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The travel time computation of microseismic waves in different directions (particularly, the diagonal direction) in three-dimensional space has been found to be inaccurate, which seriously affects the localization accuracy of three-dimensional microseismic sources. In order to solve this problem, this research study developed a method of calculating the P-wave travel time based on a 3D high-order fast marching method (3D_H_FMM). This study focused on designing a high-order finite-difference operator in order to realize the accurate calculation of the P-wave travel time in three-dimensional space. The method was validated using homogeneous velocity models and inhomogeneous layered media velocity models of different scales. The results showed that the overall mean absolute error (MAE) of the two homogenous models using 3D_H_FMM had been reduced by 88.335%, and 90.593% compared with the traditional 3D_FMM. On that basis, the three-dimensional localization of microseismic sources was carried out using a particle swarm optimization algorithm. The developed 3D_H_FMM was used to calculate the travel time, then to conduct the localization of the microseismic source in inhomogeneous models. The mean error of the localization results of the different positions in the three-dimensional space was determined to be 1.901 m, and the localization accuracy was found to be superior to that of the traditional 3D_FMM method (mean absolute localization error: 3.447 m) with the small-scaled inhomogeneous model.

The phase-to-height imaging model, as a three-dimensional (3D) measurement technology, has been commonly applied in fringe projection to assist surface profile measurement, where the efficient and accurate calculation of phase plays a critical role in precise imaging. To deal with multiple extra coded patterns and 2π jump error caused to the existing absolute phase demodulation methods, a novel method of phase demodulation is proposed based on dual variable-frequency (VF) coded patterns. In this paper, the frequency of coded fringe is defined as the number of coded fringes within a single sinusoidal fringe period. First, the effective wrapped phase (EWP) as calculated using the four-step phase shifting method was split into the wrapped phase region with complete period and the wrapped phase region without complete period. Second, the fringe orders in wrapped phase region with complete period were decoded according to the frequency of the VF coded fringes and the continuous characteristic of the fringe order. Notably, the sampling frequency of fast Fourier transform (FFT) was determined by the length of the decoding interval and can be adjusted automatically with the variation in height of the object. Third, the fringe orders in wrapped phase region without complete period were decoded depending on the consistency of fringe orders in the connected region of wrapped phase. Last, phase demodulation was performed. The experimental results were obtained to confirm the effectiveness of the proposed method in the phase demodulation of both discontinuous objects and highly abrupt objects.

The accurate measurement of slope displacement profiles using a fiber Bragg grating flexible sensor is limited due to the influence of accumulative measurement errors. The measurement errors vary with the deformation forms of the sensor, which dramatically affects the measurement accuracy of the slope displacement profiles. To tackle the limitations and improve the measurement precision of displacement profiles, a segmental correction method based on strain increments clustering was proposed. A K-means clustering algorithm was used to automatically identify the deformation segments of a flexible sensor with different bending shapes. Then, the particle swarm optimization method was adopted to determine the correction coefficients corresponding to different deformation segments. Both finite element simulations and experiments were performed to validate the superiority of the proposed method. The experimental results indicated that the mean absolute errors (MAEs) percentages of the reconstructed displacements using the proposed method for six different bending shapes were 1.87%, 5.28%, 6.98%, 7.62%, 4.16% and 8.31%, respectively, which had improved the accuracy by 26.83%, 18.94%, 29.49%, 26.35%, 7.39%, and 19.65%, respectively. Therefore, it was confirmed that the proposed correction method was competent for effectively mitigating the measurement errors and improving the measurement accuracy of slope displacement profiles, and it presented a vital significance and application promotion value.

The measurement accuracy of the intelligent flexible morphological sensor based on fiber Bragg grating (FBG) structure was limited in the application of geotechnical engineering and other fields. In order to improve the precision of intellisense for displacement, an FBG implantable flexible morphological sensor was designed in this study, and the classification morphological correction method based on conjugate gradient method and extreme learning machine (ELM) algorithm was proposed. This study utilized finite element simulations and experiments, in order to analyze the feasibility of the proposed method. Then, following the corrections, the results indicated that the maximum relative error percentages of the displacements at measuring points in different bending shapes were determined to be 6.39% (Type 1), 7.04% (Type 2), and 7.02% (Type 3), respectively. Therefore, it was confirmed that the proposed correction method was feasible, and could effectively improve the abilities of sensors for displacement intellisense. In this paper, the designed intelligent sensor was characterized by temperature self-compensation, bending shape self-classification, and displacement error self-correction, which could be used for real-time monitoring of deformation field in rock, subgrade, bridge, and other geotechnical engineering, presenting the vital significance and application promotion value.

We proposed and studied an impact detection system based on a fiber Bragg grating (FBG) sensor array and multiple signal classification (MUSIC) algorithm to determine the location and the number of low velocity impacts on a carbon fiber-reinforced polymer (CFRP) plate. A FBG linear array, consisting of seven FBG sensors, was used for detecting the ultrasonic signals from impacts. The edge-filter method was employed for signal demodulation. Shannon wavelet transform was used to extract narrow band signals from the impacts. The Gerschgorin disc theorem was used for estimating the number of impacts. We used the MUSIC algorithm to obtain the coordinates of multi-impacts. The impact detection system was tested on a 500 mm × 500 mm × 1.5 mm CFRP plate. The results show that the maximum error and average error of the multi-impacts’ localization are 9.2 mm and 7.4 mm, respectively.