Low-frequency Vibration Measurement Research Articles

Low-frequency vibration measurements in harsh environments using a frequency-modulated interferometer

Low-frequency vibration measurements in harsh environments are considerably challenging owing to strong background noise. In this study, a simple, high-dynamic-range, and high-precision vibration-measuring system using a frequency-modulated interferometer was proposed and validated. Harmonics with perfectly orthogonal phases were extracted directly from the interference signal, and noise with random frequencies was filtered using a synchronous detection method. The modulation index of the interferometer was controlled to remove the effect of Bessel functions; hence, a full-circle Lissajous diagram was obtained. The ratio of the two harmonics was used to determine the vibration; hence, the effects of intensity fluctuation and background noise can be neglected. The vibration measurement bandwidth was well controlled by controlling the modulation and cutoff frequencies of the bandpass filters. The best noise level of 1 nm/√Hz under harsh measuring conditions can be archived in the low-frequency range.

Dual straight-wing FBG accelerometer for low-frequency vibration measurement

Fiber optic accelerometers have a wide range of applications in low-frequency vibration measurement, such as in earthquake monitoring, disaster early warning, underground resource exploration, and anti-seismic monitoring projects for critical structures like dams and bridges. In response to the current issues of Fiber Bragg Gratings (FBG) accelerometers being insensitive to low-frequency vibration signals and challenging to apply in engineering, a dual straight-wing FBG accelerometer for low-frequency vibration measurement is proposed. Firstly, a sensor model is established and theoretically analyzed. Secondly, the impact of the sensor's main structural parameters on sensitivity and natural frequency is analyzed, and the sensor is simulated using ANSYS. Finally, a prototype of the sensor is developed, and a low-frequency vibration testing system is set up to test the sensor's performance. Experimental results show that the accelerometer has a natural frequency of 39.1 Hz, operates in the 5–22 Hz frequency band, and has a sensitivity of 171.7 p.m./g, a dynamic range of 69.82 dB, and a transverse interference resistance of less than 9.5%. This research provides a new reference for the development of similar sensors.

Noncontact Self-Vibration Compensated Position Sensitive Detector Based Low-Frequency Vibration Measurement

Noncontact Self-Vibration Compensated Position Sensitive Detector Based Low-Frequency Vibration Measurement

High-sensitivity dual-FBG acceleration sensor for low frequency vibration measurement

High-sensitivity dual-FBG acceleration sensor for low frequency vibration measurement

A dual oblique wing-based low-frequency FBG accelerometer

The low-frequency vibration measurement technology is significant in energy exploration, aerospace, geophysical activities, health monitoring of large engineering structures, etc. A low-frequency FBG accelerometer based on a dual oblique wing is proposed to address the issue of difficulty in accurately measuring low-frequency vibration signals in current fiber Bragg grating accelerometers. Firstly, the structure of this accelerometer was theoretically analyzed and dimension-optimized. Secondly, the static stress analysis and modal simulation analysis are carried out, and the accelerometer is developed. Finally, it is fixed on the vibration table, and the low-frequency vibration test system is built to test the performance. The experimental results show that the natural frequency of the accelerometer is 46 Hz, the working frequency band is 0.1–28 Hz, the sensitivity is 55.6 pm/g, the dynamic range is 48.94 dB, and the resistance to transverse interference of less than 5.62 %. The accelerometer designed in this paper provides a new idea for low-frequency vibration signal measurement.

Cascadable Four-Core Fiber Bragg Gratings Accelerometer for 2-D Low-Frequency Vibration Measurement

Cascadable Four-Core Fiber Bragg Gratings Accelerometer for 2-D Low-Frequency Vibration Measurement

Standard sine motion video-based virtual traceability method for monocular vision low-frequency vibration measurements.

The low-frequency vibration exists in building structures, mechanical devices, instrument manufacturing, and other fields, and is the key to modal analysis, steady-state control, and precision machining. At present, the monocular vision (MV) method has gradually become the primary choice to measure the low-frequency vibration because of its distinctive advantages in efficiency, non-contact, simplicity, flexibility, low cost, etc. Although many literature reports have demonstrated that this method has the capability to reach high measurement repeatability and resolution, its metrological traceability and uncertainty evaluation are difficult to be unified. In this study, a novel, to the best of our knowledge, virtual traceability method is presented to evaluate the measurement performance of the MV method for the low-frequency vibration. This presented method achieves traceability by adopting the standard sine motion videos and the precise position error correction model. Simulations and experiments confirm that the presented method can evaluate the amplitude and phase measurement accuracy of the MV-based low-frequency vibration in the frequency range from 0.01 to 20 Hz.

DESCRIPTIVE STATISTICAL CALIBRATION METHOD OF TRIAXIAL DIGITAL ACCELEROMETER ADXL345 AS EARTHQUAKES SENSOR

Seismic monitoring networks are the crucial elements in strong motion seismology for effective risk reduction. Low scale lateral variation of high intensity ground movement caused by earthquakes will be detected more effectively with densely located networks. However, the limitations of developing such project are rooted in expensive costs associated with the construction and installation in addition to bulky size of the conventional seismic observation system. Recently, micro-electromechanical system (MEMS) has being recognized in the applications of seismological and earthquake engineering due to the high precision obtained in these micron size semiconductor instruments and cheaper alternative for traditional seismic detector. ADXL345 is a type of digital triaxial MEMS accelerometer that is ideal for measurement of low-frequency vibrations and static accelerations of gravity, which makes it suitable for ground motion detection. Thus, this study aims at calibrating ADXL345 sensor that is required as sensing component in an affordable earthquake monitoring system with the Earthquake Benchmarking System (Penanda Aras Gempa Bumi, PAG) available in the inventory of Department of Mineral and Geoscience Malaysia, Sabah. Soil vibrations in EW (east-west or x-axis), NS (north-south or y-axis), and UD (up-down or z-axis) directions during random forces hit on the surface are recorded by both accelerometers. Acceleration magnitudes recorded by PAG and ADXL345 are extracted and data exploration is performed. Predominantly, ADXL345 measurements in horizontal and vertical ground movements are on a higher scale than the reference device. Subsequently, evaluation by using descriptive statistical analysis is chosen to produce numerical equations for data correction operations. İmplementation of the mathematical functions in ADXL345 for observing land movements in EW, NS, and UD directions resulted in decreasing the range values of output readings. Higher approximation of magnitudes of ground motion with the PAG system is achieved.

Development of a High-Precision and Low Cross-Axis Sensitivity 3-D Accelerometer for Low-Frequency Vibration Measurement

A new high-precision and low-frequency 3-D accelerometer that utilizes a symmetrical parallel vibration-sensing mechanism and a low cross-axis sensitivity high-precision 3-D sensing system is proposed in this study. The parameters of the vibration-sensing mechanism were determined by theoretical modeling and simulation analysis, and the performance of the 3-D accelerometer was tested experimentally. The dynamic response characteristics of the accelerometer were first determined using kinetic modeling, which showed reasonable amplitude–frequency and phase–frequency characteristics in the frequency range below 10 Hz. The accelerometer was calibrated using the comparison method. The sensitivities of the accelerometer in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${X}$ </tex-math></inline-formula> -, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Y}$ </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">${Z}$ </tex-math></inline-formula> -axes are 25.3, 25.3, and 21.1 V/g, respectively, with a cross-axis sensitivity of less than 1%. The resolutions of the accelerometer in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${X}$ </tex-math></inline-formula> -, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Y}$ </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">${Z}$ </tex-math></inline-formula> -axes were 48, 45, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$50 \mu \text{g}$ </tex-math></inline-formula> , respectively. The proposed accelerometer with high sensitivity and high resolution can be widely used for low-frequency microvibration measurements in engineering applications.

Prior information-based motion blur image restoration method for the low-frequency sinusoidal vibration measurements with machine vision

The sinusoidal vibration is the basic unit of motion control and measurement, which can constitute the arbitrary plane and space motions and is essential to the low-frequency vibration calibration. At present, the machine vision (MV) method has been widely applied to measure the low-frequency vibration, which can promote the improvement of low-frequency vibration calibration and metrology traceability. However, the MV method is always inevitably affected by the motion blur which decreases its measurement accuracy. In this study, a novel prior information-based motion blur image restoration method is investigated, which applies the known sinusoidal information and the Lucy-Richardson (LR) method with Non-Local (NL)-Means to eliminate the motion blur and improve the measurement accuracy. Meanwhile, the objective evaluation indexes and edge detection method are adopted to verify the restoration effect. Several simulations and actual experiment show that the investigated method can significantly improve the quality of the sinusoidal motion blur images, and further make the accuracies of the edge detection method and MV method increase 0.3 pixel and 0.3%, respectively.

A high-sensitivity FBG accelerometer and application for flow monitoring in oil wells

In this study, a cantilever beam-based fibre Bragg grating (FBG) accelerometer is presented. Two fibre supports are arranged at both ends of a cantilever beam; therefore, the FBG can be stretched longitudinally by both displacement and rotation of the free end. The principle of this sensor is analysed by the elasticity theory approach and the accuracy of the theoretical model is verified by the ANSYS modal simulation. Furthermore, the influence of key structural parameters on the sensor characteristics is analysed by Mathematica for structural optimisation. Hence, the accelerometer exhibits a resonant frequency of approximately 76 Hz, an average sensitivity of 59.3 dB re pm/g for a 1–60 Hz flat response interval and a cross-sensitivity of less than –24.43 dB (<6.1 %), which is capable of low frequency and precision vibration measurements. Finally, a flow-monitoring test is presented and the results show that it is feasible to use FBG accelerometers for flow monitoring in oil wells.

Fast frequency relocking for synchronization enhanced resonant accelerometer

Synchronization, as a unique phenomenon, has been extensively studied in biology, chaotic systems, nonlinear dynamics, quantum information, and other fields. Benefiting from the characteristics of frequency amplification, noise suppression, and stability improvement, synchronization has been gradually applied in sensing, communication, time keeping, and other applications. In the sensing field, synchronization provides a new strategy to improve the performance of sensors. However, the performance improvement is only effective within the synchronization range, and the narrow synchronization range has become a great challenge for the wide application of synchronization-enhanced sensing mechanism. Here, we propose a frequency automatic tracking system (FATS) to widen the synchronization range and track the periodic acceleration signals by adjusting the frequency of the readout oscillator in real time. In addition, a high-precision frequency measurement system and fast response control system based on FPGA (Field Programmable Gate Array) are built, and the tracking performance of the FATS for static and dynamic external signals is analyzed to obtain the optimal control parameters. Experimental results show that the proposed automatic tracking system is capable of static acceleration measurement, the synchronization range can be expanded to 975 Hz, and the relocking time is shortened to 93.4 ms at best. By selecting the optimal PID parameters, we achieve a faster relocking time to meet the requirements of low-frequency vibration measurements, such as seismic detection and tidal monitoring.

A new L-shaped rigid beam FBG acceleration sensor

Acceleration detection is an important technology in the fields of seismic monitoring, structural health monitoring and resource exploration. A FBG acceleration sensor with the combination of L-shaped rigid beam and spring structure based on bearings is proposed against the low sensitivity that predominates in the low-frequency vibration measurement by FBG acceleration sensors, where L-shaped rigid beam is utilized to amplify the vibration signal, and is fixed by the bearings at both ends to effectively suppress the transverse crosstalk. The effects of structural parameters on the sensitivity and natural frequency of the sensors were analyzed using Origin theory, and such parameters were optimized; next, static stress and modal simulation analysis was made using COMSOL; in the end, a test system was built to test the performance of the real sensors. According to the findings, the acceleration sensor, whose natural frequency is 57 Hz, is of a flat sensitivity response in the low frequency range of 1–35 Hz, with the dynamic range being 89.83 dB, the acceleration sensitivity being up to 1241.85 pm/g, the coefficient of determination R2 for the sensitivity fit is 0.9997, and the transverse crosstalk being -26.20 dB within the operating frequency band. The findings offer a reference for improving the low-frequency vibration measurement capability of FBG acceleration sensors.

An active geophone with an adjustable electromagnetic negative stiffness for low-frequency vibration measurement

The low-frequency performance of an active vibration isolation system depends on the low-frequency measurement ability of inertial sensors such as geophones. Reducing the stiffness of the interior mechanical spring may serve as an effective way to improve the low-frequency performance of a geophone. But unfortunately, this approach may lead to a nonlinear response and a stability problem. This paper develops an active geophone with an adjustable electromagnetic negative stiffness (AENS). The AENS of the proposed geophone consists of two pairs of magnet rings and coil winds and adopts a concentric nested configuration. The AENS neutralizes the positive stiffness of mechanical spring and provides a low linear composite stiffness in a stroke range of ± 4.4 mm without affecting the high-frequencies stability of the active geophone. Besides, the “drift” phenomenon caused by an initial installation misalignment of the AENS is discussed. The analyzed result shows that once the misalignment happens, the deviation from the initial position will aggravate further. Therefore, by combining the AENS with active control of a drift suppression and a force-balance, the nonlinearity and misalignment problems caused by the AENS are addressed to guarantee an improved low-frequency performance. The performance of the prototype is analyzed and validated by experiments. The results have shown that the measurable bandwidth of the prototype is 0.1 Hz ∼ 25 Hz, and the sensitivity is 275 V/(m/s).

A new type low-frequency FBG acceleration sensor based on cross reeds

PurposeThe purpose of this paper is to solve the problem of weak low-frequency vibration measurement capability of FBG accelerometer, and propose a FBG accelerometer based on cross reed.Design/methodology/approachThis study proposed a new type FBG acceleration sensor based on cross reeds. When the sensor vibrates, the mass block in the new structure rotates around the center of the cross reeds, which could eliminate the impact of friction, reduce the natural frequency of the sensor and improve its sensitivity. This study theoretically analyzed the impact of several structural parameters on the sensitivity and natural frequency of the proposed sensor and used COMSOL to perform static stress analysis and modal simulation; in this study, a test system was built to test the performance of the proposed sensor.FindingsThe test results revealed that the proposed sensor had a natural frequency of 94 Hz; within a low-frequency range of 1–65 Hz, its sensitivity response was flat, the dynamic range was 81.89 dB, the sensitivity was 243.59 pm/g and the linearity was 99.97%. The cross reeds effectively strengthened the structural stability, the relative standard deviation of the repeatability of the sensor was 0.89% and the transverse crosstalk in the working frequency band was −26.97 dB.Originality/valueThis study innovatively proposes the structure of the two symmetrical cross reeds, which can improve sensitivity by eliminating the influence of friction, and the structure of cross reeds can effectively suppress the influence of lateral crosstalk. The proposed sensor can realize real-time accurate measurement of low-frequency weak vibration signals.

A multi-cantilever beam low-frequency FBG acceleration sensor

The acquisition of 2–50 Hz low-frequency vibration signals is of great significance for the monitoring researches on engineering seismology, bridges & dams, oil & gas exploration, etc. A multi-cantilever beam low-frequency FBG acceleration sensor is proposed against the low sensitivity that predominates in the low-frequency vibration measurement by FBG acceleration sensors. Structural parameters of the sensor is subjected to simulation analysis and optimization design using the ANSYS software; the real sensor is developed based on the simulation results in the following manner: Three rectangular of the cantilever beams are evenly arranged around the mass block at 120°to improve the sensitivity and alleviate the transverse crosstalk of sensor; in the end, a performance test is performed on the sensor. According to the research findings, the sensor, whose natural frequency is approximately 64 Hz, is applicable for monitoring the low-frequency vibration signals within the range 16–54 Hz. The sensor sensitivity is approximately 87.955,{text{pm/m}};{text{s}}^{ - 2}, the linearity being greater than 99%, the transverse interference immunity being lower than 2.58%, and the dynamic range being up to 86 dB. The findings offer a reference for developing sensor of the same type and further improving the sensitivity of fiber optic acceleration sensor.

Low-Frequency Vibration Measurement Based on the Concentric-Circle Grating Projection System

In low-frequency vibration measurement field, optical dynamic 3-D measurement based on camera-projector system is a novel approach. In this system, linear sinusoidal grating is the most common projection mode, which can meet the requirements of some vibration measurement. However, the dynamic measurement range of amplitude using the combination of linear grating and Fourier transform profilometry (FTP) is limited in some vibration measurement environments, because the linear fringe is periodic. To solve the problem, this article proposes a low-frequency vibration measurement method based on the concentric-circle grating camera-projector system and FTP. The center of the circle is traced dynamically and the coordinate system is transformed with the center of the circle as the origin. The phase distribution of concentric-circle grating is obtained by coordinate system transformation and FTP. By exploring the relationship between phase and relative height, the time-varying curve of the object surface height is recovered, which contains the vibration information. The experiments compare the measurement ability of the concentric-circle and linear grating. The results show that the linear grating and concentric-circle grating with the similar amplitude resolution have different amplitude measurement range. In this experiment, the maximum measurement range of linear grating is about 2.4 mm, while that of concentric-circle grating is more than about 3.9 mm. It means that the concentric-circle grating projection method can measure a large dynamic range of amplitude under the condition that the center of the circle can be traced, and solve the problem of amplitude limitation of linear grating in the use of FTP.

Fading Noise Suppression in Φ-OTDR Based on Nearest Neighbor Analysis

Phase sensitive optical time domain reflectometry (Φ-OTDR) has been widely used in the precise acquisition of the vibration signal along the sensing optical fiber, and has attracted more and more interest. However, polarization fading and coherent fading usually lead to the phase hopping of the recovered signal, thus it is difficult to realize the continuous measurement of vibration, especially the low frequency vibration. The polarization diversity and multi-frequency detection schemes which are usually used to solve the above problems need additional hardware, thus increasing the cost and complexity of the system. In this article, we propose a statistical method based on nearest neighbor analysis. For each interrogation fiber separation, the phases of the sub-separations are evaluated and selected to reconstruct the vibration. In the experiment, the vibrations with frequencies as low as 0.2 Hz are loaded on the fiber and recovered. The results show that the method can effectively suppress the phase hopping, correct distorted vibration and improve the performance of low frequency vibration measurement of Φ-OTDR system on the basis of only numerical calculation.

Development of a High-Sensitivity Optical Accelerometer for Low-Frequency Vibration Measurement.

Low-frequency vibration is a harmful factor that affects the accuracy of micro/nano-measuring machines. Low-frequency vibration cannot be completely eliminated by passive control methods, such as the use of air-floating platforms. Therefore, low-frequency vibrations must be measured before being actively suppressed. In this study, the design of a low-cost high-sensitivity optical accelerometer is proposed. This optical accelerometer mainly comprises three components: a seismic mass, a leaf spring, and a sensing component based on a four-quadrant photodetector (QPD). When a vibration is detected, the seismic mass moves up and down due to the effect of inertia, and the leaf spring exhibits a corresponding elastic deformation, which is amplified by using an optical lever and measured by the QPD. Then, the acceleration can be calculated. The resonant frequencies and elastic coefficients of various seismic structures are simulated to attain the optimal detection of low-frequency, low-amplitude vibration. The accelerometer is calibrated using a homemade vibration calibration system, and the calibration experimental results demonstrate that the sensitivity of the optical accelerometer is 1.74 V (m·s−2)−1, the measurement range of the accelerometer is 0.003–7.29 m·s−2, and the operating frequencies range of 0.4–12 Hz. The standard deviation from ten measurements is under 7.9 × 10−4 m·s−2. The efficacy of the optical accelerometer in measuring low-frequency, low-amplitude dynamic responses is verified.

A Novel Low Frequency Vibration Measurement Method Based on Single Camera

In recent years, low frequency vibration measurement is being widely concerned in many applications, because low frequency vibration usually introduces a strong influence. The low frequency vibration is commonly measured by the laser interferometry, requiring a complicated system and a high cost laser interferometer, and its flexibility in field vibration measurement is poor; or the method using vibration transducer, requiring a transducer with known sensitivity, and its measurement precision is not high. In this paper, we propose a novel method based on single camera, which achieves low frequency vibration measurement via collecting and processing sufficient frame sequence images. The proposed method is compared with the heterodyne interferometry by measuring the vibration displacements of a long-stroke shaker simultaneously. Experimental results show the proposed method realizes <1% vibration displacement measurement precision at frequencies between 0.05 Hz-5 Hz.