Evaluating the effectiveness of ground motion intensity measures through the lens of causal inference

When solving the performance-based earthquake engineering (PBEE) integral, the engineering demand parameters (EDPs) are assumed to be independent of the "upstream" parameters used in ground motion models (e.g., magnitude and source-to-site distance) after conditioning on the intensity measure (IM). This paper formulates a methodology for evaluating this conditional independence assumption through the lens of causal inference (CI). From a causal perspective, the effect of an upstream parameter on the EDP of interest is partially mediated by the IM with the remainder having a direct influence on the EDP. An IM is judged to be desirable (from a conditional independence standpoint) if the mediated effect of the upstream parameter is maximized, which implies that the direct effect is minimized. In the language of causal inference (CI), the IM, EDP and upstream parameters are described as the "treatment", "outcome" and "confounding" variables, respectively. It then follows that the best performing IM is the one that maximizes the effect on the EDP after controlling for the upstream parameters. A semi-parametric model that employs double machine learning is used to estimate the causal effect. The methodology is demonstrated through a case study application utilizing the responses from five special steel moment frames analyzed using 240 site-agnostic ground motions. Compared to sufficiency-based assessments, the casual inference method produces findings that are more explainable using structural dynamics principles and invariant to the number of ground motions used in the evaluation.