The tomography technique is an effective way to quantitatively evaluate damage from reconstruction imaging in structure health monitoring (SHM). The reconstruction algorithm for the probabilistic inspection of damage (RAPID) algorithm based on the signal difference coefficient (SDC) feature is a promising approach due to its superior performance. This paper focuses on the influence of different patterns of PZT (Lead Zirconate Titanate) sensor array configurations, i.e., the circular, square, and parallel array, on reconstruction image qualities for evaluating hole and crack damage. Variable shape parameters are applied to account for the unequal damage distances of different actuator-sensor pairs. Considering the directionality scattering fields of cracks, the angular scattering pattern of the SDC values are studied by simulation. The SDC variations for different groups of sensing paths at the same actuator are applied to predict the crack orientation. An improved RAPID algorithm is proposed by defining an additional SDC value of 1 in the path along the predicted crack orientation, which is determined by the point of the actuator causing the minimal SDC variation and the center point of the initial reconstruction image of the crack. The results show that the improved RAPID algorithm is effective for the evaluation of crack damage. Reconstruction image qualities with three PZT sensor array configurations for both holes and cracks are compared. The research is significant for selecting the PZT sensor array configuration in SHM.

Directional piezoelectric sensors can detect the Lamb wave propagation direction to locate damage in structural health monitoring (SHM). The directivity of the round piezoelectric fiber is exploited with a 0°/45°/90° rosette configuration to acquire flexural Lamb wave signals. The directional response of the piezoelectric fiber under narrowband tone-burst excitation is theoretically deduced. Experimental tests are conducted to demonstrate the directivity and the frequency response property of the piezoelectric fiber under different excitation central frequencies in comparison with the MFC, rectangular piezoelectric sheet, and circular piezoelectric disc. Continuous wavelet transform (CWT) is applied to extract the maximum response amplitude information of the acquired Lamb wave signal at a central frequency. Experimental test results indicate that the piezoelectric fiber is capable to be used as a Lamb wave directional sensor than other piezoelectric sensors. A numerical estimation method for the Lamb wave propagation direction is proposed by defining an error function between the theoretical and experimental normalized response amplitude. The proposed method is generally applicable for different rosette configurations. Experimental results validate the accuracy of the proposed estimation method. The research results are significant to design or select the piezoelectric sensor to measure Lamb wave signals.

The large-scale rotary machine with multi-supporting, such as rotary kiln and rope laying machine, is the key equipment in the architectural, chemistry, and agriculture industries. The body, rollers, wheels, and bearings constitute a chain multibody system. Axis line deflection is a vital parameter to determine mechanics state of rotary machine, thus body axial vibration needs to be studied for dynamic monitoring and adjusting of rotary machine. By using the Riccati transfer matrix method, the body system of rotary machine is divided into many subsystems composed of three elements, namely, rigid disk, elastic shaft, and linear spring. Multiple wheel-bearing structures are simplified as springs. The transfer matrices of the body system and overall transfer equation are developed, as well as the response overall motion equation. Taken a rotary kiln as an instance, natural frequencies, modal shape, and response vibration with certain exciting axis line deflection are obtained by numerical computing. The body vibration modal curves illustrate the cause of dynamical errors in the common axis line measurement methods. The displacement response can be used for further measurement dynamical error analysis and compensation. The response overall motion equation could be applied to predict the body motion under abnormal mechanics condition, and provide theory guidance for machine failure diagnosis.

A multibody dynamic model is developed for dynamic analysis of a 5-DOF flexure-based nanopositioning stage in the projection optical system of the semiconductor lithography in this paper. The 5-DOF stage is considered as an assembly of rigid bodies interconnected by elastic flexure hinges. Considering the length effects of flexure hinges, multibody dynamic equations are established according to spatial motions of rigid bodies by using Lagrangian method. The shear effects and the torsional compliances of the commonly used circular flexure hinges are considered to enhance the modeling accuracy. The accuracies of various out-of-plane compliance formulas are also discussed. To verify the developed dynamic model, the finite element analyses (FEA) by using ANSYS and modal hammer experimental tests of the primary flexure-based composition structures and the integral 5-DOF stage are performed. The analytical modal frequencies are well in agreement with FEA and experimental test. The results are significant to analyze and optimize the 5-DOF flexure-based nanopositioning stage.

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