PSI - Issue 57

Khashayar Shahrezaei et al. / Procedia Structural Integrity 57 (2024) 711–717 K. Shahrezaei et al. / Structural Integrity Procedia 00 (2023) 000–000

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needed. In the early stages of the design development process, changes are more easily implemented at a lower cost, however, product knowledge is limited. An approach to overcome this typical design process paradox (Lindahl and Sundin, 2013) is to employ probabilistic modeling methods at an early stage of the design development process. This enables the extraction of knowledge early on, allowing the definition of both best- and worst-case scenarios, helping to navigate through uncertainties. A robust material design is a product that is insensitive to uncertainties. Hence, the source of uncertainty needs to be quantified and controlled. Controlling the source of uncertainty of the model input parameters may yield a great reduction in the model output uncertainty and an improved fatigue material behavior. Most often many sources of uncertainty occur already at the manufacturing stage. Once the source of uncertainty has been quantified, it is a prerequisite to understand how these sources of uncertainty influence the outputs of interest or material performance. This can be done using a Global Sensitivity Analysis (GSA). GSA is a well-established modeling technique that quantifies how uncertainty in the model outputs can be appor tioned to di ff erent sources of uncertainty in the model inputs (Saltelli, 2004). This modeling technique enables the identification of the input parameters that significantly a ff ect the output, the non-influential inputs, and some interac tion e ff ects within the model. Among all the global sensitivity measures Sobol’ sensitivity indices (Sobol’, 1990) are the most commonly used. Sobol’ sensitivity indices provide a robust estimation of the model sensitivity for a large number of input parameters making it favorable for high-dimensional problems. However, Sobol’s sensitivity indices are computationally intensive since it is a method based on Monte Carlo Simulations (MCS). To overcome the afore mentioned cost, a metamodel-based approach has been adopted in the present study. Metamodeling is acknowledged as an e ffi cient mathematical modeling approach to approximate costly and complex simulations. Among all the schemes of computing Sobol’s indices, one of the most e ffi cient schemes is proposed by Saltelli et al. (2010). The proposed scheme has a computational cost of N ( i + 2) for computing the Sobol’s indices (for i number of input parameters and N number of model evaluations). Nevertheless, like other MCS-based methods, this scheme requires a large number of model evaluations. Generally, an order of magnitude greater than three ensures convergence (Burnaev et al., 2017), which makes the method highly computational intensive. This motivates the development of a metamodel-based GSA to provide more e ffi cient model evaluations. The general idea of metamodeling is to approximate the behavior of a computational heavy or complex simulation using a simplified mathematical or computational model. Metamodels are commonly used in various fields, including engineering, optimization, machine learning, and computer experiments. Although metamodels are computationally e ffi cient, the construction of an appropriate metamodel still requires a number of model evaluations of the original sim ulation or process to create the preliminary Experimental Design (ED). Many types of sophisticated metamodels have been developed over the past decades and they are found in numerous engineering applications. For a comprehensive discussion of how to construct these models, authors refers to the work by Forrester et al. (2008). In order to improve accuracy in fatigue predictions the aim of this study is to incorporate statistical aspects of manufacturing defects. The present study will focus on a micromechanical simulation and the understanding of pa rameter uncertainty on e ff ective macromechanical material properties of a Carbon Fiber Reinforced Polymer (CFRP) material. In order to improve accuracy in fatigue predictions the aim of this study is to incorporate statistical aspects of manufacturing defects. Three di ff erent types of metamodels commonly used for GSA frameworks are studied, namely, Artificial Neural Networks (ANN), Polynomial Chaos Expansion (PCE), and Kriging. A case study is used to demonstrate how to determine the sensitivity of the controlling parameters on the outputs of interest. In the case study, the implemented modeling framework replaces a key step in a Multi-Scale Modeling (MSM) framework. It is an example of visualizing the strengths of the metamodel-based GSA and the amount of knowledge you can gain with less time and computational e ff ort, and how you could early in a design development process make decisions to improve fatigue behavior. 1.1. Metamodel-based GSA 1.2. Scope of this paper