Vibration Measurement Techniques Research Articles

Statistical blade tip timing measurement, Part II: High-order cumulant architecture

Blade tip timing (BTT) is a potential non-contact vibration measurement technique for rotating blades owing to its high efficiency and long service life. However, probe layout design and vibration parameter identification are critical challenges in BTT due to its inherent undersampling. To address this issue, we have proposed the concept of statistical BTT measurement which promotes efficient layouts and parameter identification methods by shifting the recovery target from the signal to itself to its statistics. In the first paper of series papers, we have developed covariance architecture for BTT measurement and signal post-processing. In this second part of series papers, we set out to develop BTT measurement from a higher-order statistic perspective. Specifically, we find that the 2qth-order cumulant retains the vibration information (frequency and amplitude) of the signal itself and it can be recovered at lower sampling rates than what is prescribed by the covariance architecture. On this basis, we propose a higher-order cumulant architecture for BTT measurement, which contains two aspects: higher-order difference layout (HODL) and higher-order cumulant-based parameter identifications. HODL is a special family of layouts that physically guarantee the availability of consecutive higher-order cumulant estimations and thus leads to a satisfactory parameter identification. To facilitate application, a series of concrete HODLs are provided for users, including a four-level nested layout and its enhanced version, and optimal fourth-order difference layout. The quantitative comparison in the simulations and experiments shows the effectiveness of the proposed higher-order cumulant architecture. Compared with the architectures developed from covariance and signal itself perspective, the proposed higher-order cumulant architecture is not only more robust to noise but also further reduces the number of required probes.

Transfer learning with cross-domain adaptation of vibro-acoustic signals for electric motor mechanical fault detection and diagnosis.

Contact-based vibration measurement techniques involving accelerometers are typically utilized for machine health monitoring and manufacturing end-of-line quality control. Acoustic signals, encompassing sound pressure and particle velocity, carry crucial information about the operational status of underlying equipment and can be utilized for detecting various machine faults. Utilizing one-dimensional Convolution Neural Networks (1D-CNN) based on deep learning for processing raw acoustic time signals has proven to be a valuable approach in detecting machinery faults, offering an effective alternative to using traditional accelerometer signals. However, the success of deep learning methods is heavily dependent on the quantity and availability of data for robust network training. When transitioning to new non-contact type sensor technology, manufacturers may face challenges due to insufficient data for training deep learning models. In such cases, leveraging existing historical accelerometer-based data becomes crucial. Transfer learning emerges as a promising solution, allowing deep learning models trained on a source domain (SD) to be applied to a separate but related target domain (TD). This paper hence introduces a domain adaptation methodology by implementing transfer learning, where the SD 1D-CNN network is trained on accelerometer signals, then the trained model weights are transferred to the TD 1D-CNN network that can process acoustic signals.

Vibration measurement technique by using OFDR with in-line interferometers

Due to their compact size, electromagnetic interference immunity, and compatibility with embedding in composite materials, optical fiber sensors have emerged as a versatile and integral solution for structural health monitoring (SHM) in various structures. Among the key contributors to the evolution of this field is the significant progress in optical frequency domain reflectometry (OFDR), a technology that offers unparalleled high resolution and sensitivity in distributed strain sensing, thereby establishing itself as an indispensable tool in the realm of SHM. Through the implementation of OFDR, we devised a distributed fiber optic sensor tailored for the precise measurement of vibration or strain within structures. In previous works, vibration monitoring has been achieved using an OFDR with an array of 20 in-line interferometers, serving as weak reflectors that not only facilitated vibration monitoring but also furnished valuable strain information. In this study takes a step further by introducing an innovative technique wherein in-line interferometers are strategically arranged in a non-uniform fashion along the optical fiber. To validate the practical utility of this technology, extensive simulations and experiments were conducted, utilizing a cantilever beam as a representative structure. The results obtained from these endeavors showcase the tangible potential and reliability of optical fiber sensors in the practical implementation of SHM across various applications. By enhancing the precision and scope of structural monitoring, optical fiber sensors equipped with non-uniform interferometer arrangements pave the way for more effective and comprehensive structural health assessment in diverse settings.

PSD estimation and modal parameter identification for random vibrations with blade tip timing measurement

Abstract Blade tip timing (BTT) is a vibration measurement technique for blade health monitoring. Most of the existing BTT analysis methods are suitable for deterministic vibration signals but are ineffective for random vibration signals that often occur in practice. Statistical analysis of BTT data is significant for random vibration analysis and improving blade monitoring efficiency. This study proposes a compressive model for power spectral density (PSD) estimation and modal parameter identification. The efficiencies of three compressive sensing algorithms, including the least absolute shrinkage and selection operator (Lasso), nonnegative least squares (NLS), and nonnegative orthogonal matching pursuit, are compared. The effects of the duration of the signal and the frequency resolution on the quality of the estimated PSD and the identified parameters are discussed. According to the analysis, to obtain accurate damping ratios, it is recommended that the duration of the signal be greater than 3000 revolutions. A Q criterion based on the half-power bandwidth is proposed to determine the set of frequency resolutions. Numerical and field tests were conducted to verify the proposed method. The results indicate that the NLS algorithm is recommended to use. The root-mean-square errors of the identified natural frequencies and damping ratios obtained by the proposed method were 0.065 Hz and 0.023%, respectively. The proposed method was verified at different rotational speeds in a field test, demonstrating the capability of the method over a wide rotational speed range and providing more opportunities to detect blade damage.

Structural intensity in thin plates and beams under transient and stationary forces using time-resolved, full-field optical slope measurements

Structural intensity, or structure-borne intensity or power flow, was introduced in the 1970s and implemented at that time using contact sensors like accelerometers. Point and contactless measurement methods removed added mass and sensor size constraints. Time-resolved and full-field vibration measurement techniques now open new perspectives for the estimation of structural intensity, but these prospects also come with many challenges. In this work, we study the applicability of optical deflectometry measurements to calculate the structural intensity in thin plates or beams under transient and stationary loadings. Since deflectometry directly provides slope fields, a slope formulation of structural intensity is proposed and evaluated. The effect of various parameters like frame rate (sampling frequency) and spatial resolution is studied from a numerical point of view on a simply-supported plate. Experimental results are then presented on a simply-supported plate and on a cantilever beam. Numerical and experimental results allow identifying the main challenges related to the implementation of structure intensity estimation using full-field and time-resolved data.

Investigation of Dynamic Characteristics of Vibrating Components and Structure Through Vibration Measurement and Operational Modal Analysis

Smooth plant production is utmost expected by plant owners since any unplanned shutdown is very much undesirable as it may incur loss of company’s profits and other repercussions. Critical operational assets such as rotating machineries and their components, e.g., motor, pump, compressor, and turbines are crucial to be monitored in ensuring continuous operation of the plant. Therefore, vibration being one of the elements in predictive maintenance is much needed. This paper addressesthe monitoring and findings for predictive maintenance on high vibration of a make-up gas compressor in one of the oil & gas and petrochemical plant in Malaysia. The conventional vibration measurement using vibration analyzer was utilized to identify the severity of the machine vibrations through the overall vibration value obtained on the motor and compressor. A specialized vibration measurement technique, namely, Operational Modal Analysis (OMA) was further deployed to verify the presence of resonance on the equipment by obtaining its dynamic characteristics, i.e., natural frequency and mode shape. The findings showed clear indication of resonance occurrence as similar frequency (112 Hz) was identified from both vibration measurement and operational modal analysis.

In situ monitoring of initial plasma electrolytic oxidation process on 60 vol. % SiCp/2009 aluminum matrix composite by sound and vibration measurement techniques.

The initial discharge process of plasma electrolytic oxidation (PEO) on the 60 vol. % SiCP/2009 aluminum matrix composite in silicate solution was in situ monitored by sound and vibration measurement techniques. The underwater sound, airborne sound, and sample vibration signals were detected in the initial 120s of the PEO process, and their generation mechanism was discussed. In terms of waveforms and spectrograms of the sound and vibration signals, the initial PEO process can be divided into five stages: conventional anodizing stage (I), glow discharge stage (Ⅱ), tiny spark discharge stage (Ⅲ), large spark discharge stage (Ⅳ), and strong spark discharge stage (Ⅴ). The sound and vibration signals during the PEO process are attributed to the evolution of bubbles, which are from the plasma discharge, electrochemical reactions, and vaporization of electrolyte under Joule heat. In stage I, these signals completely come from the bubbles produced by the evaporative electrolyte and electrochemical reactions. In stages Ⅱ-Ⅴ, the bubbles from the plasma discharge gradually become the main source of these signals with increasing discharge intensity. In addition, the spike peaks on the waveforms of these signals at stage Ⅴ are related to the strong discharge sparks. These results demonstrate that sound and vibration measurement techniques can effectively monitor the PEO discharge process.

Position sensitive detector based non-contact vibration measurement with laser triangulation method utilizing Gabor Transform for noise reduction

Measurement of vibration without having contact with the target is crucial for many applications. However, real time vibration signals are frequently mixed with various levels of dynamic noises. In this research, a non-contact type vibration measurement system based on laser triangulation method is proposed by using a PSD (Position sensitive detector) and here a single axis Brüel and Kjaer piezoelectric accelerometer is used to validate the experimental results. The primary goal of this measurement system is to develop a Gabor Transform based signal denoising technique, in order to eliminate noise from the real-time vibration data. Furthermore, PSD platform vibration, which might cause unanticipated inaccuracies in the detected vibration data, has also been eliminated by utilizing a self-vibration compensation approach using an ADXL-345 three-axis accelerometer. The self-vibration compensated vibration measurement technique has been designed using an NI (national instruments) cRIO (CompactRIO) 9074 real-time FPGA (field programmable gate array) based embedded controller. Consequently, a Gabor Transform and Expansion-based Signal Processing Technique is designed using NI cRIO-9074 real time platform to reduce external noise from the self-vibration compensated vibration data. It has been observed that the implementation of Gabor Transform has improved the performance of the system in term of enhancing the SNR (Signal-to-noise ratio).

Vibration signal separation of rotating cylindrical structure through target-less photogrammetric approach

Vibration analysis is one of the most widely used methodologies for structural health monitoring. For vibration monitoring of structures, contact-type sensors, such as gap sensors, are commonly utilized. However, these devices can add mass loading to a lightweight structure, resulting in degradation in performance of the structure. As an alternative, photogrammetric approaches, such as digital image correlation and point-tracking techniques have been proposed for vibration measurement. Despite the many advantages of image-based techniques applied by non-contact-type sensors, these are ineffective in detecting vibrations at the outer edge of a rotating cylinder-shaped structure because tracking of the speckles or targets on the backside of a structure invisible to a camera is impossible. Furthermore, vibrations occurring in structures are usually attributed to multiple factors; to identify these factors individually, the vibration signals should be detected separately. In this study, we introduce a noncontact-based vibration signal separation technique that can be used to recognize multiple factors that cause a structure to vibrate at different frequency rates. For this purpose, the vibration occurring in a structure is first detected using an edge-based vibration measurement technique. A phase-based motion magnification technique is then used to generate multiple magnified videos at different dominant frequencies. Subsequently, vibrations were detected in multiple magnified videos to separate vibration signals. To demonstrate the effectiveness of the proposed method, quantitative and qualitative assessments were conducted on both simulation and real video datasets containing vibrations with multiple frequency rates. The results generated by this method can be utilized for health monitoring of various types of structures on which targets, necessary for the general photogrammetry approach for monitoring purposes, are not attached. Furthermore, the magnified videos generated in this study can be used for the visualization and mode identification of existing vibration signals at different frequencies in a structure.

Research on the identification of asynchronous vibration parameters of rotating blades based on blade tip timing vibration measurement theory

The identification of rotating blade vibration parameters is crucial for diagnosing the health of the blades. While there are many rotating blade vibration measurement techniques, the tip timing vibration theory is currently used by most for non-contact rotating blade vibration measurements, which presents a number of challenges in its practical implementation. However, the traditional bladetip timing vibration measurement method is less involved in the calculation of vibration displacement and vibration data pre-processing and the frequency mixing problem brought on by undersampling is not fully analyzed. The majority of methods to increase measurement accuracy are studied in depth in data post-processing. The accuracy of identifying the spinning blade vibration parameters is lowered, and even identification error arises, as a result of measuring noise interference and the impact of frequency overlap. This work adjusts the calculation of blade tip vibration displacement based on the theory of blade tip timing vibration measurement and applies the Savitzky-Golay noise filtering technique to increase calculation accuracy. To combat the effect of frequency confusion brought on by undersampling and increase the precision of asynchronous vibration parameter detection of spinning blades, the synthetic phase difference spectrum correction method is adopted. In the experiments described in this work, a revolving blade is excited by an electromagnetic exciter to create vibrations at a single frequency. To determine the blade asynchronous vibration characteristics at various rotation speeds, rotating blade asynchronous vibration tests were carried out on a rotor blade table. The outcomes demonstrate that the blade asynchronous vibration parameters can be accurately identified using the parameter identification method, and the maximum vibration frequency identification error is 7.2%, demonstrating the accuracy of the blade asynchronous vibration parameter identification method.

Edge-based 3D vibration measurement of rotating cylinder-shaped structure through epipolar line-based corresponding point extraction between two camera images

Three-dimensional (3D) vibration measurements are important for monitoring rotating structures in order to reproduce the directional displacements of vibration signals such that they are similar to the actual movement. Photogrammetric techniques, which can be used to determine the relationship between 3D objects and their two-dimensional images, allow 3D vibrations in a structure to be measured without direct contact. Therefore, we herein present a multipoint 3D vibration measurement approach for rotating cylinder-shaped structures, which performs the imaging of a structure from two directions using two cameras. First, an epipolar line-based corresponding point extraction technique is applied to extract the corresponding regions of interest (ROIs) in videos acquired by the two cameras placed at 90° to the structure. Subsequently, an edge-based vibration measurement approach is used to detect vibrations in the corresponding ROIs. Noise reduction is then applied to reduce the noise, induced by the cameras or edge-based vibration measurement technique, by extracting and employing the frequencies at which the vibrations were occurring to the phase-based motion magnification technique. Subsequently, vibrations in the corresponding ROIs of the magnified videos are detected. For 3D plotting, the two vibration signals are combined. Simulation and real datasets are prepared for the qualitative and quantitative assessments of the proposed method. The simulation data results are compared with the results obtained before noise reduction, those obtained after noise reduction via bandpass filtering, and the reference data. A 3D vibration analysis is performed on the real data in multiple ROIs. The results yielded by the proposed method can be used to identify the weak points in a rotating cylinder-shaped structure that cause the structure to function abnormally.

Microphone vibration sensitivity: What it is, why it is important, and how to measure it

Microphones are designed to respond to acoustic pressure fields, but they can also be excited by external sources of mechanical vibration. In hearing aids, feedback is a difficult problem to resolve due to the high gain used to amplify sounds. The problem is worsened by the location of microphones and loudspeakers in close proximity, coupling both the acoustic and mechanical feedback paths. The first proposals of microphone vibration measurement techniques and definitional structure were published by Mead Killion in the 1970’s. Significant improvements in measurement technique have been published over the last 10 years. This talk will focus on a new measurement technique that allows for direct measurement of the “intrinsic vibration sensitivity”. The technique gives the ideal zero acoustic pressure condition at the microphone port and isolates room acoustic noise from the desired vibration signal. The noise floor of the new technique is 30 dB below previous methods, allowing for exceptionally clean measurement of primary-axis vibration sensitivity up to 10 kHz. Improvements are robust enough to enable the clean measurement of off-axis sensitivity of the microphone, which is often below 50 dBspl equivalent at 9.81 m/s2 of acceleration.

Miniaturization of Laser Doppler Vibrometers-A Review.

Laser Doppler vibrometry (LDV) is a non-contact vibration measurement technique based on the Doppler effect of the reflected laser beam. Thanks to its feature of high resolution and flexibility, LDV has been used in many different fields today. The miniaturization of the LDV systems is one important development direction for the current LDV systems that can enable many new applications. In this paper, we will review the state-of-the-art method on LDV miniaturization. Systems based on three miniaturization techniques will be discussed: photonic integrated circuit (PIC), self-mixing, and micro-electrochemical systems (MEMS). We will explain the basics of these techniques and summarize the reported miniaturized LDV systems. The advantages and disadvantages of these techniques will also be compared and discussed.

EPIPOLAR LINE-BASED LATERAL VIBRATION MEASUREMENT BY USING TWO CAMERAS

Abstract. Vibration measurement techniques can be categorized into contact-type and non-contact-type techniques. These types of techniques can add mass-loading to a lightweight structure resulting in the negative performance of a structure, because sensors, high contrast speckles or targets should be mounted on a structure. Moreover, non-contact-type vibration measurement techniques have only been tested to detect vibrations using a single camera. As the vibrations occurring at the opposite sides of a rotating structure in a region of interest (ROI) can be different from each other. For 3-dimensional (3D) vibration measurement, the same position in videos acquired from two cameras should be used. Because the videos acquired by two cameras placed perpendicular to the structure can be used to detect the vibrations in the x-direction as well as y-direction. In this study, an epipolar line-based corresponding point selection on a rotating cylindrical structure was performed, to extract the same ROIs from videos recorded by two cameras. A fundamental matrix was constructed by using the targets attached on the structure and in the background. The coordinates of the mid-pixel of the ROI in a video acquired by one camera was used to determine the epipolar line for the same ROI in the video acquired by another camera. Then an edge-based vibration measurement technique was applied to measure the vibration in the extracted ROIs. The results were used to reconstruct a 3D vibration signal. The 3D vibration measurement results can be used to effectively recognize the deformations resulting in the negative performance of a structure.

Multi-level deformation behavior monitoring of flexural structures via vision-based continuous boundary tracking: proof-of-concept study

The concept of measuring the multi-level deformation behavior of flexural structures via the extraction of continuous structural boundaries using a computer vision technique is proposed. The feasibility of using a salient-object-detection method to estimate the deformation and curvature profile of target structures from the image frames of a video recording structural vibrations is investigated. A framework is proposed for performing this salient-object-detection-based vibration measurement technique via the aid of a pre-trained deep neural network. A method for determining the curvature estimated from the boundary extracted from the deep neural network is then introduced. The accuracy of the proposed technique is validated via two experiments. The first experiment measures the curvature of a semi-circular plate under rigid body motions. The second experiment tracks the deformation of reinforced concrete beams under impact loads. Both experiments verify that the proposed method is feasible for accurately measuring the vibration profile of the target structure.

Phase-Based Displacement Sensor With Improved Spatial Frequency Estimation and Data Fusion Strategy

Phase-based vibration measurement has attra- cted a lot of attention due to its advantages of wireless, non-contact, and full-field measurement capabilities. The phase shifts across the different video frames correspond to the motion of the structure, which makes it possible to measure the vibration with the phase. However, the decoding of the phase shifts and the presence of the phase singularities make the phase-based method noise-sensitive and non-robust when concerning vibration measurement. Within this paper, an improved framework is proposed to enhance the performance of the phase-based technique for vibration measurement. A double filtering approach combined with the O’Shea refinement is introduced to decrease the phase noise to obtain accurate spatial frequency estimates. Then a confidence measure index is constructed to evaluate the reliability of phase responses to avoid the outliers induced by the phase singularities. Finally, an information fusion strategy over multiple scales is developed to enhance the accuracy and robustness of the motion estimation. Both simulated and experimental results verify the effectiveness and accuracy of the proposed framework.

Continuous video stream pixel sensor: A CNN‐LSTM based deep learning approach for mode shape prediction

Modal analysis has emerged as a globally accepted tool to formulate and optimize the behavioral functions of engineering structures, which assists in assessing structural failure and laying out a plan for their maintenance. Modal analysis aims at determining the frequencies, damping ratios, and mode shapes of the system under excitation. However, conventional mode shape measurement methods like contact sensors are prone to precision and accuracy issues owing to the sensor's weight and low spatial resolution. In this paper, we improve upon various existing methods for mode shape determination and introduce the idea of a full-field pixel sensor for mode shape prediction. The proposed computer vision-based deep learning architecture predicts the mode shape of a vibrating structure with significant precision. Besides, a ModeShape dataset consisting of the vibration recording video and finite element analysis (FEA) based label has been curated. Specifically, we introduce a convolutional neural network, long short-term memory (CNN-LSTM) computer vision-based non-contact vibration measurement technique for automated mode shape prediction. The key idea is to use each pixel of a RGB camera as a sensor and process the captured spatio-temporal data to enable mode shape prediction. Our CNN-LSTM model takes the video streams of a vibrating structure as input and yields the fundamental mode shapes. The proposed technique is non-invasive and can extract information at relatively high spatial density. The CNN-LSTM model is proficient by utilizing experimental outcomes. The robustness of the deep learning model has been scrutinized by utilizing specimens of an assortment of different materials and fluctuating dimensions.

Research on high-temperature vibration measurement method using laser Doppler interferometry

High-temperature vibration measurement plays a critical role in the design and performance testing of equipment such as aero-engine and heavy-duty gas turbines. Due to its non-contact, high accuracy, and resolution, the laser Doppler method has become one of the most commonly used vibration measurement techniques. However, one of the main problems in high-temperature vibration measurement is that the surface of the measured objects is oxidized, thus resulting in a decrease of interference signal intensity and signal-to-noise ratio. Furthermore, the aforementioned may even cause measurement failure. In this paper, an all-fiber laser Doppler velocity measurement device using a fiber optic circulator is established. Its vibration measurement performance is experimentally validated at high temperatures. The results demonstrate that this device can achieve vibration measurement within the temperature range of 300°C-1200°C with a maximum vibration speed of 1 m/s and maximum vibration acceleration of 378.4 m/s2. Relative deviation with Polytec vibrometer’s velocity results is within 1.95%. This model provides a viable solution for achieving accurate measurements of high-temperature vibration.

The CSLDV Technique for Vibration Measurement of a Plate Structure with Arbitrary Rectangular Holes

The Continuous Scanning Laser Doppler Vibrometry (CSLDV) developed on the base of the galvanometer scanner system has made it possible to quickly obtain the full-field vibration responses within an intact structure without any hole. In order to make CSLDV also suitable for testing structures with arbitrary rectangular holes, a novel method of area-partitioned continuous scanning test and mode reconstruction is further proposed in this paper. In the first step, the surface of a flat plate structure with arbitrary rectangular holes is divided into several rectangular sub regions by an appropriate area-partitioned method, and the operational deflection shape(ODS) of each sub region is obtained by a continuous scanning at constant speed. Then, considering that the ODSs of all sub regions are spliced and the relative phases among them are different, the operational deflection shape of the whole structure is reconstructed based on linear function and other process. Finally, a plate structure with two arbitrary rectangular holes was taken as an example for modal test using the proposed method. At the same time, a validated experiment was performed using the SLDV measurement. The results show the mode shapes derived from the extended CSLDV are in agreement with those from SLDV and the Modal Assurance Criterion (MAC) between the two are all greater than 0.95. This method has great potential in practical engineering applications with the advantages of high efficiency and the full-field measurement.

Baseline-Free Damage Identification Method for Lattice Sandwich Structures Based on Operational Deflection Shapes

ABSTRACT A novel baseline-free damage identification method based on high frequency operational deflection shapes (ODSs) is presented for debonding detection in lattice sandwich structures (LSSs). Two numerical models with different unit cells are constructed to analyze the vibration characteristics of a structure with debonded defect in the high-frequency band. The mode shapes and ODSs are computed numerically to investigate the local defect vibration effects. The results show that there will be obvious local vibration at the damaged location at a certain and appropriate frequency band. A baseline-free damage index calculated from ODSs is originally proposed for damage imaging. For experimental validation, we suggested an intermittent periodic excitation signal for vibration actuating, which may excite multiple ODSs at different frequencies using one measurement that significantly improve the detection efficiency. The experimental results also indicated that the proposed damage identification method is effective to locate the debonding damage in LSSs. The conclusions derived from this study are expected to provide an efficient vibration measurement technique and a practical damage detection method for LSSs, as well as other plate-like structures.