Displacement Measurement Error Research Articles

Non-iterative pose estimation method based on the polarization information via a parallelogram

As for vision-based pose estimation, which is also known as the PnP problem, non-iterative algorithms are more efficient. Precise extraction of 2D projections of feature points is important. If the projections of the feature points are not accurately extracted, the pose estimation accuracy is reduced. Under the condition of natural light, a camera captures the images of feature points, and the existence of high-light regions in the image affects the extraction accuracy of 2D projections of feature points, which reduces the number of effective feature points and leads to poor pose estimation accuracy. In the redundant cases (n > 4), redundant feature points are introduced as additional information, increasing the number of effective feature points to reduce the impact of high-light regions and improve the pose estimation accuracy. For the non-redundant cases (n = 4), it was difficult to ensure pose estimation accuracy. To solve this problem, a non-iterative pose estimation method based on the optimum polarization angle via four corner points of a parallelogram was proposed in this study. First, a model for solving optimum polarization angle was established. Thereafter, on the premise of the optimum polarization angle, the images were captured. Finally, the projections of the four corner points of a parallelogram were extracted, and the object pose was solved non-iteratively according to the four corner points. The corner point extraction experimental results show that the slope difference between the two parallel sides of each parallelogram under the condition of optimum polarization angle is less than that under the condition of natural light, thereby proving the improvement of the imaging quality. Measurement accuracy verification experiments prove that our pose estimation algorithm and the optimum polarization angle is the best combination to improve the non-iterative pose estimation accuracy in non-redundant cases. In the measurement range of −60-+60°, the angle measurement error was less than ±0.0491°. In the measurement range of 0–20 mm, the displacement measurement error was less than ±0.0435 mm.

Improving the tensile property calculations with plastic zone radius measurements in depth-sensing spherical indentation tests

Depth-sensing spherical indentation tests (SITs) have been widely used in tensile property calculations, but the accuracy and reproducibility of calculations may be significantly influenced by displacement measurement errors. Taking two representative tensile property calculation methods as examples, namely the analytical and numerical methods, the rationale as to why accurate and reproducible tensile property calculations cannot be expected from the depth-sensing SITs was discussed in detail. Subsequently, the proportional limit σ0 calculation from plastic zone radius rp measurements, which was analytically developed in the expanding cavity model (ECM) and experimentally measured by digital image correlation (DIC), was introduced to enhance the accuracy and reproducibility of the two representative methods. Principles for setting the strain threshold εth were established, and factors influencing the σ0 calculation from rp measurements were investigated through the optical system, the friction condition, the hardening behaviors of specimen materials, and the indentation depth. Through finite element calculations, it was proven that tensile property calculations at the existence of displacement measurement errors, particularly the constant error from the origin correction, can be significantly improved with the introduction of rp measurements. Similar findings were also observed in experiments on four metals that exhibited different hardening behaviors.

Measurement of energy spectrum by using 100 eyes Tomographic PIV

PIV is one of the methods to measure velocity in a flow field, but its dynamic velocity range is narrower than other flow velocimeter. This disadvantage is particularly apparent in measurements of spectrum in turbulent boundary layers, where the higher wave number side of the spectrum cannot be measured with high accuracy. In this study, we captured images of the same particle in the flow field from many different direction simultaneously, and reduced the measurement error of the particle displacement by averaging the acquired particle positions, so called ‘Multiple Eye PIV’ [Maekawa, A., Sakakibara, J., 2018, Meas. Sci. Tech., 29, 064011]. We applied this method to obtain the energy spectrum in a turbulent pipe flow aiming for resolving higher wave number. Particle images were captured by a single high-speed CMOS camera (Fastcam Nova S6, 6000 fps, Photron) through a mirror array consists of 110 flat mirrors arranged in the shape of an axisymmetric ellipsoid (Fig.1), as shown in Fig.2. The images were evaluated by Tomographic PIV method to resolve three-dimensional velocity field. Fig.3 shows energy spectrum in a pipe measured by Tomographic-PIV with number of mirrors, N, up to 100 in addition to the 2D2C-PIV with a single mirror. Although the spectrum curve for the result of Tomographic-PIV begins to depart from the reference curve at wavenumber beyond 10-1 , such wavenumber grows as N increases, and consequently the plateau of the curve appeared at lower energy. Such a downward shift of the plateau is expected due to the improvement of the dynamic velocityrange, which is approximately one order in energy, i.e. three times in velocity, found between N=4 and 100. Note that the cases of N=4 and 40 loses the dynamic range against the 2C2D-PIV case. From the above, we can summarize that the advantage of Multiple Eye PIV over the 2C2D-PIV is effective when the number of mirrors is more than 40. In this experiment, the issue is that particles images flickered. In order to resolve this issue, we tried to use fluorescent particles, and obtained a clear particle images in the following experiment. We are now analyzing whether the energy spectrum can be measured with higher accuracy due to improved resolution of the particles.

Simulation of gymnastics performance based on MEMS sensor

The development and progress of multi-sensor data fusion theory and methods have also laid the foundation for the research of human body posture tracking system based on inertial sensing. The main research in this paper is the simulation of gymnastics performance based on MEMS sensors. In the preprocessing to reduce noise interference, this paper mainly uses median filtering to remove signal glitches. This article uses virtual character models for gymnastics performances. The computer receives sensor data from the sink node of the motion capture device through a Bluetooth communication module. The unit calculates the quaternion output from the dynamic link library of sensor data processing, calculates the rotation amount and coordinate offset of each sensor node’s limb, and uses the character model to realize the real-time rendering of the virtual character model. At the same time, it controls the storage of sensor data, the drive of the model, and the display of the graphical interface. When a gesture action is about to occur, a trigger signal is given to the system to mark the beginning of the action, so as to obtain the initial data of each axis signal of the MEMS sensor. When the gesture action is completed, give the system a signal to end the action. Mark the end of the action, so that you can capture the original signal data during the beginning and end of the gesture action. In order to ensure the normal communication between PS and PL, it is necessary to test the key interfaces involved. Because the data received by the SPI acquisition module is irregular, it is impossible to verify whether the data is wrong, so the SPI acquisition module is replaced with a module that automatically increments data, and the IP core is generated, and a test platform is built for testing. The data shows that the average measurement error of X-axis displacement of the space tracking system is 8.17%, the average measurement error of Y-axis displacement is 7.51%, the average measurement error of Z-axis displacement is 9.72%, and the average error of three-dimensional space measurement is 8.7%. The results show that the MEMS sensor can accurately recognize the action with high accuracy.

INTERNAL SPECKLE PATTERN QUALITY ASSESSMENT AND OPTIMAL SELECTION OF VOXEL POINTS FOR DIGITAL VOLUME CORRELATION

Digital volume correlation (DVC) is a powerful experimental tool for quantitative 3D internal deformation measurement throughout the interior of materials or biological tissues. By comparing the volumetric images acquired at the reference and deformed states by a volumetric imaging facility (e.g., X-ray CT), DVC provides full-field displacements with subvoxel accuracy and full-field strain maps. When using DVC method for internal deformation measurement, the quality of internal speckle pattern of a test sample has an important impact on the accuracy and precision of the measured displacements. In this work, theoretical analysis and numerical simulation experiments are firstly performed to assess the quality of internal speckle patterns. The results show that the displacement measurement error of DVC is negative correlation with the sum of square of subvolume intensity gradient (SSSIG) of a subvolume. Thus, the SSSIG value of a subvolume can be used as a simple and effective metric for quality assessment of its internal speckle pattern. In practical DVC analyses, increasing the SSSIG parameter of a subvolume helps to improve the measurement accuracy and precision of DVC. Despite the SSSIG in a subvolume can be increased by enlarging its subvolume size, this simple approach, however, would lead to increased calculation burden. With a purpose to increase SSSIG without significantly increase the amount of calculation, this paper further proposes a method for optimal selection of calculation voxel points in subvolumes. Specifically, the voxel points with small gray gradients in a subvolume are excluded from DVC calculation to decrease the amount of calculation when increasing the size of the subvolume. The efficacy of the presented voxel point optimal selection method is validated by analyzing computer simulated and experimentally obtained volume images. Experimental results reveal that the proposed voxel point selection method is capable of reducing the calculation burden when increasing the subvolume size to increase the SSSIG parameters.

Grating-based 2D displacement measurement with quadruple optical subdivision of a single incident beam.

We propose a new symmetrical heterodyne grating displacement measurement method, based on 2D grating and single diffraction quadruple subdivision method. Using a dual-frequency laser with a wavelength of 632.8 nm, output power of 2.2 mW, and a 1200 l/mm 2D grating, eight diffracted light beams interfere in pairs in the X and Y directions through a turning element. The detection system's measurement accuracy was assessed experimentally. The system measurement resolution in the X and Y directions is better than 3 nm; the grating displacement measurement errors within a 10 mm range are better than ±30 nm and ±40 nm, and the repeatability error is better than ±25 nm. The method is not only applicable to nanoscale 2D displacement measurement technology but also can be used for ultra-precision positioning and ultra-precision processing, with the potential for picometer-level improvement.

Random forest assisted vector displacement sensor based on a multicore fiber.

We proposed a two-dimensional vector displacement sensor with the capability of distinguishing the direction and amplitude of the displacement simultaneously, with improved performance assisted by random forest, a powerful machine learning algorithm. The sensor was designed based on a seven-core multi-core fiber inscribed with Bragg gratings, with a displacement direction range of 0-360° and the amplitude range related to the length of the sensor body. The displacement information was obtained under a random circumstance, where the performances with theoretical model and random forest model were studied. With the theoretical model, the sensor performed well over a shorter linear range (from 0 to 9 mm). Whereas the sensor assisted with random forest algorithm exhibits better performance in two aspects, a wider measurement range (from 0 to 45 mm) and a reduced measurement error of displacement. Mean absolute errors of direction and amplitude reconstruction were decreased by 60% and 98%, respectively. The proposed displacement sensor shows the possibility of machine learning methods to be applied in point-based optical systems for multi-parameter sensing.

Multitarget fiber high-precision position detection method based on a front light source

Fiber positioning technology is widely used in spectroscopic telescopes, and the accurate identification of the fiber position on the focal plane directly affects the efficiency of the astronomical spectrum. At present, fiber positioning usually uses the “back-illuminate” technique to illuminate one end of the fiber. The other end of the fiber is used for detection. The fiber could be stressed or twisted during locator motion, resulting in a difference between the detected fiber position and the actual fiber core. However, the fiber-optic back-illuminated device in the spectrometer system increases the complexity of the system and the time loss of fiber positioning. This paper attempts to use a new method combining image processing with deep learning to identify the fiber ferrule by the front-illuminated method. We built an experimental platform in the lab and experimented with a CMOS camera and telecentric lens. We tested the repeated errors and displacement measurement errors of the two methods. A series of comparative experimental results show that the final detection accuracy of this method can meet the needs of optical fiber positioning in the laboratory, although it has not yet reached the accuracy of the back-illuminated approach. In the future, if the light source and fiber ferrule were specifically designed for the front-illuminated method, its accuracy could be further improved.

A Monocular Vision Relative Displacement Measurement Method Based on Bundle Adjustment Optimization and Quadratic Function Correction

In order to meet the requirements of high-precision target displacement measurement, this paper proposed a measurement method based on monocular vision measurement system by which the advantages of simple structure, convenient debugging, easy to install and calibrate is recognized. This method first uses the bundle adjustment algorithm with conditional constraints to optimize the solution results of the orthogonal iterative algorithm, then calculates the relative poses of the optimization results, finally establishes an error correction model to perform secondary optimization on the relative poses. The experimental results show that the method proposed in this paper can reduce more than 54% average error of displacement measurement results, and the error between the final displacement measurement results and the actual displacement values is controlled at 0.4mm level, which proves that the method has good practical value.

The Influence and Compensation Method of Eccentricity for Cylindrical Specimens in Eddy Current Displacement Measurement.

The eddy current displacement sensor (ECDS) is used to realize the precise detection of the rotor radial position in the magnetic suspension motor. The eccentricity between the probe axis and the measured surface normal reduces the measurement accuracy. An ECDS mathematical model is established to analyze the influence of the measured surface curvature and eccentricity on detection results. The eddy current density distribution law of the measured surface is obtained by using the finite element method (FEM). The experimental platform is set up based on the practical engineering structure, which contains two kinds structures of the single probe and the differential. The compensation method is introduced to reduce the error caused by the eccentricity. The displacement measurement error with and without compensation are tested separately. The results show that the largest full-scale error is less than 0.8% after compensation in the single probe structure, and 0.6% in the differential structure. For the engineering application, the orthogonal direction measured value is used as the eccentricity, and the compensation order of big then small is proposed. It is thus proved that the compensation method provides a guarantee for accurate feedback and control of the rotor radial position in the magnetic suspension motor system.

Effects of incident beam deviation from the center of a cat's eye retro-reflector on the measurement accuracy of a laser tracing system

This paper proposed a method of analyzing the measurement accuracy of a laser tracing system using the deviation of the incident beam from the center of a cat's eye retro-reflector. Based on the laser tracing system's measurement principle, a corresponding model is established to analyze the influence of the incident beam deviation from the center of cat's eye retro-reflector at the initial measurement position on the measurement accuracy. The measurement experiments verified that the influence was significant. When the deviation between the incident beam and the center of the cat's eye retro-reflector was -50 μm, the displacement measurement error was 3.5867 ± 0.0260 μm. When the deviation was 50 μm, the displacement measurement error reached 3.5939 ± 0.0189 μm. The relative displacement error between the cat's eye retro-reflector and the laser tracing system decreased the measurement system's accuracy. This study provides an important theoretical basis for evaluating and improving the accuracy and reliability of laser tracing measurement systems.

Dynamic Displacement Estimation for Long-Span Bridges Using Acceleration and Heuristically Enhanced Displacement Measurements of Real-Time Kinematic Global Navigation System.

In this paper, we propose a dynamic displacement estimation method for large-scale civil infrastructures based on a two-stage Kalman filter and modified heuristic drift reduction method. When measuring displacement at large-scale infrastructures, a non-contact displacement sensor is placed on a limited number of spots such as foundations of the structures, and the sensor must have a very long measurement distance (typically longer than 100 m). RTK-GNSS, therefore, has been widely used in displacement measurement on civil infrastructures. However, RTK-GNSS has a low sampling frequency of 10–20 Hz and often suffers from its low stability due to the number of satellites and the surrounding environment. The proposed method combines data from an RTK-GNSS receiver and an accelerometer to estimate the dynamic displacement of the structure with higher precision and accuracy than those of RTK-GNSS and 100 Hz sampling frequency. In the proposed method, a heuristic drift reduction method estimates displacement with better accuracy employing a low-pass-filtered acceleration measurement by an accelerometer and a displacement measurement by an RTK-GNSS receiver. Then, the displacement estimated by the heuristic drift reduction method, the velocity measured by a single GNSS receiver, and the acceleration measured by the accelerometer are combined in a two-stage Kalman filter to estimate the dynamic displacement. The effectiveness of the proposed dynamic displacement estimation method was validated through three field application tests at Yeongjong Grand Bridge in Korea, San Francisco–Oakland Bay Bridge in California, and Qingfeng Bridge in China. In the field tests, the root-mean-square error of RTK-GNSS displacement measurement reduces by 55–78 percent after applying the proposed method.

Research on the Effects of Calibrated Position on Digital Image Correlation Measurement of Dual Camera in Engineering Application

To explore the influence of calibration position on digital image correlation measurement of dual cameras in engineering application, an experimental method of displacement stepping for digital image correlation measurement of dual cameras under different calibration locations is designed. Through precise displacement stepping of samples, the results of digital image correlation measurement and dial gauge measurement are compared. The influence of different calibration locations on the measurement results of digital image correlation method with dual cameras is analyzed. The results show that when the calibration position and collection conditions are unified, there will be no large displacement measurement error, and the discreteness of repeated measurement results is relatively small. The calibration position has more influence on the measurement of ordinary glass in the measuring optical path than that of quartz glass. The relative error caused by calibration position is relatively large for small displacement measurement and relatively small for large displacement measurement

An Effective Accuracy Evaluation Method for LFMCW Radar Displacement Monitoring With Phasor Statistical Analysis

Non-contact displacement and vibration monitoring based on microwave interferometry is an emerging and promising technique in structural health monitoring. This paper focuses on the measurement accuracy evaluation requirements for linear frequency-modulated continuous-wave (LFMCW) radar displacement monitoring in practical applications, and presents an effective accuracy evaluation method based on phasor statistical analysis (PSA). The basic idea of the proposed method is that the phase evolution estimation error (i.e., corresponding to displacement measurement error) can be quantitatively evaluated and calculated by using the relative error statistic of the phasor amplitude tracking result across multiple sweeps. The accuracy evaluation problem and the specific procedures of the proposed PSA method are described. In addition, the detailed mathematical analysis and geometric interpretation regarding three main interference (i.e., noise, static clutter and adjacent clutter) scenarios are provided for the validation. A series of simulations and experiments are carried out to demonstrate the performance of our proposed method, which has low computational complexity, high applicability and good user friendliness.

Small Displacement Measuring System Based on MEMS Accelerometer

In order to intelligently measure the displacement of moving objects, a small displacement measuring system based on MEMS (microelectromechanical system) accelerometer is designed. Firstly, the principle and error of displacement measurement using acceleration signal are deeply analyzed. The method of fitting polynomial extremum with better correction effect is selected in the time domain to eliminate the trend term error caused by the DC component, which is the main source of error. Real-time correction algorithm is added to the time-domain integral of acceleration. On the hardware circuit, the measurement module, control module, storage module, and power module of the system are designed, respectively. Finally, the system-integrated packaging scheme is designed, which enables the system to complete the real-time acceleration measurement, velocity and displacement calculation, and data storage of the motion carrier. Through simulation experiments, it is found that the system has good antioverload capability, and the displacement measurement average accuracy can reach 0.96%, which has very important engineering significance.

Laser self-mixing interference displacement measurement based on VMD and phase unwrapping

In order to measure displacement accurately and conveniently, the laser self-mixing interference measurement method based on variational mode decomposition (VMD) and phase unwrapping is proposed. The laser self-mixing interference technology has many advantages such as high sensitivity, ease of use and compactness. The VMD method can non-recursively decompose a self-mixing interference signal into a number of intrinsic mode functions and remove noise effectively. The linewidth enhancement factor and the optical feedback level factor are measured by the hysteresis phenomenon in the self-mixing interference. The reconstruction of displacement is implemented by phase unwrapping. The displacement measurement is carried out by the self-mixing interference experimental system. The experimental results show that the displacement measurement error is less than 80 nm, which verifies the correctness of the method.

Precision Position Measurement of Linear Motors Mover Based on Temporal Image Correlation

High-precision position measurement is very important for precision motion control of a linear motor. This paper presents an accurate mover position detection method with high precision stability based on temporal image correlation and fence image for the linear motors. First, sequence fence images with the information of mover position are recorded by a position measurement system for linear motor, and the integer pixel displacement of each image is obtained by image correlation method. Then, according to the continuity of the motion, the subpixel displacement can be extracted by fitting the integer pixel displacement. Finally, the displacement and velocity curves can be calculated according to system calibration. Compared to digital image measurement used in position detection of linear motors, the proposed method can detect mover position accurately with longer measurement range and smaller uncertainty. The moving least square (MLS) algorithm is used to ensure the stability of measurement uncertainty under different motion modes. Simulations and mover position detection experiments with different motion conditions were performed to demonstrate the effectiveness of the proposed method in linear motors. In this paper, the average measurement error of displacement is 0.006 mm with the maximum displacement of 120 mm. The maximum and average relative errors are less than 0.06% and 0.017%, respectively.

Coupled velocity and temperature acoustic tomography in heated high subsonic Mach number flows

The application of acoustic tomography (AT) for simultaneous velocity and static temperature estimation has generally been restricted to low subsonic Mach number applications due to the increased complexities associated with acoustic refraction, high computational resource requirements, and a limited range of practical applications. The current work describes a novel AT method for application in such conditions and presents the results of a proof of concept laboratory jet experiment. Using a traversed set of acoustic sound source and microphones, acoustic propagation time measurements were collected at Mach 0.48 and 0.72 jet conditions (with total temperatures of 675 K) along three azimuthal orientations and used to perform AT. A comparison of intrusive and non-intrusive measurements showed that a three orientation reconstruction could approximate jet plume size and location within 1/4th of the jet’s radius. Several sensitivity studies were conducted to assess the behavior and limitations of the proposed AT method. In particular, the effects of orientation count, reconstruction resolution, and displacement measurement errors were investigated. The findings of these sensitivity studies were used to make recommendations for future experiments. This application is the first time an acoustic method is used to non-intrusively and simultaneously measure jet velocity and static temperature distributions in high subsonic Mach number flows.

Signal Error Detection and Correction of Quadrature Detectors of Laser Interferometers

Errors of laser interferometers using quadrature detectors depend not only on the interferometers themselves, but also on the electronic systems for processing quadrature signals. There are three sources of errors of quadrature detector signals that affect the displacement measurement error: the inequality of the amplitudes of quadrature signals, the phase shift of these signals (not equal to 90°), and the zero offset in each signal. A simple method for identifying and correcting these errors based on experimental data on signals obtained using analog-to-digital converters is considered. The proposed method is applicable to any interferometer with sinusoidal quadrature outputs.

Displacement Measurement Errors in Digital Image Correlation Due to Displacement Mapping Function

In the classic subset-based local digital image correlation (DIC) technique, the displacement measurement errors due to the displacement mapping function have been an important factor to improve the measurement accuracy. In general, the first-order displacement mapping function is broadly used. But, in the real experiments, the order of the deformation of the test sample is higher than that of the used displacement mapping function. So the errors due to the undermatched displacement mapping functions are existent. Although the random errors due to the overmatched shape function have been studied, the root-mean square errors (RMSEs) due to the matched or mismatched displacement mapping function are not studied. In this paper, the RMSEs of the measured displacements due to the matched or mismatched displacement mapping function are investigated experimentally by employing the simulated and real experimental speckle patterns. Moreover, the relationships between the RMSE and the subset size or the image noise are thoroughly examined. Finally, the practical implementation of DIC is recommended in terms of the subset size and the image noise.