Testing shock absorbers: Towards a faster parallelizable algorithm

Abstract

Cars are equipped with shock absorbers, which are designed to smooth out the shocks on the road. In practice, there is a need to test them. To test the shock absorbers, we need to estimate the values of the shock absorber's parameters. If we did not have any measurement errors, then two measurements would be sufficient to determine the parameters. However, in reality, there are measurement errors. Usually, in engineering practice, it is assumed that the errors are normally distributed with 0 mean, so we can use least squares method to test it. In practice, we often only know the upper bound on the measurement errors, so we have interval uncertainty. In principle, the problem of determining the parameters of the shock absorber under interval uncertainty can be solved by reducing it to several linear programming problems. However, linear programming problems take a reasonably long time O(n3.5). A natural way to speed up computations is to parallelize the algorithm. However, it is known that linear programming is provably the most difficult problem to parallelize. So instead, we propose a new algorithm for finding ranges for shock absorber's parameters, an algorithm which is not only faster but also easy-to-parallelize.