Microsphere-Based Microsensor for Miniature Motors' Vibration Measurement

We present a microsphere-based microsensor that can measure the vibrations of the miniature motor shaft (MMS) in a small space. The microsensor is composed of a stretched fiber and a microsphere with a diameter of 5 μm. When a light source is incident on the microsphere surface, the microsphere induces the phenomenon of photonic nanojet (PNJ), which causes light to pass through the front. The PNJ's full width at half maximum is narrow, surpassing the diffraction limit, enables precise focusing on the MMS surface, and enhances the scattered or reflected light emitted from the MMS surface. With two of the proposed microsensors, the axial and radial vibration of the MMS are measured simultaneously. The performance of the microsensor has been calibrated with a standard vibration source, demonstrating measurement errors of less than 1.5%. The microsensor is expected to be used in a confined space for the vibration measurement of miniature motors in industry.

Rail Corrugation Index Development by Sound-Field Excitation on the Carriage Floor of In-Service Train

The steel rail and wheel in the railway system offer a high precision and smooth-running surface. Nevertheless, the point of contact between the rail and wheel presents a critical area that can give rise to rail corrugation. This phenomenon can potentially elevate sound and vibration levels in the vicinity considerably, necessitating advanced monitoring and assessment measures. Recently, many efforts have been directed towards utilizing in-service trains for evaluating rail corrugation, and the evaluation has primarily relied on axle-box acceleration (ABA). However, the ABA measurements require a higher threshold for vibration detection. This study introduces a novel approach to rail corrugation detection by carriage floor acceleration (CFA), aimed at lowering the detection threshold. The method capitalizes on the acceleration data sensed on the carriage floor, which is induced by the sound pressure (e.g., sound-field excitation) generated at the wheel-rail contact point. An exploration of the correlation between these datasets is undertaken by simultaneously measuring both ABA and CFA. Moreover, a pivotal aspect of this research is the development of the eigenfrequency rail corrugation index (E-RCI), a mechanism that culminates energy around specific eigenfrequencies by CFA. Through this index, a focused analysis of rail corrugation patterns is facilitated. The study further delves into the stability, repeatability, and sensitivity of the E-RCI via varied measurement scenarios. Ultimately, the CFA-based rail corrugation identification is verified, establishing its practical applicability and offering a distinct approach to detecting and characterizing rail corrugation phenomena. This study has introduced an innovative methodology for rail corrugation detection using CFA, with the principal objective of lowering the detection threshold. This approach offers an efficient measurement technique for identifying rail corrugation areas, thereby potentially reducing maintenance costs and enhancing efficiency within the railway industry.

Assessment of Fiber Bragg Grating Sensors for Monitoring Shaft Vibrations of Hydraulic Turbines

The structural dynamic response of hydraulic turbines needs to be continuously monitored to predict incipient failures and avoid catastrophic breakdowns. Current methods based on traditional off-board vibration sensors mounted on fixed components do not permit inferring loads induced on rotating parts with enough accuracy. Therefore, the present paper assesses the performance of fiber Bragg grating sensors to measure the vibrations induced on a rotating shaft-disc assembly partially submerged in water resembling a hydraulic turbine rotor. An innovative mounting procedure for installing the sensors is developed and tested, which consists of machining a thin groove along a shaft line to embed a fiber-optic array that can pass through the bearings. At the top of the shaft, a rotary joint is used to extract, in real time, the signals to the interrogator. The shaft strain distribution is measured with high spatial resolution at different rotating speeds in air and water. From this, the natural frequencies, damping ratios, and their associated mode shapes are quantified at different operating conditions. Additionally, the change induced in the modes of vibration by the rotation effects is well captured. All in all, these results validate the suitability of this new fiber-optic technology for such applications and its overall better performance in terms of sensitivity and spatial resolution relative to traditional equipment. The next steps will consist of testing this new sensing technology in actual full-scale hydraulic turbines.

High-Temperature Fiber-Optic Fabry-Perot Vibration Sensor Based on Single-Crystal Sapphire

In this paper, a fiber-optic Fabry-Perot (F-P) vibration sensor that can work at 800 °C is proposed. The F-P interferometer is composed of an upper surface of inertial mass placed parallel to the end face of the optical fiber. The sensor was prepared by ultraviolet-laser ablation and three-layer direct-bonding technology. Theoretically, the sensor has a sensitivity of 0.883 nm/g and a resonant frequency of 20.911 kHz. The experimental results show that the sensitivity of the sensor is 0.876 nm/g in the range of 2 g to 20 g at an operating frequency of 200 Hz at 20 °C. The nonlinearity was evaluated from 20 °C to 800 °C with a nonlinear error of 0.87%. In addition, the z-axis sensitivity of the sensor was 25 times higher than that of the x-axis and y-axis. The vibration sensor will have wide high-temperature engineering-application prospects.

Design and Development of a MOEMS Accelerometer Using SOI Technology

The micro-electromechanical system (MEMS) sensors are suitable devices for vibrational analysis in complex systems. The Fabry-Pérot interferometer (FPI) is used due to its high sensitivity and immunity to electromagnetic interference (EMI). Here, we present the design, fabrication, and characterization of a silicon-on-insulator (SOI) MEMS device, which is embedded in a metallic package and connected to an optical fiber. This integrated micro-opto-electro-mechanical system (MOEMS) sensor contains a mass structure and handle layers coupled with four designed springs built on the device layer. An optical reading system using an FPI is used for displacement interrogation with a demodulation technique implemented in LabVIEW^®. The results indicate that our designed MOEMS sensor exhibits a main resonant frequency of 1274 Hz with damping ratio of 0.0173 under running conditions up to 7 g, in agreement with the analytical model. Our experimental findings show that our designed and fabricated MOEMS sensor has the potential for engineering application to monitor vibrations under high-electromagnetic environmental conditions.

Excitation of Mechanical Resonances in the Stationary Ring of a Mechanical Seal by a Continuously Operated Electromagnetic Acoustic Transducer

Acoustic/ultrasonic testing is now a common method in the field of nondestructive testing for detecting material defects or monitoring ongoing mechanical changes in a structure during operation. In many applications, piezoelectric transducers are used to generate mechanical waves inside the specimen. Their actual operating frequency is highly dependent on the dimensions of the transducer. Larger dimensions of the piezoelectric transducer allow for a lower operating frequency. However, these dimensions limit the use of piezoelectric transducers in certain applications where the size of the transducer is restricted due to limited installation space and when low-frequency excitation is required. One application that places these requirements on the transducer is the monitoring of mechanical seals. Here, the transducer must be mounted on the stationary ring of the seal. In this paper, a continuously operated electromagnetic acoustic transducer (EMAT) is presented as an alternative to piezoelectric transducers as a transmitter. The advantage of a EMAT is that it meets the requirements of limited sensor size (sensor area < 10 × 6 mm) and can excite mechanical waves with frequencies below 10 kHz. A structural analysis of the stationary ring shows that the first two mechanical resonances occur around 4 and 5.5 kHz. An experimental study meterologically demonstrates the ability of the EMAT to excite these first two mechanical resonances of the ring. A comparative simulation agrees well with the measurement.

Three Dimensional Membrane Vibration Measurement Using a Two Dimensional Position Sensitive Device

This study presents the outcome of research into membrane vibrations in a 3D space performed using a system based on position sensitive device (PSD) sensors. Here, measurements were conducted for harmonic vibrations. The use of such detectors for assessing the movement of objects within a plane or space requires determining the position of more than one marker. The article reviews two methods for detecting the position of several light spots on a sensor's photosensitive plane: a marker sequential control method, and a method based on Fast Fourier Transform (FFT) that employs a square wave control signal. The authors present an approach to improving measurement accuracy for both methods. They also discuss the advantages and disadvantages of each.

Combined Feature Extraction and Random Forest for Laser Self-Mixing Vibration Measurement without Determining Feedback Intensity

To measure the vibration of a target by laser self-mixing interference (SMI), we propose a method that combines feature extraction and random forest (RF) without determining the feedback strength (C). First, the temporal, spectral, and statistical features of the SMI signal are extracted to characterize the original SMI signal. Secondly, these interpretable features are fed into the pretrained RF model to directly predict the amplitude and frequency (A and f) of the vibrating target, recovering the periodic vibration of the target. The results show that the combination of RF and feature extraction yields a fit of more than 0.94 for simple and quick measurement of A and f of unsmooth planar vibrations, regardless of the feedback intensity and the misalignment of the retromirror. Without a complex optical stage, this method can quickly recover arbitrary periodic vibrations from SMI signals without C, which provides a novel method for quickly implementing vibration measurements.

Comparative In Situ Study of Dynamic Load Generated by Gravel Piles Measured by a Fiber-Optic Interferometer

Currently, all the technology used for seismic monitoring is based on sensors in the electrical domain. There are, however, other physical principles that may enable and fully replace existing devices in the future. This paper introduces one of these approaches, namely the field of fiber optics, which has great potential to be fully applied in the field of vibration measurement. The proposed solution uses a Michelson fiber-optic interferometer designed without polarization fading and with an operationally passive demodulation technique using three mutually phase-shifted optical outputs. Standard instrumentation commonly used in the field of seismic monitoring in geotechnical engineering was used as a reference. Comparative measurements were carried out during the implementation of gravel piles, which represents a significant source of vibration. For the correlation of the data obtained, the linear dependence previously verified in laboratory measurements was used. The presented results show that the correlation is also highly favorable (correlation coefficient in excess of 0.9) from the values measured in situ, with an average deviation for the oscillation velocity amplitude of the optical sensor not exceeding 0.0052.

A New Pattern Quality Assessment Criterion and Defocusing Degree Determination of Laser Speckle Correlation Method

The laser speckle correlation method has found widespread application for obtaining information from vibrating objects. However, the resolution and accuracy of the laser speckle correlation method as they relate to the defocusing degree have not been analyzed sufficiently. Furthermore, the possible methods for speckle pattern quality assessment and enhancement have not been studied. In this study, the resolution and accuracy of the laser speckle correlation method are analyzed, and it is found that they are affected by the defocusing degree and speckle pattern quality, respectively. A new speckle pattern quality criterion combining the mean intensity gradient and frequency spectrum was proposed, called CMZ. The quality of the speckle pattern is higher when the CMZ is closer to zero. The proposed criterion was verified by simulated speckle patterns and real speckle patterns with different speckle sizes, densities, and gray contrasts. In the experimental setup stage, a suitable defocusing degree can be selected based on the resolution requirement and optimal speckle size, and other experimental parameters can be determined according to the CMZ criterion. Rotation and vibration experiments verified the effectiveness of the laser speckle correlation method and confirmed the reliability of the experiment preparation based on proposed CMZ criterion.

Fiber Bragg Grating Sensors for Underwater Vibration Measurement: Potential Hydropower Applications

The present paper assesses the performance and characteristics of fiber Bragg grating sensors, with a special interest in their applications in hydraulic machinery and systems. The hydropower industry is turning to this technology with high expectations of obtaining high quality data to validate and calibrate numerical models that could be used as digital twins of key assets, further strengthening the sector’s relevant position within industry 4.0. Prior to any validation, fiber Bragg grating sensors’ ability to perform well underwater for long periods of time with minimal degradation, and their ease of scalability, drew the authors´ attention. A simplified modal analysis of a partially submerged beam is proposed here as a first step to validate the potential of this type of technology for hydropower applications. Fiber Bragg grating sensors are used to obtain the beam’s natural frequencies and to damp vibrations under different conditions. The results are compared with more established waterproof electric strain gauges and a laser vibrometer with good agreement. The presence of several sensors in a single fiber ensures high spatial resolution, fundamental to precisely determine vibration patterns, which is a main concern in this industry. In this work, the beam’s vibration patterns have been successfully captured under different excitations and conditions.

A Novel Feature Extraction and Fault Detection Technique for the Intelligent Fault Identification of Water Pump Bearings

The reliable and cost-effective condition monitoring of the bearings installed in water pumps is a real challenge in the industry. This paper presents a novel strong feature selection and extraction algorithm (SFSEA) to extract fault-related features from the instantaneous power spectrum (IPS). The three features extracted from the IPS using the SFSEA are fed to an extreme gradient boosting (XBG) classifier to reliably detect and classify the minor bearing faults. The experiments performed on a lab-scale test setup demonstrated classification accuracy up to 100%, which is better than the previously reported fault classification accuracies and indicates the effectiveness of the proposed method.

Vibration-based drilling depth estimation of bone

Drilling is one of the most common forms of tissue removal procedures, and drilling to a desired depth contributes to avoid injury to the soft tissue beyond and ensure implant stability. The deformation of the human musculoskeletal system has been a common problem in many drilling processes, making it difficult to achieve accurate estimation of the drilling depth. To remedy this problem, a dynamic model is presented to describe the relationship between the axial vibration of the drill and the feed rate. During drilling process, the amplitude of the main harmonic is estimated from the high-frequency component of the acceleration signal, while the short-time integral of the low-frequency part is calculated. Both the initial contact of the drilling tool to the bone and breakthrough are identified by comparing either the harmonic amplitude or the short-time integral. The harmonic amplitude is mapped to the data from a non-contact position sensor tracking the feed rate of the drill. Multiple drilling experiments on both a handheld device and a robotic cutting system demonstrated the effectiveness, stability and accuracy of the method when estimating depth. The mean maximum error for drilling depth estimation is less than 15% of the simulated bone thickness when using the handheld device, while the mean maximum error is less than 5% for the robotic cutting system.

Feature Space Transformation for Fault Diagnosis of Rotating Machinery under Different Working Conditions

In recent years, various deep learning models have been developed for the fault diagnosis of rotating machines. However, in practical applications related to fault diagnosis, it is difficult to immediately implement a trained model because the distribution of source data and target domain data have different distributions. Additionally, collecting failure data for various operating conditions is time consuming and expensive. In this paper, we introduce a new transformation method for the latent space between domains using the source domain and normal data of the target domain that can be easily collected. Inspired by semantic transformations in an embedded space in the field of word embedding, discrepancies between the distribution of the source and target domains are minimized by transforming the latent representation space in which fault attributes are preserved. To match the feature area and distribution, spatial attention is applied to learn the latent feature spaces, and the 1D CNN LSTM architecture is implemented to maximize the intra-class classification. The proposed model was validated for two types of rotating machines such as a dataset of rolling bearings as CWRU and a gearbox dataset of heavy machinery. Experimental results show the proposed method has higher cross-domain diagnostic accuracy than others, therefore showing reliable generalization performance in rotating machines operating under various conditions.

Performance of Optical Structural Vibration Monitoring Systems in Experimental Modal Analysis

Image-based optical vibration measurement is an attractive alternative to the conventional measurement of structural dynamics predominantly relying on accelerometry. Although various optical vibration monitoring systems are now readily available, their performance is currently not well defined, especially in the context of experimental modal analysis. To this end, this study provides some of the first evidence of the capability of optical vibration monitoring systems in modal identification using input–output measurements. A comparative study is conducted on a scaled model of a 3D building frame set in a laboratory environment. The dynamic response of the model to an impulse excitation from an instrumented hammer, and an initial displacement, is measured by means of five optical motion capture systems. These include commercial and open-source systems based on laser Doppler velocimetry, fiducial markers and marker-less pattern recognition. The performance of these systems is analysed against the data obtained with a set of high-precision accelerometers. It is shown that the modal parameters identified from each system are not always equivalent, and that each system has limitations inherent to its design. Informed by these findings, a guidance for the deployment of the considered optical motion capture systems is given, aiding in their choice and implementation for structural vibration monitoring.

Suboptimal Omnidirectional Wheel Design and Implementation

The optimal design of an omnidirectional wheel is usually focused on the minimization of the gap between the free rollers of the wheel in order to minimize contact discontinuities with the floor in order to minimize the generation of vibrations. However, in practice, a fast, tall, and heavy-weighted mobile robot using optimal omnidirectional wheels may also need a suspension system in order to reduce the presence of vibrations and oscillations in the upper part of the mobile robot. This paper empirically evaluates whether a heavy-weighted omnidirectional mobile robot can take advantage of its passive suspension system in order to also use non-optimal or suboptimal omnidirectional wheels with a non-optimized inner gap. The main comparative advantages of the proposed suboptimal omnidirectional wheel are its low manufacturing cost and the possibility of taking advantage of the gap to operate outdoors. The experimental part of this paper compares the vibrations generated by the motion system of a versatile mobile robot using optimal and suboptimal omnidirectional wheels. The final conclusion is that a suboptimal wheel with a large gap produces comparable on-board vibration patterns while maintaining the traction and increasing the grip on non-perfect planar surfaces.

Nanometer-Scale Vibration Measurement Using an Optical Quadrature Interferometer based on 3 × 3 Fiber-Optic Coupler

We propose a nanometer-scale displacement or vibration measurement system, using an optical quadrature interferometer and the post-processing technique that extracts the parameters necessary for characterizing the interferometric system. Using a 3 × 3 fiber-optic coupler, the entire complex interference signal could be reconstructed with two interference signals measured at two return ports of the coupler. The intrinsic phase difference between the return ports was utilized to obtain the quadratic part of the interference signal, which allowed one to reconstruct the entire complex interference signal. However, the two measured signals were appreciably affected by the unequal detector gains and non-uniform intrinsic phases of the coupler. Fortunately, we could find that the Lissajous curve plotted by the two signals of the interferometric system would form an ellipse. Therefore, by fitting the measured Lissajous curve to an ellipse, we could extract the parameters characterizing the actual system, which allowed the nanometer-scale measurement. Experimental results showed that a 20 kHz sinusoidal vibration with an amplitude of 1.5 nm could be measured with a standard deviation of 0.4 nm.

An In-Line Fiber Optic Fabry-Perot Sensor for High-Temperature Vibration Measurement

An in-line fiber optic Fabry–Perot (FP) sensor for high-temperature vibration measurement is proposed and experimentally demonstrated in this paper. We constructed an FP cavity and a mass on single-mode fibers (SMFs) by fusion, and together they were inserted into a hollow silica glass tube (HST) to form a vibration sensor. The radial dimension of the sensor was less than 500 μm. With its all-silica structure, the sensor has the prospect of measuring vibration in high-temperature environments. In our test, the sensor had a resonance frequency of 165 Hz. The voltage sensitivity of the sensor system was about 11.57 mV/g and the nonlinearity was about 2.06%. The sensor could work normally when the temperature was below 500 °C, and the drift of the phase offset point with temperature was 0.84 pm/°C.

Short and Long Term Measurements in Assessment of FRP Composite Footbridge Behavior

The paper presents application of different sensors for the purpose of short and long term measurements, as well as a structural health monitoring (SHM) system to assess the behavior of a novel fiber reinforced plastics (FRP) composite footbridge. The aim is to present a thorough and concise description of these sensors networks and results gathered with their aid during in situ measurement of strains, displacements, and vibrations, as only a few works are available in this field. The bridge geometry, material solutions, and properties are described at first. Then the measurement devices composing the system and subsystems of sensors are elaborated on. Subsequently, the bridge research program is described and the results are shown and discussed. Finally, it is concluded that the use of selected sensors is helpful in assessment of the behavior of the novel structure, and moreover in validation of its numerical models. The collected data confirmed many assumptions made during the bridge design process and allowed us to accept it for exploitation.

Prognosis of a Wind Turbine Gearbox Bearing Using Supervised Machine Learning

Deployment of large-scale wind turbines requires sophisticated operation and maintenance strategies to ensure the devices are safe, profitable and cost-effective. Prognostics aims to predict the remaining useful life (RUL) of physical systems based on condition measurements. Analyzing condition monitoring data, implementing diagnostic techniques and using machinery prognostic algorithms will bring about accurate estimation of the remaining life and possible failures that may occur. This paper proposes to combine two supervised machine learning techniques, namely, regression model and multilayer artificial neural network model, to predict the RUL of an operational wind turbine gearbox using vibration measurements. Root Mean Square (RMS), Kurtosis (KU) and Energy Index (EI) were analysed to define the bearing failure stages. The proposed methodology was evaluated through a case study involving vibration measurements of a high-speed shaft bearing used in a wind turbine gearbox.

Recent Progress in the Performance Enhancement of Phase-Sensitive OTDR Vibration Sensing Systems

Recently, phase-sensitive Optical Time-Domain Reflectometry (Φ-OTDR)-based vibration sensor systems have gained the interest of many researchers and some efforts have been undertaken to push the performance limitations of Φ-OTDR sensor systems. Thus, progress in different areas of their performance evaluation factors such as improvement of the signal-to-noise ratio (SNR), spatial resolution (SR) in the sub-meter range, enlargement of the sensing range, increased frequency response bandwidth over the conventional limits, phase signal demodulation and chirped-pulse Φ-OTDR for quantitative measurement have been realized. This paper presents an overview of the recent progress in Φ-OTDR-based vibration sensing systems in the different areas mentioned above.

Learning to See the Vibration: A Neural Network for Vibration Frequency Prediction

Vibration measurement serves as the basis for various engineering practices such as natural frequency or resonant frequency estimation. As image acquisition devices become cheaper and faster, vibration measurement and frequency estimation through image sequence analysis continue to receive increasing attention. In the conventional photogrammetry and optical methods of frequency measurement, vibration signals are first extracted before implementing the vibration frequency analysis algorithm. In this work, we demonstrate that frequency prediction can be achieved using a single feed-forward convolutional neural network. The proposed method is verified using a vibration signal generator and excitation system, and the result compared with that of an industrial contact vibrometer in a real application. Our experimental results demonstrate that the proposed method can achieve acceptable prediction accuracy even in unfavorable field conditions.

A High-Speed Target-Free Vision-Based Sensor for Bus Rapid Transit Viaduct Vibration Measurements Using CMT and ORB Algorithms

Bus Rapid Transit (BRT) has become an increasing source of concern for public transportation of modern cities. Traditional contact sensing techniques during the process of health monitoring of BRT viaducts cannot overcome the deficiency that the normal free-flow of traffic would be blocked. Advances in computer vision technology provide a new line of thought for solving this problem. In this study, a high-speed target-free vision-based sensor is proposed to measure the vibration of structures without interrupting traffic. An improved keypoints matching algorithm based on consensus-based matching and tracking (CMT) object tracking algorithm is adopted and further developed together with oriented brief (ORB) keypoints detection algorithm for practicable and effective tracking of objects. Moreover, by synthesizing the existing scaling factor calculation methods, more rational approaches to reducing errors are implemented. The performance of the vision-based sensor is evaluated through a series of laboratory tests. Experimental tests with different target types, frequencies, amplitudes and motion patterns are conducted. The performance of the method is satisfactory, which indicates that the vision sensor can extract accurate structure vibration signals by tracking either artificial or natural targets. Field tests further demonstrate that the vision sensor is both practicable and reliable.

Optical Tip Clearance Measurements as a Tool for Rotating Disk Characterization

An experimental investigation on the vibrational behavior of a rotating disk by means of three optical fiber sensors is presented. The disk, which is a scale model of the real disk of an aircraft engine, was assembled in a wind tunnel in order to simulate real operation conditions. The pressure difference between the upstream and downstream sides of the disk causes an airflow that might force the disk to vibrate. To characterize this vibration, a set of parameters was determined by measuring the tip clearance of the disk: the amplitude, the frequency and the number of nodal diameters in the disk. All this information allowed the design of an upgraded prototype of the disk, whose performance was also characterized by the same method. An optical system was employed for the measurements, in combination with a strain gauge mounted on the disk surface, which served to confirm the results obtained. The data of the strain gauge coincided closely with those provided by the optical fiber sensors, thus demonstrating the suitability of this innovative technique to evaluate the vibrational behavior of rotating disks.

A Method Using Optical Contactless Displacement Sensors to Measure Vibration Stress of Small-Bore Piping

In nuclear power plants, vibration stress of piping is frequently evaluated to prevent fatigue failure. A simple and fast measurement method is attractive to evaluate many piping systems efficiently. In this study, a method to measure the vibration stress using optical contactless displacement sensors was proposed, the prototype instrument was developed, and the instrument practicality for the method was verified. In the proposed method, light emitting diodes (LEDs) were used as measurement sensors and the vibration stress was estimated by measuring the deformation geometry of the piping caused by oscillation, which was measured as the piping curvature radius. The method provided fast and simple vibration estimates for small-bore piping. Its verification and practicality were confirmed by vibration tests using a test pipe and mock-up piping. The stress measured by both the proposed method and an accurate conventional method using strain gauges were in agreement, and it was concluded that the proposed method could be used for actual plant piping systems.

Detecting nano-scale vibrations in rotating devices by using advanced computational methods

This paper presents a computational method for detecting vibrations related to eccentricity in ultra precision rotation devices used for nano-scale manufacturing. The vibration is indirectly measured via a frequency domain analysis of the signal from a piezoelectric sensor attached to the stationary component of the rotating device. The algorithm searches for particular harmonic sequences associated with the eccentricity of the device rotation axis. The detected sequence is quantified and serves as input to a regression model that estimates the eccentricity. A case study presents the application of the computational algorithm during precision manufacturing processes.