ON THE STATISTICAL LINEARIZATION METHODS OF I. E. KAZAKOV

摘要

In Kazakov's pioneering papers [1, 2] on statistical linearization he proposed two methods for replacing a nonlinear system under random excitation by an approximate linear system under the same excitation. He demonstrated that in particular examples, the two methods gave different predictions for the response statistics and he suggested that an improved prediction would be obtained by averaging the two results. This suggestion is examined here from the point of view of the concept of "true" linearization defined by Kozin [3] as a linearization recipe which produces the true nonlinear response statistics when the statistics in the linearization recipe are evaluated using the probability distribution of the true nonlinear response. It is found that Kazakov 's first method is a "true" linearization for nonlinear algebraic systems, but not a "true" linearization for differential equation systems, while the second method is a "true" linearization for systems with nonlinear differential equations, but not a "true" linearization for algebraic systems. In this sense the two different methods work better on different problems. On any particular problem, however, the average of the two results often provides an estimate that is inferior to the result provided by the better of the two methods.