Optimizing slip-mean-time used in estimating non-stationary random vibration signal's PSD

The aircraft has always suffered non-stationary random vibration in the booster-phase of the launch process. Obtain the relationship between the slip-mean-time and the bias error and that between the slip-mean-time and the random error in the estimation of a non-stationary random vibration signal's power spectral density (PSD) by analyzing the estimation of the signal's variable mean square (MS). Based on this, Obtain the analytic relationship between the variable MS of a sample of a non-stationary random vibration signal and the optimum slip-mean-time which causes the smallest total error in the spectrum analysis of the signal, propose an approach for optimizing the slip-mean-time in the estimation of a non-stationary random vibration signal's PSD. Present an appliance for a signal sample of a random vibration process which is caused during an aircraft booster-phase. Used the orthogonal polynomial approximation to get the analytic format of the process's MS, confirm the optimum slip-mean-time used in estimating the signal's PSD.