Ruifu Zhang

Baseline correction of vibration acceleration signals with inconsistent initial velocity and displacement

This study improves upon the traditional polynomial detrending method in order to correct the vibration acceleration signals with inconsistent initial velocity and displacement more rationally and efficiently. When numerical integration of recorded acceleration signals using assumed initial velocity and displacement values (which are generally inconsistent with real values) is performed, baseline shift or drift phenomenon can arise in velocity and displacement curves obtained. Baseline correction must be performed if an inconsistent acceleration signal is to be used in dynamic analyses. Polynomial detrending is generally used to remove unreasonable trends in time series, but the consistency among acceleration, velocity, and displacement has not received sufficient attention. The traditional polynomial detrending method is improved by purposefully removing the shifted trends in velocity and displacement. Two inconsistent vibration signals are selected to be corrected using both the traditional method and the improved method. It was found that the traditional method does not give a satisfactory correction result, but the improved method can correct the signal to be consistent. The improved detrending method is effective in making vibration signals have consistent acceleration, velocity, and displacement.

Target-based algorithm for baseline correction of inconsistent vibration signals

A target-based baseline correction algorithm that can directly assign acceleration/velocity/displacement values equal or close to preset target values is proposed in this study for correcting vibration acceleration signals with inconsistent initial velocities and displacements. Baseline shift or drift phenomena can arise for velocity and displacement values obtained by numerical integration of recorded acceleration signals using assumed initial values that are inconsistent with reality. Two indicators, the drift ratio and amplitude ratio, are also proposed to identify the degree of baseline drift and to evaluate the results of baseline correction. The traditional polynomial detrending algorithm has typically been used to remove unreasonable trends in time series, but insufficient attention has been paid to consistency between acceleration, velocity, and displacement, which is explicitly considered in the proposed algorithm. The target-based algorithm has two implementation schemes, that is, a precise scheme and a detrending scheme, which can be selected according to the degree of baseline drift. Three inconsistent vibration signals are considered to verify the validity of the proposed algorithm. The baseline shift or drift trends can be removed effectively using the proposed target-based algorithm with the drift ratio and amplitude ratio reduced to satisfactory ranges whereas the traditional method fails to correct these signals.

Demand-Based Optimal Design of Storage Tank with Inerter System

A parameter optimal design method for a tank with an inerter system is proposed in this study based on the requirements of tank vibration control to improve the effectiveness and efficiency of vibration control. Moreover, a response indicator and a cost control indicator are selected based on the control targets for liquid storage tanks for simultaneously minimizing the dynamic response and controlling costs. These indicators are reformulated through a random vibration analysis under virtual excitation. The problem is then transformed from a multiobjective optimization problem to a single-objective nonlinear problem using the -constraint method, which is consistent with the demand-based method. White noise excitation can be used to design the tank with the inerter system under seismic excitation to simplify the calculation. Subsequently, a MATLAB-based calculation program is compiled, and several optimization cases are examined under different excitation conditions. The effectiveness of the demand-based method is proven through a time history analysis. The results show that specific vibration control requirements can be met at the lowest cost with a simultaneous reduction in base shears and overturning base moments.

Simplified variational iteration method for solving ordinary differential equations and eigenvalue problems

A simplified variational iteration method is proposed to solve high-order homogeneous or nonhomogeneous linear ordinary differential equation and ordinary differential equation eigenvalue problems more efficiently and conveniently. The simplification includes two aspects: (1) explicitly deducing the general form of the differential equation for the identification of the general Lagrange multiplier while avoiding the complexity of variational calculations during identification and (2) simplifying the iterative expressions to reduce the computational work of each iteration. Three ordinary differential equations in mechanics are solved by this simplified variational iteration method, which proves that it is valid and more concise than traditional methods. To make the method more practical, it is suggested that some complicated analytical derivations be executed numerically, thereby achieving a simplified semi-analytical variational iteration method that can be easily implemented by computer programs. The method is then used to numerically solve two complex ordinary differential equation problems derived from the continuum analysis of tall building structures: a sixth-order nonhomogeneous ordinary differential equation with complex boundary conditions and a sixth-order ordinary differential equation eigenvalue problem. Numerical computer programs are developed for these two problems, and corresponding examples are provided to verify the accuracy and efficiency of the simplified variational iteration method in solving complex ordinary differential equation problems.