Accurate Displacement Estimation Research Articles

Sensorless model-based displacement estimator for piezoelectric actuator through a practical three-stage mechanism

Piezoelectric elements (PEMs) are used in a variety of applications. In this paper, we developed a new simple sensorless method for a Piezoelectric Actuator (PEA), which includes piezostack elements and a three-stage amplification mechanism.This research focuses on a piezoelectric actuator that incorporates a three-stage amplification system, where the outcome of one stage serves as the input for the subsequent one. The actuator receives two types of inputs: the voltage applied to the piezoelectric elements and the mechanical load it carries. Its output is defined by the rotation angle observed at the end of the third amplification stage. To indirectly measure the actuator's displacement, a basic external circuit is utilized.The precise movement of these actuators is essential. To circumvent the high costs and limitations associated with highly accurate displacement sensors, there has been a growing interest in sensorless control methods. Certain electrical signals, when measured, can provide an estimation of displacement. However, induced voltage measurements are not effective for piezoelectric stacks. Two more promising measures are the voltage and current of the piezoelectric material.Given that the electrical charge on these actuators closely reflects their displacement with minimal hysteresis across a broad frequency spectrum, it's proposed that displacement can be effectively gauged through current measurements that assess charge.The core contribution of this paper is the introduction and validation, both theoretically and experimentally, of a hybrid algorithm that leverages these two electrical signals to enhance the accuracy of displacement estimates. This was confirmed using a laboratory setup.The primary benefit of this research is the presentation of a straightforward sensorless control algorithm, poised for further exploration within the realm of piezoelectric actuators. The simplicity of both the theoretical model and the sensorless technique facilitates their application across a diverse range of piezoelectric actuators and amplification systems, thereby streamlining the design, modeling, and control strategy development for various actuators.The innovation of this study stems from the application of an uncomplicated sensorless estimation algorithm, coupled with a system-level perspective on piezoelectric actuators. This approach utilizes a simple, adaptable model suitable for a wide array of applications and operational techniques.

Variational mode decomposition-based multirate data-fusion framework for estimating structural dynamic displacement by integrating vision- and acceleration-based measurements

Dynamic displacement is a crucial parameter in structural health monitoring (SHM) for assessing the safety, dependability, and suitability of structures under various types of excitations. Computer vision-based methods for dynamic displacement estimation have attracted much interest owing to their cost-effectiveness and convenience. However, these methods are limited by their low sampling rates and high data sensitivity. To compensate for these limitations, methods for combining data obtained from other sensors have been proposed. In this study, an experimental data-fusion framework for displacement estimation based on variational mode decomposition (VMD) was developed to leverage the advantages of vision- and acceleration-based measurements. The measurements were decomposed into ensembles of modes and recomposed to reconstruct the displacement with a higher accuracy and over a wider frequency range. An optimal mode recomposition method was proposed to achieve optimal mode combinations. Furthermore, this study introduced an improved vision-based displacement measurement method and a VMD-based indirect acceleration measurement method. The proposed framework was validated through four-story RC structure tests, which demonstrated that the method could enhance the accuracy of displacement estimation and extend the feasible frequency range compared with single-source displacement measurements. The method provides a promising solution for more effective health monitoring of modern structures subjected to a wide variety of dynamic loads.

A self-sensing approach for estimating suspension displacement and velocity in semi-active electromagnetic dampers

Electromagnetic damper (EMD) suspension systems have gained significant recognition for their fast response and precise control capabilities. Nonetheless, the necessity of sensor-based control escalates system costs too high and limits its application. This paper introduces an innovative self-sensing approach for semi-active EMD that aims to autonomously acquire vehicle suspension state information without external sensors. The goal is to improve the performance of vibration damping while remaining cost-efficiency. Initially, the EMD is designed and modelled, followed by an analysis of the variable damping principle of the permanent magnet synchronous motor (PMSM). The variable damping EMD model is formulated using the machine-electric coupling equation. Subsequently, a detailed explanation of the principle behind the proposed self-sensing approach is presented. Simulation results confirm its precise capability to estimate the suspension displacement and velocity even in the absence of external sensor input. Moreover, bench experiments for the EMD are conducted to validate the effectiveness of the variable damping and self-sensing approach. Experimental results indicate that the damping characteristic of the EMD can be controlled by manipulating external resistance value. In addition, accurate estimation of suspension displacement and velocity can be achieved under varying excitation conditions, even with changes in damper damping.

Data Fusion for Displacement Estimation and Tracking of UAV Quadrotor in Dynamic Motion

The fusion of MIMU and GPS data is generally used to estimate the displacement and tracking of quadrotor UAVs. Meanwhile, displacement estimation inaccuracies during dynamic motion often occur. This error is caused by noise and limited sensor sampling rate especially occurs when the quadrotor changes its attitude rapidly to generate an instantaneous horizontal force. This paper proposes data fusion based on Kalman filter to estimate orientation and displacement. Experiments were also carried out to verify displacement accuracy, i.e. in single-axis and multi-axis sensor motions. The algorithm combines data from MIMU and GPS sensors so that acceleration data is filled in points where GPS data is not available. With this method, the predicted displacement from the MIMU sensor can be corrected every second with data from the GPS and produce accurate displacement and trajectory estimates.

Evaluation of Atmospheric Phase Correction Performance in 79 GHz Ground-Based Radar Interferometry: A Comparison with 17 GHz Ground-Based SAR Data

Ground-based radar interferometry is capable of measuring target displacement to sub-mm accuracy. W-band ground-based radar has recently been investigated as a potential application for structural health monitoring. On the other hand, the application of W-band ground-based radar for natural slope monitoring is considered in this study due to its advantages in portability and recent cost-effective solutions. In radar interferometry, atmospheric phase screen (APS) is the most relevant phase disturbance that should be corrected for accurate displacement measurement. However, the APS effects in W-band radar interferometry have rarely been discussed. In this context, we study and evaluate the impacts of APS and its potential correction methods for 79 GHz ground-based radar interferometry using multiple-input and multiple-output (MIMO) radar. This paper presents an experimental investigation of a 79 GHz radar system using two types of field experiments conducted in an open flat field and a quarry site. In addition to the W-band radar system, a Ku-band (17 GHz) ground-based synthetic aperture radar (GB-SAR) system was jointly tested to compare different operating frequency bands. The result confirmed the accurate displacement estimation capability of the 79 GHz radar with an appropriate APS correction.

Sparse accelerometer-aided computer vision technology for the accurate full-field displacement estimation of beam-type bridge structures

Computer vision-based sensors are considered effective means to monitor full-field displacements; nevertheless, several limitations prevent their applications in full-scale structures. First, the accuracy of computer vision-based sensors is affected by measured distances. Second, due to the limited frame rate of cameras, computer vision-based sensors cannot record high-frequency responses. To effectively address these issues, a novel full-field displacement estimation approach based on the data fusion of camera-based measurements and limited accelerations was proposed. Full-field pseudo-static displacements were extracted from camera-based measurements, and full-field dynamic displacements were expanded by accelerations at sparse locations based on the modal superposition method. Subsequently, high-fidelity full-field displacements were obtained by data fusion. The proposed approach was numerically and experimentally verified. Further, the full-field displacements of an experimental-scale beam model and a full-scale bridge were estimated by a consumer-grade camera and several accelerometers.

AR-DIC: A Novel Automatic Optical Strategy for Displacement Measurement of the Curved-in-Place Pipe Under Dynamic Fracturing

Curved-In-Place Pipe (CIPP) technology is widely used in urban underground pipeline repair nowadays. However, the lack of automatic global displacement acquisition method makes it still quite challenging to effectively obtain the detailed displacement characteristics of the CIPP pipes under dynamic loads. Herein, we propose a cascade strategy named automatic speckle region extraction digital image correlation (AR-DIC) to achieve the dynamic, efficient and accurate displacement estimation of the CIPP pipelines, so as to determine the variation characters of the CIPP pipelines under dynamic loads. In the first stage, an improved automatic DeepLabv3+ neural network (IA-DeepLabv3+) is meticulously designed to extract the region of interest (ROI) of the CIPP pipeline speckle automatically. A dataset containing the cluttered background and the real experimental speckle are also generated to train the model parameters. Note that this is the first time an automated ROI extraction method has been proposed in CIPP, even in the DIC field. In the second stage, the digital image correlation based on scale-invariant feature transform (SIFT-DIC) algorithm is adopted to calculate the extracted ROI and get the displacement field. Finally, the proposed method is tested on both the simulated and experimental datasets. The experimental results confirm that our method can not only extract the speckle ROI region accurately, but also achieve high-precision calculation of the displacement field.

Multi-Vib

Vibration measurement is vital for fault diagnosis of structures (e.g., machines and civil structures). Different structure components undergo distinct vibration patterns, which jointly determine the structure's health condition, thus demanding simultaneous multi-point vibration monitoring. Existing solutions deploy multiple accelerometers along with their power supplies or laser vibrometers on the monitored object to measure multi-point vibration, which is inconvenient and costly. Cameras provide a less expensive solution while heavily relying on good lighting conditions. To overcome these limitations, we propose a cost-effective and passive system, called Multi-Vib, for precise multi-point vibration monitoring. Multi-Vib is implemented using a single mmWave radar to remotely and separately sense the vibration displacement of multiple points via signal reflection. However, simultaneously detecting and monitoring multiple points on a single object is a daunting task. This is because most radar signals are scattered away from vibration points due to their tilted locations and shapes by nature, causing an extremely weak reflected signal to the radar. To solve this issue, we dedicatedly design a physical marker placed on the target point, which can force the direction of the reflected signal towards the radar and significantly increase the reflected signal strength. Another practical issue is that the reflected signal from each point endures interferences and noises from the surroundings. Thus, we develop a series of effective signal processing methods to denoise the signal for accurate vibration frequency and displacement estimation. Extensive experimental results show that the average errors in multi-point vibration frequency and displacement estimation are around 0.16Hz and 14μm, respectively.

Deformation Prediction of Cihaxia Landslide Using InSAR and Deep Learning

Slope deformation monitoring and analysis are significant in the geological survey of hydraulic engineering. However, predicting future slope deformation is a vital and challenging task for engineers. The accurate estimation of slope displacement is required for the risk assessment of slope stability. This study was conducted using slope deformation data obtained by interferometric synthetic aperture radar. Five typical points of the slope in different zones were selected to establish the prediction model. Based on the observed data, a prediction model based on long short-term memory (LSTM) and autoregressive integrated moving average (ARIMA) was proposed. Firstly, ARIMA and LSTM models were used separately to predict slope deformation. Root mean square error, mean absolute error, and R2 were used to evaluate the performance of the models, and the results showed that LSTM is more effective than ARIMA. It denotes that the LSTM model can catch the trend in the data sequence with time, and ARIMA is good at predicting the bias in the stationary data sequence. Then, the predictions of ARIMA were added to the original data while the new data were fed to the LSTM model. For most data points, our LSTM-ARIMA model achieved good performance, indicating that the model is robust in slope deformation prediction. The effectiveness of the proposed LSTM-ARIMA model will enable engineers to take corresponding measures to prevent accidents before landslides occur.

A Phase Correlation Anti-Noise Displacement Estimation Method Based on PSD Phase Screening

When using digital images to obtain the displacement of a structure, noise is always a factor that greatly affects the accuracy of the displacement results. To overcome this problem, a phase-correlation improvement method, based on phase filtering by phase standard deviation (PSD), is proposed. We use PSD to remove the severe noise interference area in the cross-power spectrum matrix, then the singular value decomposition (SVD) is used to convert the two-dimensional phase to one-dimensional to reduce the difficulty of phase unwrapping. Finally, straight-line fitting is used to obtain the high-precision displacement results. Experiments were carried out using both simulated data and real data. For the simulated data, the absolute accuracy of the proposed method is around 0.3 pixels, while, for the real data, the absolute accuracy of the proposed method is 0.018 mm. The experimental results show that the method can effectively resist noise interference and still obtain accurate displacement estimation results in the case of severe noise.

Nonlinear backstepping hierarchical control of shake table using high‐gain observer

AbstractShake table testing is a common technique used to examine the responses of structures under dynamic loads. Shake table is often regulated using linear controller, such as proportional‐integral‐derivative (PID) controller. However, traditional PID control cannot consider inherent nonlinearities in the structural and control systems. In this paper, a series of novel backstepping control methods, which consider the nonlinearities in the structural and control systems, have been developed. In addition, high‐gain observers, which can provide highly accurate estimation of the shake table displacement, velocity and acceleration, are also developed. The proposed backstepping control methods and high‐gain observers are implemented in a hierarchical framework, where the high‐level backstepping controller generates the command signal for the low‐level controller to execute. A total of four hierarchical backstepping control methods, including the acceleration‐based backstepping hierarchical control (ABHC), the ABHC with high‐gain observer (ABHCO), the displacement‐based backstepping hierarchical control (DBHC) and the DBHC with high‐gain observer (DBHCO), have been implemented. Detailed parameter studies have been conducted to identify the optimized parameters for the proposed hierarchical backstepping control methods. The proposed control method is verified through a series of shake table tests. The experimental results show the ABHC, ABHCO, DBHC and DBHCO can all achieve high‐performance shake table control, especially with superior acceleration tracking over the traditional PID control. Overall, ABHCO achieves the best tracking performance for displacement, velocity and acceleration.

Bi-Directional Semi-Supervised Training of Convolutional Neural Networks for Ultrasound Elastography Displacement Estimation.

The performance of ultrasound elastography (USE) heavily depends on the accuracy of displacement estimation. Recently, convolutional neural networks (CNNs) have shown promising performance in optical flow estimation and have been adopted for USE displacement estimation. Networks trained on computer vision images are not optimized for USE displacement estimation since there is a large gap between the computer vision images and the high-frequency radio frequency (RF) ultrasound data. Many researchers tried to adopt the optical flow CNNs to USE by applying transfer learning to improve the performance of CNNs for USE. However, the ground-truth displacement in real ultrasound data is unknown, and simulated data exhibit a domain shift compared to the real data and are also computationally expensive to generate. To resolve this issue, semisupervised methods have been proposed in which the networks pretrained on computer vision images are fine-tuned using real ultrasound data. In this article, we employ a semisupervised method by exploiting the first- and second-order derivatives of the displacement field for regularization. We also modify the network structure to estimate both forward and backward displacements and propose to use consistency between the forward and backward strains as an additional regularizer to further enhance the performance. We validate our method using several experimental phantom and in vivo data. We also show that the network fine-tuned by our proposed method using experimental phantom data performs well on in vivo data similar to the network fine-tuned on in vivo data. Our results also show that the proposed method outperforms current deep learning methods and is comparable to computationally expensive optimization-based algorithms.

Enhancing sensitivity of the angular displacement measurement based on a hybrid interferometer combining parametric amplification

We theoretically investigate the angular displacement measurement based on a hybrid interferometer combining two optical parametric amplifiers (OPAs), which are used to amplify the phase-sensing intensity and squeeze shot noise. We obtain significant improvement in sensitivity for this modified hybrid interferometer over the Mach–Zehnder interferometer (MZI) combining two OPAs. Finally, the effect of losses on sensitivity is discussed and we find that our scheme has more robust compared with the modified MZI. Our results provide a more accurate angular displacement estimation which has potential applications in precision measurements and quantum sensing.

Virtual Source Synthetic Aperture for Accurate Lateral Displacement Estimation in Ultrasound Elastography.

Ultrasound elastography (USE) is an emerging noninvasive imaging technique in which pathological alterations can be visualized by revealing the mechanical properties of the tissue. Estimating tissue displacement in all directions is required to accurately estimate the mechanical properties. Despite capabilities of elastography techniques in estimating displacement in both axial and lateral directions, estimation of axial displacement is more accurate than lateral direction due to higher sampling frequency, higher resolution, and having a carrier signal propagating in the axial direction. Among different ultrasound imaging techniques, synthetic aperture (SA) has better lateral resolution than others, but it is not commonly used for USE due to its limitation in imaging depth of field. Virtual source synthetic aperture (VSSA) imaging is a technique to implement SA beamforming on the focused transmitted data to overcome the limitation of SA in depth of field while maintaining the same lateral resolution as SA. Besides lateral resolution, VSSA has the capability of increasing sampling frequency in the lateral direction without interpolation. In this article, we utilize VSSA to perform beamforming to enable higher resolution and sampling frequency in the lateral direction. The beamformed data are then processed using our recently published elastography technique, OVERWIND. Simulation and experimental results show substantial improvement in the estimation of lateral displacements.

Bridge displacement estimation by fusing accelerometer and strain gauge measurements

For large-span bridge monitoring, displacement measurement is essential. However, it remains challenging to accurately estimate bridge displacement. When displacement is calculated by the double integration of acceleration, a low-frequency drift appears in the estimated displacement. Displacement can also be estimated from strains based on the Euler–Bernoulli beam theory. However, prior knowledge of the mode shapes and the neutral axis location of the target bridge are required for strain–displacement transformation. In this study, we propose a finite impulse response filter-based displacement estimation technique by fusing strain and acceleration measurements. First, the relationship between displacement and strain is established, and the parameter associated with this strain–displacement transformation is estimated from strain and acceleration measurements using a recursive least squares algorithm. Next, the low-frequency displacement estimated from the strain measurements and the high-frequency displacement obtained from an acceleration measurement are combined for high-fidelity displacement estimation. The feasibility of the proposed technique was examined via a series of numerical simulations, a lab-scale experiment, and a field test. The uniqueness of this study lies in the fact that the displacement and the unknown parameter in strain–displacement transformation are estimated simultaneously and the accuracy of displacement estimation is improved in comparison with those of previous data fusion techniques.

A Displacement Estimated Method for Real Time Tissue Ultrasound Elastography

As an important means of medical imaging, elastic imaging is an indispensable part of mobile telemedicine. Ultrasound elastography has become a research hotspot because it can accurately measure soft tissue lesions. Displacement estimation is the most important step in ultrasound elastography. At present, the phase zero search method is an accurate and fast displacement estimation method. However, when the displacement exceeds 1/4 wavelength, it is invalid. The accuracy of block matching method is not high, but it is suitable for large displacement, so it can overcome this shortcoming. It is worth noting that the quality-guided block matching method has good robustness under complex mutation conditions. It can provide prior knowledge to increase the robustness of the phase-zero search under large displacement conditions. So we propose a novel displacement estimation method for real time tissue ultrasound elastography, which combines the quality-guided block matching method and the phase-zero search method. The experimental results show that this method is more accurate, faster and robust than other displacement estimation methods.

Adaptive Full-Order Displacement Observer for Sensorless Resonant Frequency Tracking Control of Linear Oscillatory Machines

Linear oscillatory machines are becoming more widely used in refrigeration compressors due to advantages of compact volume, little maintenance, and so on. In order to further increase the efficiency and reduce the cost of the whole system, both resonant frequency tracking control and sensorless control strategies should be implemented simultaneously. In this article, an adaptive full-order observer with simple structure and less computation is proposed, which can not only provide accurate displacement estimation signals for the system piston stroke control, but also achieve resonant frequency tracking control through the estimation of machine parameters. The system stability analysis proves the quick convergence of the proposed observer, and comprehensive simulation and experimental results demonstrate the effectiveness of the proposed algorithm.

Evaluation of liquefaction-induced lateral displacement using Bayesian belief networks

Liquefaction-induced lateral displacement is responsible for considerable damage to engineered structures during major earthquakes. Therefore, an accurate estimation of lateral displacement in liquefaction-prone regions is an essential task for geotechnical experts for sustainable development. This paper presents a novel probabilistic framework for evaluating liquefaction-induced lateral displacement using the Bayesian belief network (BBN) approach based on an interpretive structural modeling technique. The BBN models are trained and tested using a wide-range case-history records database. The two BBN models are proposed to predict lateral displacements for free-face and sloping ground conditions. The predictive performance results of the proposed BBN models are compared with those of frequently used multiple linear regression and genetic programming models. The results reveal that the BBN models are able to learn complex relationships between lateral displacement and its influencing factors as cause-effect relationships, with reasonable precision. This study also presents a sensitivity analysis to evaluate the impacts of input factors on the lateral displacement.

Load-carrying capacity evaluation of girder bridge using moving vehicle

Efficient and reliable load-carrying capacity evaluation of deficient bridges is essential for bridge maintenance and management. Based on load-carrying capacity evaluation of an existing bridge, operator can formulate strategies and implement countermeasures such as repair, strengthening or traffic regulation. Currently, static load test is used widely for evaluation of bridge load-carrying capacity. The test, however, is often considered expensive and requires massive traffic closure that hinders frequent implementation on highway or bridges in the rural area. In this paper, an efficient method for load-carrying capacity evaluation of girder bridges based on displacement under moving vehicle is proposed. The method consists of three main procedures, namely, radar-based dynamic displacement measurement under truck pass-by test, influence line extraction, and estimation of the displacement under the static load test scenario. Based on these procedures, evaluation of load-carrying capacity is conducted following the AASHTO manual. The method was verified in numerical simulations using three-dimensional finite element model of typical girder bridge under vehicle loading. Effects of vehicle weight, vehicle speed, and road roughness on the accuracy of displacement estimation were investigated in the numerical simulations. Full-scale implementation of the method was conducted on a simply supported prestressed concrete girder bridge to investigate feasibility of the proposed method and to provide guidance for practical application. The results reveal that load rating factor of the girders can be reliably evaluated. The evaluation process was also more effective and economical than the conventional method.

A new PDE-based resolution enhancement technique for the analysis of low SNR particle displacement images

Speckle images have found multiple applications in image-based measurement techniques, where the objective of measurement is the estimation of speckle displacements between two often consecutive images. Depending on the characteristics of a measurement system and its measurands, the signal-to-noise ratio (SNR) of recorded images may become low and even marginal. One solution to improve the accuracy of speckle displacement estimation in such cases is the use of super-resolution methods. In this article a robust and versatile partial differential equation based resolution enhancement method is presented for the analysis of low SNR speckle displacement signals. The application of the method to synthetic one-dimensional and two-dimensional signals as well as actual particle displacement images indicate that the method is capable of reducing noise effects and partially recovering lost correlation, which in turn makes the selection of smaller interrogation windows and achieving higher resolution and accuracy of displacement estimation possible. The method is applicable to both speckle and particle displacement images.