Diane Villanueva

Including the Effect of a Future Test and Redesign in Reliability Calculations

It is common to test components after they are designed and redesign if necessary. The reduction of the uncertainty in the probability of failure that can occur after a test is usually not incorporated in reliability calculations at the design stage. This reduction in uncertainty is accomplished by additional knowledge provided by the test and by redesign when the test reveals that the component is unsafe or overly conservative. In this paper, a methodology is developed to estimate the effect of a single future thermal test followed by redesign and to model the effect of the resulting reduction of the uncertainty in the probability of failure. Using assumed distributions of computation and experimental errors and given redesign rules, possible outcomes of the future test and redesign throughMonte Carlo sampling are obtained to determinewhat changes in probability of failure, design, andweight will occur. In addition, Bayesian updating is used to gain accurate estimates of the probability of failure after a test. These methods are demonstrated through a future thermal test on an integrated thermal protection system. Performing redesign following a single future test can reduce the probability of failure by orders of magnitude, on average, when the objective of the redesign is to restore original safety margins. Redesign for a given reduced probability of failure allows additional weight reduction.

Dynamic Design Space Partitioning for Optimization of an Integrated Thermal Protection System

In this paper, we explore the use of design space partitioning to tackle optimization problems in which each point is expensive to evaluate and there are multiple local optima. The overarching goal of the method presented in this paper is to locate all local optima rather than just the global one. Locating multiple designs provides insurance against discovering that late in the design process a design is poor due to modeling errors or overlooked objectives or constraints. The proposed strategy to locate multiple candidate designs dynamically partitions the search space among several “agents” that approximate their sub-region landscape using surrogates. Agents coordinate by exchanging points to form an approximation of the objective function or constraints in the sub-region and by modifying the boundaries of their sub-regions. Through a self-organized process of creation and deletion, agents adapt the partition as to exploit potential local optima and explore unknown regions. This idea is demonstrated on a six-dimensional analytical function, and a practical engineering example, the design of an integrated thermal protection system. Nomenclature c = center f = objective function F = objective function values associated with design of experiments in database g = constraint G = constraint values associated with design of experiments in database t = time x = design variables X = design of experiments in database ˆ f = surrogate prediction of f ˆ g = surrogate prediction of g

Accounting for future redesign to balance performance and development costs

Most components undergo tests after they are designed and are redesigned if necessary. Tests help designers find unsafe and overly conservative designs, and redesign can restore safety or increase performance. In general, the expected changes to the performance and reliability of the design after the test and redesign are not considered. In this paper, we explore how modeling a future test and redesign provides a company an opportunity to balance development costs versus performance by simultaneously designing the design and the post-test redesign rules during the initial design stage. Due to regulations and tradition, safety margin and safety factor based design is a common practice in industry as opposed to probabilistic design. In this paper, we show that it is possible to continue to use safety margin based design, and employ probability solely to select safety margins and redesign criteria. In this study, we find the optimum safety margins and redesign criterion for an integrated thermal protection system. These are optimized in order to find a minimum mass design with minimal redesign costs. We observed that the optimum safety margin and redesign criterion call for an initially conservative design and use the redesign process to trim excess weight rather than restore safety. This would fit well with regulatory constraints, since regulations usually impose minimum safety margins.

Surrogate-based agents for constrained optimization

Multi-agent systems have been used to solve complex problems by decomposing them into autonomous subtasks. Drawing inspiration from both multi-surrogate and multi-agent techniques, we dene in this article optimization subtasks that employ dierent approximations of the data in subregions through the choice of surrogate, which creates surrogatebased agents. We explore a method of design space partitioning that assigns agents to subregions of the design space, which drives the agents to locate optima through a mixture of optimization and exploration in the subregions. These methods are illustrated on two constrained optimization problems, one with uncertainty and another with small, disconnected feasible regions. It is observed that using a system of surrogate-based optimization agents is more eective at locating the optimum compared to optimization with a single surrogate over the entire design space.

Probabilistic Optimization of Integrated Thermal Protection System

The paper considers probabilistic optimization of i ntegrated thermal protection system (ITPS) that combines the thermal protection function with the structural load carrying function. For ITPS design, structural and thermal requirements usually conflict. Increased structural thickness helps carry loads bu t increases heat conduction. Designers need to allocate risk between structural and therma l failure modes. In deterministic designs, this risk allocation is implicit in the ch oice of safety factors. Probabilistic design allocates risk explicitly. This paper uses a simple case to illustrate the difference between deterministic and probabilistic risk allocation for ITPS design.. For this example the deterministic design allocates risk about equally b etween thermal and structural failure, while the probabilistic design allocates most of th e failure to thermal failure.

Accounting for Future Redesign in the Optimization of an Integrated Thermal Protection System

between the probability of redesign and the mass at the design stage. We observed that to minimize mass, designs should initially satisfy safety requirements such that most redesigns concern overly conservative designs. The additional knowledge gained from the test allows the designer to consider a smaller safety margin for the redesign to reduce the mass.

Dynamic Partitioning for Balancing Exploitation and Exploration in Constrained Optimization: A Multi-Agent Approach

In this article, we define optimization subtasks that employ different approximations of the data in subregions through the choice of surrogate, which creates surrogate-based agents. Through design space partitioning, which assigns agents to subregions of the design space, the agents solve the optimization problem in their respective subregions, and use the feasibility and objective function value to assess the value of the solutions in order to center the subregions at local and global optima. Further, we introduce methods to create agents at run-time which allows additional exploration by creating a finer partition of the design space. The end result of this dynamic partitioning is a multi-agent system that inherently balances exploitation and exploration in the design space. We illustrate this approach on a constrained optimization problem with small, disconnected feasible regions. It was observed that the agents were effective at locating global and local optima.

Decomposition of System Level Reliability-Based Design Optimization to Reduce the Number of Simulations

It is computationally expensive to evaluate the overall system level reliability when several interacting failure modes are present. Therefore, it is even more expensive to optimize considering the system level reliability that accounts for the interactions between failure modes. In this paper, we decompose the system level reliability based optimization problem using surrogates into less expensive problems with fixed risk allocation for each failure mode. In addition, the fixed risk allocation problem is transformed from a purely probabilistic problem to a deterministic one through an iterative process of updating safety factors to limit the number of calls to evaluate the reliability. We found that the number of calls to the simulation to evaluate the system level reliability was reduced by 77% with this methodology.