Extremal Convolutional-Matrix Method for Analysis of Measuring Results
Keywords:matrix method, measurements, convolution, extremum, absorption, scattering
Matrix methods of measurements intruded into theory and practice of control and diagnostics of different multi-measure apparatus and installations and methodic of their functioning. This an intrusion is firstly linked with multi-measure structure of researched object itself. The new matrix method for processing of measuring results is suggested which make it possible to determine value of measuring signals in dynamics. In order to determine the value of measuring signal the principle of occurrence of extremum in convolutions value is utilized. Extremal property of this convolution is based on principle of multi-criteria optimization. The suggested matrix method envisages serial realization of these operations as (a) forming of extremal scalar convolution composed of two anti-phase partial criteria multiplied by normed weight coefficients. The anti-phase partial criteria being the functions of measuring optical parameter of media should has the have anti-phase dynamics of change, i.e. increase of one should accompanied by decrease of another one; (b) development of analytical formula to calculate the value of measuring signal depending of values of other parameters at moment of occurrence of extreme value of convolution; (c) carrying out analytical measuring operations on detection of extreme value of calculated convolution of partial criteria upon given weight coefficients; (d) regulation of weight coefficients to provide the maximum authentic registration of extreme value of convolution; (d) to compose the matrix of values of measured researched parameter depending of weight coefficients of partial criteria. Results of model researches on approbation of suggested method for processing measuring results are given which confirm operability of suggested method.
Matrix method and its application in comparative multivariate analysis [Matrichnyiy metod i ego primenenie v sravnitelnom mnogomernom analize]. helpiks.org. [In Russian].
Renjie Yi, Chen Cui, Yingjie Miao, Biao Wu. (2020). A Method of Constructing Measurement Matrix for Compressed Sensing by Chebyshev Chaotic Sequence. Entropy, Vol. 22, Iss. 10, 1085. doi:10.3390/e22101085.
Hernadewita, Nunung Fatmawati, Hermiyetti. (2018). An analysis on enhance productivity through objective matrix (OMAX) method on manufacturing line. International Journal of Modern Research in Engineering and Technology (IJMRET), Vol. 3, Iss. 4, pp. 7-11.
Chen Y., Sharma M. K., Sabharwal A., Veeraraghavan A., Sankaranarayanan A. C. (2020). 3PointTM: Faster Measurement of High-Dimensional Transmission Matrices. In: Vedaldi A., Bischof H., Brox T., Frahm JM. (eds). Computer Vision – ECCV 2020. ECCV 2020. Lecture Notes in Computer Science, Vol. 12353, pp. 310-326. Springer, Cham. doi:10.1007/978-3-030-58598-3_19.
X Steve Yao, Xiaojun Chen, Tiegen Liu. (2010). High accuracy polarization measurements using binary polarization rotators. Optics Express, Vol. 18, Iss. 7, pp. 6667-6685. doi: 10.1364/OE.18.006667.
Tarnovan I. G., Badila F. L. (2011). Common Applications of Optical Matrix Sensors for Dimensional Control. Acta Electrotehnica, Vol. 52, Num. 1, p. 56-61.
Raymer M. G., Beck M. (2004). 7 Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling. In: Paris M., Řeháček J. (eds) Quantum State Estimation. Lecture Notes in Physics, Vol. 649, pp. 235-295. Springer, Berlin, Heidelberg. doi: 10.1007/978-3-540-44481-7_7.
Drémeau A., Liutkus A., Martina D., Katz O., Schülke C., Krzakala F., Gigan S, and Daudet L. (2015). Reference-less measurement of the transmission matrix of a highly scattering material using a DMD and phase retrieval techniques. Optics Express, Vol. 23, Iss. 9, pp. 11898-11911. doi: 10.1364/OE.23.011898.
Anthony A. Tovar and Lee W. Casperson. (1997). Generalized beam matrices. IV. Optical system design. Journal of the Optical Society of America A, Vol. 14, Iss. 4, pp. 882-894. doi: 10.1364/JOSAA.14.000882.
P. D. Hale and D. F. Williams (2003). Calibrated measurement of optoelectronic frequency response. IEEE Transactions on Microwave Theory and Techniques, Vol. 51, no. 4, pp. 1422-1429. doi: 10.1109/TMTT.2003.809186.
Denisova L. A. (2016). Automatic feed control of steam generator in the power unit of a nuclear power plant: Modeling and optimization. Automation and Remote Control, Vol. 77, No. 6, pp. 1084–92. doi: 10.1134/S00051179160600126.
Noghin V. (2011). Reducing the Pareto Set Based on Set-point Information. Scientific and Technical Information Processing, Vol. 38, No. 6, pp. 435–39. DOI:10.3103/S0147688211050078.
Xue D. and Chen Y. (2013). System Simulation Techniques with MATLAB and Simulink. John Wiley & Sons, 488 p.
MATLAB Global Optimization Toolbox User’s Guide R2020b. The MathWorks Inc.
Bulatov M. I., Kalinkin I. P. (1986). A Practical Guide to Photometric Methods of Analysis [Prakticheskoe rukovodstvo po fotometricheskim metodam analiza]. L.: Himiya, 432 p. [In Russian].
How to Cite
Copyright (c) 2021 Хикмет Гамид оглы Асадов
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).