Force identification of dynamic systems using virtual work principle

One of the key inverse problems for estimating dynamic forces acting on a structure is to determine the force expansion and the corresponding solving method. This paper presents a moving least square (MLS) method for fitting dynamic forces, which improves the existing traditional methods. The simulation results show that the force expansion order has a tiny effect on the types of forces, which indicates the MLS methods excellent ability for local approximation and noise immunity as well as good fitting function. Then, the differential equation of motion for the system is transformed into an integral equation by using the virtual work principle, which can eliminate the structural acceleration response without introducing the calculation error. Besides, the transformation derives an expression of velocity by integrating by parts, which diminishes the error propagation of the velocity. Hence, the integral equation of motion for the system has a strong constraint to noise with zero mean value. Finally, this paper puts forward an optimization method to solve the equation. The numerical stability can be enhanced as the matrix inversion calculation is avoided. Illustrative examples involving different types of forces demonstrate that the transformation of the differential equation proposed through virtual work principle can eliminate interference efficiently and is robust for dynamic calculation.