Is stochastic equivalent linearization a subtly flawed procedure?

The standard equivalent linearization procedure for estimating the mean and variance of the response of nonlinear dynamic systems has proved to be an unusually effective technique. For over forty years there has been general agreement about the procedure to be followed. Recently two independent claims have been made that the standard procedure harbors a subtle flaw. In place of the standard procedure, essentially the same alternative procedure was claimed to be the “correct” procedure, even though, in the test cases investigated, the alternative “correct” procedure produced estimates with greater errors than the “incorrect” standard procedure. The present note investigates the claim that the standard procedure is flawed and finds that: (a) there is no subtle flaw in the standard procedure; (b) the proposed alternative procedure differs from the standard procedure in that it employs a different criterion for selecting the optimum linear approximation; (c) there is also no flaw in the proposed alternative procedure; but, (d) there does not seem to be any practical advantage to using the proposed alternative, since the standard procedure is simpler and more accurate.