A Mathematical Basis for the Random Decrement Vibration Signature Analysis Technique

1982 ◽  
Vol 104 (2) ◽  
pp. 307-313 ◽  
Author(s):  
J. K. Vandiver ◽  
A. B. Dunwoody ◽  
R. B. Campbell ◽  
M. F. Cook
Keyword(s):  
Random Process ◽  
Linear Time ◽  
Signature Analysis ◽  
Gaussian Random Process ◽  
Mathematical Basis ◽  
Linear Time Invariant ◽  
Random Decrement Technique ◽  
Random Decrement ◽  
Vibration Signature ◽  
Linear Time Invariant System

The mathematical basis for the Random Decrement Technique of vibration signature analysis is established. The general relationship between the autocorrelation function of a random process and the Randomdec signature is derived. For the particular case of a linear time invariant system excited by a zero-mean, stationary, Gaussian random process, a Randomdec signature of the output is shown to be proportional to the auto-correlation of the output. Example Randomdec signatures are computed from acceleration response time histories from an offshore platform.

scholarly journals Temporal Variability in the Response of a Linear Time-Invariant Catchment System to a Non-Stationary Inflow Concentration Field

2020 ◽  
Vol 10 (15) ◽  
pp. 5356
Author(s):  
Ching-Min Chang ◽  
Kuo-Chen Ma ◽  
Mo-Hsiung Chuang
Keyword(s):  
Closed Form ◽  
Temporal Variability ◽  
Linear Time ◽  
Concentration Field ◽  
Surface Water Quality ◽  
Catchment Scale ◽  
Input Concentration ◽  
Linear Time Invariant ◽  
Linear Time Invariant System ◽  
Time Invariant

Predicting the effects of changes in dissolved input concentration on the variability of discharge concentration at the outlet of the catchment is essential to improve our ability to address the problem of surface water quality. The goal of this study is therefore dedicated to the stochastic quantification of temporal variability of concentration fields in outflow from a catchment system that exhibits linearity and time invariance. A convolution integral is used to determine the output of a linear time-invariant system from knowledge of the input and the transfer function. This work considers that the nonstationary input concentration time series of an inert solute to the catchment system can be characterized completely by the Langevin equation. The closed-form expressions for the variances of inflow and outflow concentrations at the catchment scale are derived using the Fourier–Stieltjes representation approach. The variance is viewed as an index of temporal variability. The closed-form expressions therefore allow to evaluate the impacts of the controlling parameters on the temporal variability of outflow concentration.

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