This study introduces the evolutionary tail-equivalent linearization method (ETELM) for nonlinear stochastic dynamic analysis. The method builds on the recently developed tail-equivalent linearization method (TELM) and it is designed for the class of evolutionary processes. The original TELM employs a tail-equivalent linear system (TELS) by equating the tail probability of a linear system response for a specified threshold to the first-order approximation of the tail probability of the nonlinear system response. For stationary problems, the TELS is time-independent and only one linear system needs to be defined for the specified threshold. However, for a transient input, the TELS is time dependent and an evolutionary tail-equivalent linear system (ETELS) must be defined to study the entire transient response. Algorithms are developed to determine a discrete-time ETELS based on a sequence of linearization points, and a continuous-time approximation based on Priestley’s evolutionary theory. The linearized evolutionary system is used to compute the response statistics of interest, including the first-passage probability, in first-order approximation. Numerical examples demonstrate the accuracy and limitations of the proposed method.

本研究介绍了用于非线性随机动力学分析的演化尾部等效线性化方法（ETELM）。该方法建立在最近开发的尾部等效线性化方法（TELM）上，并且针对进化过程类别而设计。原始TELM通过将指定阈值的线性系统响应的尾部概率等于非线性系统响应的尾部概率的一阶近似值，使用尾部等效线性系统（TELS）。对于平稳问题，TELS与时间无关，并且仅需为指定阈值定义一个线性系统。但是，对于瞬态输入，TELS是时间相关的，必须定义演化尾等效线性系统（ETELS）来研究整个瞬态响应。开发了基于一系列线性化点确定离散时间ETELS的算法，并基于Priestley的进化理论确定了连续时间的近似算法。线性演化系统用于以一阶近似值计算感兴趣的响应统计信息，包括第一次通过概率。数值算例表明了该方法的准确性和局限性。