Absolute Displacement Measurement Research Articles

Quasi-Zero Stiffness Vibration Sensing and Energy Harvesting Integration Based on Buckled Piezoelectric Euler Beam.

This paper presents a novel quasi-zero stiffness vibration sensing and energy harvesting integration system for absolute displacement measurements based on a buckled piezoelectric Euler beam (BPEB) with quasi-zero stiffness (QZS) characteristics. On one hand, BPEB provides negative stiffness to the system, thus creating a vibration-free point within the system and transforming the absolute displacement measurement problem into a relative motion sensing problem. On the other hand, during the measurement process, the BPEB collects the vibration energy from the system, which can provide electrical energy for low-power relative motion sensing devices and remarkably suppress the frequency range of the jump phenomenon, thereby further expanding the frequency domain measurement range of the sensing system. The research results have shown that this system can measure the absolute motion signal of the tested object in low-frequency vibration with small excitation. By adjusting parameters such as the force-electric coupling coefficient and damping ratio, the measurement accuracy of the sensing system can be improved. Furthermore, the system can convert the mechanical energy of vibrations into electrical energy to power the surrounding low-power sensors or provide partial power. This could potentially achieve self-powering integrated quasi-zero stiffness vibration sensing, offering another approach and possibility for the automation development in wireless sensing systems and the Internet of Things field.

An enhanced chromatic dispersion probe for simultaneous measurement of dual-axis absolute and relative displacement with nanometric resolutions

This paper presents an enhanced chromatic dispersion probe for simultaneous measurement of dual-axis absolute and relative displacement with nanometric resolutions based on a 4f optical system and a signal processing algorithm. In the 4f optical system, a light source is generated by a pinhole in such a way that the employed pinhole is placed on the focal planes of the two achromatic lenses, aimed at generating a low-pass filter in the frequency domain. With a smaller pinhole, side lobes of the measured spectra are effectively suppressed and the signal-to-noise ratio is optimized, resulting in an expanded absolute measurement range and improved resolution of the two axes, and an enhanced relative measurement resolution of the dual-axis. A signal processing algorithm is proposed in such a way that in the spectral curvature region of the dual-axis output spectra, the original fitted spectrum is replaced by a linear fitting line and a newly-intersected wavelength can be obtained, resulting in an expanded measurement range of the relative displacement of the dual-axis. Numerical simulation and experiments have indicated that the absolute measurement range has been expanded to 225 μm with an enhanced resolution of 40 nm, and the measurement range of the relative displacement of the dual-axis has been expanded to 370 μm with an enhanced relative measurement resolution of 90 nm.

An Absolute Displacement Measurement Method and Its Application in Ship Motion Measurement

Due to the fact that there is no static reference point in ocean space, relative measurement sensors such as laser sensors cannot be applied to the measurement of ship motion. In order to collect the motion signal of a ship in the ocean more accurately, an absolute measurement method for the motion of a ship is proposed. Firstly, the acceleration signal in the heave direction of the ship is obtained by using an acceleration sensor; secondly, the time–frequency domain integration algorithm is used to avoid the problem of the quadratic trend item and the influence of the low-frequency signal, and the ship’s heave displacement value is obtained by integration; finally, the displacement signal measured by the laser sensor and the integrated displacement signal of the acceleration sensor are compared with each other to verify the effectiveness of the absolute measurement of the heave displacement of the ship based on the acceleration sensor. At the same time, an angle sensor is used to measure the roll angle and pitch angle in the motion of the ship, form an absolute measurement system for the motion of the ship, and verify that the measurement points are arranged on the ship, which proves that the system can collect data from the ship in sea areas far from the coast. Motion signals are more advantageous.

Improved computation of Lagrangian tissue displacement and strain for cine DENSE MRI using a regularized spatiotemporal least squares method.

In displacement encoding with stimulated echoes (DENSE), tissue displacement is encoded in the signal phase such that the phase of each pixel in space and time provides an independent measurement of absolute tissue displacement. Previously for DENSE, estimation of Lagrangian displacement used two steps: first a spatial interpolation and, second, least squares fitting through time to a Fourier or polynomial model. However, there is no strong rationale for such a through-time model. To compute the Lagrangian displacement field from DENSE phase data, a minimization problem is introduced to enforce fidelity with the acquired Eulerian displacement data while simultaneously providing model-independent regularization in space and time, enforcing only spatiotemporal smoothness. A regularized spatiotemporal least squares (RSTLS) method is used to solve the minimization problem, and RSTLS was tested using two-dimensional DENSE data from 71 healthy volunteers. The mean absolute percent error (MAPE) between the Lagrangian displacements and the corresponding Eulerian displacements was significantly lower for the RSTLS method vs. the two-step method for both x- and y-directions (0.73±0.59 vs 0.83 ±0.1, p < 0.05) and (0.75±0.66 vs 0.82 ±0.1, p < 0.05), respectively. Also, peak early diastolic strain rate (PEDSR) was higher (1.81±0.58 (s-1) vs. 1.56±0. 63 (s-1), p<0.05) and the strain rate during diastasis was lower (0.14±0.18 (s-1) vs 0.35±0.2 (s-1), p < 0.05) for the RSTLS vs. the two-step method, with the former suggesting that the two-step method was over-regularized. The proposed RSTLS method provides more realistic measurements of Lagrangian displacement and strain from DENSE images without imposing arbitrary motion models.

A Moving Magnetic Grid-Type Long-Range Linear Absolute Displacement Sensor

In order to overcome the shortcomings of the traditional magnetic absolute linear displacement sensors in which cables affect the flexibility and measurement range in linear motor transmission systems, this paper proposes a novel cable-free moving magnetic grid-type long-range absolute displacement sensor. The sensor consists of a magnetic grid and a signal acquisition board. The magnetic grid is a moving component that contains two rows of permanent magnet arrays, one for relative displacement measurement and the other for the displacement interval code. The signal acquisition board is a fixed component that uses n groups of two-row Hall sensor arrays for continuous absolute displacement measurement. The principle of the sensor using the 2D magnetic field signal for the relative displacement measurement is analyzed, and a measurement method based on Hall sensor arrays for coding and absolute displacement detection over n cycles is proposed. Finally, a sensor prototype is fabricated and the experiments are performed. The experimental results show that the measurement resolution of the sensor is 5 μm, and the measurement accuracy is ±14.8 μm within the measurement range of 0-98.3 mm. The proposed sensor can realize continuous absolute displacement measurement over multiple cycles without cable binding.

A Fiber-Based Chromatic Dispersion Probe for Simultaneous Measurement of Dual-Axis Absolute and Relative Displacement.

This paper presents a fiber-based chromatic dispersion probe for the simultaneous measurement of dual-axis absolute and relative displacement with nanometric resolutions. The proposed chromatic dispersion probe is based on optical dispersion. In the probe, the employed light beam is split into two sub-beams, and then the two sub-beams are made to pass through two optical paths with different optical settings where two identical single-mode fiber detectors are located at different defocused positions of the respective dispersive lenses. In this way, two spectral signals can be obtained to indicate the absolute displacement of each of the dual-axes. A signal processing algorithm is proposed to generate a normalized output wavelength that indicates the relative displacement of the dual-axis. With the proposed chromatic dispersion probe, the absolute and relative displacement measurements of the dual-axis can be realized simultaneously. Theoretical and experimental investigations reveal that the developed chromatic dispersion probe realizes an absolute measurement range and a measurement resolution of approximately 180 μm and 50 nm, respectively, for each axis. Moreover, a relative displacement measurement range and a measurement resolution of about 240 μm and 100 nm, respectively, are achieved for the dual-axis.

Absolute displacement measurement using an inertial reference generated by linearised electromagnetic levitation

This paper proposes a novel passive absolute displacement measurement system (ADMS) utilising the electromagnetic levitation approach, instead of any mechanical spring. The most distinctive feature of the proposed ADMS is its measuring amplitude range of 30μm–1.2 mm with a lower frequency limit of 2 Hz. Consequently, a wider measuring bandwidth and higher measurement accuracy for absolute displacement signals can be realised without feedback/serve-type inertia sensors, which are usually expensive and vulnerable. Both features make the proposed system promising for of low-frequency measurement applications, such as precision vibration isolation of optical platforms in vibrational environments, anti-shake UAV platforms, monitoring of seismic wave signals, ship equipment protection and safety inspection of long-span bridges. First, the principles of the proposed ADMS are introduced. Subsequently, the measuring performance of the proposed ADMS is simulated and analysed. Finally, a prototype of the ADMS is constructed and tested. The experimental results confirm the validity of the proposed ADMS design and demonstrate its capability to measure the absolute displacement with a low-frequency and wider amplitude range.

Structural monitoring method for RC column with distributed self-sensing BFRP bars

Reinforced concrete (RC) columns may be damaged under earthquakes or wind loads, which will severely affect their bearing capacity. Current damage evaluation methods are mainly based on displacement measurement, which makes evaluating local structural damage difficult. Therefore, this study proposes an RC column structural monitoring and evaluation method based on a distributed self-sensing basalt fiber reinforced polymer (BFRP) bar with optical fiber sensors inside. First, the self-sensing BFRP bar is introduced, including the sensing principle, inner structure, and basic sensing performance. It is found that the strain sensing coefficient of the proposed self-sensing BFRP bar presents only 2.2 % difference from that of the bare optical fiber sensor, meaning the BFRP package take no negative effect on the strain sensitivity. Second, the analytical methods of curvature and displacement are established based on the strain distribution measurement, in which the influence of bond-slip on parameter calculations is mainly considered. Finally, the proposed method was well verified by the loading tests of one RC column with self-sensing BFRP bars. Among the results, the absolute displacement measurement error increase with the development of structure damage, which can be even up to several mm after the steel yielding. However, the relative displacement measurement error can be still controlled within 20 % until the structure failure of the RC column. Considering the additional long-term performance of the proposed self-sensing BFRP bar, the proposed method is expected to implement long-term monitoring of RC columns.

An Absolute Linear Displacement Sensor Based on Orthogonal Dual Traveling Wave Magnetic Field

This paper presents an absolute linear displacement sensor, which is based on orthogonal dual traveling wave magnetic field. The sensor consists of two groups of field coils and inductive coils. Two groups of field coils with ‘ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N}$ </tex-math></inline-formula> ’ and ‘ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N}$ </tex-math></inline-formula> -1’ pitches generate two groups of traveling wave magnetic field which move in orthogonal directions. Then, the mixed magnetic field is picked up and induced by two groups of inductive coils. Two roads of electrical traveling wave signals are generated. Absolute position measurement is realized by comparing the phase differences of two groups of electrical signals. Compared with the traditional structure of the absolute sensor, the sensor combines dual tracks into a single track. Accordingly, the width of the sensor can be reduced. In order to be sensed effectively, dual traveling wave magnetic fields move orthogonally. The angular separations with the direction of measurement are 45° and −45°. The structure and measurement principle of the sensor are described in detail. A sensor prototype is fabricated by printed circuit board technology, and the experiment is brought out. The experimental results show that the sensor can achieve absolute displacement measurement, and the measurement accuracy is ± <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$15 ~\mu \text{m}$ </tex-math></inline-formula> within the measurement range of 0–80 mm.

A Novel Self-Correction Method for Linear Displacement Measurement Based on 2-D Synthesis Mechanism

With increased range, the accuracy of longer-range linear displacement measurement is difficult to guarantee. According to the analysis, it is inevitable that there will be a certain margin between the direction of the calibration grating and the direction of the reading head, which will impact the longer-range linear displacement measurement. In order to eliminate this measurement error, a self-correction method based on 2-D synthesis is herein proposed. First, we describe the principle of absolute linear displacement measurement based on image recognition. Then, the error model is established, which caused by the included angle between the calibration grating and the reading head. Third, a method is proposed for obtaining the vertical offset of the calibration grating by using the vertical image sensor. Finally, we reach an error self-correction method based on 2-D synthesis. In order to test the feasibility of the proposed method, a linear displacement measuring device with a range of 200 mm was developed. After experiment, the maximum absolute error was reduced from 4.34 to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2.03~\mu \text{m}$ </tex-math></inline-formula> with the proposed error correction in the long range of 200 mm. The proposed algorithm does not depend on the assembly and installation position, and can realize self-correction of errors. So the method could lay the groundwork for improving larger range linear displacement measurement technology.

High precision angular displacement measurement based on self-correcting error compensation of three image sensors.

As the feedback link of a numerical control system, the measurement accuracy of absolute angular displacement measurements directly affects the control performance of a numerical control system. In previous research, angular displacement measurements based on dual image sensors can achieve higher measurement performance. However, the elimination of harmonic error by the dual image sensor is still limited. For this reason, this paper proposes an image-type angular displacement measurement method based on self-correction error compensation of three image sensors. First, the mathematical model of harmonic error is established, and the shortcomings of using dual image sensors to compensate the error are analyzed. Then, a high precision angular displacement measurement method based on three image sensors is proposed. Finally, the self-correction error compensation method of three image sensors is applied to the angular displacement measurement system, and the measurement performance is verified. The experimental results show that a measurement accuracy of 1.76'' can be achieved on the circular grating with a diameter of 96 mm. In contrast, the dual image sensor can only achieve a measurement accuracy of 2.88''. It is concluded that the odd number of image sensors can achieve higher measurement accuracy than the even number. This research lays a foundation for the realization of high precision image angular displacement measurement.

Accuracy of Radiographic Displacement Measurement in a Pelvic Ring Injury Model.

Pelvic ring injury outcome studies rely on radiographic assessment. To date, no study investigates the accuracy of radiographic measurement. The aim of this study was to assess the accuracy and interobserver reliability of pelvic ring displacement measurement in an injury model. We hypothesize that current radiographic measurement methods do not accurately quantify the three-dimensional pelvic ring displacement. Ten orthopaedic traumatologists evaluated 12 pelvic ring injury model displacements using AP, inlet, and outlet radiographs and axial CT images. Observers completed a survey of demographic and treatment approach strategies. Radiographic displacement measurements in axial, coronal, and sagittal planes were analyzed for accuracy using. Absolute displacement measurements were categorized with Matta and Tornetta grading system for Fleiss Kappa inter-reliability correlation evaluation. The mean age of orthopaedic traumatologists was 47.5 years (range 36 to 59) with a mean 15.3 years (range 4 to 27) of pelvic fracture surgery experience. Radiographic measurement of isolated uniplanar of pelvic displacement in axial, sagittal, or coronal plane alone was more accurate than multiplanar pelvic displacements with more than one plane of displacement, 6.6 ± 5.7 mm error compared with 9.6 ± 6.3 mm error, respectively (P = 0.0035). Measurement accuracy was greater with isolated coronal plane (4 ± 3.5 mm error) compared with isolated axial plane (9.9 ± 7.1 mm error) or isolated sagittal plane displacement (6.7 ± 4 mm error). Interrater reliability for the radiographic displacement measurement by observers showed an overall poor agreement with 0.24. Radiographic displacement measurement in these modeled pelvic ring injuries has notable inaccuracy among various measurement methods. Coronal and sagittal plane radiographic displacement measurements are more accurate compared with axial plane measurement. The reporting of radiographic displacement measurement outcomes in clinical research studies should be critically evaluated, and standardization of pelvic ring injury displacement may not be achievable with radiography. Level V.

Novel nano-scale absolute linear displacement measurement based on grating projection imaging

There is urgent demand for new absolute Linear Displacement Measurement (LDM) technology with high resolution and high precision, during the development of high-end numerical control technology. In previous research, we found that displacement measurement based on the image processing method performs well, however, the volume increases when using an imaging lens, and the system is susceptible to factors such as virtual focus. In this paper, the lensless LDM image optical path is established based on grating projection imaging, then the absolute grating coding method is operated based on M−sequence pseudo-random coding. A linear displacement subdivision algorithm is then deployed based on the digital image recognition algorithm. An LDM device with a measuring range of 250 mm was designed to test the performance of the proposed method. The device shows a measurement resolution of 1 nm and measurement accuracy of 1.76 μm in the range of 250 mm. This work lays a foundation for further research on high performance LDM technology.

Experimental Study on the Effect of Medium in Optical Path on Digital Image Correlation Measurement

To explore the effect of optical media on digital image correlation measurement, the experiments of digital image correlation measurement under different optical media conditions were carried out. By analyzing the speckle images non-special optical path medium, common ordinary glass medium and quartz glass medium in the optical path, the effect of medium change in the optical path on digital image correlation measurement is discussed. The results show that the effect of different optical media on the accuracy of digital image correlation measurement is different, and the effect of optical media on absolute displacement measurement is much greater than that of rigid body displacement measurement. The effect of optical medium on different measuring areas is also different. The effect of quartz glass state on strain measurement is greater than that of ordinary glass. The effect of optical medium on the measurement of vertical optical axis displacement is much less than that of optical axis displacement measurement. Whether ordinary glass or quartz glass is added, the measurement error of camera optical axis direction is much larger than that of vertical optical axis direction; the stability of DIC displacement measurement in different optical path media is in turn ordinary glass medium, quartz glass medium and non-special optical path medium.

A novel electromagnet-based absolute displacement sensor with approximately linear quasi-zero-stiffness

Quasi-zero-stiffness (QZS) has attracted notable interest in the study of absolute displacement measurements due to the increasing demand for displacement sensors that can be applied in harsh environments. Based on recent studies of QZS-based vibration isolators, this paper presents a novel absolute displacement sensor (ADS) with a measurement accuracy of 0.1 mm above 3 Hz. The principle of this ADS system can be described as follows: the QZS-based ADS system creates a vibration-free point; thus, the absolute motion of the base, which is fastened to the equipment to be measured, can be equivalent to its relative motion with respect to the vibration-free point. The relative motion can be indicated by the deformation of a spring mounted in the ADS system through a load cell. Instead of mechanical QZS, the proposed design adopts non-contact electromagnetic QZS, which offers several advantages: (i) by nesting ring permanent magnets into the electromagnets (coil windings), the proposed design has a much more compact structure. (ii) The non-contact nature of the electromagnetic force may result in a smaller damping coefficient and a longer fatigue life. (iii) The electromagnetic stiffness can be tuned to be approximately linear within a certain range, which eliminates the influence of the stiffness non-linearity and hence improves the measurement accuracy.

An FPGA Platform for Next-Generation Grating Encoders.

Among various nanometer-level displacement measurement methods, grating interferometry-based linear encoders are widely used due to their high robustness, relatively low cost, and compactness. One trend of grating encoders is multi-axis measurement capability for simultaneous precision positioning and small order error motion measurement. However, due to both lack of suitable hardware data processing platform and of a real-time displacement calculation system, meeting the requirements of real-time data processing while maintaining the nanometer order resolutions on all these axes is a challenge. To solve above-mentioned problem, in this paper we introduce a design and experimental validation of a field programmable gate array (FPGA)-cored real-time data processing platform for grating encoders. This platform includes the following functions. First, a front-end photodetector and I/V conversion analog circuit are used to realize basic analog signal filtering, while an eight-channel parallel, 16-bit precision, 200 kSPS maximum acquisition rate Analog-to-digital (ADC) is used to obtain digital signals that are easy to process. Then, an FPGA-based digital signal processing platform is implemented, which can calculate the displacement values corresponding to the phase subdivision signals in parallel and in real time at high speed. Finally, the displacement result is transferred by USB2.0 to the PC in real time through an Universal Asynchronous Receiver/Transmitter (UART) serial port to form a complete real-time displacement calculation system. The experimental results show that the system achieves real-time data processing and displacement result display while meeting the high accuracy of traditional offline data solution methods, which demonstrates the industrial potential and practicality of our absolute two-dimensional grating scale displacement measurement system.

Dispersion Compensation for PLCI Based on Fringe Peak Estimation and Polynomial Fitting

Polarized low-coherence interferometry (PLCI) is a promising technology to absolute displacement measurement and sensor demodulation. To avoid jump errors induced by dispersion and achieve a high response, a dispersion compensation method based on fringe peak position estimation and polynomial fitting is proposed to get rid of the dependence on the priori model and birefringence parameters, and make this method very robust. The nearly linear resolution between the envelope and ${m}$ -order PLCI fringe (PLCIF) centers are found and verified with both Gauss and non-Gauss profile broadband light sources. Then, the zero-order PLCIF is estimated and located to demodulate the measurement displacement. The demodulated results are significantly influenced by dispersion of the birefringence optical wedge and then polynomial fittings of sensing curve are conducted to raise the sensing accuracy. In comparison to the priori model and parameters based method, the proposed method can effectively avoid jump errors and has a higher accuracy than the directly envelope center method. Experimental results indicate that the measurement accuracy is higher than 19.5 nm which is enhanced by 6.88 times, the resolution is better than 2 nm, and its processing data rate can reach 35 kHz on an embedded system.

Calibration of a Piezoelectric Transducer through Laser Measurements and Numerical Simulation

A piezoelectric transducer is an electromechanical sensor which converts electrical energy (voltage signal) to mechanical energy (displacement signal) and vice versa by taking advantage of the piezoelectric crystal. Depending on the physical combination of transducer parts, sensors may have a linear or non-linear response to the input signal. In seismic tests such as ultrasonic non-destructive testing (NDT) methods, analyzing stress wave propagation through the specimen gives an assessment of its condition. The signal attenuation is an important parameter to assess the condition of specimen which can be done by having the displacement signal as an output. However, instead of the displacement signal, the piezoelectric transducer provides the voltage signal as an output. Therefore, to get reliable and accurate results, it is essential to calibrate the transducers. An appropriate calibration results in a suitable Transfer Function (TF) which can be used to properly calculate the displacement signal. In this study, the output displacement of a 1 MHz piezoelectric transducer is measured using a laser vibrometer with a nanometer resolution. Measurements and calculated TF showed at frequencies of 0.1, 1, and 1.5 MHz, TF values are 0.8, 0.08, and 0.2 respectively which is a non-linear relation between displacement (absolute signal) and voltage (relative signal) as it was expected. Then, numerical simulation is implemented as part of this study to simulate all electrical and mechanical components of the piezoelectric transducer. The simulation was verified with the absolute displacement measurements result from the laser vibrometer.

Analysis and Design of a Bioinspired Vibration Sensor System in Noisy Environment

Absolute displacement signals of vibrating platforms/objects are often needed in vibration control, signal processing, and object tracking. Motivated by the practical requirement of engineering applications, this study presents the analysis and design of a novel bioinspired dynamics vibration sensor system for absolute vibration displacement measurement. The sensor system is constructed using simple beams and springs, which indicates a possible way in achieving nonlinear quasi-zero stiffness and consequently creating a broadband vibration-free point for absolute displacement measurement in vibrating platforms. The theoretic analysis of the influence of different structure parameters on the bioinspired sensor system is conducted for achieving an excellent isolation property, and thus realizing an outstanding measurement performance. Importantly, to avoid the drawback of measurement noises from the sensor data, the square root unscented Kalman filter technique for estimating the system of the bioinspired dynamic sensor is developed, which improves the accuracy of the resulting vibration measurement. A series of simulations demonstrate the effectiveness of this novel sensor system. Experiments are also conducted using an in-house prototyped sensor testbed, to validate the displacement measurement results and assess the filter algorithms.

Advances in Capacitive, Eddy Current, and Magnetic Displacement Sensors and Corresponding Interfaces

This paper presents a review of the latest advances in the field of capacitive, inductive (eddy current), and magnetic sensors, for measurement of absolute displacement. The need for accurate displacement and position measurement in the micrometer, nanometer, and subnanometer scales has increased significantly over the last few years. Application examples can be found in high-tech industries, metrology, and space equipment. Besides measuring displacement as a primary quantity, absolute displacement sensors are also used when physical quantities such as pressure, acceleration, vibration, inertia, etc., have to be measured. A better understanding of the commonalities between capacitive, inductive, and magnetic displacement sensors, as well as the main performance differences and limitations, will help one make the best choice for a specific application. This review is based on both theoretical analysis and experimental results. The main performance criteria used are: sensitivity, resolution, compactness, long-term stability, thermal drift, and power efficiency.