ENTUCKY RANSPORTATION C ENTER. College of Engineering

Transcription

1 Research Report KTC-04-28/SPR F T K ENTUCKY RANSPORTATION C ENTER College of Engineering STATE TRAFFIC VOLUME SYSTEMS COUNT ESTIMATION PROCESS

2 Our Mission We provide services to the transportation community through research, technology transfer and education. We create and participate in partnerships to promote safe and effective transportation systems. We Value... Teamwork -- Listening and Communicating, Along with Courtesy and Respect for Others Honesty and Ethical Behavior Delivering the Highest Quality Products and Services Continuous Improvement in All That We Do For more information or a complete publication list, contact us KENTUCKY TRANSPORTATION CENTER 176 Raymond Building University of Kentucky Lexington, Kentucky (859) (859) (FAX) ktc@engr.uky.edu The University of Kentucky is an Equal Opportunity Organization

3 Research Report KTC-04-28/SPR F State Traffic Volume Systems Count Estimation Process by S. Doug Kreis, P.E. Project Management Engineer and Angie Quigley Research Engineer Kentucky Transportation Center College of Engineering University of Kentucky Lexington, Kentucky In cooperation with Transportation Cabinet Commonwealth of Kentucky The contents of this report reflect the views of the authors who are responsible for the facts and accuracy of the data presented herein. The contents do not necessarily reflect the official views or policies of the University of Kentucky, the Kentucky Transportation Cabinet, nor the Federal Highway Administration. This report does not constitute a standard, specification, or regulation. The inclusion of manufacturer names and trade names are for identification purposes and are not to be considered as endorsements. October 2004 ii

4 1. Report Number KTC-04-28/SPR F 4. Title and Subtitle 2. Government Accession No. State Traffic Volume Systems Count Estimation Process 3. Recipient s Catalog No. 5. Report Date October Performing Organization Code 7. Author(s) S.Doug Kreis, Angie Quigley 9. Performing Organization Name and Address 8. Performing Organization Report No. KTC-04-28/SPR F 10. Work Unit No. 12. Sponsoring Agency Name and Address 13. Type of Report and Period Covered Final Kentucky Transportation Cabinet State Office Building 14. Sponsoring Agency Code Frankfort Kentucky Supplementary Notes Prepared in cooperation with the Kentucky Transportation Cabinet and the Federal Highway 16. Abstract Kentucky Transportation Center College of Engineering University of Kentucky Lexington Kentucky Administration 11. Contract or Grant No. SPR The Kentucky Transportation Cabinet has an immense traffic data collection program that is an essential source for many other programs. The Division of Planning processes traffic volume counts annually. These counts are maintained in the Counts Database (CTS), which contains over 20,000 separate station locations and some traffic counts from as early as The Division of Planning currently collects traffic volume counts for all non-interstate routes on a revolving threeyear basis. Years wherein actual counts are not performed are supplemented with estimates generated by a FORTRAN program. Estimates are projected using prior actual counts by weighted linear regression methods. If an actual count is performed during the fiscal year, this count then replaces the estimated count. These traffic volume counts, both actual and estimated, are compiled into the Traffic Volume System (TVS). The focus of this project was to research potential estimating methods to fulfill the above mentioned requests and to analyze possible contributing factors to traffic volume counts such as traffic growth, population, and economic development. 17. Key Words Traffic volume counts, traffic estimation 18. Distribution Statement Unlimited, with approval of the Kentucky Transportation Cabinet 19. Security Classification (report) Unclassified 20. Security Classification (this page) Unclassified 21. No. of Pages Price iii

5 TABLE OF CONTENTS EXECUTIVE SUMMARY... VII 1.0 INTRODUCTION REVIEW OF CURRENT SYSTEMS BRIEF INTRODUCTION TO NEURAL NETWORKS DATA MANAGEMENT & SOFTWARE CAPABILITY FINAL MODEL RESULTS CONCLUSION REFERENCES APPENDIX Boone County Network Training Report Boone County Network Testing Report Boyd County Network Training Report Boyd County Network Testing Report Fayette County Network Training Report Fayette County Network Test Report Henderson County Network Training Report Henderson County Network Testing Report Jefferson County Network Training Report Jefferson County Network Testing Report Laurel County Network Training Report Laurel County Network Testing Report McCracken County Network Training Report McCracken County Network Testing Report iv

6 8.0 APPENDIX Continued 8.15 Nelson County Network Training Report Nelson County Network Testing Report Pike County Network Training Report Pike County Network Testing Report Powell County Network Training Report Powell County Network Testing Report Pulaski County Network Training Report Pulaski County Network Testing Report Warren County Network Training Report Warren County Network Testing Report Kentucky County Population Neural Network Statistical Summary v

7 LIST OF FIGURES Figure 1. Comparison of Year 2000 Actual versus Estimated Traffic Counts by Functional Class....3 Figure 2. A Multilayer Perceptron diagram....5 Figure 3. Example of a Successful Network Training....7 Figure 4. Kentucky Counties with Common Networks LIST OF TABLES Table 1. Counties requiring modified MLP networks...15 Table 2. Comparison of Neural Network and Fortran Estimates to Actual Traffic Counts...19 vi

8 Executive Summary The Kentucky Transportation Cabinet has an immense traffic data collection program that is an essential source for many other programs. The Division of Planning processes traffic volume counts annually. These counts are maintained in the Counts Database (CTS), which contains over 20,000 separate station locations and some traffic counts from as early as The Division of Planning currently collects traffic volume counts for all noninterstate routes on a revolving three-year basis. Years wherein actual counts are not performed are supplemented with estimates generated by a FORTRAN program. Estimates are projected using prior actual counts by weighted linear regression methods. If an actual count is performed during the fiscal year, this count then replaces the estimated count. These traffic volume counts, both actual and estimated, are compiled into the Traffic Volume System (TVS). This database is the source file for various reports produced by the Kentucky Transportation Cabinet. Annual Average Daily Traffic (AADT) is vital to many efforts including the Highway Information Systems and the Highway Performance Monitoring System (HPMS). AADT is reported annually to the Federal Highway Administration. With these significant contributions of the TVS, the Division of Planning has deemed necessary an evaluation of the current process for estimating traffic volume counts. Specific revisions requested were: 1. Retain a copy of historical estimates that have been replaced with actual counts. 2. Remove TVS from the mainframe. 3. Examine forecasting mechanism for possible revision to minimize erroneous outliers in estimation process. 4. Potential inclusion of growth factors into estimation process. The focus of this project was to research potential estimating methods to fulfill the above mentioned requests and to analyze possible contributing factors to traffic volume counts such as traffic growth, population, and economic development. As with any system, the quality of the data will determine the accuracy of the results. Although there has been much attention focused on the quality control of traffic counts, error is inherent to this process with so many variables in the traffic patterns and flow. Automated Traffic Recorders (ATR), which record traffic data continuously 365 days a year would be the ideal solution. These recorders would capture an accurate model of daily traffic that can only otherwise be mathematically manipulated at best. Kentucky currently has 99 ATR s, and has plans to implement additional ATR s in the future. However, with the expense of the recorders and the required maintenance involved, the implementation could be a slow process. An advantage of neural networks is their ability to allow the data to become the model, rather than imposing a presumed relational equation upon the data. With each county having its own neural network, traffic volume estimates can more vii

9 accurately reflect the traffic volumes in each county. Although the population and employment data is county-based, the addition of these growth factors will enhance the networks ability to adjust to fluctuations that might not have been detected otherwise. With this new estimating process, the advance in transportation technologies and the continuing efforts of the Division of Planning, Kentucky should remain a forerunner in transportation. viii

10 Acknowledgements We would like to express our appreciation to all who participated in this project. Clark Graves Dan Inabnitt Doug Kreis Melissa Moreland Angie Quigley John Ripy Peter Rogers Debbie Watson Greg Witt Kentucky Transportation Center Kentucky Transportation Cabinet, Division of Planning Kentucky Transportation Center Kentucky Transportation Cabinet, Division of Planning Kentucky Transportation Center Kentucky Transportation Center Kentucky Transportation Cabinet, Division of Planning Kentucky Transportation Cabinet, Division of Planning Kentucky Transportation Cabinet, Division of Planning ix

11 1.0 Introduction The Kentucky Transportation Cabinet s Division of Planning recognized that the current process for estimating traffic volumes should be evaluated and if possible, improved upon. The current system, which predicts traffic volumes using a variety of mathematical methods depending on the availability of actual data, has proven to not be sufficient for the current needs of the Division of Planning. Traffic volume is vital to many efforts of KTC. The Annual Average Daily Traffic (AADT), which is derived from both actual and estimated traffic counts, provides crucial information for the planning of new road construction, travel model design, congestion management, pavement design, air quality compliance, etc. AADT is also used to estimate state wide Vehicle Miles Traveled (VMT), which aids in compliance with the 1990 Clean Air Act Amendment. In the initial stages of this project, a search was conducted to evaluate the success of other state s traffic count estimation systems. A large part of this data was obtained from a recent report Analysis of Traffic Growth Rates, published by the Kentucky Transportation Center (1). From a survey response of 29 states, it was determined that 81% of states calculated ADT by counting traffic some years and estimating others. For these years of traffic count estimations, 43% of the states used other local road counts in the estimation process. Many states have customized programs to estimate traffic counts while some use mainstream software. There are various prediction or estimation softwares available; however some form of customization is usually required. Some states use a software package to streamline all traffic information. For example, Wisconsin, Nevada, Delaware, Washington, and Missouri use TRADAS, which is a traffic data collection, quality control, and analysis software package that can also be customized. (2) 1

12 A literature search on estimating traffic counts proved to be limited. Most information is based on urban areas. One study focusing on county roads was performed by Purdue University. A multiple regression method using aggregated data at the county level was used to predict AADT in 40 counties in Indiana. Four predictors were chosen: county population, access to other roads, location type (rural/urban), and total arterial mileage in a county. Several other studies have also been performed on AADT estimation using predictors such as county population size, location type (rural/urban), personal income level, total number of through lanes, vehicle registrations, etc (3,4,5, 6). 2.0 Review of Current Systems The first task in the TVS project was to interview the members of the Division of Planning who maintain the current Counts Database (CTS). These employees receive actual counts from various locations across the state each month. These counts are attained through permanent, portable, and index stations. There are approximately 4700 actual counts performed each year. The counts are reviewed for possible errors or flags and then entered into the system, replacing the estimated counts for those particular stations. The standard for data quality is the Count Acceptance Program, CAP, which requires data from portable stations to be +/- 10% error for any given county in a given year. The CTS file is then updated at the end of each month. The current system for estimating traffic counts is a FORTRAN program that estimates counts based on the number of actual counts in the database. If there are no counts for a particular station, the system uses a statewide average for the corresponding Functional Class. If there is one actual count, the system uses the ratio of data to the Functional Class average by linear growth rate. For two or more actual counts, a piecewise weighted linear fit of actual data points to current year. For estimates prior to first actual count, a ratio of the Functional Class average is computed for a range of one to four actual counts. For five or more actual counts, estimates prior to the first actual are computed by exponential regression. 2

13 In an earlier study performed by Kentucky Transportation Center, estimates generated by the FORTRAN program were saved before they were replaced by actual traffic counts and compared as shown in Figure 1. Comparison of Year 2000 Actual and Estimated Traffic Volume Counts Cumulative Percent (%) % Error (predicted - actual ) FC 02 FC 06 FC 07 FC 08 FC 09 Figure 1. Comparison of Year 2000 Actual versus Estimated Traffic Counts by Functional Class. Functional Class 02 has the most accurate traffic volume estimates, with 48% of the estimates generated falling within the +/- 10% error guidelines. The least accurate estimates occurred with Functional Class 09, with a sparse 17% of estimates generated resulting in +/-10 % error. The CTS database itself contains a massive amount of information such as the 18,000 plus stations, their corresponding mile markers and road numbers, functional class, and corresponding traffic data from years 1963 to 2003, with data designated as A adjusted by engineer, E engineer s estimate, or _ computer estimate. Some years contained 0 for counts prior to the implementation of the estimation program. Also included in this database is whether a road has had an impact year, or a year in which major changes have 3

14 occurred such as the construction of a large retail store in close proximity to the road. After the review of other estimating or prediction software and the CTS database, we recommended the analysis of a neural network to generate traffic volume estimations. Many different neural network software packages were analyzed, however we chose Neurosolutions software for its ease of use and compatibility. The Division of Planning also chose two factors to analyze relationally to traffic volumes: population and economic development or employment per county. The population information was easily acquired from the Kentucky State Data Center. The employment information on a county basis was limited to years 1975 and forward on computer file. This data was obtained from the Kentucky Cabinet for Workforce Development. With this factor limiting, it was determined that we would only input all data (traffic volume counts, population, and employment) beginning with the year 1975 through Brief Introduction to Neural Networks Neural networks have been employed in various fields such as finance, engineering, medicine, geology, and physics. The power of neural networks lies within its complex modeling capabilities. Neural networks are nonlinear, thus allowing the problems of prediction, classification, or control to be modeled without the inadequate approximations of linear modeling. Neural networks are applicable in any situation in which a relationship between independent variables or inputs and dependent variables or outputs exists, even if the correlation between the two is not easily ascertained. If the nature of this relationship was known, it could be modeled easily. Neural networks are loosely based on the human brain, with multiple layers of processing elements called neurons. Neurons in our brain help us to remember, think, and apply our previous experiences to any circumstance. Neural networks learn by example. A history of data is entered into the network and training 4

15 algorithms are invoked allowing the network to learn the structure of the data. If the network can learn the structure of the data, it can subsequently be used to predict data where the output is not known. A simple schematic depicts the most common neural network, a Multilayer Perceptron: Adjust weights Repeat Presentation of Data Neural Network Output Error Desired Output Figure 2. A Multilayer Perceptron diagram. As shown in Figure 2, the input data is continuously presented to the network and compared to the desired output. After each epoch, or a complete cycle of data presentation to the network, an error is computed and fed back or backpropagated to the network. The network then adjusts the weights so that the error decreases with each iteration, thus allowing the network to closely model the desired output. 4.0 Data Management & Software Capability Preceding any software simulations, the traffic volume counts had to be extracted from the CTS database. Some of the data required cleaning, as estimated 5

16 values were tagged with hyphens, adjusted values also contained the letter A, etc. Years with zeroes or no count or estimate were replaced with an interpolated value between the two closest year counts. The population and employment data were downloaded from their respective web sites into Excel TM files. An advantage to the neural network software is an option for a Microsoft Excel add-in program that allows all tasks to be performed while in Excel TM. This would allow simple data management, such as preprocessing and analyzing data, and more importantly, creating, training, and testing the neural network from within Microsoft Excel TM. There were various techniques analyzed for presenting the data to the network. For the traffic counts, data could be segregated by county or by district. Grouping the data by each district would be beneficial due to the increased amount of data for the network to process or learn and would also limit the number of different networks to 12. However, a county-based network would more accurately depict traffic volumes, but would increase the number of networks to Final Model Results A multiplayer perceptron (MLP) was used for each of the 120 counties. Within each network, 60 % of the data was used for training, 25 % for testing, and 15 % for cross validation. In a few of the counties, all of the data was used for training thus no cross validation was performed (see Table 1 in appendix). The data was presented to the network in the following order: previous year traffic counts, population, employment, and current year traffic counts. The stations were ordered just as they are in the CTS database. The network training was set to load the best weights, use cross validation, and randomize initial weights. Each network s training was terminated after 1000 epochs. A separate analysis was performed on some counties by grouping the traffic volume counts by arterials, rural and urban interstates and freeways, and 6

17 collector and local. Jefferson County, which is one of the largest counties, did not perform well in this analysis. Counties with similar traffic patterns were also grouped together as a trial network. Jefferson, Oldham, Fayette, Jessamine, Clark, Scott, and Madison counties were tested as a separate network. However, the results were not desirable and the trial was discontinued. The majority of the counties performed well with the simple MLP. Initial performance can be monitored by successful network training. As shown in Figure 3, the cross validation error and training error should approach zero. MSE versus Epoch MSE Training MSE Cross Validation MSE Epoch Figure 3. Example of a Successful Network Training. No more than 3 training sessions were required for any county to achieve a relatively high correlation coefficient (r) during testing. As a general rule, a correlation coefficient of 0.88 means that the fit of the network model to the data is reasonably good. Results from counties randomly selected from each district are shown in Appendix A. However, 48 of the counties did not perform as well with the initial network. An additional processing element was added to the network and the stations were randomized and then presented to the network. This drastically improved the network performance of these counties which are shown in Table 1. 7

18 Table 1. Counties requiring modified MLP networks. Allen Harlan McCreary Pike Anderson Harrison Magoffin Powell Barren Hart Marshall Pulaski Bell Hickman Mason Rockcastle Bourbon Kenton Mercer Rowan Breathitt Laurel Montgomery Scott Butler Lawrence Muhlenberg Shelby Caldwell Leslie Nelson Simpson Casey Letcher Nicholas Todd Christian Lincoln Ohio Washington Garrard Logan Oldham Wolfe Graves McCracken Perry Woodford An interesting observation can be made when viewing the counties on a state map as shown in Figure 4. Two similar but distinct networks were used in this project. Notice that the counties listed in Table 1 are highlighted in purple in Figure 4. The most common identifiers seem to be the presence of an interstate and/or a major highway system in a non-metropolitan area. A statistical summary for all counties can be found in the appendix. Training and cross validation results include final mean squared error (MSE) with corresponding epoch number. Testing results include normal mean squared error (NMSE) and correlation coefficient ( r ). A comparison of the neural network results with the Fortran program results are shown in Figure 5. 8

19 Figure 4. Kentucky Counties with Common Networks. 9

20 Figure 5. Analysis of Neural and Fortran Estimates to Actual Counts Traffic Volume Randomly Selected Stations Fortran Estimates Neural Network Estimates Actual Counts 10

21 Stations were randomly selected for the analysis shown in Figure 5. Some stations initially selected could not be used due to actual traffic counts for those stations not being taken during For the 50 stations depicted in Figure 5, the neural network predicted more accurate traffic estimations 76% of the time while the Fortran estimates were closer to the actual counts 24% of the time. The neural network total average percent error was % while the Fortran program total average percent error was %. See Table 2 for the complete analysis as shown in Figure 5. These results are quite promising considering the fact that the neural network performed this well while using the current traffic counts database, which contains approximately 66% Fortran estimates at any given time. An interesting evaluation of the network could be performed at the end of the next 3-year count cycle when the database would comprise entirely of estimates from the network itself. 11

22 2003 Fortran 2003 Neural County Station ID estimate % Error network estimate % Error Actual 1 1KY 001A US US KY 005D KY 007D KY 009A US 011A US 014C US 016A KY 019S KY 022A KY 025A KY KY US 030A US 034G KY 035A US 037A US TR KY 046A US 049A US US 054A FS 056A KY 059C KY KY 063A KY 065A KY 067A KY US 072A US 073B KY 076C KY KY KY KY 093B KY 097A KY KY 102A KY 105A US 106A KY KY KY US 114C KY 116A KY 118B KY Total % Error Avg % Error Total Stations Closer to Actual Count 12 (24%) 38 (76%) Table 2. Comparison of Neural Network and Fortran Estimates to Actual Traffic Counts. 12

23 6.0 Conclusion The importance of accurately estimating future traffic counts is vital for the Division of Planning. These estimations are the source for many state and federal systems, including Annual Average Daily Traffic (AADT), Highway Information Systems (HIS), and the Highway Performance Monitoring System (HPMS) to name a few. The Division of Planning has established stringent policies such as the Count Acceptance Program (CAP) to assure the quality of these traffic estimations and has also chosen to evaluate the system that produces these estimates. The current program, which has been in place since 1973, has performed well since its inception but during the latter years has begun to deviate beyond the CAP standard. This may be due to the program s linear estimation method, which does not perform well during years where traffic patterns fluctuate. This weakness of the program led to the analysis with neural networks, which are known for their ability to adapt to fluctuations. Although the initial performance of some counties with the network was not suitable, modifications to those county networks resulted in more accurate estimations. With closer analysis the similarities of these counties were found to be very high, including the presence of a major highway and/or an interstate in a non-metropolitan area. The ability of the network to adapt to these conditions with a simple change in the network structure proved invaluable. More importantly, this initially poor network performance exposed an underlying trait of these county s traffic volumes that differs from the other counties. The neural network proved to be a powerful estimating tool that can easily be adapted for specific situations. The requests made by the Division of Planning were to retain historical estimates, remove estimating program from mainframe, minimize outliers in estimation process, and to include growth factors into estimation process. The neural network only tests or produces future year estimates, thus the current and previous years remain intact. The software can 13

24 also be installed on personal computers. The network also showed promising results, achieving a 76% closer accuracy to actual counts than the Fortran estimates. Lastly, growth factors (employment and population) that largely influence traffic volumes and that were readily accessible were incorporated into the estimation process. 14

25 7.0 References 1. Allen D., Barrett M., Graves R., & Pigman J.: Analysis of Traffic Growth Rates. Final Report, Kentucky Transportation Center, Chaparral Systems Corporation The Traffic Data System Mohamad, D., Sinha, K., and Kuczek, T. An Annual Average Daily Traffic Prediction Model for County Roads. Transportation Research Board 77 th Annual Meeting. CD-Rom Cheng, C., Optimum Sampling for Traffic Volume Estimation, Ph.D. Dissertation, University of Minnesota, Fricker, J. and Saha, S. Traffic Volume Forecasting Methods for Rural State Highways. Final Report, FHWA/IN/JHRP-86/ Aldrin, M., A Statistical Approach to the Modeling of Daily Car Traffic, Traffic Engineering and Control, Vol. 36, Issue 0, 1995, pp

26 8.0 Appendix 16

27 MSE versus Epoch Best Networks Training Cross Validation Epoch # Minimum MSE Final MSE MSE 0.6 Training MSE Cross Validation MSE Epoch 8.1 Boone County Network Training Report. 17

28 Boone County Desired Output and Actual Network Output Output Current Yr Traffic Current Yr Traffic Output Exemplar 8.2 Boone County Network Testing Report. 18

29 MSE versus Epoch Best Networks Training Cross Validation Epoch # Minimum MSE Final MSE MSE Training MSE Cross Validation MSE Epoch 8.3 Boyd County Network Training Report. 19

30 Boyd County Desired Output and Actual Network Output Current Yr Traffic Current Yr Traffic Output Output Exemplar 8.4 Boyd County Network Testing Report. 20

31 Fayette County MSE versus Epoch Training MSE Cross Validation MSE Best Networks Training Cross Validation Epoch # Minimum MSE Final MSE MSE Epoch 8.5 Fayette County Network Training Report. 21

32 Fayette County Desired Output and Actual Network Output current traffic current traffic Output Output Exemplar 8.6 Fayette County Network Test Report. 22

33 Henderson County MSE versus Epoch Best Networks Training Cross Validation Epoch # Minimum MSE Final MSE MSE Training MSE Cross Validation MSE Epoch Henderson County Network Training Report. 23

34 Henderson County Desired Output and Actual Network Output Current Traffic Count Current Traffic Count Output 8000 Output Exemplar 8.8 Henderson County Network Testing Report. 24

35 0.35 Jefferson County MSE versus Epoch 0.3 Training MSE Cross Validation MSE MSE Best Networks Training Cross Validation Epoch # Minimum MSE E-05 Final MSE E Epoch 8.9 Jefferson County Network Training Report. 25

36 Jefferson County Desired Output and Actual Network Output Current Traffic Count Current Traffic Count Output Output Exemplar 8.10 Jefferson County Network Testing Report. 26

37 Laurel County MSE versus Epoch Best Networks Training Cross Validation Epoch # Minimum MSE E-05 Final MSE E MSE 0.2 Training MSE Cross Validation MSE Epoch 8.11 Laurel County Network Training Report. 27

38 Laurel County Desired Output and Actual Network Output Current Traffic Count Current Traffic Count Output Output Exemplar 8.12 Laurel County Network Testing Report. 28

39 McCracken County MSE versus Epoch Best Networks Training Cross Validation Epoch # Minimum MSE Final MSE MSE 0.25 Training MSE Cross Validation MSE Epoch 8.13 McCracken County Network Training Report. 29

40 McCracken County Desired Output and Actual Network Output Current Traffic Count Current Traffic Count Output Output Exemplar 8.14 McCracken County Network Testing Report. 30

41 Nelson County MSE versus Epoch Best Networks Training Cross Validation Epoch # Minimum MSE Final MSE MSE 0.1 Training MSE Cross Validation MSE Epoch 8.15 Nelson County Network Training Report. 31

42 Nelson County Desired Output and Actual Network Output Current Traffic Count Current Traffic Count Output Output Exemplar 8.16 Nelson County Network Testing Report. 32

43 Pike County MSE vs Epoch Best Networks Training Cross Validation Run # 2 3 Epoch # Minimum MSE Final MSE MSE Training Cross Validation Epoch 8.17 Pike County Network Training Report. 33

44 Pike County Desired Output and Actual Network Output Current Traffic Count Current Traffic Count Output Output Exemplar 8.18 Pike County Network Testing Report. 34

45 0.08 Powell County MSE versus Epoch 0.07 Best Networks Training Cross Validation Epoch # Minimum MSE E-05 Final MSE E MSE 0.04 Training MSE Cross Validation MSE Epoch 8.19 Powell County Network Training Report. 35

46 Powell County Desired Output and Actual Network Output 4000 Current Traffic Count Current Traffic Count Output Output Exemplar 8.20 Powell County Network Testing Report. 36

47 Pulaski County MSE vs Epoch Best Networks Training Cross Validation Run # 3 1 Epoch # Minimum MSE Final MSE MSE Training Cross Validation Epoch 8.21 Pulaski County Network Training Report. 37

48 Pulaski County Desired Output and Actual Network Output Current Traffic Count Current Traffic Count Output Output Exemplar 8.22 Pulaski County Network Testing Report. 38

49 Warren County MSE versus Epoch Best Networks Training Cross Validation Epoch # Minimum MSE Final MSE MSE 0.15 Training MSE Cross Validation MSE Epoch 8.23 Warren County Network Training Report. 39

50 Warren County Desired Output and Actual Network Output Current Yr Traffic Current Yr Traffic Output Output Exemplar 8.24 Warren County Network Testing Report. 40

51 Kentucky County Population, County Kentucky Adair Allen Anderson Ballard 7902 Barren Bath 9692 Bell Boone Bourbon Boyd Boyle Bracken 7766 Breathitt Breckinridge Bullitt Butler Caldwell Calloway Campbell Carlisle 5238 Carroll 9292 Carter Casey Christian Clark Clay Clinton 9135 Crittenden 9196 Cumberland 6784 Daviess Edmonson Elliott 6455 Estill Fayette ,090,381 4,129,298 4,168, ,467 17,646 17, ,284 18,680 19, ,767 20,303 20, ,363 8,424 8, ,586 39,026 39, ,271 11,421 11, ,914 29,791 29, ,265 93,787 97, ,377 19,385 19, ,629 49,516 49, ,894 28,047 28, ,379 8,458 8, ,185 16,247 16, ,998 19,280 19, ,182 64,754 66, ,294 13,523 13, ,058 13,058 13, ,467 34,723 35, ,146 89,554 89, ,374 5,392 5, ,309 10,434 10, ,215 27,470 27, ,623 15,763 15, ,728 73,071 73, ,629 34,011 34, ,938 25,242 25, ,701 9,751 9, ,421 9,450 9, ,205 7,251 7, ,924 92,211 92, ,831 11,980 12, ,793 6,828 6, ,414 15,497 15, , , ,994 41

52 Kentucky County Population, Fleming Floyd Franklin Fulton 8271 Gallatin 5393 Garrard Grant Graves Grayson Green Greenup Hancock 7864 Hardin Harlan Harrison Hart Henderson Henry Hickman 5566 Hopkins Jackson Jefferson Jessamine Johnson Kenton Knott Knox Larue Laurel Lawrence Lee 7422 Leslie Letcher Lewis ,033 14,227 14, ,335 42,241 42, ,065 48,357 48, ,711 7,678 7, ,257 8,579 8, ,280 15,681 16, ,429 24,294 25, ,498 37,877 38, ,490 24,842 25, ,666 11,784 11, ,965 37,011 37, ,474 8,538 8, ,944 95,555 96, ,832 32,528 32, ,269 18,498 18, ,841 18,163 18, ,059 45,234 45, ,396 15,666 15, ,226 5,198 5, ,570 46,603 46, ,733 13,925 14, , , , ,084 40,927 41, ,495 23,530 23, , , , ,611 17,577 17, ,060 32,266 32, ,614 13,808 14, ,980 54,998 56, ,835 16,046 16, ,984 8,040 8, ,243 12,114 11, ,119 24,985 24, ,274 14,420 14,565 42

53 Kentucky County Population, Lincoln ,852 24,249 24,648 Livingston 9062 Logan Lyon 6624 McCracken McCreary McLean 9628 Madison Magoffin Marion Marshall Martin Mason Meade Menifee 5092 Mercer Metcalfe 8963 Monroe Montgomery Morgan Muhlenberg Nelson Nicholas 6725 Ohio Oldham Owen 9035 Owsley 5036 Pendleton Perry Pike Powell Pulaski Robertson 2124 Rockcastle Rowan Russell ,923 10,017 10, ,908 27,178 27, ,247 8,384 8, ,788 65,996 66, ,334 17,537 17, ,011 10,068 10, ,343 73,553 74, ,384 13,422 13, ,428 18,603 18, ,478 30,760 31, ,607 12,626 12, ,840 16,868 16, ,651 26,896 27, ,766 6,938 7, ,043 21,219 21, ,199 10,329 10, ,825 11,877 11, ,979 23,319 23, ,247 14,491 14, ,906 31,955 31, ,549 39,416 40, ,829 6,841 6, ,197 23,424 23, ,099 49,658 51, ,785 10,977 11, ,847 4,836 4, ,760 15,063 15, ,291 29,201 29, ,319 67,954 67, ,464 13,647 13, ,095 57,796 58, ,285 2,299 2, ,842 17,050 17, ,166 22,231 22, ,513 16,669 16,822 43

54 Kentucky County Population, Scott ,337 35,385 36,462 Shelby Simpson Spencer 6801 Taylor Todd Trigg Trimble 6090 Union Warren Washington Wayne Webster Whitley Wolfe 6503 Woodford ,577 35,596 36, ,573 16,706 16, ,595 13,298 14, ,097 23,230 23, ,139 12,272 12, ,950 13,239 13, ,443 8,706 8, ,577 15,526 15, ,338 95,810 97, ,971 11,013 11, ,275 20,558 20, ,180 14,227 14, ,196 36,455 36, ,150 7,216 7, ,618 23,943 24,264 44

55 Training Cross Validation Testing County MSE Epoch # MSE Epoch # NMSE r Adair E E Allen Anderson E Ballard Barren Bath E Bell E Boone Bourbon Boyd Boyle Bracken E E Breathitt E Breckinridge Bullitt E E Butler Caldwell Calloway Campbell E Carlisle Carroll E Carter Casey E Christian Clark Clay E Clinton Crittenden * * Cumberland * * Daviess E Edmonson E Elliott Estill Fayette Fleming E Floyd Franklin Fulton Gallatin E Garrard * * Grant * * Graves E Grayson Green E * * Greenup E Hancock