Probabilistic Model of Assessing the Operational Condition of Reinforced Concrete Slabs Using the Regression Analysis Techniques

A regression analysis technique is presented, focused on statistical processing the parameters of the technical condition of reinforced concrete roof slabs obtained as a result of instrumental and visual inspection. The purpose of the study is to establish probabilistic dependences between the strength characteristics of concrete and the categories of operational suitability of structures based on a statistically representative sample. The analysis includes constructing a two-dimensional system of discrete random variables, calculating sample statistics (mathematical expectation, variance, standard deviation), testing hypotheses about the type of dependence between variables, determining correlation coefficients, and approximating empirical data with the use of a quadratic regression model. In addition, a normalized probability density function is formed based on which an assessment of the probability of a serviceable state of structures in a given strength range is made. The results of the study demonstrate a high degree of dependence between the strength characteristics and the operational state of the slabs, which confirms the feasibility of using the regression approach to analyze the technical condition of building elements. The proposed algorithm can be used in engineering practice for probabilistic reliability assessment, residual resource forecast and optimization of measures for the technical maintenance of structures. The work is based on present day trends in the integration of mathematical statistics and reliability theory in the problems of construction diagnostics and monitoring