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Journal articles on the topic 'Form Error Evaluation'

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Author: Grafiati

Published: 14 March 2023

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1

Cui, Changcai, Bing Li, Fugui Huang, and Rencheng Zhang. "Genetic algorithm-based form error evaluation." Measurement Science and Technology 18, no. 7 (May 9, 2007): 1818–22. http://dx.doi.org/10.1088/0957-0233/18/7/004.

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2

Namboothiri, V. N. Narayanan, and M. S. Shunmugam. "Form error evaluation using L1-approximation." Computer Methods in Applied Mechanics and Engineering 162, no. 1-4 (August 1998): 133–49. http://dx.doi.org/10.1016/s0045-7825(97)00338-1.

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3

Jiang, Qimi, Hsi-Yung Feng, Yujun Wang, and Can Fang. "Batch circular form error characterization and evaluation." Precision Engineering 47 (January 2017): 223–30. http://dx.doi.org/10.1016/j.precisioneng.2016.08.007.

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4

Weber, Timothy, Saeid Motavalli, Behrooz Fallahi, and S. Hossein Cheraghi. "A unified approach to form error evaluation." Precision Engineering 26, no. 3 (July 2002): 269–78. http://dx.doi.org/10.1016/s0141-6359(02)00105-8.

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5

Kase, K., A. Makinouchi, T. Nakagawa, H. Suzuki, and F. Kimura. "Shape error evaluation method of free-form surfaces." Computer-Aided Design 31, no. 8 (July 1999): 495–505. http://dx.doi.org/10.1016/s0010-4485(99)00046-9.

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6

Yang, Tai-Hung, and J. Jackman. "A Probabilistic View of Problems in Form Error Estimation." Journal of Manufacturing Science and Engineering 119, no. 3 (August 1, 1997): 375–82. http://dx.doi.org/10.1115/1.2831116.

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Form error estimation techniques based on discrete point measurements can lead to significant errors in form tolerance evaluation. By modeling surface profiles as random variables, we show how sample size and fitting techniques affect form error estimation. Depending on the surface characteristics, typical sampling techniques can result in estimation errors of as much as 50 percent. Another issue raised in the fitting approach is the metric p selection for the fitting objective. We show that for p = 2 and p = ∞, the selection does not appear to significantly affect the estimation of form errors.

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7

Xie, Jin, Jia Long Guo, and Jing Xu. "Evaluation and Measurement of 3D Form Errors of Ground Curve Surface." Key Engineering Materials 359-360 (November 2007): 513–17. http://dx.doi.org/10.4028/www.scientific.net/kem.359-360.513.

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Evaluation and measurement of form errors distributed on 3D ground curved surface are proposed due to the difficulty of processing measured points of 3D ground curve surface in comparison with axisymmetric curved surface. First form curved surface grinding is conducted by arc-shaped diamond grinding wheel, second ground curved surface is measured by contact measurement to obtain 3D measuring data, next transfer mode from CNC grinding to measuring reference frames is established, then effective and applicable 3D compensation arithmetic for probe sphere error is introduced, finally 3D form errors are investigated in connection with reference frame transfer and probe sphere compensation. It is confirmed that form error PV of is improved form 203 m / 8 cm2 is obtained by using reference frame transfer and probe sphere compensation, enhancing measuring accuracy by about 29 %.

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8

Zhu, Xiangyang, Han Ding, and Michael Y. Wang. "Form Error Evaluation: An Iterative Reweighted Least Squares Algorithm*." Journal of Manufacturing Science and Engineering 126, no. 3 (August 1, 2004): 535–41. http://dx.doi.org/10.1115/1.1765144.

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This paper establishes the equivalence between the solution to a linear Chebyshev approximation problem and that of a weighted least squares (WLS) problem with the weighting parameters being appropriately defined. On this basis, we present an algorithm for form error evaluation of geometric features. The algorithm is implemented as an iterative procedure. At each iteration, a WLS problem is solved and the weighting parameters are updated. The proposed algorithm is of general-purpose, it can be used to evaluate the exact minimum zone error of various geometric features including flatness, circularity, sphericity, cylindericity and spatial straightness. Numerical examples are presented to show the effectiveness and efficiency of the algorithm.

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9

Wang, Meng, Lifeng Xi, and Shichang Du. "3D surface form error evaluation using high definition metrology." Precision Engineering 38, no. 1 (January 2014): 230–36. http://dx.doi.org/10.1016/j.precisioneng.2013.08.008.

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10

Su, Na, and Hui Guo. "Research on the Profile Error Evaluation and Visualization of Free-Form Surface." Applied Mechanics and Materials 43 (December 2010): 560–64. http://dx.doi.org/10.4028/www.scientific.net/amm.43.560.

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To solve the problem of evaluating profile error of surface, theoretical surface was built by interpolating design points at the method of bicubic Non-Uniform Rational B-Spline(NURBS). Measuring points were gained by laser measurement, and the mathematical model was built for computing the error. The particle swarm optimization (PSO) was applied to compute the minimum distance from measuring points to design surface, which can evaluate profile error of surface accurately. At the same time, MATLAB software was used to realize visualization of profile error evaluation of free-form surface. Experiments show that the proposed optimization can obtain precise result, the method is feasible, visualization makes geometric feature observed more intuitive and there is important practical significance.

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11

Pathak, Vimal Kumar, and Amit Kumar Singh. "Form Error Evaluation of Noncontact Scan Data Using Constriction Factor Particle Swarm Optimization." Journal of Advanced Manufacturing Systems 16, no. 03 (August 2017): 205–26. http://dx.doi.org/10.1142/s0219686717500135.

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Form error evaluation of manufactured parts is one of the crucial aspects of precision coordinate metrology. With the advent of technology, the noncontact data acquisition techniques are replacing the conventional machines like coordinate measuring machine (CMM). This paper presents an optimization technique to evaluate minimum zone form errors, namely straightness, circularity, flatness and cylindricity using constriction factor-based particle swarm optimization (CFPSO) algorithm. Addition of constriction factor helps in accelerating the convergence property of CFPSO. Initially, a simple minimum zone objective function is formulated mathematically for each form error and then optimized using the proposed CFPSO. Primarily, the results of the proposed method for form error evaluation are compared with the literature results. Furthermore, the data obtained from noncontact 3D scanner is processed and the results of form error evaluation using CFPSO algorithm are compared with Steinbichler’s INSPECT PLUS software results. It was found that the results obtained using the proposed CFPSO algorithm are fast and better as compared with other evolutionary techniques like genetic algorithm (GA), previous literatures and software results. Furthermore, to ensure effectiveness of the proposed method statistical analysis ([Formula: see text]-test) was performed. CFPSO results for large dimension of problem show significant difference in computation time as compared with GA. The CFPSO algorithm provides 27.25%, 7.5% and 6.38% improvements in circularity, flatness and cylindricity, respectively, in comparison to RE software results, for determination of minimum zone error. Thus, the methodology presented helps in improving the accuracy and for speeding up of the automated inspection process generally performed by CMMs in industries.

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12

Chiabert, Paolo, Manuela De Maddis, Suela Ruffa, and Jambul Yusupov. "Probabilistic method in form error evaluation: comparison of different approaches." International Journal of Advanced Manufacturing Technology 92, no. 1-4 (February 27, 2017): 447–58. http://dx.doi.org/10.1007/s00170-017-0144-1.

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13

Fei, Liu, Liu Dan, Liang Lin, Xu Guanghua, Zhang Qing, and Meng Zixia. "Sampling strategy and error estimation for evaluation of quadratic form error using Cartesian coordinate data." IET Science, Measurement & Technology 11, no. 7 (October 1, 2017): 839–46. http://dx.doi.org/10.1049/iet-smt.2016.0470.

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14

Qu, Zhi Yong, and Jun Wei Han. "Evaluation Method to Determine Radial Error of Spindle Units on Simulation Turntable." Key Engineering Materials 460-461 (January 2011): 311–16. http://dx.doi.org/10.4028/www.scientific.net/kem.460-461.311.

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Many errors including radial error influence the accuracy of simulation turntable, which is a crucial equipment in hardware-in-the-loop simulation system. The aim of this paper is to propose a new method of radial error motion separation of rotating spindle on a simulation turntable. Based on transformation matrix and small angle approximation, gesture transformation matrix with various error items is achieved. As a result of this analysis, form errors of master ball are corrected and the eccentricity from the rotation error of a spindle is separated. This radial error analysis is carried out when this measurement result is applied to a simulation turntable. Furthermore, this study also permits the user to know how to minimize some error sources of the spindle system.

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15

Yu, D. P., X. Zhong, Y. S. Wong, G. S. Hong, W. F. Lu, and H. L. Cheng. "An automatic form error evaluation method for characterizing micro-structured surfaces." Measurement Science and Technology 22, no. 1 (December 13, 2010): 015105. http://dx.doi.org/10.1088/0957-0233/22/1/015105.

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16

Samuel, G. L., and M. S. Shunmugam. "Evaluation of sphericity error from form data using computational geometric techniques." International Journal of Machine Tools and Manufacture 42, no. 3 (February 2002): 405–16. http://dx.doi.org/10.1016/s0890-6955(01)00124-9.

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17

Carley, Michael. "Closed-Form Evaluation of Potential Integrals in the Boundary Element Method." Journal of Theoretical and Computational Acoustics 28, no. 02 (March 3, 2020): 1950014. http://dx.doi.org/10.1142/s2591728519500142.

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A method is presented for the closed-form evaluation of the singular and near-singular integrals arising in the Boundary Element Method solution of the Helmholtz equation. An error analysis is presented for the numerical evaluation of such integrals on a plane element, and used to develop a criterion for the selection of quadrature rules. The analytical approach is based on an optimized expansion of the Green’s function for the problem, selected to limit the error to some required tolerance. Results are presented showing accuracy to tolerances comparable to machine precision.

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18

Yi, Bowen, Ruibin Liang, Xiaosun Wang, Shijing Wu, and Nuodi Huang. "Free-form surface form error evaluation based on smaller-scale sampling points in touch-trigger probing." Precision Engineering 76 (July 2022): 255–60. http://dx.doi.org/10.1016/j.precisioneng.2022.03.019.

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19

Cui, Changcai. "Form error evaluation of circles based on a finely-designed genetic algorithm." Chinese Journal of Mechanical Engineering (English Edition) 17, no. 01 (2004): 59. http://dx.doi.org/10.3901/cjme.2004.01.059.

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20

Namboothiri, V. N. Narayanan. "On determination of sample size in form error evaluation using coordinate metrology." International Journal of Production Research 37, no. 4 (March 1999): 793–804. http://dx.doi.org/10.1080/002075499191526.

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21

Lang, Ailei, Zhanjie Song, Gaiyun He, and Yicun Sang. "Profile error evaluation of free-form surface using sequential quadratic programming algorithm." Precision Engineering 47 (January 2017): 344–52. http://dx.doi.org/10.1016/j.precisioneng.2016.09.008.

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22

Venkaiah, N., and M. S. Shunmugam. "Evaluation of form data using computational geometric techniques—Part I: Circularity error." International Journal of Machine Tools and Manufacture 47, no. 7-8 (June 2007): 1229–36. http://dx.doi.org/10.1016/j.ijmachtools.2006.08.010.

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23

Venkaiah, N., and M. S. Shunmugam. "Evaluation of form data using computational geometric techniques—Part II: Cylindricity error." International Journal of Machine Tools and Manufacture 47, no. 7-8 (June 2007): 1237–45. http://dx.doi.org/10.1016/j.ijmachtools.2006.08.011.

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24

Sushchenko, S. P., P. V. Pristupa, P. A. Mikheev, and V. V. Poddubny. "Evaluation of the efficiency of forward error correction of transport protocol data blocks." Proceedings of Tomsk State University of Control Systems and Radioelectronics 23, no. 4 (December 25, 2020): 35–39. http://dx.doi.org/10.21293/1818-0442-2020-23-4-35-39.

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A model of a transport connection controlled by a transport protocol with the technology of forward error correction in the selective failure mode in the form of a discrete-time Markov chain is proposed. The model takes into account the influence of the protocol parameters, the level of errors in the communication channels, the round-trip delay and the technological parameters of forward error correction on the throughput of the transport connection. The analysis of the dependence of the advantages of the transport protocol with forward error correction over the classical transport protocol is carried out.

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25

Denis, S. A., and G. L. Samuel. "Harmonic-analysis-based method for separation of form error during evaluation of high-speed spindle radial errors." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 226, no. 5 (February 15, 2012): 837–52. http://dx.doi.org/10.1177/0954405411434868.

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26

Delgado Gracia, Jorge. "Compensated Evaluation of Tensor Product Surfaces in CAGD." Mathematics 8, no. 12 (December 14, 2020): 2219. http://dx.doi.org/10.3390/math8122219.

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In computer-aided geometric design, a polynomial surface is usually represented in Bézier form. The usual form of evaluating such a surface is by using an extension of the de Casteljau algorithm. Using error-free transformations, a compensated version of this algorithm is presented, which improves the usual algorithm in terms of accuracy. A forward error analysis illustrating this fact is developed.

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27

Halkacı, H. S., Ö. Mavi, and O. Yigit. "Evaluation of form error at semi-spherical tools by use of image processing." Measurement 40, no. 9-10 (November 2007): 860–67. http://dx.doi.org/10.1016/j.measurement.2007.06.006.

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28

Mainar, E., and J. M. Peña. "Running Error Analysis of Evaluation Algorithms for Bivariate Polynomials in Barycentric Bernstein Form." Computing 77, no. 1 (December 5, 2005): 97–111. http://dx.doi.org/10.1007/s00607-005-0149-8.

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29

Cui, Changcai, Shiwei Fu, and Fugui Huang. "Research on the uncertainties from different form error evaluation methods by CMM sampling." International Journal of Advanced Manufacturing Technology 43, no. 1-2 (August 14, 2008): 136–45. http://dx.doi.org/10.1007/s00170-008-1681-4.

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30

Liu, J., and Guang Lin Wang. "Pneumatic Measurement Approach for Form Tolerances of Inner Hole in Spool Valve." Applied Mechanics and Materials 42 (November 2010): 480–84. http://dx.doi.org/10.4028/www.scientific.net/amm.42.480.

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Pneumatic measurement and genetic algorithm based approach for form tolerances, including the cylindricity error, circularity error and straightness error of axis, of inner hole in spool valve are studied in this paper. A differential pressure type of pneumatic comprehensive measurement approach is put forward, which applies the pneumatic nozzle scanning measurement principle. The minimum zone evaluation and calculation approach for form tolerances based on an improved genetic algorithm is presented considering the characteristics of the measuring point. Finally, the automatic measurement experiment is developed, which can simultaneously measure and evaluate the form tolerances of inner hole in one process.

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31

Polini, Wilma, and Andrea Corrado. "A kinematic approach for error modelling in drilling." Engineering Computations 36, no. 4 (May 13, 2019): 1364–83. http://dx.doi.org/10.1108/ec-11-2018-0511.

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Purpose The purpose of this paper is to model how geometric errors of a machined surface (or manufacturing errors) are related to locators’ error, workpiece form error and machine tool volumetric error. A kinematic model is presented that puts into relationship the locator error, the workpiece form deviations and the machine tool volumetric error. Design/methodology/approach The paper presents a general and systematic approach for geometric error modelling in drilling because of the geometric errors of locators positioning, of workpiece datum surface and of machine tool. The model can be implemented in four steps: (1) calculation of the deviation in the workpiece reference frame because of deviations of locator positions; (2) evaluation of the deviation in the workpiece reference frame owing to form deviations in the datum surfaces of the workpiece; (3) formulation of the volumetric error of the machine tool; and (4) combination of those three models. Findings The advantage of this approach lies in that it enables the source errors affecting the drilling accuracy to be explicitly separated, thereby providing designers and/or field engineers with an informative guideline for accuracy improvement through suitable measures, i.e. component tolerancing in design, machining and so on. Two typical drilling operations are taken as examples to illustrate the generality and effectiveness of this approach. Research limitations/implications Some source errors, such as the dynamic behaviour of the machine tool, are not taken into consideration, which will be modelled in practical applications. Practical implications The proposed kinematic model may be set by means of experimental tests, concerning the industrial specific application, to identify the values of the model parameters, such as standard deviation of the machine tool axes positioning and rotational errors. Then, it may be easily used to foresee the location deviation of a single or a pattern of holes. Originality/value The approaches present in the literature aim to model only one or at most two sources of machining error, such as fixturing, machine tool or workpiece datum. This paper goes beyond the state of the art because it considers the locator errors together with the form deviation on the datum surface into contact with the locators and, then, the volumetric error of the machine tool.

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32

Yu, Yang, and Ping Liu. "Evaluation of Cutting Error in Five-Axis Free-Form Surface Milling for Table-Tilting Type Machine." Advanced Materials Research 472-475 (February 2012): 2125–28. http://dx.doi.org/10.4028/www.scientific.net/amr.472-475.2125.

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Accuracy of machined workpiece is one of the most important considerations for any manufacturer. The present study aims to establish a new algorithm for evaluating the cutting Error in five-axis free-form surface milling for table-tilting type machine. The cutting error evaluating algorithms consider the kinematics of the machine and the tool geometry as well as the local geometries of the machined free-form surface. Based on these algorithms, the present study develops a new error compensation method. Finally, experimental results show that the tool paths generated by the present procedure have better machining efﬁciency.

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33

He, G. Y., H. J. Zheng, Ying Tian, and Jian Liu. "Measurement and Evaluation of the Geometric Error of Precision Machined Spherical Surface." Advanced Materials Research 53-54 (July 2008): 261–64. http://dx.doi.org/10.4028/www.scientific.net/amr.53-54.261.

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This paper is principally concerned with the form error measurement and evaluation of the spherical surface after precision machining. According to the minimum zone condition, the definition of sphericity error is first analyzed. To obtain the minimum sphericity error from the form data, an approximations technique is devised. First the method is modeled, then the process of approximations is constructed, and finally software for data processing is programmed. Six steel bolls of φ50 are measured on a coordinate measurement machine (CMM) in the Measurement experiment. The experiment results indicate that the geometric approximations technique can give an accurate solution with high efficiency.

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34

Yang, Yang, Ming Li, Chen Wang, and QingYue Wei. "Cylindricity Error Evaluation Based on an Improved Harmony Search Algorithm." Scientific Programming 2018 (July 19, 2018): 1–13. http://dx.doi.org/10.1155/2018/2483781.

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The cylindricity error is one of the basic form errors in mechanical parts, which greatly influences the assembly accuracy and service life of relevant parts. For the minimum zone method (MZM) in international standards, there is no specific formula to calculate the cylindricity error. Therefore, the evaluation methods of the cylindricity error under the MZM have been widely concerned by international scholars. To improve the evaluation accuracy and accelerate the iteration speed of the cylindricity, an improved harmony search (IHS) algorithm is proposed and applied to compute the cylindricity. On the basis of the standard harmony search algorithm, the logistic chaotic initialization is introduced into the generation of initial solution to improve the quality of solutions. During the iterative process, the global and local search capabilities are balanced by adopting the par and bw operators adaptively. After each iteration, the Cauchy mutation strategy is adopted to the best solution to further improve the calculation precision of the IHS algorithm. Finally, four test functions and three groups of cylindricity error examples were applied to validity verification of the IHS algorithm, the simulation test results show that the IHS algorithm has advantages of the computing accuracy and iteration speed compared with other traditional algorithms, and it is very effective for the application in the evaluation of the cylindricity error.

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35

Zhang, Qiushuang, Xin Jin, Zhongqing Zhang, Zhijing Zhang, and Zhihua Liu. "An Evaluation Method for Spatial Distribution Uniformity of Plane Form Error for Precision Assembly." Procedia CIRP 76 (2018): 59–62. http://dx.doi.org/10.1016/j.procir.2018.01.015.

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36

Ayuningtyas, Dea Rahmanita, Lailatul Karimah, Silvi Intan Cahyaningsih, and Chafit Ulya. "Analysis of Language Errors in the “Larise” Magazine Article at SMP Negeri 8 Surakarta." Edunesia : Jurnal Ilmiah Pendidikan 3, no. 1 (January 2, 2022): 55–65. http://dx.doi.org/10.51276/edu.v3i1.214.

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This study aims to analyze language errors and their interpretations at the level of syntax, morphology, and Indonesian Spelling System as well as to increase knowledge and insight about how to write properly and correctly according to the language rules that have been regulated in the KBBI and PUEBI. This research uses descriptive qualitative research method. The data in this study are in the form of words (not numbers) sourced from Larise magazine in an article entitled "Philosophy of Kidungan Jawa "Ana Kidung Rumeksa ing Wengi" published on Sunday, October 11, 2020. The data collection technique in this study is a note-taking technique, namely: by reading Larise magazine as a data source. The analysis used in this study is an interactive analysis which includes the steps of a) data collection, b) error identification, c) error explanation, d) error classification, and e) error evaluation. In this study, an analysis of errors in writing rules was carried out at the level of syntax, morphology, and accuracy in the use of Indonesian Spelling (EBI). Errors at the syntactic level are in the form of errors in the use of effective sentences, errors at the morphological level are affixation errors, and errors related to Indonesian spelling include errors in using punctuation marks, using capital letters, using standard words, using prepositions, and using particles

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37

Ali, Salah H. R. "Performance Investigation of CMM Measurement Quality Using Flick Standard." Journal of Quality and Reliability Engineering 2014 (July 17, 2014): 1–11. http://dx.doi.org/10.1155/2014/960649.

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Quality of coordinate measuring machine (CMM) in dimension and form metrology is designed and performed at the NIS. The experimental investigation of CMM performance is developed by using reference Flick standard. The measurement errors of corresponding geometric evaluation algorithm (LSQ, ME, MC, and MI) and probe scanning speed (1, 2, 3, 4, and 5 mm/s) are obtained through repeated arrangement, comparison, and judgment. The experimental results show that the roundness error deviation can be evaluated effectively and exactly for CMM performance by using Flick standard. Some of influencing quantities for diameter and roundness form errors may dominate the results at all fitting algorithms under certain circumstances. It can be shown that the 2 mm/s probe speed gives smaller roundness error than 1, 3, 4, and 5 mm/s within 0.2 : 0.3 μm. It ensures that measurement at 2 mm/s is the best case to satisfy the high level of accuracy in the certain condition. Using Flick standard as a quality evaluation tool noted a high precision incremental in diameter and roundness form indication. This means a better transfer stability of CMM quality could be significantly improved. Moreover, some error formulae of data sets have been postulated to correlate the diameter and roundness measurements within the application range. Uncertainty resulting from CMM and environmental temperature has been evaluated and confirmed the quality degree of confidence in the proposed performance investigation.

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38

Han, Yanjun, Lei Zhang, Cheng Fan, Wule Zhu, and Anthony Beaucamp. "Theoretical Study of Path Adaptability Based on Surface Form Error Distribution in Fluid Jet Polishing." Applied Sciences 8, no. 10 (October 3, 2018): 1814. http://dx.doi.org/10.3390/app8101814.

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In the technology of computer-controlled optical surfacing (CCOS), the convergence of surface form error has a close relationship with the distribution of surface form error, the calculation of dwell time, tool influence function (TIF) and path planning. The distribution of surface form error directly reflects the difference in bulk material removal depth across a to-be-polished surface in subsequent corrective polishing. In this paper, the effect of path spacing and bulk material removal depth on the residual error have been deeply investigated based on basic simulation experiments excluding the interference factors in the actual polishing process. With the relationship among the critical evaluation parameters of the residual error (root-mean-square (RMS) and peak-to-valley (PV)), the path spacing and bulk material removal depth are mathematically characterized by the proposed RMS and PV maps, respectively. Moreover, a variable pitch path self-planning strategy based on the distribution of surface form error is proposed to optimize the residual error distribution. In the proposed strategy, the influence of different bulk material removal depths caused by the distribution of surface form error on residual error is compensated by fine adjustment of the path spacing according to the obtained path spacing optimization models. The simulated experimental results demonstrate that the residual error optimization strategy proposed in this paper can significantly optimize the overall residual error distribution without compromising the convergence speed. The optimized residual error distribution obtained in sub-regions of the polished surface is more uniform than that without optimization and is almost unaffected by the distribution of parent surface form error.

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39

Wu, Cheng, and Jian Zhen Yu. "Evaluation of linear regression techniques for atmospheric applications: the importance of appropriate weighting." Atmospheric Measurement Techniques 11, no. 2 (March 2, 2018): 1233–50. http://dx.doi.org/10.5194/amt-11-1233-2018.

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Abstract. Linear regression techniques are widely used in atmospheric science, but they are often improperly applied due to lack of consideration or inappropriate handling of measurement uncertainty. In this work, numerical experiments are performed to evaluate the performance of five linear regression techniques, significantly extending previous works by Chu and Saylor. The five techniques are ordinary least squares (OLS), Deming regression (DR), orthogonal distance regression (ODR), weighted ODR (WODR), and York regression (YR). We first introduce a new data generation scheme that employs the Mersenne twister (MT) pseudorandom number generator. The numerical simulations are also improved by (a) refining the parameterization of nonlinear measurement uncertainties, (b) inclusion of a linear measurement uncertainty, and (c) inclusion of WODR for comparison. Results show that DR, WODR and YR produce an accurate slope, but the intercept by WODR and YR is overestimated and the degree of bias is more pronounced with a low R2 XY dataset. The importance of a properly weighting parameter λ in DR is investigated by sensitivity tests, and it is found that an improper λ in DR can lead to a bias in both the slope and intercept estimation. Because the λ calculation depends on the actual form of the measurement error, it is essential to determine the exact form of measurement error in the XY data during the measurement stage. If a priori error in one of the variables is unknown, or the measurement error described cannot be trusted, DR, WODR and YR can provide the least biases in slope and intercept among all tested regression techniques. For these reasons, DR, WODR and YR are recommended for atmospheric studies when both X and Y data have measurement errors. An Igor Pro-based program (Scatter Plot) was developed to facilitate the implementation of error-in-variables regressions.

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40

Suradi and Nurwati Djam’an. "Students’ Error on Proof of The Group with “Satisfy Axioms Proof” based on Newman Error Analysis." Journal of Physics: Conference Series 2123, no. 1 (November 1, 2021): 012024. http://dx.doi.org/10.1088/1742-6596/2123/1/012024.

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Abstract This study aims to analyze students’ errors in solving proof problems on group theory, focus on proofs with satisfying axioms proof. The analysis used refers to the Newman Error Analysis, namely: reading, understanding, transformation, process skills, and coding. The participants in this study consisted of students at the Mathematics Department that enrolled in the group theory course during the odd semester of the 2021/2022 academic year in Universitas Negeri Makassar. Research data was obtained through tests, followed by interviews based on student answers from the test. Based on the results of the error analysis conducted in this study, it can be concluded that: (1) There were no reading errors; (2) Comprehension error was incorrectly write down the meaning of what is known from the problem in symbolic form; (3) Transformation error was error determining the type of proof, mistake write down a formula to show an axiom in the group; (4) Process skill error was an error using arithmetic operations for the validity of an axiom; and (5) Encoding error was an error in writing the final answer, wrong evaluation to conclude.

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Xiong, Pan, Shuan Li Yuan, and Shao Jie Cheng. "Statistical Properties of the Unsymmetrical P-Norm Distribution." Key Engineering Materials 439-440 (June 2010): 1153–58. http://dx.doi.org/10.4028/www.scientific.net/kem.439-440.1153.

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The distribution of observation errors is determined according to their magnitudes by using the distribution collocation test method or figure method taking into account the result, sample total, the interval density etc. It is therefore difficult to get the specific type of error distribution of observations by conventional methods. In analyzing the actual situation of the observation error distribution using their statistical properties, this paper proposes the use of unsymmetrical distribution to express the true distribution of the observation errors. The P-norm distribution is a generalized form of a group of error distributions, and from the statistical properties of random errors we can arrive at an unsymmetrical P-norm distribution according to the practical situation of the occurrence of random errors. The common P-norm distribution is the specific case of this distribution. This paper deduces the density function equation of the unsymmetrical P-norm distribution, obtained the statistical properties of the distribution function and the evaluation of precision index. By choosing appropriate value for p, we can get closer to the distribution function of the true error distribution.

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He, Gaiyun, Mei Zhang, and Zhanjie Song. "Error evaluation of free-form surface based on distance function of measured point to surface." Computer-Aided Design 65 (August 2015): 11–17. http://dx.doi.org/10.1016/j.cad.2015.02.004.

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Dhanish, P. B., and M. S. Shunmugam. "An algorithm for form error evaluation — using the theory of discrete and linear Chebyshev approximation." Computer Methods in Applied Mechanics and Engineering 92, no. 3 (November 1991): 309–24. http://dx.doi.org/10.1016/0045-7825(91)90019-3.

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Wu, C. T., and C. K. Chen. "Study on the Form Error Evaluation Model of a Conical-Shank Ball-End Milling Cutter." International Journal of Advanced Manufacturing Technology 18, no. 12 (December 2001): 851–62. http://dx.doi.org/10.1007/pl00003953.

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Pan, Wei Min, Xin Ye, and Ning Ning Kong. "Solid-Sealed Polar Pole CMM Digital Measurement and Error Evaluation." Key Engineering Materials 621 (August 2014): 627–32. http://dx.doi.org/10.4028/www.scientific.net/kem.621.627.

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Solid-sealed polar pole embed Vacuum quenching pot and related conductive part in an easily solidified insulating material such as epoxy resin, making the whole Breaker as a uniform component, decreasing its overall dimension. CMM is widely used in many sectors. Using CMM is one of the most effective ways to carry out for dimension data comparing other measuring method. In the contact, a precise digital measurement is carried out for the key mounting dimension and space tolerance of form and position, then calculating and analyzing the measuring result, and then guarantee the mounting dimension, providing a basis for solid-sealed Vacuum quenching and guide sleeve research such as heat resistance, deformation, tolerance and Fits, etc, which improve the conformity and accuracy of solid-sealed Vacuum quenching.

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ISHIKAWA, KEN-ICHI, DAIJI KIMURA, KENTA SHIGAKI, and ASAKO TSUJI. "A NUMERICAL EVALUATION OF VACUUM POLARIZATION TENSOR IN CONSTANT EXTERNAL MAGNETIC FIELDS." International Journal of Modern Physics A 28, no. 20 (August 7, 2013): 1350100. http://dx.doi.org/10.1142/s0217751x13501005.

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Hattori–Itakura have recently derived the full Landau-level summation form for the photon vacuum polarization tensor in constant external magnetic fields at the one-loop level. The Landau-level summation form is essential when the photon momentum exceeds the threshold of the pair creation of charged particles in a magnetic field stronger than the squared mass of the charged particle. The tensor has three different form factors depending on the tensor direction with respect to the external magnetic field. The renormalization is nontrivial because these form factors are expressed in terms of double or triple summation forms. We give a numerical UV subtraction method which can be applied to numerically evaluate the form factors in constant external magnetic fields. We numerically investigate the photon vacuum polarization tensor in the form of the Landau-level summation and estimate the systematic errors coming from truncation of the Landau-level summation in a parameter region realized in heavy ion collision experiments. We find that the error is practically controllable at an O(10-2) level for electrons and muons in strong magnetic fields expected in heavy ion collisions in the experimentally feasible kinematic parameter regions.

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Klein, Itzik, Sagi Filin, Tomer Toledo, and Ilan Rusnak. "Assessment of Aided-INS Performance." Journal of Navigation 65, no. 1 (November 25, 2011): 169–85. http://dx.doi.org/10.1017/s0373463311000609.

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Aided Inertial Navigation Systems (INS) systems are commonly implemented in land vehicles for a variety of applications. Several methods have been reported in the literature for evaluating aided INS performance. Yet, the INS error-state-model dependency on time and trajectory implies that no closed-form solutions exist for such evaluation. In this paper, we derive analytical solutions to evaluate the fusion performance. We show that the derived analytical solutions manage to predict the error covariance behavior of the full aided INS error model. These solutions bring insight into the effect of the various parameters involved in the fusion of the INS and an aiding sensor.

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Spirrison, Charles L., and Keith Noland. "The Original vs an Abbreviated Version of the Treatment Evaluation Inventory: Systematic Measurement Error." Psychological Reports 69, no. 3 (December 1991): 763–66. http://dx.doi.org/10.2466/pr0.1991.69.3.763.

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The Treatment Evaluation Inventory was used by 164 undergraduates to rate the acceptability of each of six treatments. The differences between the (scale-corrected) total score and the total of items representing the short form were analyzed. Analysis suggested that the short form, as compared to the original scale, systematically underestimates the acceptability of overcorrection and overestimates the acceptability of differential reinforcement of other behavior.

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Wen, Xiulan, Yibing Zhao, Youxiong Xu, and Danghong Sheng. "Quasiparticle Swarm Optimization for Cross-Section Linear Profile Error Evaluation of Variation Elliptical Piston Skirt." Mathematical Problems in Engineering 2012 (2012): 1–15. http://dx.doi.org/10.1155/2012/761978.

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Variation elliptical piston skirt has better mechanical and thermodynamic properties and it is widely applied in internal combustion engine in recent years. Because of its complex form, its geometrical precision evaluation is a difficult problem. In this paper, quasi-particle swarm optimization (QPSO) is proposed to calculate the minimum zone error and ellipticity of cross-section linear profile, where initial positions and initial velocities of all particles are generated by using quasi-random Halton sequences which sample points have good distribution properties and the particles’ velocities are modified by constriction factor approach. Then, the design formula and mathematical model of the cross-section linear profile of variation elliptical piston skirt are set up and its objective function calculation approach using QPSO to solve the minimum zone cross-section linear profile error is developed which conforms to the ISO/1101 standard. Finally, the experimental results evaluated by QPSO, particle swarm optimization (PSO), improved genetic algorithm (IGA) and the least square method (LSM) confirm the effectiveness of the proposed QPSO and it improves the linear profile error evaluation accuracy and efficiency. This method can be extended to other complex curve form error evaluation such as cam curve profile.

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Keele, John, Tara McDaneld, Ty Lawrence, Jenny Jennings, and Larry Kuehn. "Estimation of Pool Construction and Technical Error." Agriculture 11, no. 11 (November 4, 2021): 1091. http://dx.doi.org/10.3390/agriculture11111091.

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Pooling animals with extreme phenotypes can improve the accuracy of genetic evaluation or provide genetic evaluation for novel traits at relatively low cost by exploiting large amounts of low-cost phenotypic data from animals in the commercial sector without pedigree (data from commercial ranches, feedlots, stocker grazing or processing plants). The average contribution of each animal to a pool is inversely proportional to the number of animals in the pool or pool size. We constructed pools with variable planned contributions from each animal to approximate errors with different numbers of animals per pool. We estimate pool construction error based on combining liver tissue, from pulverized frozen tissue mass from multiple animals, into eight sub-pools containing four animals with planned proportionality (1:2:3:4) by mass. Sub-pools were then extracted for DNA and genotyped using a commercial array. The extracted DNA from the sub-pools was used to form super pools based on DNA concentration as measured by spectrophotometry with planned contribution of sub-pools of 1:2:3:4. We estimate technical error by comparing estimated animal contribution using sub-samples of single nucleotide polymorphism (SNP). Overall, pool construction error increased with planned contribution of individual animals. Technical error in estimating animal contributions decreased with the number of SNP used.

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