## 1 Introduction
To address these challenges, this paper proposes a new reliability analysis method for complex structural systems with multiple failure modes, utilizing an adaptive AdaBoost model that enhances both accuracy and effectiveness in assessing the reliability of complex structures. Adaptive iteration continuously optimizes the sampling center through proactive sampling. During this process, the effectiveness of the sample is quantitatively evaluated by measuring the ratio of the number of samples falling into the ineffective region to the total number of samples. The AdaBoost algorithm is a strong integrated learning method for low-bias prediction tasks, which are not easy to overfit during training [25]. The method employs a training dataset with different weights to construct different weak basis classifiers. Each data sample is then assigned a weight that indicates its importance as a training sample, and all samples have the same weight in the first iteration. In the ensuing iterations, the weight assigned to misclassified samples is elevated (or alternatively, the weight attributed to correctly classified samples is proportionately diminished), causing the new classifier to pay increasing attention to misclassified samples that may gather near the classification edge, thereby ultimately reducing the error rate [26; 27; 28]. Many scholars around the world have actively engaged in in-depth research on the AdaBoost algorithm, evaluating its application effects and proposing practical and feasible improvements [29; 30; 31; 32; 33; 34]. For example, [PERSON] et al. [31] presented an innovative approach to the naval gun hydraulic system fault diagnosis based on the BP-AdaBoost model. [PERSON] et al. [32] proposed a new polynomial chaos expansion surrogate modeling method utilizing AdaBoost for uncertainty quantification. [PERSON] [33] artfully integrated the enhanced AdaBoost algorithm with the backpropagation neural network model, employing an evolutionary optimization algorithm to refine the model and proposing a mechanical structure reliability calculation method grounded in this advanced framework. [PERSON] et al. [34] proposed a real BP AdaBoost algorithm based on weighted information entropy to solve the problems of low prediction accuracy and poor reliability of the software reliability model of the single neural network. [PERSON] et al. [35; 36; 37] proposed a new hybrid adaptive Kriging model and a water-cycle algorithm based on reliability assessment learning and optimization strategies, subsequently applying it to offshore wind turbine monopole and offshore wind power towers. [PERSON], [PERSON], et al. [38] proposed a machine learning (ML) algorithm to provide prediction models for determining the seismic response, seismic performance curve and earthquake failure probability curve of brbf. [PERSON], [PERSON], and [PERSON] [39] solved the problem of seismic probability and risk assessment of reinforced concrete shear walls (RCSWs) by introducing a stacked machine learning (stacked ML) model based on Bayesian optimization (BO), genetic algorithm (GA), particle swarm optimization (PSO), and gradient-based optimization (GBO) algorithms. The IDA curves (MIDA) and seismic probability curves of this model have a good curve-fitting ability. The subsequent sections of this paper will be meticulously organized into three sections. Section 2 will thoroughly explore the distinctive characteristics of complex structures in the context of multiple failure modes, the methodology for adaptive sample selection, and the principle underlying the iterative AdaBoost algorithm. Additionally, it outlines a process for assessing the reliability of mechanical structures based on the AdaBoost surrogate model. The Section 3 validates the effectiveness and precision of the AdaBoost surrogate model in evaluating multi-failure mode complex structures through three illustrative examples and discusses their computational results.