# Condition Rating Prediction Using an Interactive Deterioration Model Development Package
## 6 Comparison of Deterioration Models for Wyoming Bridges
### Assessment of Various Modeling Strategies Using DMDP  
To compare the performances of the stochastic models, we evaluated the normalized prediction errors for the deck, superstructure, and substructure elements. Figure 12 presents the normalized prediction errors for the condition ratings five years later (i.e., using data from 2013 to predict the conditions in 2018) depending on the classification tree level. In general, the prediction error slightly decreased, particularly for the percentage prediction and logistic regression algorithms. As the quantity of inspection data was insufficient for optimization when a high classification tree level was considered, the result was inferior in terms of the prediction error. A similar effect was observed for the Weibull distribution. Although the deterioration shapes for the percentage prediction and logistic regression algorithms were almost identical across numerous subsets, the logistic regression algorithm generally exhibited superior performance to the percentage prediction algorithm. Overall, the classification tree scheme, while common, does not seem to provide dramatically improved predictions.  
Figure 13 presents the normalized prediction errors for the investigated stochastic methods depending on the prediction years, for which a three-level of classification tree was used. The Weibull distribution exhibited the best result for the deck, whereas the logistic regression algorithm was superior for the other elements.  
Figure 11: Superstructure deterioration models for a subset of Wyoming bridges associated with “DST 1” (cast-in-place concrete), “BRW 4” (range between 4 and 6 m), and “DL 5” (MS 18), using (**a**) percentage prediction, (**b**) logistic regression, (**c**) optimization, (**d**) Weibull distribution.  
Figure 12: Normalized prediction error comparison of stochastic methods depending on the level of classification tree for (**a**) deck, (**b**) superstructure, and (**c**) substructure.  
Figure 13: Normalized prediction error comparison of stochastic methods depending on prediction years for (**a**) deck, (**b**) superstructure, and (**c**) substructure.  
The DMDP provides plots for the distribution of predicted condition ratings for the bridges inspected a particular year, which can be selected by the user. The predicted condition ratings were rounded to count the number of bridges for each condition. The predicted distribution was compared with the actual inspection data to examine the performance of the investigated algorithm. Figure 14 illustrates the distribution of two- and four-year predictions (i.e., using data from 2013) for the deck of all Wyoming bridges when the logistic regression algorithm was used without considering classification. Likely, due to the lack of repair information, the increase in the condition ratings was unable to be captured. In same manner, the distribution comparison was conducted using the second level of classification, as shown in Figure 15. Although minor improvement was observed when compared to Figure 14, the overall forecasting pattern only resulted in minor changes.