From Empirical Bayes to Full Bayes: Methods for Analysing Traffice Safety Data, October 25, 2004

Traffic safety engineers are among the early adopters of Bayesian statistical tools for analyzing crash data. As in many other areas of application, empirical Bayes methods were their first choice, perhaps because they represent an intuitively appealing, yet relatively easy to implement alternative to purely classical approaches. With the enormous progress in numerical methods made in recent years and with the availability of free, easy to use software that permits implementing a fully Bayesian approach, however, there is now ample justification to progress towards fully Bayesian analyses of crash data. The fully Bayesian approach, in particular as implemented via multi-level hierarchical models, has many advantages over the empirical Bayes approach. In a full Bayesian analysis, prior information and all available data are seamlessly integrated into posterior distributions on which practitioners can base their inferences. All uncertainties are thus accounted for in the analyses and there is no need to pre-process data to obtain Safety Performance Functions and other such prior estimates of the effect of covariates on the outcome of interest. In this slight, fully Bayesian methods may well be less costly to implement and may result in safety estimates with more realistic standard errors. In this manuscript, we present the full Bayesian approach to analyzing traffic safety data and focus on highlighting the differences between the empirical Bayes and the full Bayes approaches. We use an illustrative example to discuss a step-by-step Bayesian analysis of the data and to show some of the types of inferences that are possible within the full Bayesian framework.

From Empirical Bayes to Full Bayes: Methods for Analyzubg Traffic Safey Data, October 25, 2004

Traffic safety engineers are among the early adopters of Bayesian statistical tools for analyzing crash data. As in many other areas of application, empirical Bayes methods were their first choice, perhaps because they represent an intuitively appealing, yet relatively easy to implement alternative to purely classical approaches. With the enormous progress in numerical methods made in recent years and with the availability of free, easy to use software that permits implementing a fully Bayesian approach, however, there is now ample justification to progress towards fully Bayesian analyses of crash data. The fully Bayesian approach, in particular as implemented via multi-level hierarchical models, has many advantages over the empirical Bayes approach. In a full Bayesian analysis, prior information and all available data are seamlessly integrated into posterior distributions on which practitioners can base their inferences. All uncertainties are thus accounted for in the analyses and there is no need to pre-process data to obtain Safety Performance Functions and other such prior estimates of the effect of covariates on the outcome of interest. In this light, fully Bayesian methods may well be less costly to implement and may result in safety estimates with more realistic standard errors. In this manuscript, we present the full Bayesian approach to analyzing traffic safety data and focus on highlighting the differences between the empirical Bayes and the full Bayes approaches. We use an illustrative example to discuss a step-by-step Bayesian analysis of the data and to show some of the types of inferences that are possible within the full Bayesian framework.

Evaluation of Appropriate Maintenance, Repair and Rehabilitation Methods for Iowa Bridges, TR-429, 2003

Most states, including Iowa, have a significant number of substandard bridges. This number will increase significantly unless some type of preventative maintenance is employed. Both the Iowa Department of Transportation and Iowa counties have successfully employed numerous maintenance, repair and rehabilitation (MR&R) strategies for correcting various types of deficiencies. However, successfully employed MR&R procedures are often not systematically documented or defined for those involved in bridge maintenance. This study addressed the need for a standard bridge MR&R manual for Iowa with emphasis for secondary road applications. As part of the study, bridge MR&R activities that are relevant to the state of Iowa have been systematically categorized into a manual, in a standardized format. Where pertinent, design guidelines have been presented. Material presented in this manual is divided into two major categories: 1) Repair and Rehabilitation of Bridge Superstructure Components, and 2) Repair and Rehabilitation of Bridge Substructure Components. There are multiple subcategories within both major categories that provide detailed information. Some of the detailed information includes step-by-step procedures for accomplishing MR&R activities, material specifications and detailed drawings where available. The source of information contained in the manual is public domain technical literature and information provided by Iowa County Engineers. A questionnaire was sent to all 99 counties in Iowa to solicit information and the research team personally solicited input from many Iowa counties as a follow-up to the questionnaire.

Retrofit Methods for Distortion Cracking Problems in Plate Girder Bridges, TR-436, 2003

This report is formatted to independently present four individual investigations related to similar web gap fatigue problems. Multiple steel girder bridges commonly exhibit fatigue cracking due to out-of-plane displacement of the web near the diaphragm connections. This fatigue-prone web gap area is typically located in negative moment regions of the girders where the diaphragm stiffener is not attached to the top flange. In the past, the Iowa Department of Transportation has attempted to stop fatigue crack propagation in these steel girder bridges by drilling holes at the crack tips. Other nondestructive retrofits have been tried; in a particular case on a two-girder bridge with floor beams, angles were bolted between the stiffener and top flange. The bolted angle retrofit has failed in the past and may not be a viable solution for diaphragm bridges. The drilled hole retrofit is often only a temporary solution, so a more permanent and effective retrofit is required. A new field retrofit has been developed that involves loosening the bolts in the connection between the diaphragm and the girders. Research on the retrofit has been initiated; however, no long-term studies of the effects of bolt loosening have been performed. The intent of this research is to study the short-term effects of the bolt loosening retrofit on I-beam and channel diaphragm bridges. The research also addressed the development of a continuous remote monitoring system to investigate the bolt loosening retrofit on an X-type diaphragm bridge over a number of months, ensuring that the measured strain and displacement reductions are not affected by time and continuous traffic loading on the bridge. The testing for the first three investigations is based on instrumentation of web gaps in a negative moment region on Iowa Department of Transportation bridges with I-beam, channel, and X-type diaphragms. One bridge of each type was instrumented with strain gages and deflection transducers. Field tests, using loaded trucks of known weight and configuration, were conducted on the bridges with the bolts in the tight condition and after implementing the bolt loosening retrofit to measure the effects of loosening the diaphragm bolts. Long-term data were also collected on the X-diaphragm bridge by a data acquisition system that collected the data continuously under ambient truck loading. The collected data were retrievable by an off-site modem connection to the remote data acquisition system. The data collection features and ruggedness of this system for remote bridge monitoring make it viable as a pilot system for future monitoring projects in Iowa. Results indicate that loosening the diaphragm bolts reduces strain and out-of-plane displacement in the web gap, and that the reduction is not affected over time by traffic or environmental loading on the bridge. Reducing the strain in the web gap allows the bridge to support more cycles of loading before experiencing fatigue, thus increase the service life of the bridge. Two-girder floor beam bridges may also exhibit fatigue cracking in girder webs.

Methods for Estimating Annual Exceedance-Probability Discharges for Streams in Iowa, Based on Data through Water Year 2010, TR-519, 2013

A statewide study was performed to develop regional regression equations for estimating selected annual exceedance- probability statistics for ungaged stream sites in Iowa. The study area comprises streamgages located within Iowa and 50 miles beyond the State’s borders. Annual exceedanceprobability estimates were computed for 518 streamgages by using the expected moments algorithm to fit a Pearson Type III distribution to the logarithms of annual peak discharges for each streamgage using annual peak-discharge data through 2010. The estimation of the selected statistics included a Bayesian weighted least-squares/generalized least-squares regression analysis to update regional skew coefficients for the 518 streamgages. Low-outlier and historic information were incorporated into the annual exceedance-probability analyses, and a generalized Grubbs-Beck test was used to detect multiple potentially influential low flows. Also, geographic information system software was used to measure 59 selected basin characteristics for each streamgage. Regional regression analysis, using generalized leastsquares regression, was used to develop a set of equations for each flood region in Iowa for estimating discharges for ungaged stream sites with 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probabilities, which are equivalent to annual flood-frequency recurrence intervals of 2, 5, 10, 25, 50, 100, 200, and 500 years, respectively. A total of 394 streamgages were included in the development of regional regression equations for three flood regions (regions 1, 2, and 3) that were defined for Iowa based on landform regions and soil regions. Average standard errors of prediction range from 31.8 to 45.2 percent for flood region 1, 19.4 to 46.8 percent for flood region 2, and 26.5 to 43.1 percent for flood region 3. The pseudo coefficients of determination for the generalized leastsquares equations range from 90.8 to 96.2 percent for flood region 1, 91.5 to 97.9 percent for flood region 2, and 92.4 to 96.0 percent for flood region 3. The regression equations are applicable only to stream sites in Iowa with flows not significantly affected by regulation, diversion, channelization, backwater, or urbanization and with basin characteristics within the range of those used to develop the equations. These regression equations will be implemented within the U.S. Geological Survey StreamStats Web-based geographic information system tool. StreamStats allows users to click on any ungaged site on a river and compute estimates of the eight selected statistics; in addition, 90-percent prediction intervals and the measured basin characteristics for the ungaged sites also are provided by the Web-based tool. StreamStats also allows users to click on any streamgage in Iowa and estimates computed for these eight selected statistics are provided for the streamgage.