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Optimization of any aerospace product results in increasing payload capacity of space vehicles. Essentially weight, volume and cost are the main constraints. Design optimization studies for aerospace system are increasingly gaining importance. The problem of optimum design under uncertainty has been formulated as reliability-based design optimization. The reliability based optimization, which includes robustness requirements leads to multi-objective optimization under uncertainty. In this paper Reliability, based design optimization study is carried out under linear constraint optimization to minimize the weight of a nitrogen gas bottle with specified target reliability. Response surface method considering full factorial experiment is used to establish multiple regression equation for induced hoop stress and maximum strain. Necessary data pertaining to design, manufacturing and operating conditions are collected systematically for variability study. Structural reliability is evaluated using Advanced First-Order Second-Moment Method (AFOSM). Finally, optimization formulation established and it has been discussed in this paper.

In design, much research deals with cases where design variables are deterministic thus ignoring possible uncertainties present in manufacturing or environmental conditions. When uncertainty is considered, the design variables follow a particular distribution whose parameters are defined. Probabilistic design aims to reduce the probability of failure of a system by moving the distribution parameters of the design variables. The most popular method to estimate the probability of failure is a Monte Carlo Simulation where, using the distribution parameters, many runs are generated and the number of times the system does not meet specifications is counted. This method, however, can become time-consuming as the mechanistic model developed to model a physical system becomes increasingly complex. From structural reliability theory, the First Order Reliability Method (FORM) is an efficient method to estimate probability and efficiently moves the parameters to reduce failure probability. However, if the mechanistic model is too complex FORM becomes difficult to use. This paper presents a methodology to use approximating functions, called 'metamodels', with FORM to search for a design that minimizes the probability of failure. The method will be applied to three examples and the accuracy and speed of this metamodel-based probabilistic design method will be discussed. The speed and accuracy of three popular metamodels, the response surface model, the Radial Basis Function and the Kriging model are compared. Later, some theory will be presented on how the method can be applied to systems with a dynamic performance measure where the response lifetime is required to computer another performance measure.

Most systems have multiple inputs that comprise of a mixture of excitations and component parameters. Excitations are different from component parameters in that they are always functions of time. In mechanical systems, these include applied forces, applied displacements, system settings, systems configurations and operating conditions. It would be convenient to include multiple excitations and multiple component parameters in a meta-model to take advantage of the inherent computation speed needed for timely probability-based design optimization.

In the development of the meta-model in this paper, we treat the component parameters in the same manner as the excitations and thus, in both cases, form time-sampled vectors. A design-of-experiments training regime creates a single input matrix, and using the mechanistic model, a single output matrix. Finally, a simple, explicit, meta-model is developed that turns an arbitrary vector of contiguous multiple excitations and multiple component parameters into the corresponding output vector (herein, the response). The approach provides an appealing and efficient solution to the multiple, mixed input problem, and in addition, requires only off-the-shelf computer software. The efficacy of the meta-model is shown through probability-based design optimization (PBDO) of a tire-wheel assembly, modelled as a mass-spring-damper system with nonlinear hysteresis, under a combination of practical inputs.

This paper presents a method to simulate the construction of a caisson breakwater in order to evaluate the risks involved in its construction. A computer model of the construction process that a contractor would follow to build a caisson breakwater was developed, with the wave climate for each month of the duration of works modeled using data obtained from the NOWPHAS Reports. Possible damage to the caisson was determined using a deformation-based reliability design method that included sliding, tilting, overturning of the caisson and erosion of the toe armour and foundation material. The model included possible delays due to adverse weather, reconstruction of damaged sections and construction accidents. By using the Monte Carlo simulation technique, the expected cost and time to finish the breakwater could be obtained, allowing to determine the risk associated with the breakwater construction. Thus, it is possible to determine when would be the most appropriate time to begin construction and the likelihood of encountering problems during the construction phase. A case study of the breakwater construction for Honshu island in Japan is shown, with the results comparing well with the experience of Japanese contractors.

In this study, the performance-based design method developed for a conventional solid-wall caisson breakwater is extended to a perforated-wall caisson breakwater. First, to verify the mathematical model to calculate the sliding distance of a perforated-wall caisson, hydraulic experiment is conducted. A good agreement is shown between the model and experimental results. The developed performance-based design method is then compared with the conventional deterministic method in different water depths. Both the expected sliding distance and the exceedance percentage of total sliding distance during the structure lifetime decrease shorewards outside the surf zone, but they increase again toward the shore inside the surf zone. The performance-based design method is either more economical or less economical than the deterministic method depending on which design criterion is used. If the criterion for expected sliding distance or exceedance percentage is used in the ultimate limit state, the former method is less economical than the latter outside the surf zone, whereas the two methods are equally economical inside the surf zone. However, if the breakwater is designed to satisfy the criterion for exceedance percentage in the repairable limit state, the former method is more economical than the latter in all water depths.