Technical Manual for Veda Software

Transcription

1 Technical Manual for Veda Software N All passes data Proofing data only IX X I, V and IX are same coordinate. II, VI and X are same coordinate. III and VII are same coordinate. IV and VIII are same coordinate. Pass No.=3 VII Pass No.=2 V II I Pass No. =1 I VI II VI IV II Legend of Pass No E Y axis (North) Azimuth Lag Distance Lag Tolerance Lag 1 Lag 2 Lag 3 Lag 4 Bandwidth Azimuth tolerance X axis (East)

2 1. Report No. MN/RC Title and Subtitle Technical Manual for Veda 7. Author(s) 2. Government Accession No. N/A 3 Recipient Catalog No. N/A 5. Report Date August Performing Organization Code N/A 8. Performing Organization Report No. George Chang, Qinwu Xu, Jason Dick, and Jennifer Rutledge of the Transtec Group Inc. 9. Performing Organization Name and Address The Transtec Group, Inc Balcones Drive Austin TX Sponsoring Agency Name and Address This effort is sponsored jointly by Mn/DOT and FHWA. Minnesota Dept. of Transportation Consultant Services Section, Mail Stop John Ireland Boulevard St. Paul, Minnesota Supplementary Notes N/A 10. Work Unit No. (TRAIS) N/A 11. Contract or Grant No. Mn/DOT Contract No Type of Report and Period Covered Final report (draft) 14. Sponsoring Agency Code N/A 16. Abstract Intelligent compaction (IC) is an emerging technology, and for some applications it is mature enough for implementation in field compaction of pavement materials. IC data are often massive and new to DOTs and industries. Thus, it requires practical guidelines and protocol to assist DOTs and industries to properly manage the IC data in order to provide support for decision-making and quality control/acceptance (QC/QA). Therefore, there is an immediate need to develop IC Data Management Protocol to fulfill these needs, and on a local level, to assist with Minnesota s current implementation efforts. The tool would be used by research personnel for further development and refinement of the Minnesota Department of Transportation s (MnDOT) draft specifications and by the Inspectors for review of uniformity and assistance in the determination of areas for QA spot testing. Features are included to analyze defection data from sonic test rolling (STR). This document is a technical manual to describe in details on the methods and algorithms of the IC and STR data management tool - Veda. 17. Key words Compaction, intelligent compaction, roller, data, viewing, analysis, pavement performance. 18. Distribution Statement No restrictions. This document is available to the public through the National Technical Information Service, Springfield, Virginia Security Classif. (of this report) Unclassified 20. Security Classif. (of this page) Unclassified 21. No. of Pages 22. Price i

3 SI* (MODERN METRIC) CONVERSION FACTORS APPROXIMATE CONVERSIONS TO SI UNITS Symbol When You Know Multiply By To Find Symbol LENGTH in inches 25.4 millimeters mm ft feet meters m yd yards meters m mi miles 1.61 kilometers km AREA in 2 square inches square millimeters mm 2 ft 2 square feet square meters m 2 yd 2 square yard square meters m 2 ac acres hectares ha mi 2 square miles 2.59 square kilometers km 2 VOLUME fl oz fluid ounces milliliters ml gal gallons liters L ft 3 cubic feet cubic meters m 3 yd 3 cubic yards cubic meters m 3 NOTE: volumes greater than 1000 L shall be shown in m 3 MASS oz ounces grams g lb pounds kilograms kg T short tons (2000 lb) megagrams (or "metric ton") Mg (or "t") TEMPERATURE (exact degrees) o F Fahrenheit 5 (F-32)/9 Celsius or (F-32)/1.8 ILLUMINATION fc foot-candles lux lx fl foot-lamberts candela/m 2 cd/m 2 FORCE and PRESSURE or STRESS lbf poundforce 4.45 newtons N lbf/in 2 poundforce per square inch 6.89 kilopascals kpa APPROXIMATE CONVERSIONS FROM SI UNITS Symbol When You Know Multiply By To Find Symbol LENGTH mm millimeters inches in m meters 3.28 feet ft m meters 1.09 yards yd km kilometers miles mi AREA mm 2 square millimeters square inches in 2 m 2 square meters square feet ft 2 m 2 square meters square yards yd 2 ha hectares 2.47 acres ac km 2 square kilometers square miles mi 2 VOLUME ml milliliters fluid ounces fl oz L liters gallons gal m 3 cubic meters cubic feet ft 3 m 3 cubic meters cubic yards yd 3 MASS g grams ounces oz kg kilograms pounds lb Mg (or "t") megagrams (or "metric ton") short tons (2000 lb) T TEMPERATURE (exact degrees) o C Celsius 1.8C+32 Fahrenheit ILLUMINATION lx lux foot-candles fc cd/m 2 candela/m foot-lamberts fl FORCE and PRESSURE or STRESS N newtons poundforce lbf kpa kilopascals poundforce per square inch lbf/in 2 *SI is the symbol for th e International System of Units. Appropriate rounding should be made to comply with Section 4 of ASTM E380. (Revised March 2003) ii o C o F

4 Technical Manual for Veda Final Report Prepared by: George Chang, Qinwu Xu, Jason Dick, and Jennifer Rutledge The Transtec Group, Inc Balcones Dr. Austin, TX For: Minnesota Department of Transportation Office of Materials and Road Research 395 John Ireland Blvd, St. Paul, MN And Federal Highway Administration Office of Pavement technology 1200 New Jersey Ave., SE Washington, DC August 2011 This report represents the results of research conducted by the authors and does not necessarily represent the views or policies of the Minnesota Department of Transportation. This report does not contain a standard or specified technique. The authors and the Minnesota Department of Transportation do not endorse products or manufacturers. Trade or manufacturers names appear herein solely because they are considered essential to this report. iii

5 TABLE OF CONTENTS Acknowledgement...1 Introduction 2 Basic Univariate Statistics...5 Methodology...5 Implementation...6 Histogram 8 Methodology...8 Implementation...8 Semi-variogram...10 Methodology...10 Introduction...10 Algorithm of semi-variogram...11 Implementation...15 Compaction Curves...17 Methodology...17 Implementation...17 Correlation Analysis...19 Methodology...19 Implementation...20 Fixed Interval Analysis...22 Methodology...22 Implementation...22 Linear failure Analysis...24 Methodology...24 Implementation...25 References 27 LIST OF TABLES LIST OF FIGURES Figure 1. Time history data vs. post-processed data (Sakai America)...3 iv

6 Figure 2. All passes data and proofing data (Sakai America)...4 Figure 3. Basic univariate statistics report in Veda...7 Figure 4. Histogram report in Veda....9 Figure 5. Description of a typical experimental and exponential semi-variogram and its parameters...10 Figure 6. Location and lag vectors...11 Figure 7. Direction for a semi-variogram analysis...12 Figure 8. Nodal data used for semi-variogram analysis within a given lag distance...13 Figure 9. Experimental semi-variogram Figure 10. Curve fits of theoretical Semi-variogram models...15 Figure 11. Semi-variogram report...16 Figure 12. Compaction Curve Report...18 Figure 13. Data extracted from a circular area centering a point test location Figure 14. Correlation Report...21 Figure 15. User-defined start/stop locations and lots...22 Figure 18. Linear Failure Analysis...23 Figure 15. User-defined start/stop locations and moving average base length...24 Figure 16. Zoom in to user-defined start locations and moving average base length...24 Figure 17. Refined segments to produce data points for moving average computation Figure 18. Linear Failure Analysis...26 v

7 Acknowledgement This document would not have been possible without the partial sponsorship from MnDOT and the FHWA. The authors would also like to specifically acknowledge the following individuals for their contribution to this document: MnDOT: Glenn Engstrom, Chief Geotechnical Engineer, Terry Beaudry, Grading, Base and Aggregate Engineer, and Rebecca Embacher, Assistant Grading and Base Engineer. FHWA: Victor (Lee) Gallivan 1

8 Introduction Veda (pronounced as "Vehda" - means "knowledge") is a generic software for viewing and analyzing geospatial data. Currently, the applications are limited for intelligent compaction (IC) and sonic test rolling (STR). Veda can now import data from various intelligent compaction machines and STR device, then perform standardized data processing and reporting. Users should follow the step-by-step instructions in the IC Data Management Guidelines and STR Data Management Guidelines to setup/collect/export data for specific vendors' systems prior to importing data to Veda. This document focuses on the methods and algorithm for the IC and STR analyses. The IC and STR analyses target various types of data sets. Generally, IC-related data include postprocessed IC measurement values (ICMV) and other measurements from vendors software and in-situ point test data collected with other devices. Please refer to the companion report IC Data Management Guidelines and STR Data Management Guidelines for further details. IC vendors often store IC data in two different forms: Time History Data and Post-Processed Data (see Figure 1). Time History Data: Time history data record the raw IC data during compaction operations. They normally include one data point at the bottom center of the drum at a point in time, usually at 10 Hz resulting a sampling rate at approximately 1 ft/sec. Post-Processed Data: The Time History Data can be post-processed (sometimes in real-time for some vendors solutions) to produce data in finer meshes, often by duplicating data points over the drum width at a 1 ft. interval. Some vendors also provide users options to store the post-processed data in all-passes or proofing form. 2

9 N N-E coordinates of *.gps are here which is center of drum..... N-E coordinates of *.pln are here which is center of mesh. These coordinates are calculated by AithonMT using *.gps data and setting data. E (Courtesy of Sakai) Figure 1. Time history data vs. post-processed data (Sakai America). The post-processed data can be in two sub-forms: All-Passes Data and Proofing Data. These two forms can be imported to Veda. All-Passes Data: As this term indicates, All-Passes Data include all passes within a given mesh (e.g., coverage I through X in Figure 2). Proofing Data: The Proofing Data contain only the last passes within a given mesh (e.g., coverage VII, VIII, IX, and X in Figure 2). 3

10 N All passes data Proofing data only IX X I, V and IX are same coordinate. II, VI and X are same coordinate. III and VII are same coordinate. IV and VIII are same coordinate. Pass No.=3 VII Pass No.=2 V III Pass No. =1 I VIII VI IV II Legend of Pass No E (Courtesy of Sakai) Figure 2. All passes data and proofing data (Sakai America). The structure of Veda data analyses is summarized as follows: Proof data analysis o Basic statistics and Histogram o Fix interval report (if the start and end locations are selected and the fix lot length is defined) o Correlation with point test data (if available) o Linear failure analysis (for STR data only) o Semi-variogram (optional) All-passes data analysis o Basic statistics and Histogram o Semi-variogram (optional) o Compaction curves o Correlation with point test data (if available) The followings detail the methods and implementation of the above analyses. 4

11 Basic Univariate Statistics Methodology The basic univariate statistics for a population or data set consists of the followings: mean value variance standard deviation skewness Kurtosis excess min values max values ranges coefficient of variations counts lower 95% confidence limits for mean high 95% confidence limits for mean lower 95% confidence limits for variance high 95% confidence limits for variance sum of weights The confidence intervals for the mean and variance are computed if the sample is assumed to be from a normal population. Definition for selected statistics reports are presented below: The sample arithmetic mean is defined as follows: 1 x = n n x i i= 1 (1) Where, 5

12 n x i : number of data points; : data values. Sample standard deviation is defined as follows: n 1 2 σ = ( x i x) (2) n 1 i= 1 Where, x : sample mean value. Coefficient of variance is determined as follows: σ cov = (3) x Sample skewness, a measure of the degree of asymmetry of a distribution is determined as follows: n ( x x) 3 i / n i Skewness = (4) n 3 / 2 2 ( xi x) / n i Sample excess/kurtosis, the degree of peakedness of a distribution, is determined as follows: n ( x x) 4 i / n i Kurtosis = 3 (5) n 2 2 ( xi x) / n i Currently, only selected statistics are reported including: minimum, maximum, mean, standard deviation, coefficients of variation, and sample size. Implementation The basic univariate statistics function in Veda is implemented by utilizing an IMSL function call, UVSTA (IMSL, 2007). If users setup target values for passing score, % of Target Achieved and Target Status (i.e., pass or failed) will be included in the report. % of Target Achieved means the percentage of data that meet the target values (i.e., for ICMV, it is equal or greater than the target value; it is the opposite for sonic test rolling deflection data). Target Status means that whether the area of interest is a pass or fail based on the minimum requirement of percentage of data meeting the target 6

13 values. An example report is illustrated as follows: Figure 3. Basic univariate statistics report in Veda. 7

14 Histogram Methodology The histogram is a graphical display of tabular frequencies, shown as adjacent rectangles. The histogram (tabular frequency) of a specific interval is computed as the percentage of the quantity within that interval over the total quantity of observation. Table 1 shows the tabular frequency for a sample with size of 27. Table 1. An example of histogram analysis Interval Width Quantity (Q) Freqency % % % % % % Implementation The histogram function in Veda is implemented by utilizing an IMSL function call, OWFRQ, to tally observations into a one-way frequency table (IMSL, 2007). An example report is illustrated as follows: 8

15 Figure 4. Histogram report in Veda. 9

16 Semi-variogram Methodology Introduction A semi-variogram is a plot of the average squared differences between data values as a function of separation distance, and is a common tool used in geostatistical studies to describe spatial variation. A typical semi-variogram plot is presented in Figure 5. The semi-variogram is defined as one-half of the average squared differences between data values that are separated at a distance h (Isaaks and Srivastava 1989). If this calculation is repeated for many different values of lag distances (as long as the sample data will support) the result can be graphically presented as experimental semi-variogram shown as circles in Figure 5. More details on experimental semi-variogram calculation procedure are available elsewhere in the literature (e.g., Clark and Harper 2002, Isaaks and Srivastava 1989). To obtain an algebraic expression for the relationship between separation distance and experimental semivariogram, a theoretical model is fit to the data. Some commonly used models include linear, spherical, exponential, and Gaussian models. An exponential semi-variogram is illustrated in Figure 5 as solid line. Semivariogram Effective Range R* (3R to 5R) (For Exponential or Gaussian models) Range, R Experimental Semivariogram Exponential Semivariogram Scale, C Sill C + C 0 Range: As the separation distance between pairs increase, the corresponding semivariogram value will also generally increase. Eventually, however, an increase in the distance no longer causes a corresponding increase in the semivariogram, i.e., where the semivariogram reaches a plateau. The distance at which the semivariogram reaches this plateau is called as range. Longer range values suggest greater spatial continuity or relatively larger (more spatially coherent) hot spots. Sill: The plateau that the semivariogram reaches at the range is called the sill. A semivariogram generally has a sill that is approximately equal to the variance of the data. Nugget, C 0 Separation Distance (m) Nugget: Though the value of the semivariogram at h = 0 is strictly zero, several factors, such as sampling error and very short scale variability, may cause sample values separated by extremely short distances to be quite dissimilar. This causes a discontinuity at the origin of the semivariogram and is described as nugget effect. (Isaaks and Srivastava, 1989) Figure 5. Description of a typical experimental and exponential semi-variogram and its parameters Three important features to construct a theoretical semi-variogram include: sill (C+C 0 ), range (R), and nugget (C 0 ). These parameters are briefly described in Figure 5. Arithmetic expressions and detailed descriptions of theoretical models can be found elsewhere in the literature (e.g., Clark and Harper 2002, Isaaks and Srivastava 1989). For the semi-variogram analysis in Veda, the sill, range, and nugget values during theoretical model fitting were determined by checking the models for goodness using the modified Cressie goodness fit 10

17 method (see Clark and Harper 2002) and cross-validation process (see Isaaks and Srivastava 1989). From a theoretical semi-variogram model, a low sill and longer range of influence represent best conditions for uniformity, while the opposite represents an increasingly non-uniform condition. Algorithm of semi-variogram Data conversion Spatial variability/continuity depends on the detailed distribution of the physical attributes. Attributes with highly skewed data distribution present problems in variogram calculation and the extreme values have significant impact on variogram. Therefore, raw data are transformed to the logarithmical scale prior to the semi-variogram analysis: Z = log 10 ( z) (6) Where, z : data value such as ICMV. Location and lag vector definition Next, the location vector and lag vector are defined for a 2-dimentional (2-D) space (Figure 6). Location vector (μ+h) Lag vector (h) Location vector (μ) Origin Figure 6. Location and lag vectors. 11

18 Direction and model parameter definition The direction specification for the semi-variogram analysis is then defined as shown in Figure 7. The direction (and its angle), lag number, interval for lag distance, bandwidth, and total length (distance) are specified. Y axis (North) Azimuth Lag Tolerance Lag 3 Lag 4 Bandwidth Lag Distance Lag 1 Lag 2 Azimuth tolerance X axis (East) Figure 7. Direction for a semi-variogram analysis. Calculation of semi-variogram: The semi-variogram for a lag distance is defined as the average squared difference of data values separated approximately by lag distance, for all possible locations: Where, {[ Z ( u) Z( u )] } 2 2γ ( h ) = E + h (7) μ : location; h : lag distance ( h could be constant for the same lag area). The variogram can be re-expressed as follows: 2γ ( h) = 1 + N( h) N ( h) [ Z( u) Z( u h) ] 2 (8) Where, N (h) : the number of pairs for lag distance h of a specific lag area The semi-variogram is then attained as follows: 12

19 1 2 γ ( h) = [ Z( u) Z( u + h) ] (9) 2N( h) N ( h) Figure 8 shows that the nodal data used to determine the semi-variogram for a given lag distance. Y axis (North) Lag 1 Lag 2 Lag 3 Lag 4 Figure 8. Nodal data used for semi-variogram analysis within a given lag distance. Model fit The resulting semi-variogram values for lag distances are plotted as an experimental semi-variogram (in Figure 9). Variogram γ (h) No correlation Increase variability Lag distance (h) Figure 9. Experimental semi-variogram. 13

20 Various mathematical models can be used to fit the experimental semi-variogram: including power model, exponential model, and Gaussian model, etc. Power model: c h r( h) = a. (10) a Exponential model: 3h r( h) = c 1 exp (11) a Gaussian model: 2 9h r ( h) = c 1 exp 2 (12) a Where, a, c : model parameters. Based on the geospatial data collected from intelligent compaction, it appears that the exponential model provides better fit than other models. Figure 10 shows an example of an experimental semi-variogram of IC data and fitted curves with the exponential, Gaussian, and power model, respectively. Once a theoretical semi-variogram fit is performed, the parameters such as nugget, sill, scale, and range can be found. 14

21 Semivariogram Experimental semi-variogram Exponential model Gaussian model Pow er model Lag distances (m) Figure 10. Curve fits of theoretical Semi-variogram models. Implementation The semi-variogram function in Veda is implemented using an algorithm similar to the GAMV function of the GSLIB geostatistical software library (Deutsch and Journel, 1998). The fitting of theoretical semivariogram is implemented by using an IMSL function, BCNLS, solving a nonlinear least-squares problem subject to bounds on the variables and general linear constraints (IMSL, 2007). The exponential model is used for the curve fitting. Currently, some inputs are fixed with default values as follows Parameters Default Number of lags 10 Lag distance 4 Lag tolerance 2 Angle of direction 45 Angle tolerance 90 horizontal bandwidth 50 Dip angle 0 Dip angle tolerance 0 Vertical bandwidth 50 Standardize sills? No Tail variable 1 Head variable 1 Semivariogram type Traditional semivariogram 15

22 An example report is illustrated as follows: Figure 11. Semi-variogram report. 16

23 Compaction Curves Methodology Compaction curves indicate the trend of compaction effects versus roller passes. The optimal roller pass count can be determined from a compaction curve, e.g., data from a test strip. Compaction curves can also be produced from different stages or sections of constructions to monitor the efficiency of compaction. To build a compaction curve, the following steps should be followed: Define a zone or compaction area for analysis; Compute mean values of ICMV for data corresponding to each roller pass; Plot mean ICMV values against roller pass counts; Fit the data points to a second-order polynomial function; Obtain the fitted coefficients and the R 2 value. The second-order polynomial function is defined as follows: RMV 2 = a + b n + c n (13) Where, a,b,and n c : fitted coefficients; : roller pass count. Implementation The compaction curve function in Veda is implemented using the SVIGP function (group data for each pass count), the UVSTA function (obtain mean values via univariate statistics) and the RCURV function (perform polynomial curve fit) (IMSL, 2007). An example report is illustrated as follows: 17

24 Figure 12. Compaction Curve Report. 18

25 Correlation Analysis Methodology The correlation between the in-situ point measurements (e.g. density, deflection) and the ICMV is expressed with linear function fit following the steps. Extract ICMV data points within a circular area (typical 1 m of radius) centering the location of a point test. (Figure 13) Compute mean values of ICMV from the extracted data. Plot mean values of extracted IC data vs. point test values. Perform linear fit to the above data points and report fitted equations and R 2. 2 m Figure 13. Data extracted from a circular area centering a point test location. The least square method was used for the linear fit between ICMV (Y) and spot measurements (X): Y = a + b X (14) Where, a b : intercept of linear function; : slope of the linear function. 19

26 Cov( x, y) b = = Var( x) i ( x x)( y i i ( x x) i i y) 2 (15) a = y b x (16) Where, Cov is the covariance Var( x) x 2 = σ ( ). The R 2 value is used to rate the goodness of fit: R 2 = 1 SS SS err tot (17) Where SS SS tot err 2 = ( y y) is the total sum of squares; i i 2 = ( y f ) is the residual sum of squares; i i i f i y i : estimated data; : observed data. Implementation The correlation analysis in Veda is implemented using an algorithm similar to the CIRCLE_IMP_CONTAINS_POINT_2D function of the Geopak software library to extract data (Joes, B. 1993) and the IMSL RCURV function to perform polynomial curve fit (IMSL, 2007). An example report is illustrated as follows: 20

27 Figure 14. Correlation Report 21

28 Fixed Interval Analysis Methodology The fixed interval analysis is to analyze data in a linear lot-by-lot fashion. Based on user-defined start and stop location as well as the lot length, this analysis will produce analysis results for lots along the data stream (e.g. road ways). Figure 15. User-defined start/stop locations and lots. The data stream is divided into lots, and data within each lot are analyzed. Based on user-defined failure criteria for the measurement values, percentage of failure segments is computed. Pass or fail will then be determined similar to that for the basic stats. Implementation The fixed interval analysis in Veda is implemented using an algorithm described above. An example report is illustrated as follows: 22

29 Figure 16. Linear Failure Analysis 23

30 Linear failure Analysis Methodology The linear failure analysis is to analyze data in a linear moving average fashion. Based on user-defined start and stop location as well as the moving average base length, this analysis will produce moving averaged values vs. linear distance along the data stream (e.g. road ways). Figure 17. User-defined start/stop locations and moving average base length. Figure 18. Zoom in to user-defined start locations and moving average base length. 24

31 The data stream is divided into fine segments, and data values with fine segments are average to produce mean values for subsequent moving average. Based on user-defined failure criteria for the measurement values, percentage of failure segments is computed. Pass or fail will then be determined based on userdefined threshold for percentage of failed segments. Figure 19. Refined segments to produce data points for moving average computation. Implementation The linear failure analysis in Veda is implemented using an algorithm described above. Currently, linear failure analysis is only available to analyze sonic test rolling data. An example report is illustrated as follows: 25

32 Figure 20. Linear Failure Analysis 26

33 References Clark, I., and W. Harper. Practical Geostatistics rd edition, Ecosse North America Llc, Columbus, OH, Deutsch, C. V., and Journel, A.G. GSLIB: Geostatistical Software Library and User s Guide, second edition, Isaaks, E.H., and R.M Srivastava. An Introduction to Applied Geostatistics. Oxford Univ. Press, New York, Joe, B., GEOMPACK Users Guide,

34 Contact Information Glenn Engstrom, P.E. Mn/DOT 395 John Ireland Blvd, St. Paul, MN (651) George Chang, P.E., PhD The Transtec Group, Inc 6111 Balcones Dr. Austin, TX (512) Fax (512) Report Prepared by George Chang, P.E., PhD Qinwu Xu Jason Dick Jennifer Rutledge The Transtec Group, Inc.