Designers should try to design systems that are resilient to adverse conditions during a system’s lifetime. The resilience of a system under time-dependent adverse conditions can be assessed by modeling the degradation and recovery of the system’s components. Decision makers in a firm should attempt to find the optimal design to make the system resilient to the various adverse conditions. A risk-neutral firm maximizes the expected profit gained from fielding the system, but a risk-averse firm may sacrifice some profit in order to avoid failure from these adverse conditions. The uniqueness of this paper lies in its model of a design firm’s risk aversion with a utility function or Value-at-Risk (VAR) and its use of that model to identify the optimal resilient design for the risk-averse firm. These risk-averse decision-making methods are applied to a design firm determining the resilience of a new engineered system. This paper significantly advances the engineering design discipline by modeling the firm’s appetite for risk within the context of designing a system that can fail due to degradation in the presence of adverse events and can respond to and recover from failure. Since the optimization model requires a complex Monte Carlo simulation to evaluate the objective function, we use a ranking and selection method and Bayesian optimization to find the optimal design. This paper incorporates the design of the wind turbine and the reliability and restoration of the turbine’s components for both risk-neutral and risk-averse decision makers. The results show that in order to make the system more resilient, risk-averse firms should pay a larger design cost to prevent catastrophic costs of failure. In this case, the system is less likely to fail due to the high resilience of its physical components.

Flexibility in engineering system design: •Flexibility in system design and implications for aerospace systems (Saleh et.al 2003) •A flexible and robust approach for preliminary engineering design based on designer's preference (Nahmet.al, 2007) •A real options approach to hybrid electric vehicle architecture design for flexibility (Kang et.al 2016) •Our research: •Simulation optimization •Long range uncertainty •Add flexibility and robustness to design

A new sequential sampling method, named sequential exploration-exploitation with dynamic trade-off (SEEDT), is proposed for reliability analysis of complex engineered systems involving high dimensionality and a wide range of reliability levels. The proposed SEEDT method is built based on the ideas of two previously developed sequential Kriging reliability methods, namely efficient global reliability analysis (EGRA) and maximum confidence enhancement (MCE) methods. It employs Kriging-based sequential sampling to build a surrogate model (i.e., Kriging model) that approximates the performance function of an engineered system, and performs Monte Carlo simulation on the surrogate model for reliability analysis. A new acquisition function, referred to as expected utility (EU), is developed to sequentially locate a computationally efficient set of sample points for constructing the Kriging model. The SEEDT method possesses three technical contributions: (i) defining a new utility function with several desirable properties that facilitates the joint consideration of exploration and exploitation over the course of sequential sampling; (ii) introducing a new exploration-exploitation trade-off coefficient that dynamically weighs exploration and exploitation to achieve a fine balance between these two activities; and (iii) developing a new convergence criterion based on the uncertainty in the prediction of the limit-state function (LSF). The effectiveness of the proposed method in reliability analysis is evaluated with several mathematical and practical examples. Results from these examples suggest that, given a certain number of sample points, the SEEDT method is capable of achieving better accuracy in predicting the LSF than the existing sequential sampling methods.

Designing resilient engineered systems that can sense and withstand adverse events and recover from the effects of the adverse events is increasingly seen as an important goal of engineering design. This paper proposes a value-driven design for resilience (VD2R) framework in order to enable the assessment of system resilience and the optimization of decision variables (or design characteristics) that maximize the value of the system for a firm. The VD2R framework possesses three unique features that allow system resilience and value to be addressed in a theoretically founded and explicit way. First, it assesses the time-dependent resilience of an engineered system by explicitly modeling the redundancy, robustness, and restoration of the system. This assessment captures the stochastic behavior of degradation and restoration and their impact on system resilience. Second, it encompasses a value model that links time-dependent system resilience to a design firm's future profit. Third, the VD2R framework offers an efficient optimization method to solve high-dimension, mixed-integer decision-making models. The proposed framework is demonstrated with a case study, where the resilience of a series-parallel system is modeled and its design characteristics optimized.

Research Problem •Determine how resilience should be integrated into a firm’s design decisions •Optimize design for a risk-averse firm that incorporates resilience

Engineered systems often operate in uncertain environments. Understanding different environments under which a system will operate is important in engineering design. Thus, there is a need to design systems with the capability to respond to future changes. This research explores designing a hybrid renewable energy system while taking into account long-range uncertainties of 20 years. The objective is to minimize the expected cost of the hybrid renewable energy system over the next 20 years. A design solution may be flexible, which means that the design can be adapted or modified to meet different scenarios in the future. The value of flexibility can be measured by comparing the expected cost without flexibility and expected cost with flexibility. The results show that a flexible design for hybrid renewable systems can decrease the expected cost by approximately 30%.

Designing complex systems with many parameters requires computationally expensive simulations and selecting both discrete and continuous design parameters. How to optimize design when future conditions may change, or when system is used differently than expected?