## 1 Introduction  
Reinforced concrete (RC) columns serve as critical load-bearing elements in building and bridge structures, effectively distributing loads across large-span spaces and enhancing structural stability and load-bearing capacity. Consequently, their damage evolution mechanisms have long been a primary research focus in structural engineering. Eccentric compression--a common loading condition in frame edge columns and bridge piers subjected to lateral loads--induces a stress gradient across the section. This gradient drives a progressive, multi-stage damage process, spanning from microcrack initiation and propagation to macroscopic failure [1, 2, 3]. Traditional damage assessment techniques, such as strain gauge monitoring and visual inspection, are constrained by insufficient spatial resolution and struggle to quantitatively characterize the dynamic evolution of internal microcracks. In contrast, acoustic emission (AE) technology enables the high-sensitivity, non-destructive monitoring of internal damage in concrete structures by detecting high-frequency elastic waves released during material fracture [4; 5; 6]. Critically, AE signals generated by damage in eccentrically compressed RC columns exhibit significant complexity due to stress gradient effects. This complexity arises from coupled mechanisms, including lateral crack propagation in the tension zone, longitudinal cracking in the compression zone, and interfacial delamination [7; 8; 9]. The central challenge, therefore, lies in analyzing these multi-stage damage mechanisms and crack evolution through the spatiotemporal distribution of AE signal characteristics. Recent research has extensively explored AE signal characteristics in concrete structures, consistently demonstrating the applicability of AE parameters for characterizing complex damage mechanisms in composite materials. These parameters exhibit high sensitivity to incipient damage, enabling effective identification of damage stages and crack modes [10]. [PERSON] et al. [11] established a three-stage damage evolution process (initial damage, damage propagation, and damage failure) in concrete through analysis of cumulative ring count curves during uniaxial compression tests. Utilizing AE parameters (average frequency, rise angle value, and energy), [PERSON] [12] successfully distinguished tensile micro-cracking, macro-cracking, and fiber pull-out (the phenomenon of fibers being pulled out during the expansion of concrete tensile cracks) mechanisms in fiber-reinforced concrete beams. Advances in machine learning have introduced novel approaches for damage pattern classification through clustering of multi-parametric AE signals, where algorithms including K-means, hierarchical clustering, and Gaussian mixture models (GMMs) are widely employed for AE feature analysis [13; 14]. Resultant clustering outputs facilitate damage-type identification [15; 16]. As a straightforward hard-clustering algorithm, K-means has demonstrated efficacy in clustering AE feature signals. Distinct clusters exhibit characteristic energy and amplitude ranges, enabling the correlation of cluster signatures with specific concrete damage mechanisms. [PERSON] et al. [17] employed the K-means clustering of AE parametric features during studies on concrete crack propagation under monotonic and fatigue loading, successfully identifying four damage mechanisms in conventional concrete: cement matrix cracking, aggregate sliding, interfacial transition zone (ITZ) fracture, and aggregate fracture. In contrast, GMM constitute a soft-clustering approach that better accommodates irregular data distributions by permitting probabilistic cluster memberships. [PERSON] et al. [18] introduced a machine learning-enhanced rise angle (RA)-average frequency (AF) segmentation scheme for clustering AE signals of known crack patterns. Their comparative evaluation of four clustering techniques confirmed GMM's superior classification accuracy.