# Research on the Reliability of Bridge Structure Construction Process System Based on Copula Theory
## 1 Introduction
[6] used a non-probabilistic element model and interval mathematics to deal with the uncertainty in structural damage detection, and proposed a non-probabilistic agent model based on Wavelet Weighted Least Squares Support Vector Machine (WWLS-SVM) to solve the uncertainty problem in vibration-based damage detection. Through practical application, it was proven that the performance of the method was better than the direct finite element model, and less computation was required. [PERSON] et al. [7] established an integrated monitoring system using global navigation satellite systems (GNSS) observation. The system is mainly used to study the deformation behavior and displacement prediction of suspension highway bridges, taking into account the effects of wind, temperature, humidity, and traffic load during operation and short-term measurement. The results showed that the predicted displacement obtained by artificial neural network (ANN) and adaptive neuro-fuzzy inference systems (ANFIS) provides a significant improvement for predicting the structural deformation of suspension highway bridges based on GNSS observations. [PERSON] et al. [8], by applying the extreme value function theory to structural damage detection, provided a useful tool for structural health monitoring, and carried out numerical and experimental tests and verifications by using engineering application examples in different fields. This research laid a solid foundation for structural health monitoring in the field of extreme function theory (EFT) and extreme value theory (EVT) in the future. [PERSON] et al. [9], by integrating building information modeling (BIM) with health monitoring and early warning, achieved the goal of integrating bridge operation, management, and maintenance, provided visual and information-based bridge conditions for bridge management and maintenance departments, and then provided information-based data assistance and decision support. Through analysis, it was found that the research on structural fault at home and abroad mostly focuses on structural fault monitoring and prediction, while the research on structural fault analysis based on system reliability theory is relatively lacking. At present, scholars at home and abroad have carried out a series of studies on the reliability analysis of bridge structural systems. Since the structural system has many components and complex forms, which are difficult to calculate accurately, a series of more practical approximation methods have been derived, and these calculation methods can be roughly divided into two categories: \"point estimation method\" and \"interval estimation method\" [10]. Point estimation method mainly includes the Monte-Carlo method, direct numerical integration method, and approximate numerical calculation method [11]. The Monte-Carlo method mainly relies on computerized cyclic tests to respond to the response or performance of the structure as a whole by changing the parameters or design variables of the structural system. It is not only applicable to the reliability analysis of individual members, but also can approximate the failure of the system. However, since the accuracy of the Monte-Carlo method is based on a large amount of data, it is less applicable in the reliability analysis of large structural systems. The direct numerical integration method, as the name implies, solves the system reliability by directly calculating a multidimensional numerical integral. The probability of failure of a structural system composed of failure modes in the series becomes a problem of calculating a dimensional integral. However, the calculation process is very complicated and difficult to apply in practical engineering. Moreover, as the dimension of integration increases, the computational volume and error of integration grow exponentially, and the feasibility and accuracy are relatively low.