Method and device for determining a regularity

A method to detect and determine a regularity of a cyclically fluctuating scientific or technical QUANTITY-A, comprising the steps of:

• determining, using a detector, values Ai of QUANTITY-A;
• automatically storing, in a computer memory of a computer connected to said detector, said values Ai;
• choosing, using a processor of said computer, a homogenous function W(Ai, Ai+1, . . . ) which maps at least two determined values of QUANTITY-A to a value of type angle (WINKEL), said homogeneous function fulfilling the criteria:
• W(apositiv*Ai, apositiv*Ai+1, . . . )=W(Ai, Ai+1, . . . ) for all apositiv, where apositiv can be any positive number, which evidences for a natural number k≧1 forbidden combinations of values of type angle (WINKEL) in which a combination of WINKEL(n) and WINKEL(n+1) is forbidden, if the back-transformation of W(Ai, Ai+1, . . . )=WINKEL(n) and W(Ai+k, Ai+k+1, . . . )=WINKEL(n+1) either is not possible or does exclusively allow solutions A, for which at least one complete definition set of (A→W) becomes zero or at least one value of A becomes singular, for which said back-transformation evidences a central allowed combination of values of type angle, where a central allowed combination of angles lies in the intersection of manifolds, which are formed by forbidden combinations of angles;
• mapping, using said homogenous function W(Ai, Ai+1, . . . ), at least two determined values A1, A2, . . . to a value WINKEL1;
• mapping, using said homogenous function W(Ai, Ai+1, . . . ), at least two determined values A1+k, A2+k, . . . with said value k to a value WINKEL2;
• mapping, using said homogenous function W(Ai, Ai+1, . . . ), at least two determined values A1+m, A2+m, . . . with m>k to a value WINKEL3;
• producing an implicit rule of behavior as an equation according to G[WINKEL(n+1), WINKEL(n), . . . ]=F[WINKEL(n), . . . ;
• p1, p2, . . . ],
• wherein said bi- or multivariate function G[WINKEL(n+1), WINKEL(n), . . . ] evidences singularities for combinations of WINKEL(n+1) and WINKEL(n), which belong to a set of forbidden combinations of angles, or G[WINKEL(n+1), WINKEL(n), . . . ] can be represented as a bounded univariate function of such a singular multivariate function;
• wherein said bi- or multivariate function G[WINKEL(n+1), WINKEL(n), . . . ] evidences a central singularity for a central allowed combination of WINKEL(n+1), WINKEL(n), . . . , wherein a central singularity of bi- or multivariate function G evidences a convex neighborhood of arbitrary size of combinations of angles, in which said bi- or multivariate function G assumes any value of a finite or infinite interval;
• determining said parameters p1, p2, . . . of said function F[WINKEL(n), . . . ;
• p1, p2, . . . ] by adjusting the implicit rule of behavior to values WINKEL1, WINKEL2, WINKEL3, . . . , said adjustment being based on residuals of a form R(n)=G[WINKEL(n+1), WINKEL(n), . . . ]−F[WINKEL(n), . . . ;
• p1, p2, . . . ] with WINKEL(1)=WINKEL1, WINKEL(2)=WINKEL2, . . . , being achieved either by a type of interpolation or approximation or with the help of other regression methods to adjust the parameters, using said function G[WINKEL(n+1), WINKEL(n), . . . ]=F[WINKEL(n), . . . ;
• p1,p2, . . . ] to express said regularity;
• and
• outputting an expression of regularity for a use selected from the group consisting of controlling a process, problem/change detection and diagnosis.