Moving force identification based on sparse regularization combined with moving average constraint

ØSparse regularization and moving average constraint are used for moving force identification.ØIdentified moving forces have sparse representation and stable local average values.ØIdentified moving forces are robust and not sensitive to calibration errors of sensors.ØPerformance is better than l1-norm regularization and moving average Tikhonov methods. An accurate input-output mathematical model is the basis of moving force identification (MFI). However, an absolutely accurate mathematical model between moving forces and structural responses is difficult to be established due to some practical reasons, such as calibration error, modelling error, and so on. An inaccurate input-output relationship may lead to some unreasonable MFI results, for example, an obvious fluctuation of the trend lines in moving forces. To tackle this problem, a constrained sparse regularization-based method is proposed for MFI in this study. Wherein, structural responses obtained from sensors with calibration errors are taken as the inputs. A system matrix reflecting the input-output relationship is formulated in the consideration of unknown moving forces and initial conditions. Sparse regularization is adopted for ensuring that the identified forces are sparse and robust. The constrained condition is expressed as a non-negative function. This function is defined via a strategy named moving average and applied for reflecting the degree of fluctuation of the trend lines for the moving forces. The constrained problem is solved as a standard form of l1-norm regularization via relaxing the constrained condition appropriately. Numerical simulations and experimental studies are conducted for assessing the effectiveness and feasibility of the proposed method. Effects of different calibration errors of sensors are discussed in detail. Illustrated results show that the proposed method can reconstruct the moving forces with a good performance. Some related issues are discussed as well.