Search results for: measurement error.

Authors: S. Pullteap

Abstract:

In this paper, a fiber based Fabry-Perot interferometer is proposed and demonstrated for a non-contact displacement measurement. A piece of micro-prism which attached to the mechanical vibrator is served as the target reflector. Interference signal is generated from the superposition between the sensing beam and the reference beam within the sensing arm of the fiber sensor. This signal is then converted to the displacement value by using a developed program written in visual Cµ programming with a resolution of λ/8. A classical function generator is operated for controlling the vibrator. By fixing an excitation frequency of 100 Hz and varying the excitation amplitude range of 0.1 – 3 Volts, the output displacements measured by the fiber sensor are obtained from 1.55 μm to 30.225 μm. A reference displacement sensor with a sensitivity of ~0.4 μm is also employed for comparing the displacement errors between both sensors. We found that over the entire displacement range, a maximum and average measurement error are obtained of 0.977% and 0.44% respectively.

Keywords: Non-contact displacement measurement, extrinsicfiber based Fabry-Perot interferometer, interference signal, zerocrossingfringe counting technique.

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Authors: Hassam Ahmed, Yuanzhi Liu, Yassine Selami, Wei Tao, Hui Zhao

Abstract:

The purpose of this research is to develop a real time axial force measurement system for a smart bearing through the use of strain-gauges, whereby the data acquisition is performed by an Arduino microcontroller due to its easy manipulation and low-cost. The measured signal is acquired and then discretized using a Wheatstone Bridge and an Analog-Digital Converter (ADC) respectively. For bearing monitoring, a real time monitoring system based on Internet of things (IoT) and Bluetooth were developed. Experimental tests were performed on a bearing within a force range up to 600 kN. The experimental results show that there is a proportional linear relationship between the applied force and the output voltage, and the error R squared is within 0.9878 based on the regression analysis.

Keywords: Bearing, force measurement, IoT, strain gauge.

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Authors: Tung-Hui Hsu, Wen-Yuh Jywe

Abstract:

Five-axis computer numerical control (CNC) machine tools (three linear and two rotary axes) are ideally suited to the fabrication of complex work pieces, such as dies, turbo blades, and cams. The locations of the axis average line and centerline of the rotary axes strongly influence the performance of these machines; however, techniques to compensate for eccentric error in the rotary axes remain weak. This paper proposes optical (Non-Bar) techniques capable of calibrating five-axis CNC machine tools and compensating for eccentric error in the rotary axes. This approach employs the measurement path in ISO/CD 10791-6 to determine the eccentric error in two rotary axes, for which compensatory measures can be implemented. Experimental results demonstrate that the proposed techniques can improve the performance of various five-axis CNC machine tools by more than 90%. Finally, a result of the cutting test using a B-type five-axis CNC machine tool confirmed to the usefulness of this proposed compensation technique.

Keywords: Calibration, compensation, rotary axis, five-axis computer numerical control (CNC) machine tools, eccentric error, optical calibration system, ISO/CD 10791-6

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Authors: Chompunut Jantarasorn, Chutima Prommak

Abstract:

This paper presents an intensive measurement studying of the network performance analysis when IEEE 802.11g Wireless Local Area Networks (WLAN) coexisting with IEEE 802.15.4 Wireless Personal Area Network (WPAN). The measurement results show that the coexistence between both networks could increase the Frame Error Rate (FER) of the IEEE 802.15.4 networks up to 60% and it could decrease the throughputs of the IEEE 802.11g networks up to 55%.

Keywords: Wireless performance analysis, Coexistence analysis, IEEE 802.11g, IEEE 802.15.4.

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Authors: Soo-young Ye, Gi-Ryon Kim, Dong-Keun Jung, Seong-wan Baik, Gye-rok Jeon

Abstract:

In this paper, algorithm estimating the blood pressure was proposed using the pulse transit time (PTT) as a more convenient method of measuring the blood pressure. After measuring ECG and pressure pulse, and photoplethysmography, the PTT was calculated from the acquired signals. Thereafter, the system to indirectly measure the systolic pressure and the diastolic pressure was composed using the statistic method. In comparison between the blood pressure indirectly measured by proposed algorithm estimating the blood pressure and real blood pressure measured by conventional sphygmomanometer, the systolic pressure indicates the mean error of ±3.24mmHg and the standard deviation of 2.53mmHg, while the diastolic pressure indicates the satisfactory result, that is, the mean error of ±1.80mmHg and the standard deviation of 1.39mmHg. These results are satisfied with the regulation of ANSI/AAMI for certification of sphygmomanometer that real measurement error value should be within the mean error of ±5mmHg and the standard deviation of 8mmHg. These results are suggest the possibility of applying to portable and long time blood pressure monitoring system hereafter.

Keywords: Blood pressure, Systolic, Diastolic, Pulse transit time.

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Authors: Zhengkun Guo, Yanbin Li, Wenqing Wang, Bo Zou

Abstract:

Active radar and sonar systems often report Doppler measurements in addition to the position measurements such as range and bearing. The tracker can perform better by making full use of the Doppler measurements. However, due to the high nonlinearity of the Doppler measurements with respect to the target state in the Cartesian coordinate systems, those measurements are not always fully exploited. This paper mainly focuses on dealing with the Doppler measurements as well as the position measurements in Polar coordinates. The Statically Fused Converted Position and Doppler Measurements Kalman Filter (SF-CMKF) with additive debiased measurement conversion has been presented. However, the exact compensation for the bias of the measurement conversion are multiplicative and depend on the statistics of the cosine of the angle measurement errors. As a result, the consistency and performance of the SF-CMKF may be suboptimal in the large angle error situations. In this paper, the multiplicative unbiased position and Doppler measurement conversion for two-dimensional (Polar-to-Cartesian) tracking are derived, and the SF-CMKF is improved by using those conversion. Monte Carlo simulations are presented to demonstrate the statistic consistency of the multiplicative unbiased conversion and the superior performance of the modified SF-CMKF (SF-UCMKF).

Keywords: Measurement conversion, Doppler, Kalman filter, estimation, tracking.

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Authors: M. T. Anwar, P. K. Lala, P. Thenappan

Abstract:

This paper presents the decoder design for the single error correcting and double error detecting code proposed by the authors in an earlier paper. The speed of error detection and correction of a code is largely dependent upon the associated encoder and decoder circuits. The complexity and the speed of such circuits are determined by the number of 1?s in the parity check matrix (PCM). The number of 1?s in the parity check matrix for the code proposed by the authors are fewer than in any currently known single error correcting/double error detecting code. This results in simplified encoding and decoding circuitry for error detection and correction.

Keywords: Decoder, Hsiao code, Parity Check Matrix, Syndrome Pattern.

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Authors: Sijie Fu, Pascal-Henry Biwolé, Christian Mathis

Abstract:

Among modern airflow measurement methods, Particle Image Velocimetry (PIV) and Particle Tracking Velocimetry (PTV), as visualized and non-instructive measurement techniques, are playing more important role. This paper conducts a comparative experimental study for airflow measurement employing both techniques with the same condition. Velocity vector fields, velocity contour fields, voticity profiles and turbulence profiles are selected as the comparison indexes. The results show that the performance of both PIV and PTV techniques for airflow measurement is satisfied, but some differences between the both techniques are existed, it suggests that selecting the measurement technique should be based on a comprehensive consideration.

Keywords: PIV, PTV, airflow measurement.

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Authors: O. P. Sharma, V. Janyani, S. Sancheti

Abstract:

Data rate, tolerable bit error rate or frame error rate and range & coverage are the key performance requirement of a communication link. In this paper performance of MFSK link is analyzed in terms of bit error rate, number of errors and total number of data processed. In the communication link model proposed, which is implemented using MATLAB block set, an improvement in BER is observed. Different parameters which effects and enables to keep BER low in M-ary communication system are also identified.

Keywords: Additive White Gaussian Noise (AWGN), Bit Error Rate (BER), Frequency Shift Keying (FSK), Orthogonal Signaling.

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Authors: Frydrysiak M., Zięba J., Tęsiorowski Ł.

Abstract:

In this paper authors presented the research of textile electroconductive materials, which can be used to construction sensory textronic shirt to breath frequency measurement. The full paper also will present results of measurements carried out on unique measurement stands.

Keywords: Electroconductive fibres, textile sensor, textronic, respiratory rhythm measurement.

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Authors: Hae-Yeoun Lee

Abstract:

Reversible watermarking that not only protects the copyright but also preserve the original quality of the digital content have been intensively studied. In particular, the demand for reversible watermarking has increased. In this paper, we propose a reversible watermarking scheme based on interpolation-error shifting and error pre-compensation. The intensity of a pixel is interpolated from the intensities of neighboring pixels, and the difference histogram between the interpolated and the original intensities is obtained and modified to embed the watermark message. By restoring the difference histogram, the embedded watermark is extracted and the original image is recovered by compensating for the interpolation error. The overflow and underflow are prevented by error pre-compensation. To show the performance of the method, the proposed algorithm is compared with other methods using various test images.

Keywords: Reversible watermarking, High capacity, High quality, Interpolated error shifting, Error pre-compensation.

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Authors: Heesung Lee, Joonkyung Sung, Euntai Kim

Abstract:

This paper proposes a method which reduces power consumption in single-error correcting, double error-detecting checker circuits that perform memory error correction code. Power is minimized with little or no impact on area and delay, using the degrees of freedom in selecting the parity check matrix of the error correcting codes. The genetic algorithm is employed to solve the non linear power optimization problem. The method is applied to two commonly used SEC-DED codes: standard Hamming and odd column weight Hsiao codes. Experiments were performed to show the performance of the proposed method.

Keywords: Error correcting codes, genetic algorithm, non-linearpower optimization, Hamming code, Hsiao code.

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Authors: Beata Czarnacka-Chrobot

Abstract:

Unsatisfactory effectiveness of software systems development and enhancement projects is one of the main reasons why in software engineering there are attempts being made to use experiences coming from other engineering disciplines. In spite of specificity of software product and process a belief had come out that the execution of software could be more effective if these objects were subject to measurement – as it is true in other engineering disciplines for which measurement is an immanent feature. Thus objective and reliable approaches to the measurement of software processes and products have been sought in software engineering for several dozens of years already. This may be proved, among others, by the current version of CMMI for Development model. This paper is aimed at analyzing the approach to the software processes and products measurement proposed in the latest version of this very model, indicating growing acceptance for this issue in software engineering.

Keywords: CMMI for Development (1.3), ISO/IEC standards, measurement and analysis process area, software process measurement, software product measurement.

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Authors: T. Hirner, J. Polec

Abstract:

This paper describes a new method of unequal error protection (UEP) for region of interest (ROI) with embedded zerotree wavelet algorithm (EZW). ROI technique is important in applications with different parts of importance. In ROI coding, a chosen ROI is encoded with higher quality than the background (BG). Unequal error protection of image is provided by different coding techniques. In our proposed method, image is divided into two parts (ROI, BG) that consist of more important bytes (MIB) and less important bytes (LIB). The experimental results verify effectiveness of the design. The results of our method demonstrate the comparison of the unequal error protection (UEP) of image transmission with defined ROI and the equal error protection (EEP) over multiple noisy channels.

Keywords: embedded zerotree wavelet (EZW), equal error protection (EEP), region of interest (ROI), RS code, unequal error protection (UEP)

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Authors: Yu-Sheng Lee, Qi An

Abstract:

Offset mismatch, gain mismatch, and time-skew error between time-interleaved channels limit the performance of time-interleaved analog-to-digital converters (TIADC). This paper focused on the time-skew error. A new technique for calibrating time-skew error in M-channels TIADC is described, and simulation results are also presented.

Keywords: Calibration, time-skew error, time-interleavedanalog-to-digital converters.

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Authors: Cuiran Li, Jianli Xie, Chengshu Li

Abstract:

In the paper, the performance of quasi-synchronous CDMA (QS-CDMA) system, which can allow an increased timing error in synchronized access, is discussed. Average BER performance of the system is analyzed in the condition of different access timing error and different asynchronous users by simulation in AWGN channel. The results show that QS-CDMA system is shown to have great performance gain over the asynchronous system when access timing error is within a few chips and asynchronous users is tolerable. However, with access timing error increasing and asynchronous users increasing, the performance of QS-CDMA will degrade. Also, we can determine the number of tolerable asynchronous users for different access timing error by simulation figures.

Keywords: Code-division multiple access, Quasi-SynchronousCDMA, Access timing error

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Authors: Vasco A. P. Cadavez, Fernando C. Monteiro

Abstract:

The objective of this study was to develop and compare alternative prediction equations of lean meat proportion (LMP) of lamb carcasses. Forty (40) male lambs, 22 of Churra Galega Bragançana Portuguese local breed and 18 of Suffolk breed were used. Lambs were slaughtered, and carcasses weighed approximately 30 min later in order to obtain hot carcass weight (HCW). After cooling at 4º C for 24-h a set of seventeen carcass measurements was recorded. The left side of carcasses was dissected into muscle, subcutaneous fat, inter-muscular fat, bone, and remainder (major blood vessels, ligaments, tendons, and thick connective tissue sheets associated with muscles), and the LMP was evaluated as the dissected muscle percentage. Prediction equations of LMP were developed, and fitting quality was evaluated through the coefficient of determination of estimation (R2 e) and standard error of estimate (SEE). Models validation was performed by k-fold crossvalidation and the coefficient of determination of prediction (R2 p) and standard error of prediction (SEP) were computed. The BT2 measurement was the best single predictor and accounted for 37.8% of the LMP variation with a SEP of 2.30%. The prediction of LMP of lamb carcasses can be based simple models, using as predictors the HCW and one fat thickness measurement.

Keywords: Bootstrap, Carcass, Lambs, Lean meat

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Authors: Rabiˆı DARITI, El Mamoun SOUIDI

Abstract:

Linear error-block codes are a natural generalization of linear error correcting codes. The purpose of this paper is to generalize some results on the packing and the covering radii to the error-block case. We study their properties when a code undergoes some specific modifications and combinations with another code. We give a few bounds on the packing and the covering radii of these codes.

Keywords: Linear error-block codes, π-distance, Correction capacity, Packing radius, Covering radius.

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Authors: Wenlong Feng, Zhenchun Du, Jianguo Yang

Abstract:

To decrease the grating scale thermal expansion error, a novel method which based on multiple temperature detection is proposed. Several temperature sensors are installed on the grating scale and the temperatures of these sensors are recorded. The temperatures of every point on the grating scale are calculated by interpolating between adjacent sensors. According to the thermal expansion principle, the grating scale thermal expansion error model can be established by doing the integral for the variations of position and temperature. A novel compensation method is proposed in this paper. By applying the established error model, the grating scale thermal expansion error is decreased by 90% compared with no compensation. The residual positioning error of the grating scale is less than 15μm/10m and the accuracy of the machine tool is significant improved.

Keywords: Thermal expansion error of grating scale, error compensation, machine tools, integral method.

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Authors: Belkacem Laimouche

Abstract:

With the field of Artificial Intelligence (AI) experiencing exponential growth, fueled by technological advancements that pave the way for increasingly innovative and promising applications, there is an escalating need to develop rigorous methods for assessing their performance in pursuit of transparency and equity. This article proposes a metrology-inspired statistical framework for evaluating bias and explainability in AI systems. Drawing from the principles of metrology, we propose a pioneering approach, using a concrete example, to evaluate the accuracy and precision of AI models, as well as to quantify the sources of measurement uncertainty that can lead to bias in their predictions. Furthermore, we explore a statistical approach for evaluating the explainability of AI systems based on their ability to provide interpretable and transparent explanations of their predictions.

Keywords: Artificial intelligence, metrology, measurement uncertainty, prediction error, bias, machine learning algorithms, probabilistic models, inter-laboratory comparison, data analysis, data reliability, bias impact assessment, bias measurement.

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Authors: Hadi Taghvafard

Abstract:

We present a new quadrature rule based on the spline interpolation along with the error analysis. Moreover, some error estimates for the reminder when the integrand is either a Lipschitzian function, a function of bounded variation or a function whose derivative belongs to Lp are given. We also give some examples to show that, practically, the spline rule is better than the trapezoidal rule.

Keywords: Quadrature, Spline interpolation, Trapezoidal rule, Numericalintegration, Error analysis.

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Authors: Phornpat Chewasoonthorn, Surat Kwanmuang

Abstract:

Indoor positioning technologies have been evolved rapidly. They augment the Global Positioning System (GPS) which requires line-of-sight to the sky to track the location of people or objects. In this study, we developed an error correction method for an indoor real-time location system (RTLS) based on an ultra-wideband (UWB) sensor from Decawave. Multiple stationary nodes (anchor) were installed throughout the workspace. The distance between stationary and moving nodes (tag) can be measured using a two-way-ranging (TWR) scheme. The result has shown that the uncorrected ranging error from the sensor system can be as large as 1 m. To reduce ranging error and thus increase positioning accuracy, we present an online correction algorithm using the Kalman filter. The results from experiments have shown that the system can reduce ranging error down to 5 cm.

Keywords: Indoor positioning, ultra-wideband, error correction, Kalman filter.

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Authors: M. S. Kang, D. H. Kim, J. S. Yoon, B. S. Park, J. K. Lee

Abstract:

Since straightness error of linear motor stage is hardly dependent upon machining accuracy and assembling accuracy, there is limit on maximum realizable accuracy. To cope with this limitation, this paper proposed a servo system to compensate straightness error of a linear motor stage. The servo system is mounted on the slider of the linear motor stage and moves in the direction of the straightness error so as to compensate the error. From position dependency and repeatability of the straightness error of the slider, a feedforward compensation control is applied to the platform servo control. In the consideration of required fine positioning accuracy, a platform driven by an electro-magnetic actuator is suggested and a sliding mode control was applied. The effectiveness of the sliding mode control was verified along with some experimental results.

Keywords: Linear Motor Stage, Straightness Error, Friction, Sliding Mode Control.

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Authors: Ching-Tsan Chiang, Sheng-Jie Yang, Jing-Kai Huang

Abstract:

The purpose of this research is to develop and apply the RSCMAC to enhance the dynamic accuracy of Global Positioning System (GPS). GPS devices provide services of accurate positioning, speed detection and highly precise time standard for over 98% area on the earth. The overall operation of Global Positioning System includes 24 GPS satellites in space; signal transmission that includes 2 frequency carrier waves (Link 1 and Link 2) and 2 sets random telegraphic codes (C/A code and P code), on-earth monitoring stations or client GPS receivers. Only 4 satellites utilization, the client position and its elevation can be detected rapidly. The more receivable satellites, the more accurate position can be decoded. Currently, the standard positioning accuracy of the simplified GPS receiver is greatly increased, but due to affected by the error of satellite clock, the troposphere delay and the ionosphere delay, current measurement accuracy is in the level of 5~15m. In increasing the dynamic GPS positioning accuracy, most researchers mainly use inertial navigation system (INS) and installation of other sensors or maps for the assistance. This research utilizes the RSCMAC advantages of fast learning, learning convergence assurance, solving capability of time-related dynamic system problems with the static positioning calibration structure to improve and increase the GPS dynamic accuracy. The increasing of GPS dynamic positioning accuracy can be achieved by using RSCMAC system with GPS receivers collecting dynamic error data for the error prediction and follows by using the predicted error to correct the GPS dynamic positioning data. The ultimate purpose of this research is to improve the dynamic positioning error of cheap GPS receivers and the economic benefits will be enhanced while the accuracy is increased.

Keywords: Dynamic Error, GPS, Prediction, RSCMAC.

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Authors: Mazidah Tajjudin, Norhashim Mohd Arshad, Ramli Adnan

Abstract:

Fractional-order controller was proven to perform better than the integer-order controller. However, the absence of a pole at origin produced marginal error in fractional-order control system. This study demonstrated the enhancement of the fractionalorder PI over the integer-order PI in a steam temperature control. The fractional-order controller was cascaded with an error compensator comprised of a very small zero and a pole at origin to produce a zero steady-state error for the closed-loop system. Some modification on the error compensator was suggested for different order fractional integrator that can improve the overall phase margin.

Keywords: Fractional-order PI, Ziegler-Nichols tuning, Oustaloup's Recursive Approximation, steam temperature control.

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Authors: Irina Pyrlina

Abstract:

This article presents the results of a study conducted to identify operational risks for information systems (IS) with service-oriented architecture (SOA). Analysis of current approaches to risk and system error classifications revealed that the system error classes were never used for SOA risk estimation. Additionally system error classes are not normallyexperimentally supported with realenterprise error data. Through the study several categories of various existing error classifications systems are applied and three new error categories with sub-categories are identified. As a part of operational risks a new error classification scheme is proposed for SOA applications. It is based on errors of real information systems which are service providers for application with service-oriented architecture. The proposed classification approach has been used to classify SOA system errors for two different enterprises (oil and gas industry, metal and mining industry). In addition we have conducted a research to identify possible losses from operational risks.

Keywords: Enterprise architecture, Error classification, Oil&Gas and Metal&Mining industries, Operational risks, Serviceoriented architecture

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Authors: Muhibul Haque Bhuyan, Md. Refat Sarder

Abstract:

If a person can monitor his/her oxygen saturation level intermittently then he/she can identify his/her condition early and thus he/she can seek a doctor’s help. This paper reports the design, simulation, and implementation of a low-cost pulse oxygen saturation measurement device based on a reflective photoplethysmography (PPG) system using an integrated circuit sensor as the fundamental component of this health status checking device. The measurement of the physiological parameter is the blood oxygen saturation level (SpO₂) in the peripheral capillary. This work has been implemented using an Arduino Uno R3 microcontroller along with this sensor integrated circuit (IC). The system is designed in the Proteus environment and then simulated to check its performance. After that, the hardware implementation is performed. We used a clipping type optical sensor to sense the arterial oxygen saturation level of blood signal from the fingertips of an individual and then transformed it into the digital data in the microcontroller through its programming its instruction. The designed system was tested by measuring the SpO₂ level for several people of different ages, from 12 to 57 years of age. Besides, the same people were tested using a standard machine purchased from the market. Test results were found very satisfactory as the average percentage of error was very low, 1.59% only.

Keywords: Digital pulse oxygen saturation level, oximeter, measurement, design, simulation, implementation, proteus, Arduino Uno microcontroller.

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Authors: Sutthawee Suwannarat, Thanate Khaorapapong, Mitchai Chongcheawchamnan

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In this paper, an ultrasonic technique is proposed to predict oil content in a fresh palm fruit. This is accomplished by measuring the attenuation based on ultrasonic transmission mode. Several palm fruit samples with known oil content by Soxhlet extraction (ISO9001:2008) were tested with our ultrasonic measurement. Amplitude attenuation data results for all palm samples were collected. The Feedforward Neural Networks (FNNs) are applied to predict the oil content for the samples. The Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) of the FNN model for predicting oil content percentage are 7.6186 and 5.2287 with the correlation coefficient (R) of 0.9193.

Keywords: Non-destructive, ultrasonic testing, oil content, fresh palm fruit, neural network.

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Authors: Wen-Yuh Jywe, Bor-Jeng Lin, Jing-Chung Shen, Jeng-Dao Lee, Hsueh-Liang Huang, Ming-Chen Cho

Abstract:

The dynamical contouring error is a critical element for the accuracy of machine tools. The contouring error is defined as the difference between the processing actual path and commanded path, which is implemented by following the command curves from feeding driving system in machine tools. The contouring error is resulted from various factors, such as the external loads, friction, inertia moment, feed rate, speed control, servo control, and etc. Thus, the study proposes a 2D compensating system for the contouring accuracy of machine tools. Optical method is adopted by using stable frequency laser diode and the high precision position sensor detector (PSD) to performno-contact measurement. Results show the related accuracy of position sensor detector (PSD) of 2D contouring accuracy compensating system was ±1.5 μm for a calculated range of ±3 mm, and improvement accuracy is over 80% at high-speed feed rate.

Keywords: Position sensor detector, laser diode, contouring accuracy, machine tool.

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Authors: Jinho Kim, Dongik Shin, Deokwon Yun, Changsoo Han

Abstract:

Rotating stages in semiconductor, display industry and many other fields require challenging accuracy to perform their functions properly. Especially, Axis of rotation error on rotary system is significant; such as the spindle error motion of the aligner, wire bonder and inspector machine which result in the poor state of manufactured goods. To evaluate and improve the performance of such precision rotary stage, unessential movements on the other 5 degrees of freedom of the rotary stage must be measured and analyzed. In this paper, we have measured the three translations and two tilt motions of a rotating stage with high precision capacitive sensors. To obtain the radial error motion from T.I.R (Total Indicated Reading) of radial direction, we have used Donaldson's reversal technique. And the axial components of the spindle tilt error motion can be obtained accurately from the axial direction outputs of sensors by Estler face motion reversal technique. Further more we have defined and measured the sensitivity of positioning error to the five error motions.

Keywords: Donaldson's reversal methods, Estler face motionreversal method, Error motion, sensitivity, T.I.R (Total IndicatedReading).

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