An Uncertainty Model for Strain Gages Using Monte Carlo Methodology

For the purpose of validation and identification of mechanical systems, measurements are indispensable. However, they require knowledge of the inherent uncertainty to provide valid information. This paper describes a method on how to evaluate uncertainties in strain measurement using electric strain gages for practical engineering applications. Therefore, a basic model of the measurement is deduced that comprises the main influence factors and their uncertainties. This is performed using the example of a project dealing with strain measurement on the concrete surface of a large-span road bridge under static loading. Special attention is given to the statistical modeling of the inputs, the underlying physical relationship, and the incorporation and the impact of nonlinearities for different environmental conditions and strain levels. In this regard, also experiments were conducted to quantify the influence of misalignment of the gages. The methodological approach used is Monte Carlo simulation. A subsequent variance-based sensitivity analysis reveals the degree of nonlinearity in the relationship and the importance of the different factors to the resulting probability distribution. The developed scheme requires a minimum of expert knowledge of the analytical derivation of measurement uncertainties and can easily be modified for differing requirements and purposes.