A half-century of stochastic equivalent linearization

Tom Caughey was a major pioneer in the development of the stochastic equivalent linearization procedure for estimating the mean and variance of the response of a non-linear system to random excitation. The present note describes a number of interesting episodes in the history of the linearization technique that have arisen in the past half-century. The standard procedure is described for the zero-mean case where an approximate response distribution with undetermined mean square is chosen and equivalent linearization is used to fix an optimum estimate of the mean-square response. Three linearization criteria are considered. The notion of ‘true’ linearization is discussed in light of one of Tom's widely overlooked results. It is noted that ‘true’ linearization is embedded in different criteria for oscillators and for memory-less systems. Two one-parameter families of probability shape are shown together with the resulting mean-square estimates furnished by the three criteria. Some miss-steps in the history of equivalent linearization are recounted: an early conjecture by one of the pioneers proved to be false, and an alternative to the standard procedure went unrecognized for 27 years. Copyright © 2005 John Wiley & Sons, Ltd.