The hidden belief rule base model (HBRB) which can utilize both hybrid expert’s experience and experimental data has become a useful method for hidden behavior forecasting of complex system in many applications. But the traditional HBRB model is one-step forecasting model, which means that it can only utilize the limited information in very short time instant. In fact, one-step forecasting method is incomplete because the future behavior of a complex system is generated through multiple historical stats in different time instant. Therefore, a time-delay hidden BRB forecasting model (THBRB) is designed, where the input with multiple time instant of the HBRB model is considered, and the corresponding reasoning process is also designed. Further, an optimization method based on projection covariance matrix adaption evolution strategy (P-CMA-ES) algorithm is used to train the initial THBRB model. A case study is established to prove the advantage of the proposed method, and the experiment results show that the proposed THBRB model can predict the future hidden behavior of complex system effectively.

可以同时利用混合专家的经验和实验数据的隐藏信念规则库模型（HBRB）已成为在许多应用中用于复杂系统隐藏行为预测的有用方法。但是传统的HBRB模型是一步式预测模型，这意味着它只能在非常短的时间内利用有限的信息。实际上，单步预测方法是不完善的，因为复杂系统的未来行为是通过不同时间的多个历史统计信息生成的。因此，设计了一种时延隐藏BRB预测模型（THBRB），其中考虑了HBRB模型的多个瞬时输入，并设计了相应的推理过程。进一步，提出了一种基于投影协方差矩阵自适应进化策略（P-CMA-ES）算法的优化方法来训练初始THBRB模型。通过实例研究证明了该方法的优越性，实验结果表明所提出的THBRB模型可以有效地预测复杂系统的未来隐藏行为。