A Nonhomogeneous Markov Chains For Degeneration Behaviour Of RC Flexural Members’ Long-term Performance And Its Bayesian Updating

For reinforced concrete components exposed to a chloride salt environment,proposing a prediction model of the degradation process by considering its durability and bearing capacity,and then updating the model continuously with new information has been the prevailing method in concrete long-term performance learning.However,this method has the major flaw of not being able to incorporate the outputs of the degradation model itself.However,only the specific inspection indicator results in updating parameters in it,which means the degradation development is predetermined artificially.To address this issue,this thesis unifies the results from both the model and state evaluation,and proposes a time-series model that can be updated with the new information from the output of it.Specific updating methods are suggested.The method proposed in this thesis constructs a non-homogeneous Markov chain model to simulate the long-term performance degradation process.It also establishes a corresponding evaluation system for structural components in service,which matches the model’s output results.Then based on the current state evaluation results,the Bayesian update for the time-dependent equation of the Markov model’s state transition matrix is presented.A probabilistic description of the long-term performance degradation process is realized by integrating commonality and individuality.The main research contents and conclusions are as follows.(1)The thesis reviews the research on the long-term performance degradation of concrete components resulting primarily from steel corrosion in a chloride salt environment.It then develops a machine learning model that takes several factors into account,including material properties(water-cement ratio,type and amount of active minerals),environmental factors(type of environment,temperature,humidity),and time,to form an input-output relationship with low generalization error and easy interpretation and the ability to quantitative forecast.Then the complicated combined influence of these factors in parameters(surface chloride ion concentration,chloride ion diffusion coefficient and steel corrosion rate),especially the starting and ending ranges of their effects is analyzed,to form an empirical equation.(2)The empirical equation is then substituted into the existing research to optimize the control equation of the long-term performance degradation process,which follows the order of “the chloride transfer-steel corrosion-rust expansion crack formation and development-material property degradation-structural performance degradation.” The distribution laws of uncertain parameters in the equation are explored,and a set of timeseries data on the width of rust expansion cracks and the remaining bending bearing capacity of the components are obtained through sampling.Using these two indicators,the thesis divides the durability,bearing capacity,and long-term performance degradation process into separate discrete states and determines the probability of the structure being in each defined state at any time.It then constructs a state transition matrix and a nonhomogeneous Markov chain model to simulate the long-term performance degradation process.Finally,the response and sensitivity of degradation to material characteristics,geometric conditions and exposure environments are compared.(3)Considering environmental correction and the steel corrosion state,data mining and physical experiments are applied in this thesis to obtain the probability expression of the correlation between non-destructive electrochemical testing indicators,such as the half-cell potential,corrosion current,and concrete resistivity.The probability distribution of the inspection indicators at the critical state of depassivation is studied,and then a mapping relationship between these indicators and the defined discrete states is established by using a membership function.The AHP-DEMATEL principle is used to determine the weight of importance of each inspection indicator in the structural state evaluation.Finally,a comprehensive evaluation system of long-term performance state is established,which takes the inspection indicators as the input and the probability of the current components in each defined state as the output.The model can then be updated by using the new information to obtain a more accurate and reliable long-term performance degradation prediction of the structural components.(4)A mathematical method is proposed to describe the long-term performance degradation process of the structures based on the evaluation results of their current state.Starting from the established non-homogeneous Markov chain model,the time-dependent function of the diagonal elements of the transition matrix is obtained as prior knowledge by regression.The current state evaluation results are input into the Markov model,and the time-varying law of the posterior diagonal elements in the period from the start of the current time is determined by employing the joint tree method.The Bayesian method is used to incorporate the prior function with the posterior samples to obtain the posterior function that reveals the time-varying law of the diagonal elements as well as the corresponding posterior Markov model.Then the influence of both ways to obtain the time-varying law of the posterior diagonal elements and their confidence values of them on the prediction results is studied.The feasibility of the proposed mathematical method is verified by the reduced-scale beam test and engineering cases.It is believed that the posterior model prediction results incorporate both the results of the prior model and the current state evaluation,integrating commonality and individuality.The innovation of this thesis lies in the establishment of a time-series model based on the non-homogeneous Markov chain model for simulating the long-term performance degradation process of reinforced concrete components.The mathematical method for dynamically updating the Markov model based on the state evaluation results of the components is proposed.The problem of not being able to incorporate the current state evaluation results in the updating process of the time-series model is solved,which fills the gap of limited prediction accuracy caused by only incorporating specific inspection indicators results.Finally,the mathematical method proposed in the thesis is not only available for the long-term performance research of reinforced concrete components but also provides modeling strategies to realize dynamic updating of process simulation in time-series models by using state evaluation results.The limitation of the thesis is that it only focuses on the concrete long-term performance at the component level and has not yet ascended to the structural level.