Method and device for determining a fault in a technical system
AssigneeSiemens Aktiengesellschaft
InventorsGeorg Denk, Oliver Schein
Life of this patent
Estimating the term…
Abstract
A technical system that is subject to a malfunction is described with an implicit stochastic differential equation system. An approximative solution of the system is determined in that a discrete approximation process is realized. The discrete approximation process is realized according to the following rule: −(C+hα2G)·{tilde over (X)}πn+1={−(1−γ)C+h(1+γα1−α2)G}·{tilde over (X)}πn+ +{−γC+h(γ−α1γ)G}·{tilde over (X)}πn+1 +hα2s(πn+1)+h(1+γα1−α2)s(πn)+ +h(γ−α1γ)s(πn−1)+ +B(πn)·ΔWn+γB(πn)·ΔWn−1 The disturbance {tilde over (X)}πn+1 is determined by iterative solution of the approximation process.
Claims24
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
- −(C+hα2G)·{tilde over (X)}πn+1={−(1−γ)c+h(1+γα1−α2)G}·{tilde over (X)}πn+
- +{−γC+h(γ−α1γ)G}·{tilde over (X)}πn+1
- +hα2s(πn+1)+h(1+γα1−α2)s(πn)+
- +h(γ−α1γ)s(πn−1)+
- +B(πn)·ΔWn+γB(πn)·ΔWn−1
- wherein
- á1, á2, á 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)}πn+1 is a realization of said approximation process at a supporting point Ôn+1,
- {tilde over (X)}πn is a realization of said approximation process at a supporting point Ôn,
- {tilde over (X)}πn−1 is a realization of said approximation process at a supporting point Ôn−1,
- ΔWn−1:Wπn−Wπn−1 is a difference value between a second value Wπn at said supporting point Ôn and said second value Wn−1 at said supporting point Ôn−1, and;
- iteratively solving for disturbance of said approximation process.
An apparatus for determining a malfunction of a technical system that is subject to a malfunction, comprising:
- a processor unit, wherein said system is describable with 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 a status of the 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,
- wherein said processor unit determines an approximative solution of said implicit stochastic differential equation system by a discrete approximation process operating according to a rule
- −(C+hα2G)·{tilde over (X)}πn+1={−(1−γ)c+h(1+γα1−α2)G}·{tilde over (X)}πn+
- +{−γC+h(γ−α1γ)G}·{tilde over (X)}πn+1
- +hα2s(πn+1)+h(1+γα1−α2)s(πn)+
- +h(γ−α1γ)s(πn−1)+
- +B(πn)·ΔWn+γB(πn)·ΔWn−1
- wherein
- á1, á2, á are predetermined parameters from the interval,
- 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)}πn+1 is a realization of said approximation process at a supporting point Ôn+1,
- {tilde over (X)}πn is a realization of said approximation process at a supporting point Ôn,
- {tilde over (X)}πn−1 is a realization of said approximation process at a supporting point Ôn−1,
- ΔWn−1:Wπn−Wπn−1 is a difference value between a second value Wπn at said supporting point Ôn and said second value Wπn−1 at said supporting point Ôn−1 and;
- disturbance {tilde over (X)}πn+1 is determined by iterative solution of said approximation process by said processor.
Dependencies are inferred from the claim text.