Force identification in time domain based on dynamic programming

Introducing Bellman’s Principle of Optimality into the dynamic programming equation, a new method is proposed for identifying the time history of the input excitation. The method can eliminate large fluctuations in the identified results which are commonly existed in the present identification techniques. With the state-space formulation and the least square error method, the objective function is established between measured and identified system responses. Introducing the Newmark integration, a discrete equation of motion is deduced based on the system displacement, velocity and acceleration response. Then Bellman’s Principle of Optimality is used for the minimization of the objective function to estimate the excitation forces; finally the dynamic programming method of identification formulations is deduced. Trigonometric function excitation and normal stochastic excitation are applied for the simulation study. Satisfactory results are achieved even when the measurement noise is taken into the measurement system responses.