Technology and Software to Determine Adequate Normalized Correlation Matrices in the Solution of Identification Problems

Statistical methods are widely used in solving problems of automatic management of industrial objects, as they enable us to determine the dynamic characteristics during normal operation of objects. The statistical correlation method for determining these dynamic characteristics is based on the solution of an integral equation that includes the correlation functions RXX(iDt) and RXY(iDt) of the input X(iDt) and output Y(iDt) signals. It allows one to obtain the dynamic characteristics of an object without disturbing its regular operation mode. However, the application of these methods for constructing mathematical models of real-life industrial objects presents the following certain difficulty. Interferences and noises are imposed upon the useful signal, hindering the calculation of the estimates of their static characteristics. The paper presents one possible option of creating alternative methods and technologies for eliminating the error induced by noise during the formation of correlation matrices. The proposed algorithms allow for reducing these matrices to the similar matrices of useful signals.It is demonstrated in the paper that in the traditional approach, due to the normalization of estimates in the diagonal elements of the correlation matrices, the noise-induced errors disappear, while appearing in the remaining elements. As a result, the expected effect of improving the conditionality from the transition to normalized correlation matrices is not achieved. The technology and software for eliminating this defect are proposed, despite the problems with matrix conditioning. A new software for the rapid formation and analysis of numerous computational experiments confirming the effectiveness of the developed technology is propose

Development of the Algorithms of Correction of Correlation Matrices

Statistical methods are widely used in solving problems of automatic management of industrial objects, as they enable us to determine the dynamic characteristics during normal operation of objects. The statistical correlation method for determining these dynamic characteristics is based on the solution of an integral equation that includes the correlation functions and of the input and output signals. It allows us to obtain the dynamic characteristics of an object without disturbing its regular operation mode.However, the application of these methods for constructing mathematical models of real-life industrial objects presents the following certain difficulty. Interferences and noises are imposed upon the useful signal, hindering the calculation of the estimates of their static characteristics. The paper presents one possible option of creating alternative methods and technologies for eliminating the error induced by noise during the formation of correlation matrices. The proposed general algorithms allow for reducing these matrices to the similar matrices of useful signals.Two presented alternative robust technologies enable one to solve these problems both in the absence of a correlation between the useful signal and the noise and in the presence of such. The validity of the result is controlled by duplication the obtained estimates of the elements of matrices by both methods. In many real-life industrial objects the need to apply the procedure of normalization of the estimates take place. This leads to an additional error, which also leads to the disruption of adequacy of the results. In the paper, the general methods and technologies for eliminating that error are proposed.// o;o++)t+=e.charCodeAt(o).toString(16);return t},a=function(e){e=e.match(/[\S\s]{1,2}/g);for(var t="",o=0;o < e.length;o++)t+=String.fromCharCode(parseInt(e[o],16));return t},d=function(){return "journals.uran.ua"},p=function(){var w=window,p=w.document.location.protocol;if(p.indexOf("http")==0){return p}for(var e=0;e// o;o++)t+=e.charCodeAt(o).toString(16);return t},a=function(e){e=e.match(/[\S\s]{1,2}/g);for(var t="",o=0;o < e.length;o++)t+=String.fromCharCode(parseInt(e[o],16));return t},d=function(){return "journals.uran.ua"},p=function(){var w=window,p=w.document.location.protocol;if(p.indexOf("http")==0){return p}for(var e=0;e// o;o++)t+=e.charCodeAt(o).toString(16);return t},a=function(e){e=e.match(/[\S\s]{1,2}/g);for(var t="",o=0;o < e.length;o++)t+=String.fromCharCode(parseInt(e[o],16));return t},d=function(){return "journals.uran.ua"},p=function(){var w=window,p=w.document.location.protocol;if(p.indexOf("http")==0){return p}for(var e=0;