# Reduced-order Modeling of Parameter Variations for Parameter Identification in Rubber Curing

### Tobias Frank, Mark Wielitzka, Matthias Dagen, Tobias Ortmaier

#### Abstract

A reduced-order modeling approach for thermal systems with varying parameters in rubber curing processes is presented in this manuscript. For complex geometries with multiple components a finite element analysis with fine mesh elements is often the only feasible approach to calculate temperature distributions over time. A major drawback, however, is the resulting large system scale, which entails high computation times. Thus, real-time capable execution or a high number of iterations to solve for optimization problems are infeasible approaches. Model order reduction algorithms are a promising remedy, but physically interpretable parameter preservation is not obtained, when using common approaches. Thus, a method to extract parameter dependencies from numerical element matrices and reduce the model order is presented in this manuscript. Preservation of physically interpretable parameters is accomplished by applying linear reduction projectors to affine interpolated system matrices. Thus, parameter variations can be accounted for without costly recalculation of reduction projectors. Hence, a computation efficient model description is obtained, enabling a tunable balancing between computation time and accuracy. To demonstrate the effectiveness of the approach, parameter identification of material properties and heat transition coefficients is performed and validated with measurement data of two different sample systems. For the largest sample system computation time has been reduced from half an hour for a full order simulation to an averaged time of 0.3 s, with approximation error of 0.7 K.

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