Method and device for signal analysis, process identification and monitoring of a technical process
First Claim
1. Device for carrying out consistent, expanded, fast and collinearity-free multiple regression in recursive form, for the purpose of the analysis or control of a technical process, comprising:
- a processor (2) calculating the best Q regression models from data in a memory for the correlation matrix (123) which can be obtained via the unit for correlation calculation (132) from the memory (122) for the covariance matrix, and the memory for the regressor variances (115) entered or calculated beforehand, which are utilized for correction of the diagonal elements of the correlation matrix, andthat the regression models are classified in terms of their residue variance by the regression unit (102) of the processor (2), which is bus-controlled by the control and addressing unit (101), the residual variance of the model, regressor numbers and coefficients being deposited in the memory (116) provided for that purpose, andthat a locking memory (110), a memory for the diagonal elements and the dependent column of the regression matrix (111), a memory for the recursion matrix (113) with the offset-memory (112) belonging to the recursion matrix and a memory for the regression numbers (114) are provided for the realization of the recursive method, andthat the regression unit (102) must perform several actions for the recursion level p, includingthat first of all those regressors are determined which make a small contribution to the model, and if necessary the regressors are locked (110), the offset for the recursion matrix is stored (112), the regressor rows of the new recursion matrix (113) and the new diagonal elements and the dependent column (111) are calculated, and the residual regressor numbers (114) stored,that those regressors, located within the collinearity cone of the current model, are determined and locked (110) with the help of the data from the memory for the regressor variances (115),that the most significant regressor from those remaining is searched, that regressor is selected which yields the model with the smallest residual variance and at the same time passes the F test known from statistics, andthat, in the event of an unsuccessful search, the residual variance of the current model is utilized for the classification of this model between the best Qs, with the help of the residual variances of the models (116) already found, in which case, if the residual variance is smaller or equal to the largest stored residual variance, or currently less than Q models were found, the residual variance, the regression numbers and coefficients are stored in memory for the best models (116), and thereafter the regression unit (102) returns to the recursion level p-1, and its context is loaded from the corresponding memories (110 through
114),that, in the event of a successful search for a significant regressor, the group of regressors within the collinearity cone of the best regressor is found with the values of the regressor variances (115),that each of these regressors is incorporated into the model individually, one after the other, while the remaining ones from the collinear group remain locked (110), and with the precondition that none of the regression coefficients already found undergoes a sign change, the rows of the recursion matrix (113) for the new regressor and the new diagonal elements and the dependent column (111) are calculated and the recursion level p+1 selected,that, after processing of the collinear regressors, the change is made to the recursion level p-1, its context being loaded from the corresponding memories (110 through
114).
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Abstract
Method and device for modelling the variables relevant to a process as a function of other parameters describing or influencing the process, termed regressors, by means of multiple regression for the purpose of process identification, monitoring, analysis and control or regulation. The classical method of stepwise multiple regression is expanded by the introduction of the so-called collinearity cone into a recursive method yielding all "best" collinearity-free regression models. The method is completed by giving consideration to the regression errors and by restriction to the absolutely necessary matrix elements. Stable regression models of various sizes are thus produced with little expenditure of time. Further, either linear or nonlinear regression functions permit a more accurate process analysis or modelling. By automatic learning in the case of newly occurring combinations of regressive values, it is also possible to apply the process to process monitoring, control and regulation.
42 Citations
10 Claims
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1. Device for carrying out consistent, expanded, fast and collinearity-free multiple regression in recursive form, for the purpose of the analysis or control of a technical process, comprising:
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a processor (2) calculating the best Q regression models from data in a memory for the correlation matrix (123) which can be obtained via the unit for correlation calculation (132) from the memory (122) for the covariance matrix, and the memory for the regressor variances (115) entered or calculated beforehand, which are utilized for correction of the diagonal elements of the correlation matrix, and that the regression models are classified in terms of their residue variance by the regression unit (102) of the processor (2), which is bus-controlled by the control and addressing unit (101), the residual variance of the model, regressor numbers and coefficients being deposited in the memory (116) provided for that purpose, and that a locking memory (110), a memory for the diagonal elements and the dependent column of the regression matrix (111), a memory for the recursion matrix (113) with the offset-memory (112) belonging to the recursion matrix and a memory for the regression numbers (114) are provided for the realization of the recursive method, and that the regression unit (102) must perform several actions for the recursion level p, including that first of all those regressors are determined which make a small contribution to the model, and if necessary the regressors are locked (110), the offset for the recursion matrix is stored (112), the regressor rows of the new recursion matrix (113) and the new diagonal elements and the dependent column (111) are calculated, and the residual regressor numbers (114) stored, that those regressors, located within the collinearity cone of the current model, are determined and locked (110) with the help of the data from the memory for the regressor variances (115), that the most significant regressor from those remaining is searched, that regressor is selected which yields the model with the smallest residual variance and at the same time passes the F test known from statistics, and that, in the event of an unsuccessful search, the residual variance of the current model is utilized for the classification of this model between the best Qs, with the help of the residual variances of the models (116) already found, in which case, if the residual variance is smaller or equal to the largest stored residual variance, or currently less than Q models were found, the residual variance, the regression numbers and coefficients are stored in memory for the best models (116), and thereafter the regression unit (102) returns to the recursion level p-1, and its context is loaded from the corresponding memories (110 through
114),that, in the event of a successful search for a significant regressor, the group of regressors within the collinearity cone of the best regressor is found with the values of the regressor variances (115), that each of these regressors is incorporated into the model individually, one after the other, while the remaining ones from the collinear group remain locked (110), and with the precondition that none of the regression coefficients already found undergoes a sign change, the rows of the recursion matrix (113) for the new regressor and the new diagonal elements and the dependent column (111) are calculated and the recursion level p+1 selected, that, after processing of the collinear regressors, the change is made to the recursion level p-1, its context being loaded from the corresponding memories (110 through
114). - View Dependent Claims (2, 3, 4, 5, 6, 7)
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8. Method for the analysis or control of a technical process with the aid of regression models, which are calculated in recursive form by means of consistent, expanded, fast and collinearity-free multiple regression, in short CEFSR, for the variables relevant to the process, as a function of other parameters describing or influencing the process, termed regressors, characterized by the fact
that a number of supplementary, freely selectable, linear and nonlinear functions of the regressors are calculated from the entry matrix U with L rows corresponding to the number of input channels and V columns corresponding to the size of the sample, and thus a preliminary matrix X is generated with N rows, with N much greater than L, and the same number of columns as U, which is used to calculate the covariance matrix XX'"'"', that the correlation matrix is calculated from the covariance matrix and the diagonal elements are corrected with the help of the individual regressor variances, that a regression model for the variable declared as dependent is calculated with the covariance matrix by means of a recursive method containing the following steps for one recursion level, that first of all, the regressors are determined, which make a small contribution to the model, in order to remove them from the model and lock them for the further recursion levels, in which case, if there are such regressors, the recursion matrix as well as the diagonal elements and the independent column of the regression matrix must be calculated anew for recursion level p, that the regressors located inside the collinearity cone of a regression space are locked, that the most significant regressor from the remaining ones is found by means of the F test, that, in the event of an unsuccessful search, the residual variance is used by the current model for the classification of this model between the best Qs, with the aid of the residual variances of the models already found, in which case, if the residual variance is smaller or equal to the largest stored residual variance, or at present fewer than Q models were found, the residual variance, the regressor numbers and coefficients are stored, and where, as the next step, the recursion level p-1 is selected, that, when the search is successful, the set of regressors is determined, which lie within the collinearity cone of the best regressor, that each of these regressors is incorporated into the model individually, in sequence, while the others, belonging to the collinear set, are locked and, with the precondition that none of the regression coefficients already determined has undergone a sign change, the rows of the recursion matrix for the new regressor and the diagonal elements and the independent column is calculated and the recursion level p+1 selected, that, after the processing of the collinear regressors, a change is made to recursion level p-1.
Specification