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This paper presents a new technique to estimate the dynamic displacement based on strain mode shapes of beam structures with strain sensors. Strain mode shapes are first estimated from the cross-correlation function of the measured dynamic strain data. Then, the displacement mode shapes can be estimated from the strain mode shapes based on the displacement-strain relation. For an oscillating beam structure under service conditions, the dynamic response can be expressed as the superposition of their corresponding mode shapes weighed by the corresponding modal coordinates. Thus, by knowing the strain mode shapes and strain data, the corresponding modal coordinates can be estimated. The dynamic displacement can then be estimated by the obtained displacement mode shapes and modal coordinates. This method is verified by numerical simulations of a simply supported beam subjected to impulsive excitation and earthquake excitation. Experimental tests of a simply supported beam under various hammering excitations are also conducted to verify the effectiveness of the proposed method. Both the numerical and test results show that the proposed method can estimate the dynamic displacement of beam structures with high accuracy.

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Orientation estimation from magnetic, angular rate, and gravity (MARG) sensor array is a key problem in mechatronic-related applications. This paper proposes a new method in which a quaternion-based Kalman filter scheme is designed. The quaternion kinematic equation is employed as the process model. With our previous contributions, we establish the measurement model of attitude quaternion from accelerometer and magnetometer, which is later proved to be the fastest (computationally) one among representative attitude determination algorithms of such sensor combination. Variance analysis is later given enabling the optimal updating of the proposed filter. The algorithm is implemented on real-world hardware where experiments are carried out to reveal the advantages of the proposed method with respect to conventional ones. The proposed approach is also validated on an unmanned aerial vehicle during a real flight. Results show that the proposed one is faster than any other Kalman-based ones and even faster than some complementary ones while the attitude estimation accuracy is maintained.

In this study, the recently developed analytical mode decomposition with Hilbert transform was extended to the decomposition of a non-stationary and nonlinear signal with two or more amplitude-decaying and frequency-changing components. The bisecting frequency in the analytical mode decomposition became time-varying, and could be selected between any two adjacent instantaneous frequencies estimated from a preliminary wavelet analysis. The mathematical foundation for this new extension was integration of the bisecting frequency over time so that the original time series is actually decomposed in the phase domain. Parametric studies indicated that the analytically derived components are insensitive to the selection of bisecting frequency and the presence of up to 20% noise, sufficiently accurate when the sampling rate meets the Nyquist–Shannon sampling criterion, and applicable to both narrowband and wideband frequency modulations even when the signal amplitude decays over time. The proposed analytical mode decomposition is superior to the empirical mode decomposition and wavelet analysis in the preservation of signal amplitude, frequency and phase relations. It can be directly applied for system identification of buildings with time-varying stiffness.

This paper uses strains measured by fiber Bragg grating (FBG) sensors to estimate the static or dynamic deflection curve of bending beam structures. The deflection estimation method is only based upon the geometric equations of a beam structure without knowing the material information. At each cross section of a beam structure, two FBG strain sensors are installed, and the curvature at the cross section can be estimated by using the two measured strains from the geometric equation. Then the curvature function is assumed as a polynomial function and the coefficients can be estimated using least squares method. Finally, the deflection curve is estimated by integrating the curvature function twice. For dynamic deflection estimation, since only the geometric equations are used, and at each time step, the geometric equations can be also used for a dynamic system. Therefore, at each time step, the deflection can be estimated using the proposed method and the dynamic deflection can be finally obtained. The method is verified by the simulations of a continuous beam under static loads and experimental tests of a simply supported beam under various static loads. A simply support beam under moving loads is also simulated to verify the method for dynamic deformation estimation. All the numerical and test results show that the method can estimate the static and dynamic deflection curve of beam structures with a high accuracy.

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