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Material substitution in legacy system engineering (LSE) with fuzzy logic principles

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The focus of this research is to investigate methods for material substitution for the purpose of re-engineering legacy systems that involves incomplete information about form, fit and function of replacement

The focus of this research is to investigate methods for material substitution for the purpose of re-engineering legacy systems that involves incomplete information about form, fit and function of replacement parts. The primary motive is to extract as much useful information about a failed legacy part as possible and use fuzzy logic rules for identifying the unknown parameter values. Machine elements can fail by any number of failure modes but the most probable failure modes based on the service condition are considered critical failure modes. Three main parameters are of key interest in identifying the critical failure mode of the part. Critical failure modes are then directly mapped to material properties. Target material property values are calculated from material property values obtained from the originally used material and from the design goals. The material database is searched for new candidate materials that satisfy the goals and constraints in manufacturing and raw stock availability. Uncertainty in the extracted data is modeled using fuzzy logic. Fuzzy member functions model the imprecise nature of data in each available parameter and rule sets characterize the imprecise dependencies between the parameters and makes decisions in identifying the unknown parameter value based on the incompleteness. A final confidence level for each material in a pool of candidate material is a direct indication of uncertainty. All the candidates satisfy the goals and constraints to varying degrees and the final selection is left to the designer's discretion. The process is automated by software that inputs incomplete data; uses fuzzy logic to extract more information and queries the material database with a constrained search for finding candidate alternatives.

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Date Created
  • 2011

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Uncertainty modeling for nonlinear and linear heated structures

Description

This investigation focuses on the development of uncertainty modeling methods applicable to both the structural and thermal models of heated structures as part of an effort to enable the design

This investigation focuses on the development of uncertainty modeling methods applicable to both the structural and thermal models of heated structures as part of an effort to enable the design under uncertainty of hypersonic vehicles. The maximum entropy-based nonparametric stochastic modeling approach is used within the context of coupled structural-thermal Reduced Order Models (ROMs). Not only does this strategy allow for a computationally efficient generation of samples of the structural and thermal responses but the maximum entropy approach allows to introduce both aleatoric and some epistemic uncertainty into the system.

While the nonparametric approach has a long history of applications to structural models, the present investigation was the first one to consider it for the heat conduction problem. In this process, it was recognized that the nonparametric approach had to be modified to maintain the localization of the temperature near the heat source, which was successfully achieved.

The introduction of uncertainty in coupled structural-thermal ROMs of heated structures was addressed next. It was first recognized that the structural stiffness coefficients (linear, quadratic, and cubic) and the parameters quantifying the effects of the temperature distribution on the structural response can be regrouped into a matrix that is symmetric and positive definite. The nonparametric approach was then applied to this matrix allowing the assessment of the effects of uncertainty on the resulting temperature distributions and structural response.

The third part of this document focuses on introducing uncertainty using the Maximum Entropy Method at the level of finite element by randomizing elemental matrices, for instance, elemental stiffness, mass and conductance matrices. This approach brings some epistemic uncertainty not present in the parametric approach (e.g., by randomizing the elasticity tensor) while retaining more local character than the operation in ROM level.

The last part of this document focuses on the development of “reduced ROMs” (RROMs) which are reduced order models with small bases constructed in a data-driven process from a “full” ROM with a much larger basis. The development of the RROM methodology is motivated by the desire to optimally reduce the computational cost especially in multi-physics situations where a lack of prior understanding/knowledge of the solution typically leads to the selection of ROM bases that are excessively broad to ensure the necessary accuracy in representing the response. It is additionally emphasized that the ROM reduction process can be carried out adaptively, i.e., differently over different ranges of loading conditions.

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Date Created
  • 2019