BAYESIAN Inference Based Parameter Calibration of a Mechanical Load-Bearing Structure’s Mathematical Model

Abstract

Load-bearing structures with kinematic functions like a suspension of a vehicle and an aircraft landing gear enable and disable degrees of freedom and are part of many mechanical engineering applications. In most cases, the load path going through the load-bearing structure is predetermined in the design phase. However, if parts of the load-bearing structure become weak or suffer damage, e.g. due to deterioration or overload, the load capacity may become lower than designed. In that case, load redistribution can be an option to adjust the load path and, thus, reduce the effects of damage or prevent further damage. For an adequate numerical prediction of the load redistribution capability, an adequate mathematical model with calibrated model parameters is needed. Therefore, the adequacy of an exemplary load-bearing structure’s mathematical model is evaluated and its predictability is increased by model parameter uncertainty quantification and reduction. The mathematical model consists of a mechanical part, a friction model and the electromagnetic actuator to achieve load redistribution, whereby the mechanical part is chosen for calibration in this paper. Conventionally, optimization algorithms are used to calibrate the model parameters deterministically. In this paper, the model parameter calibration is formulated to achieve a model prediction that is statistically consistent with the data gained from an experimental test setup of the exemplary load-bearing structure. Using the R2 sensitivity analysis, the most influential parameters for the model prediction of interest, i.e. the load path going through the load-bearing structure represented by the support reaction forces, are identified for calibration. Subsequently, BAYESIAN inference based calibration procedure using the experimental data and the selected model parameters is performed. Thus, the mathematical model is adjusted to the actual operating conditions of the experimental load-bearing structure via the model parameters and the model prediction accuracy is increased. Uncertainty represented by originally large model parameter ranges can be reduced and quantified.KeywordsAdaptive systemsUncertainty quantificationBAYESIAN inferenceParameter calibration