Abstract
During vibration tests, loads need to be measured for machine components such as bearings, mounts, lugs, etc. As load cells cannot be placed at certain locations in the interior, strain gauges are used instead to measure the strain. But we need a load strain relation for the components. Most of the real-life components experience axial, bending, and torsional loads. Hence a multi-dimensional force strain relationship needs to be established for each component. Hence, prior to the actual tests, calibration tests are performed, on each component separately. These calibration tests are most often static load tests, in which load is applied in one direction at a time in small increments of load. In addition to the unidirectional loads, combined loads are also applied to establish complete load strain surface. Multidimensional load strain data is compiled and pre-processed to develop a multivariable load-strain relationship. The load-strain relationship is later used to back out loads from the strain data. Currently methods such as Newton-Raphson, plate smoothing spline, surface fitting, etc. are used to develop this relationship. Newton-Raphson is an iterative technique which solves for the loads simultaneously at each strain points. This method iterates till the error is small to achieve convergence. Newton-Raphson and surface fitting methods require structured data for developing multivariable load-strain relationship. However, deriving load-strain relations for complex geometries exhibiting highly nonlinear relationships is mathematically complex and computationally expensive. Also, formulation of these methods limits the use of large number of variables (more than 3). In this paper, an ensemble of MARS (Multi variate adaptive regression spline) along with Adaboost boosting algorithm has been explored to predict loads from strain data by developing multivariable correlation between loads and strains. MARS is an improved multivariable spline regression technique that generates piecewise polynomial functions between the variables and automatically determines the number & size of segment to achieve high accuracy or best fit on nonlinear problems. With complex high dimensional and noisy non-linear problem, Adaboost helps to reduce overfitting and improve the performance of the MARS model. The proposed method is well suited for dealing with large number of variables and developing complex non-linear load-strain relationship as it doesn’t require any structured data or iterations like existing methods to backout loads. The proposed method reduces the run time by more than 90% as compared to the conventional methods without compromising on accuracy. The advantages of the proposed method over conventional techniques have been demonstrated in this paper.
