# The Application of Structural Reliability and Sensitivity Analysis in Engineering Practice
## 1 Introduction  
Sensitivity analysis is used to attain an in-depth understanding and categorization of the sources of uncertainty describing the loads and material parameters of a structure. The objective of this analysis is to ascertain the impact of these uncertainties on the structure's response. Sensitivity analysis methods are fundamentally divided into local and globalmethods. Local sensitivity analysis methods [1; 2; 3] investigate the influence of altering a single random parameter on the structure's response, specifically in the vicinity of a chosen point, typically the design point. Differential analysis methods dominate in this category. In this local method, sensitivity indices can be defined at a specific point in the probability space through the use of partial derivatives. The main disadvantage of local sensitivity analysis depends on the choice of the nominal point. Global sensitivity analysis methods focus on examining the behavior of a structure's response influenced by any number of random parameters across the entire probability space. Currently, a number of measures have been suggested, which are widely used in engineering practice. In [4], the author describes the examination of scatterplots, regression analysis, correlation analysis, partial correlation analysis, statistical tests for patterns based on gridding, entropy tests for patterns based on gridding, nonparametric regression analysis, two-dimensional Kolmogorov-Smirnov test, and tests for patterns based on distance measures. [PERSON], [PERSON], and [PERSON] [5; 6; 7] propose moment independent sensitivity indicators. A promising method for sensitivity analysis of models with uncertainty is also the Bayesian and Gaussian process method. Bayesian inference methods allow for updating probabilities based on new data and previous information. The introduction of Markov Chain Monte Carlo (MCMC) algorithms, such as Metropolis-Hastings and Gibbs sampling, made it possible to efficiently perform Bayesian inference on a large scale. MCMC algorithms allow for the generation of samples from posterior distributions, which is crucial for the practical application of Bayesian methods. In reliability analysis, Bayesian inference methods allow for updating initial assumptions about the limit function and parameters of the distributions, using information about the performance of the structure obtained at a later time. The use of Bayesian networks in sensitivity analysis is particularly valuable because it allows for the study of how changes in input values affect the model output in the context of uncertainty. Bayesian networks offer a flexible approach that takes into account both uncertainties in the data and dependencies between variables. In article [8] is proposed an enhanced Hierarchical Sparse Bayesian Learning (eHSBL) model for SHM field data forecasting and interpretation, correlation analysis, and uncertainty analysis. The proposed eHSBL model was used for the Tsing Ma Bridge (TMB), which is characterized by heterogeneities and high uncertainties. This interesting approach was successful in detecting and identifying damage for the SHM benchmark problem of Tianjin Yonghe Bridge [9]. In order to properly assess the structural performance of tall buildings, it is necessary to take into account uncertainties from various sources. In paper [10], the authors analyzed the seismic resistance of a 42-story building with a composite steel frame and a cast iron tubular core. In their research, they used a probabilistic method that takes into account various types of uncertainties. The uncertainties in the fragility analysis included the effects of loads, annual discount rate, cost index, and recovery time, as well as unknown parameters in the demand model. In this paper, the Bayesian updating rule is used to determine the posterior distribution of unknown parameters in the demand model.