An Explanation to the VTI FILTER documents

Transcription

1 VTI notat 39A VTI notat 39A- An Explanation to the VTI FILTER documents Wavelength, λ (m) (Ω) 3 (n) RoadRuf Matlab code (Device E 3) Displacement power spectral density (m 3 ) FILTER Section: Q DAF test track 3 Surface: Concrete Section length: 4 m Speed/Run: 6/3 8 Spatial frequency, n (cycles/m) Angular spatial frequency, Ω (rad/m) Author Peter Andrén & Leif Sjögren Research division Measurement Technology and Methods Project number 85 Project name Sponsor Distribution Road surface measurement, methods and necessary accuracy KFB/VV Free

2 Foreword During the cause of the FILTER project the Swedish National Road and Transportation Research Institute has been working on a project financed by the Swedish Transport & Communications Research Board and the Swedish National Road Administration concerning the required accuracy of road measuring devices In this work we made extensive use of data from the FILTER project, resulting in the documentation found on the Compact Disc We distribute this material as we ve found it useful as a tool for browsing through the data, and hope that you will find it useful too Please direct all questions of a technical nature to Peter Andrén on peterandren@vtise NB This documentation is not a part of the official FILTER documentation The official documentation describing the longitudinal analysis can be found in FILTER Experiment: Analyses of the Longitudinal Profiles and Indices by Ducros, D-M, Petkovic, L, et al Linköping, -5-8 Leif Sjögren VTI notat 39A-

3 Contents Foreword Introduction 5 The DeviceXNNpdf documents 7 3 Comparison with RoadRuf 4 An IRI comparison for all devices 3 5 About the PDF documents 5 6 Bibliography 7 VTI notat 39A-

4 Introduction This document explains how to read the PDF documents on the VTI-FILTER CD Apart from the reading instructions a comparison with the RoadRuf program for the IRI and PSD Matlab functions is included A small comparison of the calculated IRI for the different devices has also been added at the end of the document We can see that all devices behave reasonably well in that aspect I have analyzed the test section profiles from the original CD from Daniel-Marc Ducros, LCPC In the case of Device C 5 new profiles were delivered after the test, as some problem had occurred in the post processing (each profile was a cumulative sum instead of the profile) I use the notation Device Code - Test Section - Speed - Repetition to refer to a certain test profile, eg Device D 6 - W for the third repetition in sixty on test section W for device D 6 The work presented in this, and accompanying, documents has been done with Matlab for the number crunching, and pdfl A TEX for typesetting and document production The documents presenting the results from the devices and the Primal were created in one 3 hour Matlab session on May 5, This Matlab session created almost 75 PostScript figures and about 7, lines of L A TEX code in twenty-one documents Another major computer session converted the figures to the Portable Document Format and compiled the PDF-documents This resulted in the twenty-one PDF-documents on this CD, altogether containing more than 56 pages Despite the large size of this job both Matlab and pdfl A TEX behaved very well However, due to the vast amount of documentation, I haven t been able to check all results for errors If you find anything that s obviously wrong, very strange or if there s room for improvements please contact me on peterandren@vtise Feel free to contact me about other things concerning these documents: if you want the Matlab source code, need more information on some specific detail, or just about anything else (The Matlab source code isn t distributed on this CD as it was in a state of ad hoc at the time when the CDs were made My plan is to comment the code, remove unused parts and put it in public domain Mail me if you re interested in receiving a copy) Many thanks to Daniel-Marc Ducros at LCPC, France for many rewarding discussions concerning various details of longitudinal road profile analysis, and other topics as well Peter Andrén, -5-7 VTI notat 39A- 5

5 The DeviceXNNpdf documents On the Compact Disc where this document is found, you can also find documents named DeviceXNNpdf where X is the group code, and NN is the device number, following the FILTER notation This document contains an explanation of how to read and understand the DeviceXNNpdf documents The document starts with a table (as in Table below) on the first page giving information on for which test sections and at what speeds the device has delivered data The normal procedure was that three repetitions were carried out for each speed and test section If the device in question hasn t delivered data for any tests that place in the table is marked with a dash ( ), and if not all three repetitions were carried out, this is marked with with a footnote comment in the table The optimum speed is printed in red For a few devices (C, C 3, F9 and F3) the optimum speed is said to be 99 km/h This is not necessarily true, as 99 was supposed to be used as a code for the optimum speed The true optimum speed for these devices should be documented elsewhere Table : Example of Device Information Table Device E 3 Analyzed tests Test section Speed Speed Speed 3 O 9 P 6 7 Q 6 7 R 7 S U V W X Y Z Only repetition 3 Only repetition 3 Only repetitions and 3 The second table contains a summary of all the tests carried out by the device The data in this table can also be found at the more detailed presentation further back in the document The first three columns (denoted TEST INFORMATION) give the test section, the speed and the repetition The other columns contain results collected in this table for easy comparison The meaning of the other columns will be explained when the detailed analysis is explained VTI notat 39A- 7

6 Table : Example of All Test Section Table See Table 4 and 5 for the notation TEST INFORMATION CORRELATION PIARC RMS FRENCH RMS IRI Road Speed Run R u R a l p p f f f 3 I v I p O O O O O O O O O P P P Z Z After the two tables follows a more detailed presentation of all the analyzed road profiles Each and every analyzed profile is presented with a set of three pages, as illustrated in facsimiles in Figure (a-c) The first page is made up of three tables and four graphs The first table, at to the top of the page, gives some general information on the device, test section, speed and repetition analyzed The top graph shows the two profiles to be compared The Primal profile is presented just as it was delivered, and the device profile after detrending with a best fit (least-square sense) three-order polynomial This detrending is carried out to increase the numerical stability in the resampling function Profile height Profile height 4 Device Profile Compared With The Primal Profile Device: A Speed: 6 km/h Section: O - DAF Repetition: test track Primal Device A Distance [m] Distance [m] G v /G p IRI [mm/m] Wavelength [m] Spatial frequency [/m] Distance [m] Data derived from the height profile, after the metres high pass detrending Adjusted coefficient The longitudinal Vehicle IRI ( ) Primal IRI ( ) Unadjusted coefficient of correlation ( ) of correlation ( ) adjustment ( ) Root Mean Square of for five wavelength bands ( is the wavelength in metres) PIARC short PIARC long Short Medium Long wave ( ) wave ( ) wave ( ) wave ( ) wave ( ) (Ω) Displacement power spectral density (m 3 ) Wavelength, λ (m) (n) 3 Primal Device A FILTER Section: O DAF test track Surface: Concrete Section length: 4 m Speed/Run: 6/ 9 Spatial frequency, n (cycles/m) Angular spatial frequency, Ω (rad/m) (Ω) Displacement power spectral density (m 3 ) Wavelength, λ (m) (n) 3 Primal Device A FILTER Section: O DAF test track Surface: Concrete Section length: 4 m Speed/Run: 6/ 9 Spatial frequency, n (cycles/m) Angular spatial frequency, Ω (rad/m) (a) First page (b) Second page (c) Third page Figure : Facsimiles of one set of pages presenting one repetition (Device A - O ) 8 VTI notat 39A-

7 Coeff of corr Length adjustment Figure : Correlation In the second graph 5 meters on each side of the Primal profile has been cut off The device profile is trimmed so that maximum correlation between the two profiles is achieved The correlation for different positions can be seen in the Figure In this example (Device A - P ) the best correlation occurred after about meters, ie the test started meters early This process will make sure that the profile to profile comparisons are as fair as possible The coefficient of correlation for the unadjusted and longitudinally adjusted case are presented in the table at the bottom of the page (here Table 4) In some cases the adjusted profiles have a lower coefficient of correlation than the unadjusted ones The explanation to this is that both profiles (device and Primal) are high-pass filtered with a ten meter filter before the maximum correlation is searched (this will focus the search algorithm on shorter, more identifying, wavelengths) However, when the maximum correlation of the longitudinally adjusted profiles is calculated the meter high-passed filtered profiles are used, and the coefficient of correlation might change slightly This will usually not influence very much, unless the maximum correlation is very low (eg Device B - U //3) The second and third pages (Figure (b c)) contains the Power Spectral Density (PSD) functions for the both profiles These graphs are made according to the ISO 868 standard [4] The second page presents the PSD profile for all possible spatial frequencies from to (ie from 5 to meter s wavelength) The same function smoothed in octave bands for center spatial frequencies up to 3, in third-octave bands from 496 to 5, and twelfth-octave bands for the higher frequencies is presented on page three A quote (usually called transfer function) between the smoothed PSD for the device profile and Primal profile is given in the third graph on Figure (a) The last graph in Figure (a) is the International Roughness Index (IRI) for the profiles IRI values have been calculated for three meter sections, as this was considered to be detailed but still not too detailed The second table at the bottom of page one presents the coefficient of correlation for the unadjusted and longitudinally adjusted profiles, as well as the length of the adjustment Next, the IRI for the entire profiles are given The IRI code follows the Table 4: Example of the correlation and IRI table Data derived from the height profile, after the meters high pass detrending Unadjusted coefficient of correlation (R u) Adjusted coefficient of correlation (R a) The longitudinal adjustment (l) Vehicle IRI (I v) Primal IRI (I p) VTI notat 39A- 9

8 recommendations from (a draft version of) Sayers article On the Calculation of IRI from Longitudinal Road Profile [9] A comparison between my Matlab code and RoadRuf is given in Section 3 The last table presents a few root mean square values for the transfer function between the two PSD function, ie the third graph on page one These RMS values have been divided into five wavelength bands according to the PIARC recommendations, and to what in Sweden is called the French wavelength bands The RMS computation is done mainly to get a numerical representation of the transfer function Table 5: Example of the correlation and IRI table Root Mean Square of G v /G p for five wavelength bands (λ is the wavelength in meters) PIARC short PIARC long Short Medium Long wave (p ) wave (p ) wave (f ) wave (f ) wave (f 3 ) λ 5 5 < λ 5 λ 3 3 λ 3 3 λ VTI notat 39A-

9 3 Comparison with RoadRuf In order to validate the behavior of the Matlab code used a comparison with the RoadRuf software [] was conducted A continuous IRI profile (ie no averaging over subsections) was calculated with the Matlab code The road profile (in this case Device C 5 - R ) was then written to the ERD format, analyzed in RoadRuf, and read into the Matlab routine for comparison and plotting The result was very satisfactory, and is presented in the figure below As can be seen the two profiles more or less coincide, and the difference between them (in the order of 5 mm/m) can safely be ignored A similar test was carried out for the Power Spectral Density code The figure on next page shows the result Again, there s nothing crucial to complain about IRI [mm/m] 4 3 Continuous IRI profiles for Device C 5 R 75 RoadRuf Matlab code Sample 6 x Difference between the continuous IRI profiles for Device C 5 R IRI [mm/m] Sample Figure 3: IRI comparison VTI notat 39A-

10 Wavelength, λ (m) (Ω) 3 (n) RoadRuf Matlab code (Device E 3) Displacement power spectral density (m 3 ) FILTER Section: Q DAF test track 3 Surface: Concrete Section length: 4 m Speed/Run: 6/3 8 Spatial frequency, n (cycles/m) Angular spatial frequency, Ω (rad/m) Figure 3: PSD comparison VTI notat 39A-

11 4 An IRI comparison for all devices Ability to measure the IRI is one of the most important features of any road surface measuring equipment Figure 4 below summarizes all the IRI values delivered for all devices at all speeds As can be seen in the figure all devices produce a similar result The differences that can be seen are most likely mainly due to the position on the test section more than the capability of the device Figure 4 on next page illustrates how the different devices have performed on the different test sections IRI from the Primal is drawn as a red line across the graphs IRI O P Q R S U V W X Y Z Road Figure 4: IRI comparison A A B 6 B 7 B 9 B C C C 3 C 5 D 6 D 7 D 8 D 9 E E 3 F 7 F 9 F 3 G 3 G 33 Primal VTI notat 39A- 3

12 IRI on Z IRI on Y IRI on X IRI on W IRI on V IRI on U IRI on S IRI on R IRI on Q IRI on P IRI on O Device number Figure 4: IRI comparison 4 VTI notat 39A-

13 5 About the PDF documents All PDF documents on this CD have both an outline and a thumbnail mode (Figure 5 and 5, respectively) Admittedly, the thumbnail are very small, but at least I have found them useful for just browsing through the documents If you experience any problems printing the documents, try using PostScript Level in the printing dialogue box Figure 5: PDF document in outline mode Figure 5: PDF document in thumbnail mode VTI notat 39A- 5

14 6 Bibliography [] B de WIT, E Kempkens, L Sjögren, and D-M Ducros The FILTER Experiment Technical Note 999/, FEHRL, 999 [] G Descornet Inventory of High-Speed Longitudinal and Transverse Road Evenness Measuring Equipment in Europe Technical Note 999/, FEHRL, 999 [3] D-M Ducros, L Petkovic, G Descornet, B Berlemont, M Alonso Anchelo, S Yanguas, W Jendryka, and P Andrén FILTER Experiment - Analysis of Longitudinal Measurements Technical Note /, FEHRL, [4] Mechanical vibration Road surface profiles Reporting of measured data ISO 868:995(E), International Organization for Standardization (ISO), [5] Georg Magnusson and Peter Andrén Matematisk beskrivning av vägytor och longitudinella vägprofiler VTI-Notat 4, Statens väg- och transportforskningsinstitut, Linköping, [6] Georg Magnusson, Sven Dahlstedt, and Leif Sjögren Mätning av vägytans longitudinella jämnhet, metoder och nödvändig noggrannhet VTI-rapport 475, Statens väg- och transportforskningsinstitut, Linköping, [7] PIARC International Experiment to Harmonise Longitudinal and Transverse Profile Measurement and Reporting Procedures Draft [8] PIARC Caractéristiques de Surface des Chaussées IV Symposium International SURF, Nantes, France, May 4 [9] Michael W Sayers On the calculation of international roughness index from longitudinal road profile, pages Transportation Research Record 5 Transportation Research Board, Washington, D C, USA, 995 Pavement-Vehicle Interaction and Traffic Monitoring [] University of Michigan Transportation Research Institute (UMTRI) RoadRuf: Software for Analyzing Road Profiles Web site: [] M Willett, G Magnusson, and B Ferne FILTER - Theoretical Study of Indices Technical Note /, FEHRL, VTI notat 39A- 7