# Condition Rating Prediction Using an Interactive Deterioration Model Development Package
## 2 Background  
The technical literature on the bridge deterioration model and BMS is reviewed in this section. The deterioration models provide a mathematical evidence for decision making process including life cycle cost (LCC) estimation [16; 17] and establishment for maintenance strategies [18; 19; 20]. The deterioration models are classified as deterministic or stochastic on the basis of the contribution of uncertainty to the transition between condition ratings. Deterministic models are developed by estimating the average condition ratings of the bridge inventory according to age (or year built) [21]. Although deterministic deterioration models are convenient for analyzing the inspection data, they do not reflect the transitions between condition ratings or other historic information. Stochastic deterioration models are designed to overcome these issues and have been adopted in many U.S. states [4; 19; 21]. The Markov chain process has been implemented extensively to estimate the transition probabilities between condition ratings. The cumulative damage is assessed as a decrease in condition states over transition periods [22]. The elements of transition probability matrix are estimated using the condition history of various civil infrastructures, i.e., asphalt pavement [6], sewers [23], and bridges [4; 24; 25; 26]. Although Markovian models are difficult in terms of implementing current condition and expressing condition states for all elements in a group of bridges with a single number, Markov chain process is still effective in considering historical inspection data, being widely used to reflect uncertainties in the deterioration process [27; 28]. Alternatively, the sojourn time in each condition rating is modeled statistically. In reliability, the hazard rate function is modeled with Weibull distribution and the sojourn time is then estimated on the basis of the exponential of cumulated hazard function [29; 30]. The sojourn time is used to estimate elements of transition probability matrix for the Markov chain process, being named as the semi-Markov method [31]. Bayesian techniques have been implemented to quantify the uncertainties from the prior information such as the assumed structural conditions and inspection data, and are used to update the posterior models [32; 33; 34]. Recently, artificial intelligence techniques including artificial neural network, data fusion, and machine learning has been used to develop deterioration models and to establish maintenance strategies [35; 36; 37; 38]. NBI inspection data is often used for the development of deterioration models. Owing to the increase in inspection data, the more sophisticated deterioration model can be developed by separating bridges into multiple groups. [PERSON] et al. (1987) proposed a zoning technique to estimate transition probability matrices for every 6-year period [39]. Explanatory variables are used to group bridges and the deterioration models are developed for each [25; 40; 41; 42; 43]. Instead of leaning on the expert judgement for the selection of explanatory variables, [PERSON] et al. (2017) proposed a framework based on a penalty regression quantifying the significance target variables [20]. [PERSON] and [PERSON] (2020) identified significant features among NBI data using random forest technique and developed Bayesian network models for deterioration prediction for each group [35]. Several studies focused on the performance comparison among existing and newly proposed methods. [PERSON] et al. (2010) compared the deterioration models developed by Markov chain and Weibull distribution approaches and concluded that the Weibull shows better performance due to the duration independence assumption in the inspected data [4]. [PERSON] et al. (2015) developed the Markov chain Monte Carlo simulation technique, with the superior performance being verified by the prediction model when it was compared with two other existing methods [44]. [PERSON] et al.