# A Story-Based Random Structure Modeling Method for Regional Buildings Earthquake Loss Estimation
## 1 Introduction  
Currently, earthquake loss estimation methods for regional buildings can be broadly categorized into classification and statistical methods based on historical seismic damage data and elastic-plastic analysis methods based on structural models [1; 2]. The former is a data-driven method, and the reliability of the calculation results depends mainly on the accumulation of historical seismic hazard data. In contrast, there is still a need for more historical seismic hazard data [3; 4], and their practical application is limited to a certain extent [5]. At the same time, the assessment results of this type of method are biased toward the macro, the assessment accuracy of individual needs to be improved, and it is difficult to reflect the differences between individual buildings of the same type. With the development of the structural finite element method and dynamic nonlinear integration method, the structural model-based elastoplastic analysis method has the advantages of a high accuracy, low cost and equipment needs, and convenient and fast implementation, which has a broader application prospect. The prerequisite for implementing this methodis to categorize buildings based on their characteristics and create corresponding simplified models, which is fundamental for conducting large-scale analyses. HAZUS [6], a widely used regional disaster assessment software from America, can assess and predict the economic losses, casualties, and injuries of buildings and various types of infrastructure caused by earthquakes [7; 8], and similar systems have been developed in other countries or regions based on it [9; 10; 11]. HAZUS categorizes buildings into 36 types based on their construction materials, structural forms, number of stories, and seismic design codes. However, HAZUS is based on the Capacity Spectrum Method (CSM) to simplify all kinds of buildings into a single-degree-of-freedom system. The damaged state of the whole structure is unique, which is not able to reflect the distribution of the loss inside the building, while in practice, the distribution of the loss of the medium- and high-rise buildings tends to be more concentrated in some stories, with a large discrepancy between these stories. Meanwhile, HAZUS uses Push-over analysis to obtain the seismic capacity curve of the building. The seismic response of the structure is only controlled by the first vibration mode while ignoring the influence of higher-order modes, which is a big difference between the results of the response analysis under the condition of ground shaking with impulses in the near-field and the response analysis by taking into account the influence of the higher-order vibration modes [8; 11; 12]. Moreover, HAZUS needs help with the problem of database adaptability, and the applicability of the seismic hazard model and the repair cost ratios for all levels of damage states are poor for regions outside North America [13], which is significantly different from actual damage. The Pacific Earthquake Engineering Research Center (PEER) proposed the second generation of Performance-Based Earthquake Engineering (PBEE) [14], which has changed from emphasizing the \"mechanical performance\" and \"safety performance\" of structures to highlighting the \"economic performance\" of structures [15; 16]. The seismic performance assessment of buildings methodology [17] published by FEMA best reflects the concept and connotation of the second generation of PBEE. Academics and other stakeholders have widely recognized it since its introduction [18; 19]. The methodology divides components with the same seismic demand parameters into performance groups (e.g., shear walls on the same story in the same direction). Based on the fragility function and the consequence function of the performance group, the Monte Carlo method is used to simulate and obtain the building's economic losses, casualties, and repair time. This methodology can ensure a high computational accuracy, but the premise is that detailed building construction information is required.