Fuzzy pattern modeling of self-pierce riveting for data from experiments and computer simulations

Abstract

Modeling forms the basis for optimal control of complex technical processes in the context of industry 4.0 development and, hence, for high product quality as well as efficient production. For the mechanical joining process of self-pierce riveting with 11 input and 5 output variables, two modeling approaches based on (1) experimental data and (2) FEM computer simulation are outlined and performed. A physical modeling approach is ruled out due to the high problem dimensionality and complex nonlinear dynamic relationships between input and output variables. Alternatively, data-based approaches lead to Artificial Intelligence (AI) model designs. The experimental approach is cost- and resource-consuming; therefore, only a relatively small data set can be collected. Here, we present results from experimental trials that serve as representatives and are generalized by a description with high-dimensional parametric membership functions (fuzzification). The fuzzification procedure is also applied to the FEM computer simulation results. In principle, it can provide an arbitrarily large database. However, consequently, time- and computational effort increase considerably. Both data sets form the basis for parallel model building using the AI method of local fuzzy pattern models, which can be used to describe highly nonlinear input-output relationships by error-minimizing partitioning. Finally, the comparison of the results of the two modeling approaches is outlined. Finally, a coupled modeling strategy and future model adaptation are proposed.

Perspective Chapter: Quality Determination of Hydraulic Pumps with Adaptive Fuzzy Pattern Classifiers to Reduce the Risk for Quality Management

“…In special cases the amount for d l/r ! ∞ changes to a sharply described class (red color in Figure 4) [3,13].…”

“…The fuzzy potential function points to the theoretical possibility of multidimensional membership functions. Hence, one-dimensional membership functions define the membership function in N-dimensional space  N Therefore, the exceptional advantage of the potential function is that a suitable conjunctive combination of several fuzzy sets/logic can be used to obtain a multivariate membership function in parametric form [3,13]. The normalized function (a ¼ 1) with N dimension is given by…”

“…Therefore, theoretical modeling would only be an inaccurate model of the system. Since we need to simplify the input data, we are often forced to accept a certain degree of inaccuracy and uncertainty in mathematical models, which then cannot achieve acceptable results for the dynamic behavior of the systems [3,4]. In such situations, a data-based controlled nonlinear black-box system provides a reasonable approximation to nonlinear systems.…”

“…In such situations, a data-based controlled nonlinear black-box system provides a reasonable approximation to nonlinear systems. In these approaches, models are built based on the process's measured input and output data, requiring little or no physical or formal information [3]. The literature shows that black-box models, such as neural networks and fuzzy logic-based models, are widely used to build fault diagnostic models from measured input/output data [5][6][7].…”

“…The literature shows that black-box models, such as neural networks and fuzzy logic-based models, are widely used to build fault diagnostic models from measured input/output data [5][6][7]. These approaches perform better than statistical models [1] and mathematical equations [3].…”