Patent Document ID: 9582618
Application ID: 15000725
Patent Status: 1

Claim One:
1. A method of fault diagnosis comprising: determining, using processing circuitry, scheduling parameters of a system wherein the system includes a plurality of subsystems; determining, using the processing circuitry, diagnostic parameters of the system; generating, using the processing circuitry, a linear parameter varying (LPV) model wherein the model relates an input, the diagnostic parameters, and the scheduling parameters to an output; calculating a first vector estimate x Qo associated with a first matrix by applying 
 {circumflex over (x)} Q 0 =(ρ(ξ) {circle around (x)}ψ 0 T ( k )) † y 0 ( k ) where ρ(ξ) is a deviation vector, ψ o is a data matrix, and y o is an output vector; identifying the LPV model by estimating recursively using singular value decomposition matrices using data obtained by perturbing one or more diagnostic parameters and the first matrix which is determined with no perturbations, wherein the identifying includes applying the following formulation: 
 {circumflex over (x)} Q i =(ρ(ξ) {circle around (x)}ψ i T ( k )Δγ i ) † ( y i ( k )−ψ i T ( k ) {circumflex over (Q)} 0 ρ( k )); 
 {circumflex over (x)} Q ij =(ρ(ξ) {circle around (x)}ψ ij T ( k )Δγ i Δγ j ) † ( y ij ( k )−ψ ij T ( k )( {circumflex over (Q)} 0 (ξ)+ {circumflex over (Q)} i (ξ)Δγ i +{circumflex over (Q)} j (ξ)Δγ j )ρ(ξ)); 
 and 
 {circumflex over (x)} Q ijk =(ρ(ξ) {circle around (x)}ψ ijk T ( k )Δγ i Δγ j Δγ k ) † ( y ijk ( k )−ψ ijk T ( k )( {circumflex over (Q)} 0 +{circumflex over (Q)} i (ξ)Δγ i +{circumflex over (Q)} j (ξ)Δγ j +{circumflex over (Q)} k (ξ)ρ(ξ)Δγ k +{circumflex over (Q)} ij (ξ)ρ(ξ)Δγ i Δγ j )ρ(ξ)) where x Qi , x Qij , x Qijk are vector estimates associated with matrices; monitoring each of the plurality of subsystems as a function of the identified LPV model; scheduling the LPV model to track variations in an operating regime; and diagnosing one more faults of one or more components of the system using the generated LPV model.