1 Evaluation of Multiple Indicators for Stream Channel Stability Near Bridges in the United States: Multi-Criteria Prioritization and Ranking with Differential Weights, Stepwise Aggregations, Hasse Diagrams, Poset Cumulative Rank Frequency Operators, and Markov Chain Monte Carlo Methods By G.P. Patil1, Jessica Newlin2, K. Sham Bhat1, and Michael Kase1 1Center for Statistical Ecology and Environmental Statistics, Department of Statistics, 2Department of Civil and Environmental Engineering, The Pennsylvania State University, University Park, PA 16802, USA NSF Project Officer: Larry Brandt EPA Project Officer: Barbara Levinson This material is based upon work partially supported by (i) the National Science Foundation under Grant No. 0307010, (ii) The United States Environmental Protection Agency under Grant No. CR-83059301 and (iii) The United States Environmental Protection Agency under Grant No. R-828684 Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the agencies. [DRAFT] Technical Report Number 2006-0504 TECHNICAL REPORTS AND REPRINTS SERIES May 2006 Center for Statistical Ecology and Environmental Statistics Department of Statistics The Pennsylvania State University University Park, PA 16802 G. P. Patil Distinguished Professor and Director Tel: (814)865-9442 Fax: (814)865-1278 Email: [email protected] http: //www.stat.psu.edu/~gpp http://www.stat.psu.edu/hotspots DGOnline News Environmental and Ecological Statistics-SpringeriTable of Contents 1 Introduction................................................................................................................. 1 1.1 General description of bridge program............................................................... 1 1.2 Description of indicators – Methods of data collection ...................................... 1 1.3 Research Questions............................................................................................. 5 2 Description of Analysis Methods................................................................................ 7 2.1 Hasse diagrams ................................................................................................... 7 2.2 Poset Prioritization.............................................................................................. 9 2.3 POSAC.............................................................................................................. 14 2.4 2-Dimensional MPOSAC ................................................................................. 17 2.5 One-Way ANOVA F-scores............................................................................. 17 2.6 Spearman’s Correlation Coefficient ................................................................. 17 2.7 Concordance ..................................................................................................... 17 2.8 METEOR .......................................................................................................... 18 2.9 Rank Range Run ............................................................................................... 19 3 Analysis Results........................................................................................................ 20 3.1 Hasse diagrams ................................................................................................. 20 3.2 Poset Prioritization Ranking ............................................................................. 28 3.3 POSAC.............................................................................................................. 31 3.4 2-Dimensional MPOSAC ................................................................................. 37 3.5 One-Way ANOVA F-scores............................................................................. 38 3.6 Spearman’s Correlation Coefficient ................................................................. 38 3.7 Concordance ..................................................................................................... 39 3.8 Rankings ........................................................................................................... 41 3.9 Rank Range Run ............................................................................................... 42 3.10 METEOR .......................................................................................................... 49 4 Conclusions............................................................................................................... 5211 Introduction 1.1 General description of bridge program The data set we use for this paper is a data set of the Federal Highway Administration with 49 bridges with the goal of determining the main causes of bridge failure. One data set used in this analysis consists of 49 bridge sites and 13 indicators that are described by Johnson (2005). There is an important need to determine the causes of the failure of bridges over waterways, and the determination of the indicators most influential in stream stability is vital. The 49 bridge sites cross response-type streams. Four different stream classifications are considered response-type streams. They are dune-ripple, riffle-pool, plane-bed, and modified channels. The overall goal of this analysis is to investigate an existing stream stability assessment method to determine if the indicators are necessary and sufficient for the ranking of bridge crossings based on the stability of the channel. The primary causes of bridges failure are foundation and pier scour, channel movement, and hydraulic forces (Richardson and Huber, 1991). There are many ways to assess the overall risk of bridge failure. In the most recent works, Johnson (2005) proposed an assessment tool for determining the condition of channel stability near bridges. This method is based on a rapid assessment method proposed by Johnson et al. (1999). It provides a systematic, preliminary assessment of stream channel stability with respect to bridge crossings. 1.2 Description of indicators – Methods of data collection Here we have 13 indicators, which the investigators group into four different groups, a two-level hierarchy with four subindices. The investigators experimented with two indices, one, which was an average of the all 13 indicators, the other the average of the four