Patent ID: 6556954
Filing Date: 2003-04-29
Classification: G06F

Abstract:
A method for determining a malfunction of a technical system that is subject to a malfunction, comprising the steps of:obtaining a status of said system by a processor unit, said system being describable by an implicit stochastic differential equation system with a form C*(t)+G*x(t)+s(t)+B*v(t)=0, wherein C references a first matrix, (t) references a derivation of said status of said system after a time that is described by a time variable t, G references a second matrix, s(t) references a system function of independent system quantities, B references a third matrix and v(t) references a noise function, determining an approximative solution of said implicit stochastic differential equation system by a discrete approximation process, wherein said discrete approximation process is operating according to a rule âˆ’(C+h&agr;2G)Â·{tilde over (X)}&pgr;n+1={âˆ’(1âˆ’&ggr;)c+h(1+&ggr;&agr;1âˆ’&agr;2)G}Â·{tilde over (X)}&pgr;n++{âˆ’&ggr;C+h(&ggr;âˆ’&agr;1&ggr;)G}Â·{tilde over (X)}&pgr;n+1 +h&agr;2s(&pgr;n+1)+h(1+&ggr;&agr;1âˆ’&agr;2)s(&pgr;n)++h(&ggr;âˆ’&agr;1&ggr;)s(&pgr;nâˆ’1)++B(&pgr;n)Â·&Dgr;Wn+&ggr;B(&pgr;n)Â·&Dgr;Wnâˆ’1 â€ƒwherein Ã¡1, Ã¡2, Ã¡ are predetermined parameters from the interval [0, 1], h:=T/N, is a step width in an output time interval, whereby T is a predetermined value that is subdivided into N sub-intervals, {tilde over (X)}&pgr;n+1 is a realization of said approximation process at a supporting point Ã”n+1, {tilde over (X)}&pgr;n is a realization of said approximation process at a supporting point Ã”n, {tilde over (X)}&pgr;nâˆ’1 is a realization of said approximation process at a supporting point Ã”nâˆ’1, &Dgr;Wnâˆ’1:W&pgr;nâˆ’W&pgr;nâˆ’1 is a difference value between a second value W&pgr;n at said supporting point Ã”n and said second value Wnâˆ’1 at said supporting point Ã”nâˆ’1, and; iteratively solving for disturbance of said approximation process.