximation and coordination

Problem: Complex systems are composed of many interdependent subsystems with a level of complexity that exceeds the ability of a single designer. One way to address this problem is to partition the complex design problem into smaller, more manageable design tasks that can be handled by multiple design teams. Partitioning-based design methods are decision support tools that provide mathematical foundations, and computational methods to create such design processes. Managing the interdependency among these subsystems is crucial and a successful design process should meet the requirements of the whole system which needs coordinating the solutions for all the partitions after all. Approach: Partitioning and coordination should be performed to break down the system into subproblems, solve them and put these solutions together to come up with the ultimate system design. These two tasks of partitioning-coordinating are computationally demanding. Most of the proposed approaches are either computationally very expensive or applicable to only a narrow class of problems. These approaches also use exact methods and eliminate the uncertainty. To manage the computational complexity and uncertainty, we approximate each subproblem after partitioning the whole system. In engineering design, one way to approximate the reality is using surrogate models (SM) to replace the functions which are computationally expensive to solve. This task also is added to the proposed computational framework. Also, to automate the whole process, creating a knowledge-based reusable template for each of these three steps is required. Therefore, in this dissertation, we first partition/decompose the complex system, then, we approximate the subproblem of each partition. Afterwards, we apply coordination methods to guide the solutions of the partitions toward the ultimate integrated system design. Validation: The partitioning-approximation-coordination design approach is validated using the validation square approach that consists of theoretical and empirical validation. Empirical validation of the design architecture is carried out using two industry-driven problems namely the a hot rod rolling problem’, ‘a dam network design problem’, ‘a crime prediction problem’ and ‘a green supply chain design problem’. Specific sub-problems are formulated within these problem domains to address various research questions identified in this dissertation. Contributions: The contributions from the dissertation are categorized into new knowledge in five research domains: • Creating an approach to building an ensemble of surrogate models when the data is limited – when the data is limited, replacing computationally expensive simulations with accurate, low-dimensional, and rapid surrogates is very important but non-trivial. Therefore, a cross-validation-based ensemble modeling approach is proposed. • Using temporal and spatial analysis to manage the uncertainties - when the data is time-based (for example, in meteorological data analysis) and when we are dealing with geographical data (for example, in geographical information systems data analysis), instead of feature-based data analysis time series analysis and spatial statistics are required, respectively. Therefore, when the simulations are for time and space-based data, surrogate models need to be time and space-based. In surrogate modeling, there is a gap in time and space-based models which we address in this dissertation. We created, applied and evaluated the effectiveness of these models for a dam network planning and a crime prediction problem. • Removing assumptions regarding the demand distributions in green supply chain networks – in the existent literature for supply chain network design, there are always assumptions about the distribution of the demand. We remove this assumption in the partition-approximate-compose of the green supply chain design problem. • Creating new knowledge by proposing a coordination approach for a partitioned and approximated network design. A green supply chain under online (pull economy) and in-person (push economy) shopping channels is designed to demonstrate the utility of the proposed approach