Detection and Isolation of Simultaneous Additive and Parametric Faults in Nonlinear Stochastic Dynamical Systems

Table 1

Statistics of magnitudes 𝑋 and 𝑌 under the 𝐻₀ and 𝐻₁ hypotheses.

Hypothesis	𝐻0	𝐻1
𝐸[𝑋]	0	𝑘𝜑𝐿𝑃^2𝑇,𝑆
Var[𝑋]	Var[𝑋∣𝐻0]	Var[𝑋∣𝐻0]
𝐸[𝑌]	𝑅𝜖	𝑘^2𝜑𝐿𝑃^2𝑇,𝑆+𝑅𝜖
Var[𝑌]	𝑅^2𝜖𝜆^2𝑇^2(2𝜆𝑇−1)	𝑅^2𝜖𝜆^2𝑇^2(2𝜆𝑇−1)+4𝑘^2Var[𝑋∣𝐻0]
Cor[𝑋,𝑌]	0	2𝑘Var[𝑋∣𝐻0]