No abstract

Recently, design for additive manufacturing has been proposed to maximize product performance through the rational and integrated design of the product, its materials, and their manufacturing processes. Searching design solutions in such a multidimensional design space is a challenging task. Notably, no existing design support method is both rapid and tailored to the design process. In this study, we propose a holistic approach that applies data-driven methods in design search and optimization at successive stages of a design process. More specifically, a two-step surrogate model-based design method is proposed for the embodiment and detailed design stages. The Bayesian network classifier is used as the reasoning framework to explore the design space in the embodiment design stage, while the Gaussian process regression model is used as the evaluation function for an optimization method to exploit the design space in detailed design. These models are constructed based on one dataset that is created by the Latin hypercube sampling method and then refined by the Markov Chain Monte Carlo sampling method. This cost-effective data-driven approach is demonstrated in the design of a customized ankle brace that has a tunable mechanical performance by using a highly stretchable design concept with tailored stiffnesses.

a b s t r a c tUncertainties are ubiquitous and unavoidable in process design and modeling. Because they can significantly affect the safety, reliability and economic decisions, it is important to quantify these uncertainties and reflect their propagation effect to process design. This paper proposes the application of generalized polynomial chaos (gPC)-based approach for uncertainty quantification and sensitivity analysis of complex chemical processes. The gPC approach approximates the dependence of a process state or output on the process inputs and parameters through expansion on an orthogonal polynomial basis. All statistical information of the interested quantity (output) can be obtained from the surrogate gPC model. The proposed methodology was compared with the traditional Monte-Carlo and Quasi Monte-Carlo sampling-based approaches to illustrate its advantages in terms of the computational efficiency. The result showed that the gPC method reduces computational effort for uncertainty quantification of complex chemical processes with an acceptable accuracy. Furthermore, Sobol's sensitivity indices to identify influential random inputs can be obtained directly from the surrogated gPC model, which in turn further reduces the required simulations remarkably. The framework developed in this study can be usefully applied to the robust design of complex processes under uncertainties.

a b s t r a c tRecently, distributed order systems as a generalized concept of fractional order have been a major focus in science and engineering areas, and have rapidly extended application across a wide range of disciplines. However, only a few numerical methods are available for analyzing the distributed order systems. This paper proposes a novel numerical scheme to analyze the behavior of single input single output linear systems in the time domain with a single distributed order differentiator/integrator by using operational matrix technique. The proposed method reduces different analysis problems to a system of algebraic equations by using block pulse functions, which makes it easy to handle an arbitrary input. Numerical examples were used to illustrate the accuracy and computational efficiency of the proposed method. The proposed method was found to be an efficient tool for analyzing linear distributed order systems.

a b s t r a c tStochastic spectral methods are widely used in uncertainty propagation thanks to its ability to obtain highly accurate solution with less computational demand. A novel hybrid spectral method is proposed here that combines generalized polynomial chaos (gPC) and operational matrix approaches. The hybrid method takes advantage of gPC's efficient handling of large parameter uncertainties and overcomes its limited applicability to systems with relatively highly correlated inputs. The hybrid method's use of operational matrices allows analyses of systems with low input correlations without suffering its restriction to small parameter uncertainties. The hybrid method is aimed to propagate uncertainties in fractional order systems with random parameters and random inputs with low correlation lengths. It is validated through several examples with different stochastic uncertainties. Comparison with Monte Carlo and gPC demonstrates the superior computational efficiency of the proposed method.