22SISO - MAE591 RANDOM DATA Single-input/single-output...

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MAE591 RANDOM DATA Single-input/single-output relationships (Random Vibration) Response of a linear time-invariant discrete dynamic system : x t () h Hf τ y t y t hx t d ()( ) ) =− = −∞ ∞∞ ∫∫ ττ τττ 0 τ For stationary processes: Mean value [] µτ τ τ τ τ τ ττµ πτ y jf f x E y t Ehx hE x t d E x thd Ext h e d H == −= = = [() ] [ ()( ) ] () [( ) ] ] () ] 0 0 0 2 0 0 0 τ τ Correlation functions R Extyt E h xtxt d h Extxt d h R d h R xy xx xx [()( ) ] ()()( ) () [()( ) ] ( ) ξ τ ξ ξ ξτ ξ ξ ξ τ ξ ξ τ =+ = + = = 0 00 τ η Similarly, RE y t y t E h h x t x d hh E x t x t d d hh R d d hhR yy xx xx ) ] )( ) ()() [( ) ] ()() ( ) ) ( ) ξ η ξ τ η ξ η ξη ξ τηξ η τξηξ τ = + + =−∗ ∗ 0 0 0 0 Summary : Wiener- Khinchin relation + Convolution theorem Correlation relationship Spectral relationship
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This note was uploaded on 11/21/2009 for the course ME . taught by Professor . during the Spring '09 term at Korea University.

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