###### Abstract  
A reliability analysis method based on least squares support vector machines with an improved particle swarm optimization algorithm (IPSO-LSSVM) is proposed to calculate the reliability of concrete gravity dams when explicit nonlinear limit-state functions are difficult to obtain accurately. First, the main failure modes of concrete gravity dams and their influencing factors are determined. Second, Latin hypercube sampling is used to create samples. A finite element calculation batch program of concrete gravity dams is written to calculate the safety indexes of each sample. Third, based on the samples, the IPSO-LSSVM model is established to replace the finite element calculation. Finally, the failure probability of concrete gravity dams is obtained by using the Monte Carlo (MC) method. The case study for a typical concrete gravity dam in the Yunnan Province of China shows that the dam is reliable because the failure probability is \(8.87\times 10^{-5}\). The proposed reliability analysis method is efficient and feasible for calculating the reliability of concrete gravity dams. concrete gravity dam; reliability analysis method; improved particle swarm optimization algorithm; least squares support vector machine; Monte Carlo method +
Footnote †: journal: Applied  
**Critical Design**  
**2022** 20  
To overcome the limitations of the application of the above-mentioned traditional reliability analysis methods, many scholars have conducted useful research. [PERSON] et al. [7] proposed the third-order moment method based on the study of the primary second-order moment method, which improved the accuracy of the reliability calculation results. [PERSON] et al. [8] proposed a second fourth-order moment calculation method for reliability calculations based on the first fourth-order moment of the second-order approximation of the functional function and proved its simplicity and accuracy. [PERSON] et al. [9] proposed a reliability analysis method for gravity dams based on the Hermite orthogonal polynomial approximation method and illustrated the correctness and effectiveness of the proposed method by arithmetic examples. [PERSON] et al. [10] proposed a sensitivity-assisted MC simulation method in which second-order derivatives were introduced to improve the accuracy of reliability calculations. [PERSON] et al. [11] proposed a bootstrap-compensated MC method to reduce the computation time of reliability by introducing the concept of augmented samples. The importance sampling method [12] is an improved MC method, which is mainly used to improve the efficiency of simulation calculations. [PERSON] et al. [13] discussed that a change in the location of the implicit functional function fitting point in the traditional response surface method can affect the results of structural reliability calculations, indicating that the accuracy of response surface method calculations at the checkpoint is closely related to the location of the checkpoint. [PERSON] et al. [14] proposed a weighted dynamic response surface reliability analysis method based on the cat swarm algorithm, which overcomes the drawback of the MC method that requires a large number of repeated samples. [PERSON] [15] proposed a reliability solution method for the response surface of a high-dimensional model combined with the first-order reliability method to solve the structural reliability. [PERSON] et al. [16] proposed a new method for solving implicit functional function reliability problems, which does not require the derivation of response surface functions of random variables in the process of calculating reliability. [PERSON] et al. [17] used locally propagated samples to track the response surface function, and an important feature of this algorithm is that the alternative model advances with the choice of samples, enabling the algorithm to converge quickly to the response surface. [PERSON] et al.