# The Application of Structural Reliability and Sensitivity Analysis in Engineering Practice
## 1 Introduction
Based on the research, it can be concluded that taking into account the uncertainty of unknown parameters involved in the demand model has a significant impact on the estimation of fragility, expected costs, and seismic resistance of the structure. In [11], a hybrid AI-Bayes-based methodology is proposed for fragility estimation of tall buildings subjected to multiple earthquakes and winds. The proposed method is capable of fragility estimation to consider both epistemic and aleatoric uncertainties. The AI-Bayes-based method discussed in this paper provides great assistance in quantifying various uncertainties and improving the reliability of multi-hazard resilience assessment of tall buildings. Paper [12] presents the application of a hybrid Bayesian copula method to assess the wind-induced risk of tall buildings, taking into account various uncertainties. Bayesian theorem is used to develop posterior probability distributions of unknown parameters in the marginal probability distribution of wind speed and direction, as well as in the demand model for fragility estimates. On the other hand, the copula technique is used to develop a joint probability model of wind speed and direction. For this purpose, the corresponding marginal distributions of the variables discussed will be used. The application of this study shows that epistemic uncertainty has an obvious impact on both the probability of total damage based on deformation and comfort. Based on the collected results, we can conclude that the presented framework based on the Bayesian approach can well take into account the epistemic uncertainty related to unknown model parameters and random uncertainty. [PERSON] and [PERSON] [13; 14; 15] assess sensitivity via variance decomposition. Methods derived from the analysis of the variance of a structure's response, after describing the model's input uncertainties with appropriate probability distributions, can decompose the variance into components attributed to individual background variables and their combinations. The sensitivity of a structure's response to changes in parameters is quantified by calculating the partial variance. Methods derived from variance analysis facilitate a comprehensive exploration of the input variables' realization space, enabling the detection of all interactions within the computational model of the problem. Their use can be observed not only in civil engineering problems, but also in issues related to medicine. Papers [16; 17] are related to the modeling of systems containing implants used in abdominal hernia repair. Such models are often burdened with many uncertainties. In order to assess the influence of individual random variables, Sobolev indices calculated using the polynomial chaos expansion method were used. The polynomial chaos expansion is a method that allows approximation of the computational model using a series of multivariate polynomials. In [18], the authors developed a polynomial chaos expansion in mechanical problems, proposing a spectral stochastic finite element method. In many engineering problems, we can also use the polynomial chaos expansion method to calculate the global Sobol sensitivity indices [19; 20]. In [21], efficient sampling methods are used to estimate the principal and total effect indices. For high failure probability, Monte Carlo simulation is derived to calculate sensitivity indices. In the case of small failure probability values, combined methods with importance sampling procedure and truncated importance sampling procedure are used to improve the computational efficiency. In [22], the relation of variance-based sensitivity measures to the directional cosines of the most probable failure point in an underlying independent standard normal space is discussed. Moreover, the authors point out the fact that there are one-to-one relations between them for linear limit state functions of normal random variables. The authors show that these discussed relations can provide a good approximation of variance-based sensitivities for general reliability problems.