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WIM Data Analysts Manual


Section 5. Steps for Monitoring System Calibration from Office

SECTION 3 and SECTION 4 focus on data QC procedures that are intended to ensure that a WIM system is operating to the best of its capabilities. Although such procedures are intended to identify significant size and weight accuracy problems due to improper system settings, malfunctioning components, or traffic operational anomalies, they are not designed to monitor the "fine tuning" of a system's calibration.

The objectives of the calibration monitoring procedures discussed in this section include:

  • Maintain system calibration throughout the life of the system.
  • Verify the desired effects of calibration factor adjustments on WIM weight, axle spacing, and vehicle length outputs.
  • Identify weigh sensors that are intermittently and/or subtly malfunctioning.
  • Adjust calibration factors for a weigh sensor exhibiting calibration drift pending onsite recalibration using test trucks.
  • Temporarily assign calibration factors for a weigh sensor replacement pending onsite recalibration using test trucks.
  • Schedule onsite calibrations/validation for sites with most need when funding and/or resources for running test trucks is limited.

5.1. GENERATE WEIGHT AND AXLE SPACING STATISTICS FOR SAMPLE OF TRUCK TRAFFIC STREAM

The method of this monitoring is to use large traffic stream samples (at least seven consecutive days of validated data) of a selected truck type or types (typically the Class 9's Type 3S2) to generate reports displaying statistical data on:

  • Steer axle and gross vehicle weight distributions.
  • Individual outputs of right and left weigh sensors.
  • Effect of speed on weight.
  • Axle spacings (and thereby speed).

For sites that have a significant number of the Class 11's Type 2S12 or the Class 12's Type 3S12 statistical data can be generated for checking overall vehicle length calibration.

For calibration monitoring analyses to be effective using these recommended procedures, it is imperative that the data used for the samples have passed all data QC checks. Also, data for days when the truck volumes and/or operating characteristics may not be typical, such as a major holiday, should not be used in the sample. If a particular month contains days with invalid data and/or days with atypical truck traffic such that a consecutive seven-day sample cannot be obtained, simply substitute the same day(s) of the week from the closest week in the same month to make up a composite week's sample. It is important that the traffic stream sample, regardless of the vehicle class(es) or type(s) selected for analysis, include only "real" trucks. Smaller power units such as pickups, Class 5s pulling trailers (see Figure 59), recreational vehicles pulling trailers or autos can skew the statistics.

Figure 59. Photo. This vehicle combination may conform to a Class 9 Type 2S3 under some classification schemes. This photo shows a pickup (Class 5) pulling a three-axle trailer, a combination that may be misclassified by some systems as a Class 9. Other smaller power units pulling trailers, recreational vehicles pulling trailers or autos can skew the statistics if these are common at a site. It is important that the traffic stream sample, regardless of the vehicle class (es) or type(s) selected for analysis, include only "real" trucks.
Figure 59. Photo. This vehicle combination may conform to a Class 9 Type 2S3 under some classification schemes.

For sites with low volumes of Class 9 vehicles, the sample should be for 14 consecutive days. It is up to the data analyst to determine what size sample is actually needed to perform a meaningful calibration monitoring analysis, but it is noted that the contractor performing the Phase II calibration monitoring for the LTPP Specific Pavement Study (SPS) Traffic Pooled Fund Study obtained 14 day samples for any site for which a seven-day sample would typically contain less than 1500 Class 9 Type 3S2 vehicles.

It is also important to note that these calibration monitoring procedures are intended to supplement, not replace, onsite calibrations using test trucks. Based upon analyses of the traffic stream statistics that indicate one or more sensors are not maintaining calibration (referred to as "calibration drift") or otherwise not reporting accurate weights, the analyst may deem it necessary to do one of the following:

  • Call for an immediate onsite validation/recalibration with test trucks.
  • Make calibration factor adjustments from the office deemed necessary to maintain calibration until test trucks can be run at the site.

In discussing and making recommendations on calibration monitoring procedures, examples of reports generated by a custom software program as well as tables and graphs from an off-the-shelf spreadsheet program will be displayed. Although the discussions may state something to the effect that "this report should be generated...", the intent is that information and statistics similar to what is included in the displayed example should be generated for review by the analyst. It is not intended that the programs used for example purposes be considered as the only recommended tools to generate necessary statistics.

The reports and graphs used for the following examples were generated by the "WIMSys" application of "CTWIM Suite" which is available from Caltrans at http://www.dot.ca.gov/hq/traffops/trucks/datawim/install.htm. A Power Point presentation on the CTWIM's WIMSys application can be downloaded on the same website (http://www.dot.ca.gov/hq/traffops/trucks/datawim/install.htm).

Figure 60 displays a report for a seven-day sample of Class 9 vehicles for a site with weigh sensors installed in the system's lane numbers 1 and 2 (northbound), and 5 and 6 (southbound). GVW distributions are displayed in 5.0 k ranges for each lane. The dashed line following the "30.0 TO 34.9" row is the typical break point for empty Class 9 trucks and the dashed line following the "75.0 TO 79.9" row is the GVW legal limit. This particular site experiences a moderate volume of both empty and loaded Class 9 trucks. This report, generated for a seven-day sample immediately following a system's being calibrated or validated using test trucks, provides an excellent reference for distribution comparisons with subsequent analyses.

Figure 60. Tabular Report. Distribution of lane counts by GVW, for site with mix of both loaded and empty Class 9 vehicles. This figure displays a report for a seven-day sample of Class 9 vehicles for a site with weigh sensors installed in the system's lane numbers 1 and 2 (northbound), and 5 and 6 (southbound). GVW distributions are displayed in 5.0 kip ranges for each lane. The dashed line following the "30.0 TO 34.9" row is the typical break point for empty Class 9 trucks and the dashed line following the "75.0 TO 79.9" row is the GVW legal limit. The counts and percentages shown in the table for all the lanes indicate that this particular site experiences a moderate volume of both empty and loaded Class 9 trucks. This type report, generated for a seven-day sample immediately following a system's being calibrated or validated using test trucks, provides an excellent reference for distribution comparisons with subsequent analyses.
Figure 60. Tabular Report. Distribution of lane counts by GVW, for site with mix of both loaded and empty Class 9 vehicles.

Figure 61 displays the same gross weight distributions but in graphical format. It is apparent that Lane #6 weights are a bit lighter than those for Lane #1. However, it must be noted that many WIM sites with bidirectional lanes do not experience the same GVW distribution patterns for each direction. For this sample, Lane #1 has more loaded than unloaded Class 9s whereas Lane #6 has more unloaded than loaded Class 9s. It is not uncommon for these patterns to change by day of week (hence the need for a sample from seven continuous days) or by season of the year (hence the need for tracking over time, as will be discussed later). Regardless of the Class 9 Type 3S2 empty versus loaded distribution mix, it is typical for the empty distributions to peak at "30 TO <35" k (as they do in this example) when using the five k ranges. The loaded distributions peak will vary a bit depending upon a particular site's truck operating characteristics, but the peak will typically occur at "70 TO <75" or "75 TO <80" k. For this example, the Lane #6 loaded peak being at the "65 TO 70" distribution is a bit suspicious, but its empty peak appears to be reasonable.

Figure 61. Report Graph. Distribution of lane counts by GVW, for site with mix of both loaded and empty Class 9 vehicles. This figure displays a chart of the distribution of lane counts by gross vehicle weight for a seven-day sample of Class 9 vehicles, for a site with weigh sensors installed in lane numbers 1 and 2 (northbound), and 5 and 6 (southbound). The X-axis is the gross vehicle weight in 5-kip ranges, and the Y-axis is the vehicle counts. The chart shows a mix of empty and loaded vehicles for all lanes, as the distributions exhibit two peaks. The empty trucks distributions peak at 30 to 35 kips, while the loaded trucks distributions peaks vary from 65 to 80 kips for the different lanes. For this example, the Lane #6 loaded peak being at the 65 to 70 kip distribution is a bit suspicious, but its empty peak appears to be reasonable.  It is apparent that Lane #6 weights are a bit lighter than those for Lane #1. However, it must be noted that many WIM sites with bidirectional lanes do not experience the same GVW distribution patterns for each direction. For this sample, Lane #1 has more loaded than unloaded Class 9s whereas Lane #6 has more unloaded than loaded Class 9s. It is not uncommon for these patterns to change by day of week (hence the need for a sample from seven continuous days) or by season of the year.
Figure 61. Report Graph. Distribution of lane counts by GVW, for site with mix of both loaded and empty Class 9 vehicles.

Figure 62 displays the same report as that displayed in Figure 60, but this report is for a seven-day sample from a site on a long haul route in the middle of the desert. As would be expected, this site has a very low percentage of empty Class 9s.

Figure 62. Tabular Report. Distribution of lane counts by GVW, site with very few empty Class 9 vehicles.  This figure displays a report for a seven-day sample of Class 9 vehicles for a site with weigh sensors installed in the system's lane numbers 1 through 4. GVW distributions are displayed in 5.0 kip ranges for each lane. The dashed line following the "30.0 TO 34.9" row is the typical break point for empty Class 9 trucks and the dashed line following the "75.0 TO 79.9" row is the GVW legal limit. This particular site is on a long haul route in the middle of the desert. As would be expected, this site has a very low percentage of empty Class 9s.
Figure 62. Tabular Report. Distribution of lane counts by GVW, site with very few empty Class 9 vehicles.

Figure 63 displays the same gross weight distributions but in graphical format.

Figure 63. Report Graph. Distribution of lane counts by GVW, site with very few empty Class 9 vehicles. This figure displays a chart of the distribution of lane counts by gross vehicle weight for a seven-day sample of Class 9 vehicles, for a site with weigh sensors installed in lane numbers 1 through 4. The X-axis is the gross weight in 5-kip ranges, and the Y-axis is the vehicle counts. The chart shows that this particular site has a very low percentage of empty Class 9 vehicles, and there is no peak observed around gross vehicle weights of 20 to 35 kips. The loaded trucks distributions peak at 70 to 80 kips for all lanes.
Figure 63. Report Graph. Distribution of lane counts by GVW, site with very few empty Class 9 vehicles.

When reviewing GVW distributions, the analyst is trying to identify the following:

  • Reasonableness of empty and loaded peak distributions given site's truck operational characteristics.
  • Consistency of overall distribution patterns with:
    • Those in previous reports.
    • Those in a report for a sample taken immediately following the last onsite calibration or validation using test trucks.

For sites that do have seasonal variations in truck operational characteristics, it may take a couple years to verify that the changes in GVW distributions are due to these variations and not calibration drift. It is always a good idea to perform an onsite validation using test trucks the first time a site's GVW distributions change.

The next step is to check the weight outputs of each individual sensor and to monitor the effects of speed on the Axle 1 weight and GVW outputs for each lane.

A key element in the monitoring of a system's calibration and weigh sensor performance is the assumption that for a large traffic stream sample of Class 9 vehicles the average right and left steer axle weights should be approximately equal. A 2004 study (Nichols and Bullock 2004) determined this to be a logical assumption based upon a review of vehicle geometry with several truck manufacturers and an accounting for the effect of roadway cross slope. Regardless of any argument that this assumption is not "ground truth", the monitoring of the balance between the average right and left steer axle weights is an excellent tool for identifying any drift in a sensor's calibration or any subtle problem in a sensor's performance. It is recognized that some Type I WIM systems have double threshold weighing whereby each right and left wheel track has two weigh sensors instead of one. However, such a system reports, as data elements, a single right wheel weight and a single left wheel weight for each axle for each individual vehicle record. In discussions related to right and left weigh sensors, such sensors will be treated as single sensors even though in some cases a system may actually have two right sensors and two left sensors.

Onsite calibrations are typically based upon the test vehicles' static axle weights (as opposed to individual right and left static wheel weights) as reference values for determining WIM error. Therefore, it is recommended that prior to running test trucks, a sampling of the traffic stream's Class 9 data be obtained and the right and left sensor calibration factors be adjusted such that the traffic stream's average right and left steer axle WIM weights will be approximately equal. For example, if a pre-calibration Class 9 traffic stream sampling for Lane #1 showed an Axle 1 Right Wheel average of 5.2 k and an Axle 1 Left Wheel average of 5.6k, the calibration factors for the system's Lane #1 would be adjusted as per the calculations displayed in Figure 64. These right and left sensor factors would then be equally increased or decreased based upon the WIM error as determined from test truck axle weight data. This procedure would apply to each lane being calibrated.

Figure 64. Procedure.  Pre calibration - right and left sensor balance. Onsite calibrations are typically based upon the test vehicles' static axle weights (as opposed to individual right and left static wheel weights) as reference values for determining WIM error. Therefore, it is recommended that prior to running test trucks, a sampling of the traffic stream's Class 9 data be obtained and the right and left sensor calibration factors be adjusted such that the traffic stream's average right and left steer axle WIM weights will be approximately equal. This figure provides an outline of the procedure and calculations to follow. The example uses the average Axle-1 weights, that is 5.2 kips for the right wheel and 5.6 kips for the left wheel, for a total axle weight of 10.8 kips. Therefore, the desired average weight for both wheels would be 5.4 kips, that is 0.2 kips or 4 percent more on the right wheel weight, and 0.2 kips or 4 percent less in left wheel weight.  Therefore the existing calibration factors of 3200 for the right sensor and 3500 for the left sensor are adjusted accordingly. That is the right sensor calibration factor is multiplied by 1.04 to become 3328, and the left sensor calibration factor is multiplied by 0.96 to become 3360.
Figure 64. Procedure. Pre calibration - right and left sensor balance.

Another key element in system calibration and calibration monitoring is the recognition that vehicle speed is a very important aspect of a system's proper calibration. ASTM E 1318 states, under Section 7.5.5.5, "Every vehicle interacts with the road surface differently at different speeds, but about the same at the same speed." Typically, the loaded Class 9 vehicles travel at approximately the same speeds as the unloaded Class 9 vehicles for a WIM site with all of the conditions listed below:

  • A significant volume of Class 9s.
  • Truck traffic that maintains a steady cruising speed.
  • A roadway grade of less than 0.5 percent.

Figure 65 displays a report for LANE #1 for the same seven-day Class 9 sample used for the report and graph displayed in Figure 62 and Figure 63.

Figure 65. Report. Distribution of Class 9 weights and axle spacings by speed for one lane, flat roadway grade. This figure shows a report of the distribution of average weights and spacings by speed, for a system's LANE #1seven-day sample of Class 9 vehicles. The figure highlights items to be checked when using this report. Item 1, is the consistency of the Axle 1's average right and left wheel weights, and maintenance of the balance between the two. For this sample the right and left weights are 5.7 and 5.6 respectively, that is only 0.1 k apart, which is acceptable. Any shift in this balance suggests that a sensor may be intermittently malfunctioning. The consistency of the standard deviation for Axle 1's average right and left wheel weights it to be checked as well. For this sample both average weights have a standard deviation of 0.4 k, which is acceptable.  Given good site and traffic conditions, these standard deviations should typically not exceed 0.5 k. Item 2, involves sites with favorable geometry and traffic conditions, and it is the consistency of the average Steer Axle and Gross Vehicle Weights throughout the speed ranges for which a significant number of the Class 9 vehicles are travelling. For this sample the average GVW for the "45.0 TO 49.9" speed distribution is approximately four percent higher than for the higher speed distributions. Item 3, is the reasonableness and consistency of the percentage of overweight vehicles in the sample. Even though there are no weigh stations in the immediate vicinity of this WIM site, it is very doubtful if 25.5 percent of the Class 9 vehicles would actually be cited for being overweight if statically weighed. Most vehicles passing through this site are "long haul" and will at some point have to go through a weigh station, so therefore the 25.5 percent of overweight vehicles in this report needs to be investigated. Item 4, is the reasonableness and consistency of the Tractor Tandem Axles average spacing and its standard deviation.  For most locations in the U.S., the Type 3S2 vehicle's average spacing should be 4.3 feet, as shown in this report.
Figure 65. Report. Distribution of Class 9 weights and axle spacings by speed for one lane, flat roadway grade.

When reviewing a report similar to the one displayed in Figure 65, the analyst should check the following (refer to the numbered blocks highlighted in Figure 65):

1. Consistency of the Axle 1's average right and left wheel weights, and maintenance of the balance between the two.

For this sample the right and left weights are only 0.1 k apart, which is acceptable. Although some WIM sites are exceptions and a site's variance in seasonal truck operational characteristics may come into play, the Class 9 average steer axle wheel weight should remain relatively consistent. A concurrent change in both weights suggests either calibration drift or a change in truck operational characteristics. Once the right and left average weights are brought into balance (no more than 0.2 k difference), they should remain balanced. Any shift in this balance suggests that a sensor may be intermittently malfunctioning.

1. Consistency of the standard deviation for Axle 1's average right and left wheel weights.

For this sample both average weights have a standard deviation of 0.4 k, which is acceptable. Given good site and traffic conditions, these standard deviations should typically not exceed 0.5 k. If either of these standard deviations starts to increase, it is an indication that the sensor may be malfunctioning on an intermittent or subtle basis.

2. For sites with ideal geometry and traffic conditions, consistency of the average Steer Axle and Gross Vehicle Weights throughout the speed ranges for which a significant number of the Class 9 vehicles are travelling.

For this sample the average GVW for the "45.0 TO 49.9" speed distribution is approximately four percent higher than for the higher speed distributions. Given that the sample comes from a rural interstate roadway with high-speed traffic, it could very well be that the calibration or validation test trucks were not run at speeds this low in deriving data for verifying or determining calibration factors. Regardless of site and traffic conditions, the Figure 65 report should be generated for a traffic stream sample immediately following an onsite calibration or validation using test trucks. For a system to be properly calibrated, the system's calibration factors should be based upon data from test trucks that were run throughout the entire operating range of a significant majority (at least 80 percent) of the truck traffic stream.

It is recognized that at many WIM sites a majority of the truck traffic stream travels at speeds well above the posted speed limit. It is not in any way recommended that an agency run test trucks exceeding posted speed limits in the absence of jurisdictional approval. However, it would certainly be beneficial if an agency could obtain proper approval for running test trucks at speeds consistent with the truck traffic stream flow.

3. Reasonableness and consistency of the percentage of overweight vehicles in the sample.

Even though there are no weigh stations in the immediate vicinity of this WIM site, it is very doubtful if 25.5 percent of the Class 9 vehicles would actually be cited for being overweight if statically weighed. Most vehicles passing through this site are "long haul" and will at some point have to go through a weigh station. There are at least a couple reasons why a WIM system, even if well calibrated, might flag a relatively high percentage of its trucks as being in violation of weight limits (assuming the system is programmed to use the actual weight violation parameters in-lieu of allowing some tolerance):

  • For the Class 9 Type 3S2 to achieve maximum allowable GVW (typically 80 k) both tandems must be loaded as closely as possible to the maximum allowable tandem weight (typically 34 k). As such, if the WIM reads just a slight percent high for any of a tandem's wheels the vehicle will be flagged as overweight. Although a WIM system's slight overestimates and underestimates of static weights may be well within accuracy tolerances and average out overall in terms of reported weight, weight violation flags do not average out, and a WIM system's reporting of weight violation percentage based upon a sample's dynamic weight readings may be somewhat higher than if the same sample were weighed statically.
  • To get a better ride on the open road, it is quite common for a trucker to move a vehicle's king pin setting back a bit to shift weight from the steer axle to the tractor's drive tandem following an exit from a weigh station. This revised king pin setting could well result in the drive tandem's being overweight even if statically reweighed. It is also somewhat common for a trucker to move the semi-trailer's slider tandem, which shifts weight from one tandem to the other. Such king pin setting and trailer tandem slider settings are readjusted before entering the next weigh station, but at the time these vehicles pass through a WIM site they may very well actually be in violation of weight limits.

4. Reasonableness and consistency of the Tractor Tandem Axles average spacing and its standard deviation.

For most locations in the U.S., the Type 3S2 vehicle's average spacing should be 4.3 feet. This would also apply if the sample included the Class 9 Type 32 (although the power unit is not technically a "tractor"). This average (or a tight standard deviation) would not apply if the sample includes Class 9 Type 2S3 vehicles. For locations that have Canadian truck traffic or specialty truck types, consideration would need to be given to observed axle spacing configurations and the percentage of such atypical vehicles.

Figure 66 displays the same report as that in Figure 65 but for a seven-day Class 9 sample from LANE #4 of a site that has a long two percent uphill grade approach in that lane's direction. As is obvious from the vehicle gross average weights column, such weights drop drastically for the speed ranges above 50 mi/h. This is due to the fact that the heavier the vehicle the less ability the vehicle has to maintain a cruising speed. For the fully loaded vehicles, with exception of those with the most powerful engines, their speed has dropped considerably by the time they reach the WIM site.

Figure 66. Report. Distribution of Class 9 weights and axle spacings by speed for one lane, uphill grade. This figure shows a report of the distribution of average weights and spacings by speed, for a system's LANE #4 seven-day sample of Class 9 vehicles. This report is for a site that has a long two percent uphill grade approach in that lane's direction. From the vehicle gross average weights column, weights drop drastically for the speed ranges above 50 miles per hour. This is due to the fact that the heavier the vehicle the less ability the vehicle has to maintain a cruising speed. For the fully loaded vehicles, with exception of those with the most powerful engines, their speed has dropped considerably by the time they reach the WIM site.
Figure 66. Report. Distribution of Class 9 weights and axle spacings by speed for one lane, uphill grade.

Installing WIM systems on roadways with grades greater than 0.5 percent should be avoided for several reasons listed below.

  • Due to the lower speeds of the loaded trucks, the onsite calibration with test trucks must encompass a larger range of speeds to properly calibrate the system.
  • One or both of the test trucks may not be able to attain the higher speeds necessary for proper calibration.
  • When a truck is passing through the site under heavy throttle, weight is transferred from the steer axle to the drive axle(s). Although the WIM may accurately determine the dynamic wheel weights, they are not accurate estimates of the truck's static wheel weights.
  • The empty trucks travelling at the higher speeds may be passing the slower trucks through the site.
  • Since the loaded and empty trucks travel at different speeds, the calibration monitoring is more difficult to perform.
    • This report should be generated for a seven-day traffic stream sample immediately following a legitimate onsite calibration or validation with test trucks to use as a reference for subsequent comparisons.

Figure 67 displays a report for a seven-day sample for the same site, time frame, and lane as the Figure 66 report, but this report is for Class 11 vehicles. The only difference in the two report formats is that instead of providing statistics on Class 9 axle spacings, statistics are provided for the Class 11 overall vehicle length and wheelbase (Axles 1 through 5). For Class 11 Type 2S12s, the overall vehicle length typically exceeds the wheelbase by approximately six feet, so, in comparing the sample's average vehicle length and average wheelbase, the difference should be approximately six feet. This report was designed for use by California, which calibrates its systems for overall vehicle lengths and has a significant number of Class 11 vehicles at many of its WIM sites. It is recognized that many states' WIM sites have very few Class 11 vehicles and as such would have no need to generate reports for Class 11 samples.

Figure 67. Report. Distribution of Class 11 weights, vehicle length, and wheelbase by speed for one lane. This figure shows a report of the distribution of average weights and spacings by speed, for a system's LANE #4 seven-day sample of Class 11 vehicles. For Class 11 Type 2S12s, the overall vehicle length typically exceeds the wheelbase by approximately six feet, so, in comparing the sample's average vehicle length and average wheelbase, the difference should be approximately six feet.
Figure 67. Report. Distribution of Class 11 weights, vehicle length, and wheelbase by speed for one lane.

SECTION 4 discussed the use of Excel by the LTPP contractor for performing extensive WIM data analyses. This Excel workbook was expanded to generate some of the statistical information contained in the CTWIM WIMSys reports for use in calibration monitoring. In that an agency's WIM data analyst may find it easier and/or more practical to use a spreadsheet or database program for performing calibration monitoring than using the CTWIM WIMSys application, portions of the Excel workbook used for the LTPP study are described in the following examples. For any data analyst desiring to create spreadsheets with the calibration monitoring features displayed in Figure 68 through Figure 72, Excel ASCII Import workbooks and documentation are provided online at www.QualityWIM.com.

For most of the LTPP study sites a seven-day sample is used. For a few sites with low truck volumes a 14-day sample is used. As previously noted, for the calibration monitoring to be meaningful only data that has passed QC checks for days which have typical truck traffic should be included in the samples. The workbook that is used for the following examples is for one lane (the LTPP test section lane) and as such does not provide for user input of other lanes. The workbooks which are provided online at www.QualityWIM.com allow the user to enter a specific lane number, in addition to the vehicle class, when generating the tables and graphs.

Also, regardless of what type of traffic stream sampling is performed and what statistics are generated for calibration monitoring, it is imperative to perform a minimum seven-day sampling immediately following a system's onsite calibration or validation using test trucks, and to generate the set of statistics to be used as a reference set for comparison with subsequent sampling statistics.

Figure 68 displays the entire worksheet, which includes calibration monitoring tables and a graph, as well as other tables useful for the monitoring of weigh sensor performance. The Classes listed in these tables are based upon a scheme whereby vehicles with five or more axles are classified as listed below. Note that these classes are utilized solely for the purpose of performing analyses using this worksheet. They are not intended to conform to schemes used to classify vehicles in compliance with the Traffic Monitoring Guide requirements for general data submission. The analyst will need to perform post-processing of the downloaded WIM data to generate the following classes by specific vehicle configuration type.

  • CLASS 9: Type 3S2
  • CLASS 10: Type 3S3
  • CLASS 11: Type 2S12
  • CLASS 12: Type 3S12
  • CLASS 14: Type 32

Figure 68. Screen shot. "Tables" Worksheet. This figure is a snapshot of an entire worksheet, which includes calibration monitoring tables and a graph, as well as other tables useful for the monitoring of weigh sensor performance. The Classes listed in these tables are based upon a scheme whereby vehicles with five or more axles are classified as Class 9 Type 3S2, Class 10 Type 3S3, Class 11 Type 2S12,	Class 12 Type 3S12, and Class 14 Type 32. Note that these classes are utilized solely for performing analyses using this worksheet. They are not intended to conform to schemes used to classify vehicles in compliance with the Traffic Monitoring Guide requirements for general data submission. The analyst will need to perform post-processing of the downloaded WIM data to generate the following classes by specific vehicle configuration type.
Figure 68. Screen shot. "Tables" Worksheet.

The portions of this worksheet useful for calibration monitoring include those described below.

Figure 69 displays average weights and their standard deviations for each listed vehicle class's steer axle wheel weights, steer axle weight, and GVW. Analyses of these statistics have been discussed previously.

Figure 69. Screen shot. Weight statistics for calibration monitoring and tracking. This figure displays a table with average weights and their standard deviations for vehicle Class 9 through Class 14, steer axle (Axle-1) wheel weights, steer axle (Axle-1) weight, and GVW. These statistics are used for calibration monitoring and tracking.
Figure 69. Screen shot. Weight statistics for calibration monitoring and tracking.

Figure 70 displays statistics for each listed class as discussed below.

  • OVERWEIGHT- Analysis of this statistic has been discussed previously.
  • INVALID WEIGHT- More pertinent to sensor performance than calibration monitoring.
  • AX1 WHEEL <3.0 - The CTWIM WIMSys application filters out any record for which the vehicle's right or left steer axle weight is less than 3.0 k. This spreadsheet does not filter out such records, but displays how many of the right and left steer axle weights are less than 3.0 k. To use the sample for calibration monitoring purposes, these should be a very low percentage. If the percentage increases for either right or left weight, it is an indication of either intermittent sensor malfunction or an increased number of truck wheels not fully hitting the sensor.
  • CLASS 9 AXLE 2-3 SPACE - Analysis of this statistic has been discussed previously.
  • CLASS 11 - The correlation between the Class 11's wheelbase and overall vehicle length has been discussed previously.
  • CLASS 14 - For those sites with a significant number of the Type 32 truck trailer (a Class 9 using Traffic Monitoring Guide criteria), this vehicle's overall length is typically approximately six feet longer than the Axle 1 to Axle 5 wheelbase.

Figure 70. Screen shot. Additional statistics for calibration monitoring and tracking. This figure displays a table with statistics for Class 9 through 14 vehicles, including the count and percentage of overweight vehicles, count and percentage of vehicles with invalid weight flags, count and percentage of the right and left steer axle weights that are less than 3 kips, the average and standard deviation of the Class 9 vehicles Axle 2-3 spacing, the average wheelbase and average overall vehicle length for Class 11 and Class 14 vehicles.
Figure 70. Screen shot. Additional statistics for calibration monitoring and tracking.

Figure 71 displays the GVW distribution plot for the vehicle class entered into Cell B29 by the analyst. Also plotted are the average speed and the number of Invalid Measurement weights in conjunction with the GVW plot.

Figure 71. Screen shot. GVW distribution plot. This figure displays a GVW distribution plot for the vehicle class selected by the analyst, in this case Class 9. The X-axis is the GVW in kips, and the Y-axis is the vehicle counts.  A secondary Y-axis is used on the right with the average speed in miles per hour.  Also plotted are the number of Invalid Measurement weights in conjunction with the GVW plot.
Figure 71. Screen shot. GVW distribution plot.

Figure 72 displays weights versus speeds in two different ways for the class of vehicle entered by the analyst into Cell B29 (see Figure 71). As discussed previously, for a site with suitable roadway geometry and traffic conditions, the empty and loaded trucks typically travel at approximately the same speeds. For "Speed Range" distributions that have a significant number of samples the "Avg GVW" should be reasonably consistent among those distributions, and for "GVW Range" distributions that have a significant number of samples the "Avg Speed" should be reasonably consistent among those distributions.

Figure 72. Screen shot. Weights versus speed statistics. This figure displays weights versus speeds in two different ways for a seven-day Class 9 vehicles sample, as selected by the analyst using this spreadsheet. This site's roadway geometry and traffic conditions are favorable, therefore the table shows that the empty and loaded trucks travel at approximately the same speeds.
Figure 72. Screen shot. Weights versus speed statistics.

5.2. MONITORING TRUCK TRAFFIC STREAM STATISTICS OVER TIME

Up to this point this Section's examples and discussion have focused on generating and analyzing traffic stream truck traffic statistics for individual samples. It is recommended that this be performed routinely on a monthly basis, as well as any time calibration factors are revised for a particular system, or a system undergoes equipment or software modifications. The following examples and discussion will focus on monitoring and tracking these statistics over time to accomplish the items listed below:

  • Identifying true calibration drift as opposed to seasonal variations in a site's truck operational characteristics.
  • Verifying the effects of calibration factor adjustments on traffic stream weights.
  • Identifying degradation of a weigh sensor's performance.

Figure 73 displays the monthly GVW distribution plots over a one-year time frame using the seven-day Class 9 traffic stream sample sets used for the Figure 68 through Figure 72 statistics screen shots. This site is located on a long haul interstate route with high truck volumes. As is obvious from the plots, there are variations in the volumes but the loading characteristics are extremely consistent. It is noted that the GVW graph uses 2.5 k distributions, which identifies weight distribution variations to a much finer degree than the more typical graphs using 5.0 k distributions.

Figure 73. Graph. Traffic stream Class 9 GVW distribution plots for 12 consecutive months, long haul high volume. This figure displays the monthly GVW distribution plots over a one-year time frame using seven-day Class 9 traffic stream sample sets for a site that is located on a long haul interstate route with high truck volumes. The X-axis is the gross weight in 2.5-kip ranges, and the Y-axis is the vehicle counts. The plots show that even though there are variations in the volumes, the loading characteristics are extremely consistent. The peak for the loaded trucks distributions occurs around 77.5 kips.
Figure 73. Graph. Traffic stream Class 9 GVW distribution plots for 12 consecutive months, long haul high volume.


Figure 74 displays the monthly steer axle weight distributions for the same sample as that used for the GVW plots displayed in Figure 73. The weight of a tractor-semitrailer's steer axle increases only slightly as the loading of the trailer(s) is increased. As such, monitoring of the steer axle is an excellent tool for identifying calibration problems or subtle system operational problems. Although tracking of steer axle weight distributions over time may of benefit, the more routine checks such as those described in Section 5.1 (e.g.: discussions regarding Figure 52 and Figure 65) are of much greater importance.

Figure 74. Graph. Traffic stream Class 9 Axle 1 weight distribution plots for 12 consecutive months. This figure displays the monthly Axle 1 weight distribution plots over a one-year time frame using seven-day Class 9 traffic stream sample sets for a site that is located on a long haul interstate route with high truck volumes. The X-axis is the Axle 1 weight in 0.2-kip ranges, and the Y-axis is the vehicle counts. The plots show that even though there are variations in the volumes, the loading characteristics are extremely consistent. The peak for the loaded trucks distributions occurs around 11.2 kips.
Figure 74. Graph. Traffic stream Class 9 Axle 1 weight distribution plots for 12 consecutive months.


Figure 75 displays the GVW distributions for a site with low truck volumes and a high percentage of empty trucks for the spring season months of three consecutive years. After tracking traffic stream GVW plots beyond the first year, seasonal comparisons can start to be made. For this example, there are variations in volumes but it is evident there is little, if any, calibration drift taking place.

Figure 75. Graph. Class 9 GVW distribution plots for spring season over three-year period, local traffic. This figure displays the GVW distributions for a site with low truck volumes and a high percentage of empty trucks for the spring season months of three consecutive years. The X-axis is the gross weight in 2.5-kip ranges, and the Y-axis is the vehicle counts. The peak for the empty trucks distributions occurs between 35 and 40 kips. After tracking traffic stream GVW plots beyond the first year, seasonal comparisons can start to be made. For this example, there are variations in volumes but it is evident there is little, if any, calibration drift taking place.
Figure 75. Graph. Class 9 GVW distribution plots for spring season over three-year period, local traffic.


Figure 76 displays the GVW distribution plots over a one-year time frame using 14-day Class 9 traffic stream sample sets. This site is located on a rural route with very low truck volumes and experiences extreme snow and ice conditions. Although there are definable empty and loaded distributions, they are not nearly as pronounced or consistent as in the long haul high truck volume site displayed in Figure 73. Sites such as this are more difficult to monitor for calibration in that the truck operating characteristics are not consistent.

Figure 76. Graph. GVW distribution plots for 12 consecutive months, low volume. This figure displays the GVW distribution plots over a one-year time frame using 14-day Class 9 traffic stream sample sets for a site. The X-axis is the gross weight in 2.5-kip ranges, and the Y-axis is the vehicle counts. The peak for the empty trucks distributions occurs between 35 and 40 kips, while the peak for the loaded trucks distributions occurs between 77.5 and 82.5 kips. This site is located on a rural route with very low truck volumes and experiences extreme snow and ice conditions. Although there are definable empty and loaded distributions, they are not very pronounced or consistent. Sites such as this one are more difficult to monitor for calibration in that the truck operating characteristics are not consistent.
Figure 76. Graph. GVW distribution plots for 12 consecutive months, low volume.

5.3. EFFECTS OF CALIBRATION FACTOR ADJUSTMENTS ON TRUCK TRAFFIC STREAM DATA

Figure 77 displays the monthly Class 9 traffic stream GVW distribution plots over a one-year time frame, but this system had its calibration factors decreased by four percent in late June. The effects are dramatic, particularly on the loaded peak distribution. It is noted that the drop in weights starting in July was initially attributed to calibration drift. This example emphasizes the importance of considering any weight calibration factor adjustments when performing calibration monitoring.

Figure 77. Graph. Class 9 GVW distribution plots for 12 consecutive months, weight shift. This figure displays the monthly Class 9 traffic stream GVW distribution plots over a one-year time frame for a site. The X-axis is the gross weight in 2.5-kip ranges, and the Y-axis is the vehicle counts. The peak for the empty trucks distributions occurs between 30 and 37.5 kips, while the less pronounced peak for the loaded trucks distributions occurs between 72.5 and 85 kips. This system had its calibration factors decreased by four percent in late June. The effects are dramatic, particularly on the loaded peak distribution that shifted from 77.5 to 85 in May and June, to 72.5 to 80 afterwards. It is noted that the drop in weights starting in July was initially attributed to calibration drift. This example emphasizes the importance of considering any weight calibration factor adjustments when performing calibration monitoring.
Figure 77. Graph. Class 9 GVW distribution plots for 12 consecutive months, weight shift.

Procedures for performing onsite calibrations and validations using test trucks are not within the scope of this Manual. However, it is of benefit to the data analyst to be able to analyze the test truck data for the purpose of comparing such data with the traffic stream data, and determining the effect of calibration factor adjustments on the traffic stream weights. If the analyst must make the assumption that the calibration was performed correctly, the best tool for use by the analyst is a graph displaying the test trucks' GVW WIM error by speed plots. WIM error is determined by comparing a test truck's static weight with its corresponding WIM reported dynamic weight. For example, if a test truck's static GVW is 75.0 k and, for a particular run, the WIM reports a GVW of 76.0 k, the GVW WIM error for that truck's run is +1.3 percent, as calculated from the following equation:

WIM Error = 100*[(GVWWIM - GVWstatic)/ GVWstatic]

In addition, it must be remembered that system calibration and its monitoring is performed on an individual lane basis. The Excel workbook used to generate the test trucks' GVW WIM error by speed plots in the following examples is available online at www.QualityWIM.com, along with the corresponding detailed documentation.

Figure 78 actually displays two individual graphs that have been sized and aligned to exhibit the importance of considering speed when performing calibrations, or when analyzing the effect of calibration factor adjustments on the WIM weights for the truck traffic stream. The top graph displays the percent of WIM GVW error for each run for two test trucks. The solid symbols ("PRE VAL") are for the WIM GVW errors using the system's weight calibration factors in effect at the start of the first set of test truck runs and the non-solid symbols ("POST VAL") are for the WIM GVW errors using the system's weight calibration factors as adjusted based upon the PRE VAL test truck data. The amount of adjustment for each of four of the system's five calibration speed points, in percent, is displayed immediately above the corresponding speed.

As is evident from the plots, it would appear that for the higher speeds, either the desired effect of the adjustment was not achieved or a mistake was made in either calculating the adjustment or entering the revised factor for the 60 mi/h speed point. The calibration factor for the 70 mi/h speed point probably should have also been increased. The lower graph displays the site's truck traffic stream speeds in comparison to the speeds at which WIM error data was obtained by the calibration test trucks. Although the posted speed limit in effect at the site probably prevented the test trucks from making runs at higher speeds, it is evident in comparing the two graphs that a majority of the runs made by the test trucks were meaningless. In effect, the calibration factor adjustments will probably have little noticeable effect on the WIM weights outputs for the truck traffic stream.

Figure 78. Graphs. Calibration test truck GVW WIM error versus speed plots, and truck traffic stream speeds versus calibration test truck speeds plots. This figure displays two individual graphs that have been sized and aligned to exhibit the importance of considering speed when performing calibrations, or when analyzing the effect of calibration factor adjustments on the WIM weights for the truck traffic stream. The top graph displays the percent of WIM GVW error for each run for two test trucks. The X-axis is the speed in miles per hour, and the Y-axis is weight error in percent. The graph shows the WIM GVW errors using the system's weight calibration factors in effect at the start of the first set of test truck runs and the WIM GVW errors using the system's weight calibration factors as adjusted based upon the test truck data. The amount of adjustment for each of four of the system's five calibration speed points, in percent, is displayed immediately above the corresponding speed. The lower graph displays the site's truck traffic stream speeds in comparison to the speeds at which WIM error data was obtained by the calibration test trucks. The X-axis is the speed in miles per hour, and the Y-axis is the percent count. Although the posted speed limit in effect at the site probably prevented the test trucks from making runs at higher speeds, it is evident in comparing the two graphs that the majority of the vehicles are traveling at speeds higher than the speeds used for the calibration with test trucks.  In effect, the calibration factor adjustments will probably have little noticeable effect on the WIM weights outputs for the truck traffic stream.
Figure 78. Graphs. Calibration test truck GVW WIM error versus speed plots, and truck traffic stream speeds versus calibration test truck speeds plots.

Figure 79 displays, for the system calibrated shown in Figure 78, the Class 9 traffic stream GVW distributions for samples from the two months preceding and the two months following the calibration factor adjustments. Although the "Oct" empty truck distribution is somewhat random, it is evident that the factor adjustments had no noticeable effect on the traffic stream WIM weights.

Figure 79. Graph. Class 9 traffic stream GVW distribution plots before and after calibration factor adjustments. This figure shows the Class 9 traffic stream GVW distributions for samples for two months preceding (July and August 2007) and two months following (September and October 2007) calibration factor adjustment for a system. The X-axis is the gross weight in 2.5-kip ranges, and the Y-axis is the vehicle counts. The peaks for the empty trucks distributions are scattered between 27.5 and 40 kips, while the more consistent peaks for the loaded trucks distributions occur at 80 kips. Although the empty truck distribution for October is somewhat random, it is evident that the factor adjustments had no noticeable effect on the traffic stream WIM weights.
Figure 79. Graph. Class 9 traffic stream GVW distribution plots before and after calibration factor adjustments.

Another issue regarding calibrations utilizing test trucks that must be considered by the data analyst is that even when proper trucks are used and the calibration procedures are performed correctly, different trucks or pairs of trucks may get different results in terms of WIM error.

Figure 80 displays the GVW distributions for the monthly samples over a 15-month period for a site during which time no calibration factor adjustments were made. As is evident from the plots, the loaded distribution peak and to some extent the empty trucks peak remained extremely consistent over the entire period indicating that no calibration drift occurred.

Figure 80. Graph. Class 9 traffic stream GVW distribution plots over period with no calibration factor changes. This figure displays the GVW distributions for the monthly Class 9 (seven-day) samples over a 15-month period for a site during which time no calibration factor adjustments were made. The X-axis is the gross weight in 2.5-kip ranges, and the Y-axis is the vehicle counts. The peak for the empty trucks distributions occurs between 30 and 37.5 kips, while the peak for the loaded trucks distributions occurs at 77.5 kips. The plots indicate that the loaded distribution peak and to some extent the empty trucks peak remained extremely consistent over the entire period indicating that no calibration drift occurred.
Figure 80. Graph. Class 9 traffic stream GVW distribution plots over period with no calibration factor changes.

Figure 81 displays the percent WIM GVW error plots for two different sets of test truck runs (two trucks each), 16 months apart, at the site displayed in Figure 80. The solid symbols ("JUN '06") are for the WIM GVW errors verifying the system's weight calibration factors in effect at the time. The non-solid symbols ("OCT '07") are for the WIM GVW errors using those same calibration factors, based upon the second set of test truck runs 16 months later. At the higher speeds there is a significant difference in the WIM error between the two sets of test truck runs even though the traffic stream data indicates that no calibration drift occurred during the time between the two sets of test truck runs.

Figure 81. Graph. Calibration test truck GVW WIM error versus speed plots. This graph displays the percent of WIM GVW error for each run for two test trucks. The X-axis is the speed in miles per hour, and the Y-axis is gross vehicle weight error in percent. The graph shows the percent WIM GVW error plots for runs 16 months apart. The runs in Jun of 2006 were done to verify the system's weight calibration factors in effect at the time. The runs in October of 2007 were done using those same calibration factors, based upon the second set of test truck runs 16 months later. At higher speeds there is a significant difference in the WIM error between the two sets of test truck runs; even though the traffic stream data indicates that no calibration drift occurred during the time between the two sets of test truck runs.
Figure 81. Graph. Calibration test truck GVW WIM error versus speed plots.

Figure 82 displays the percent of WIM GVW error for the initial set of runs for the "OCT '07" validation displayed in Figure 81, as well as the follow-up set of runs after calibration factor adjustments. The non-solid symbols ("PRE-VAL") are for the WIM GVW errors using the system's weight calibration factors that had been in effect for the preceding 16 months and the solid symbols ("POST-VAL") are for the WIM GVW errors using the system's weight calibration factors as adjusted based upon the PRE-VAL test truck data. The percentage of factor adjustment for each of the system's five calibration speed points is shown above the corresponding speed. As is evident from the plots, it would appear that the desired effects were attained, although as the speeds increase, the difference in WIM error between the two trucks also increases.

Figure 82. Graph. Calibration test truck GVW WIM error x speed plots, before and after factor adjustments. This graph displays the percent of WIM GVW error for each run for two test trucks. The X-axis is the speed in miles per hour, and the Y-axis is gross vehicle weight error in percent. This graph displays the percent of WIM GVW error for the initial set of runs for the validation a validation in October of 2007, as well as a follow-up set of runs after calibration factor adjustments. The plots indicate that the desired effects were attained, although as the speeds increase, the difference in WIM error between the two trucks also increases.
Figure 82. Graph. Calibration test truck GVW WIM error x speed plots, before and after factor adjustments.

From a test truck data standpoint this would be deemed a successful calibration. However, from the standpoint of monitoring the effects of calibration factors on the traffic stream's WIM weights it is like trying to hit a moving target, as evidenced by Figure 83.

Figure 83 displays the effects of three different sets of calibration factor adjustments, which were based upon test truck data, on the traffic stream WIM weights over a two-year period for the site displayed in Figure 80 through Figure 82. It would appear that in actuality the WIM system has maintained its calibration very well, whereas the WIM error based upon test truck data has been inconsistent for the initial calibration and three subsequent sets of validation/recalibrations. For the loaded trucks, it would appear that the WIM weights generated utilizing calibration factors based upon test truck data for the initial calibration and the October 2007 runs are too high. However, WIM weights generated utilizing calibration factors based upon test truck data for the June 2006 and April 2008 runs appear to be too low.

To anybody not paying attention to the various calibration factor changes it would appear that this system is not maintaining its calibration. In fact, it is being extremely consistent and is simply doing what it is being programmed to do. Perhaps at some point system accuracy might benefit from simply splitting the differences of the test truck data sets' WIM errors. One thing a graph such as Figure 83 illustrates is the excellent linearity of the system in that the traffic stream WIM weight outputs change in direct relationship to the changes in the calibration factors.

Figure 83. Graph. Effects of calibration factor adjustments on traffic stream WIM weights. This figure displays the GVW distributions for the Class 9 (seven-day) samples for a site, over a two-year period that involved three different sets of calibration factor adjustments. The X-axis is the gross weight in 2.5-kip ranges, and the Y-axis is the vehicle counts. The peak for the empty trucks distributions occurs between 32.5 and 35 kips, while the peaks for the loaded trucks distributions are scattered between 75 and 82.5 kips. For the loaded trucks, it would appear that the WIM weights generated utilizing calibration factors based upon test truck data for the initial calibration and the October 2007 runs are too high. However, WIM weights generated utilizing calibration factors based upon test truck data for the June 2006 and April 2008 runs appear to be too low.
Figure 83. Graph. Effects of calibration factor adjustments on traffic stream WIM weights.

Figure 84 displays an example of tracking the statistics from the monthly Class 9 traffic stream samples in conjunction with any hardware, software/firmware, or system settings (including calibration factors) that may have an effect on the system's output of weights. This tracking sheet is for the site displayed in Figure 80 through Figure 83. As this tracking sheet is filled out each month, the analyst can make various determinations in regard to a system's maintenance of calibration and the effects of system modifications, as described below.

Figure 84. Screen shot. Tracking of system modifications and monthly calibration monitoring statistics. This figure displays a screen shot of a spreadsheet for tracking the statistics from the monthly Class 9 traffic stream samples in conjunction with any hardware, software/firmware, or system settings (including calibration factors) that may have an effect on the system's output of weights. As this tracking sheet is filled out each month, the analyst can make various determinations in regard to a system's maintenance of calibration and the effects of system modifications.
Figure 84. Screen shot. Tracking of system modifications and monthly calibration monitoring statistics.

  • In June 2006, factors for both right and left sensors were decreased 4.0 percent based upon test truck data. Was the desired effect on weights achieved?
    • Yes, for the July 2006 sample, the average GVW dropped between four and five percent, and the average steer axle weight dropped between three and four percent.
  • For the 16 months following the June 2006 calibration:
    • Is the system exhibiting any calibration drift?
      • Although the average GVW drops gradually from 50.1 k to 46.4 k (seven percent) before starting to increase again, the loaded distribution peaks per the GVW distribution plots (Figure 80) remain quite steady. This would indicate the calibration is not drifting. Also, the fact that by the 2007 summer months these weights have returned to their 2006 summer weights indicates that the decrease in average weights is probably attributable to a seasonal change in truck operating characteristics.
    • Are the right and left weigh sensors in balance and exhibiting acceptable standard deviations?
      • With exception of the July 2007 sample, the right and left balances are ok; standard deviations are marginal, but there is no indication of sensor problems.
    • In January 2007, the scale sensor interface card was replaced. Did this replacement affect the weight output?
      • No, all weight statistics remained reasonably constant.
    • Is the Axle 2-3 spacing remaining constant at 4.3?
      • Yes.
    • Is the overweight percentage remaining constant?
      • Yes.
  • In October 2007, factor adjustments were made based upon test truck data. Was the desired effect on weights achieved?
    • Yes, for the October 2007 sample, the average GVW increased between four and five percent, and the average steer axle weight between five and six percent.
  • For the months following the October 2007 calibration, is the system exhibiting any calibration drift?
    • The GVW is increasing. However, the increasing weight output of only the right weigh sensor and corresponding increase in its standard deviation, in conjunction with increasing "Invalid" and "Unequal Detection" flag percentages, indicate a sensor problem, not a calibration drift problem.
  • In February 2008, balancing of right and left weight outputs was attempted by lowering right sensor's calibration factors. Was the desired effect on the weights achieved?
    • Yes, for the March 2008 sample, the right weight output is back to where it was following the October 2007 calibration.
    Note that this action is only a temporary measure to make data as accurate as possible pending resolving the right sensor problem.
  • In April 2008, firmware was upgraded. Did this upgrade affect the weight output?
    • No, all weight statistics remained reasonably constant.
  • In April 2008, there was onsite repair work on weigh sensors, a firmware upgrade, and adjustment of calibration factors from the office based upon a small traffic stream sample. Are the WIM weights where they should be in readiness for a planned onsite validation using test trucks?
    • No, a five-day sample indicates the following:
      • Although the Axle 1 weight is consistent with that following the October 2007 calibration, the GVW is almost 10 percent higher.
      • The right and left weights are slightly out of balance.
    • Calibration factors were adjusted from the office again.
  • In April 2008, there were factor adjustments based upon test truck data. Was the desired effect on weights achieved?
    • In some respects, yes. Based upon the May 2008 sample, the loaded peak indicates lower weight readings, although it is back to where it was following the June 2006 calibration (refer to the GVW distribution plots displayed in Figure 82). It is also noted that the weight statistics are now very close to those immediately following the June 2006 calibration.

As an example from another site, Figure 85 displays the GVW distributions for the monthly samples over an 11-month period. Validations with test trucks were performed in August 2007, with no calibration factor adjustments. In March 2008, calibration factor increases were made which would affect only the weights of the very low percentage of slower moving trucks. As is evident from both the loaded and empty truck distribution peaks, this system is reporting WIM weights that are too high. The empty peaks are consistently at the "35.0-37.5" k distribution instead of "30.0-32.5" or "32.5-35.0" as is typical. The loaded peaks, although moving around a bit, are at times in excess of the maximum GVW limit of 80 k. Why is this problem not being corrected by running test trucks? Again, the answer is speed.

Figure 85. Graph. Class 9 GVW distribution plots, empty and loaded peaks too heavy. This figure displays the monthly Class 9 traffic stream GVW distribution plots over an 11- month time frame for a site. The X-axis is the gross weight in 2.5-kip ranges, and the Y-axis is the vehicle counts. The peak for the empty trucks distributions occurs between 35 and 37.5 kips, while the peaks for the loaded trucks distributions are occurs between 77.5 and 82.5 kips. It is evident from both the loaded and empty truck distribution peaks, that this system is reporting WIM weights that are too high.  The empty peaks are consistently at the "35.0-37.5" k distribution instead of "30.0-32.5" or "32.5-35.0" as is typical. The loaded peaks, although moving around a bit, are at times in excess of the maximum GVW limit of 80 k. Even though calibrations with test trucks were performed during this time frame, the system is still reporting weights too high.
Figure 85. Graph. Class 9 GVW distribution plots, empty and loaded peaks too heavy.

Figure 86, like Figure 78, displays two individual graphs that have been sized and aligned to exhibit the importance of considering speed when performing calibrations, or when analyzing the effect of calibration factor adjustments on the WIM weights for the truck traffic stream. However, this example portrays a system that really has not been calibrated even though time and resources were expended to go through the motions of performing a validation/calibration using test trucks.

The top graph displays the percent of WIM GVW error for each run for the two test trucks. The solid symbols ("PRE-VAL") are for the WIM GVW errors using the system's weight calibration factors in effect at the start of the first set of test truck runs. The non-solid symbols ("POST-VAL") are for the WIM GVW errors using the system's weight calibration factors as adjusted based upon the PRE-VAL test truck data. The percentage of factor adjustment for each of the system's five calibration speed points is displayed immediately above the corresponding speed. As is evident from the plots, it would appear that the desired effects were attained even though there was an obvious problem with the PRE-VAL Truck 2 data. The WIM error plots follow the "0%" error axis for the 41 mi/h to 57 mi/h speed range. The problem is that very few traffic stream trucks are traveling within this speed range as evidenced by the lower graph. Figure 87 exhibits additional rationale for the statement that the system "…really has not been calibrated."

Figure 87 displays weight by speed range statistics for a seven-day Class 9 sample from this site using a portion of the Excel table discussed previously in regard to Figure 72. This table indicates that the range of speeds traveled by the calibration test trucks cover only five percent of the speed range traveled by the Class 9 traffic stream (which, per the lower graph in Figure 86, corresponds with all of the truck traffic stream speeds). This table also indicates that the average steer axle weights and average GVW for 77 percent of the Class 9s are considerably higher than that for the very small sample within the speed range covered by the calibration test truck data. This is probably the reason that the Class 9 traffic stream GVW distributions displayed in Figure 85 suggest that the system's weight readings are too high. The system has simply not been calibrated (or validated) for speeds above 55 mi/h.

Figure 86. Graphs. Calibration test truck GVW WIM error x speed plots and truck traffic stream speeds versus calibration test truck speeds plots, ineffective calibration. This figure displays two individual graphs that have been sized and aligned to exhibit the importance of considering speed when performing calibrations, or when analyzing the effect of calibration factor adjustments on the WIM weights for the truck traffic stream. This example portrays a system that really has not been calibrated even though time and resources were expended to go through the motions of performing a validation/calibration using test trucks. The top graph displays the percent of WIM GVW error for each run for the two test trucks. The X-axis is the speed in miles per hour, and the Y-axis is the weight error in percent.  The data shows WIM GVW errors using the system's weight calibration factors in effect at the start of the first set of test truck runs and the WIM GVW errors using the system's weight calibration factors as adjusted based upon the first run of test trucks. The percentage of factor adjustment for each of the system's five calibration speed points is displayed immediately above the corresponding speed.  As is evident from the plots, it would appear that the desired effects were attained even though there was an obvious problem with the first run truck #2 data. The WIM error plots follow the zero percent error axis for the 41 to 57 mile per hour speed range. The problem is that very few traffic stream trucks are traveling within this speed range as evidenced by the lower graph.
Figure 86. Graphs. Calibration test truck GVW WIM error x speed plots and truck traffic stream speeds versus calibration test truck speeds plots, ineffective calibration.

Figure 87. Screen shot. Weights versus speed statistics, ineffective calibration. This figure displays weight by speed range statistics for a seven-day Class 9 sample using a portion of an Excel table. This table indicates that the range of speeds traveled by the calibration test trucks cover only five percent of the speed range traveled by the Class 9 traffic stream. This table also indicates that the average steer axle weights and average GVW for 77 percent of the Class 9s are considerably higher than that for the very small sample within the speed range covered by the calibration test truck data. The system has simply not been calibrated (or validated) for speeds above 55 mi/h.
Figure 87. Screen shot. Weights versus speed statistics, ineffective calibration.

5.4. ADJUSTMENT OF CALIBRATION FACTORS BASED UPON TRUCK TRAFFIC STREAM DATA

This section has provided recommended procedures and methods of analyses that can be performed by the Office Data Analyst to monitor a WIM system's calibration. A recap of problems that may become apparent to the analyst in performing calibration monitoring, as well as options available to the analyst to improve the system's accuracy will be provided. However, in that for certain situations the adjusting of calibration factors based upon analyses of traffic stream data instead of only test truck data will be offered as an option, the appropriateness and validity of such factor adjustments need to be addressed first. There are several reasons that may prompt the analyst to adjust calibration factors, including the following:

  • Balancing weight outputs of right and left sensors.
    • If the analyst uses proper procedures to modify calibration factors for the sole purpose of balancing the right and left sensor weight outputs, and such modifications do not affect any increase or decrease in axle weights, it should not be necessary to validate calibration by use of test truck data. However, verification that steer axle weights and GVW have not changed must be conducted by subsequent sampling and data analysis of the traffic stream.
  • Maintaining accuracy pending test truck validation/recalibration.
    • In order to continue collecting accurate data it may be beneficial to modify calibration factors based upon traffic stream data as an interim measure until such time that onsite validation and/or recalibration by use of test trucks can be performed to address one of the following:
      • The analyst can confirm that calibration drift is occurring.
      • A weigh sensor has been replaced or repaired.
      • System software/firmware has been modified or an electronic component repaired or replaced.

    If the test truck data indicates that the interim calibration factors resulted in data conforming to accuracy requirements such data may be disseminated. If the test truck data indicates that the interim factors did not result in data conforming to accuracy requirements, such data should be purged or its use limited.

  • Inconsistent test truck data.
    • As displayed in Figure 81, even testing by use of proper procedures using test trucks that meet testing requirements may result in test truck data varying by five percent or more in terms of determining WIM error. Also, as displayed in Figure 83, such differences in test truck data, particularly over a period of time, may make it apparent to the analyst that the data would probably be more accurate if the differences in the test truck data were averaged out in order to calculate calibration factor adjustments.
    • In the absence of evidence that test truck data is invalid, any determination of calibration factors based upon considerations other than the most current test truck data is not "truth in data". However, analyses of test truck data to determine what factors will result in a system's best estimates of static weights are much more of an art than a science. The extent to which the analyst is allowed to utilize subjective procedures in determining calibration factor adjustments is a policy decision. It is also noted that a site must have somewhat consistent (and thereby predictable) truck operating characteristics for an analyst to consider "trusting" traffic stream data statistics in questioning the reliability of test truck data.
  • Ineffective or useless test truck data.
    • Figure 86 and Figure 87 display examples of a test truck calibration that was ineffective due to the fact that the test truck speeds covered only a very small percentage of the speeds traveled by the truck traffic stream. The only way to obtain test truck data that would be useful in properly calibrating the system used for this example would be to run the test trucks at speeds up to at least 65 mi/h, which would be in violation of the 55 mi/h posted speed limit. This, obviously, cannot be recommended.
    • However, it is suggested that for such a site, the owner agency discuss the situation with both its legal department and the appropriate enforcement agency to determine if there is a possible solution. For example, the use of marked pilot and/or shadow vehicles for the trucks or some type of signing on the trucks might be deemed an adequate procedure to permit the test truck to run at the same speeds as the truck traffic stream.
    • In the absence of having test truck data to properly determine calibration factors, the agency has two choices, described below.
      1. Accept the fact that the system is not calibrated and acknowledge such when disseminating data.
      2. Subject to a site's having somewhat consistent truck operating characteristics, adjust the calibration factors to provide weights consistent with predictable weights over the range of speeds traveled by the truck traffic stream. It is acknowledged that this is not "truth in data", but neither is weight data based upon calibration factors that are not based upon test truck data.

5.5. RESOLVING ACCURACY PROBLEMS IDENTIFIED BY MONITORING OF TRUCK TRAFFIC STREAM

Typical calibration monitoring problems and options for improving a system's accuracy include those described below.

5.5.1. Gross Weight Distribution

If distributions appear to be unreasonable and/or inconsistent, continue analyses to determine if it is potentially due to one of the items listed below.

  • Change in average weight outputs.
    • Either the right or left Axle 1.
    • Both right and left Axle 1.
  • Calibration factors changed.
  • Calibration factors based upon inconsistent test truck results.
    • Consider adjusting calibration factors using combination of traffic stream data and review of test truck data from all calibration/validation sessions.
  • Calibration factors for entire range of speeds traveled by truck traffic stream not based upon valid test truck data.
    • Consider adjusting calibration factors for each speed point based upon traffic stream data.
  • Calibration drift.
    • If confirmed to be probable, adjust calibration factors based upon traffic stream data as interim measure until such time calibration can be checked by use of test trucks.
  • Seasonal change in truck operating characteristics.
    • Need minimum one year of tracking distributions.
5.5.2. Individual Sensor Weight Outputs
  • If Axle 1 weights and GVWs appear to be accurate but Axle 1 right and Axle 1 left average weights are different by more than 0.2 k, adjust both right and left sensor's factors to bring right and left average weights into balance (see Figure 88). This should have no effect on either the Axle 1 weight or the GVW.
  • If Axle 1 weight and GVW weight have both increased or decreased, and the entire increase or decrease is attributable to a weight output change in either the right or left sensor, adjust the factors for only the sensor for which the weights have changed (see Figure 88). The percentage change in GVW output should be approximately half of the percentage of change in the sensor's factor.
    • Note that regardless of whether the sensor's weight output change is attributable to subtle malfunction or actual calibration drift (which would be unusual for just one of the two sensors), calibration should be verified by test trucks as soon as possible.
  • If a significant change is noted in either the right or left Axle 1 average weight:
    • Check calibration factor.
    • If calibration factor is correct, perform real-time diagnostics and extensive data analyses (per SECTION 4) of sensor for potential malfunction.
  • If there is more than a 0.1 k increase in either sensor's average weight standard deviation, perform real-time diagnostics and extensive data analyses (per SECTION 4) of sensor for potential malfunction.

Figure 88. Procedure. Procedures and examples for adjusting calibration factors based upon traffic stream data statistics. This figure presents sample calculations and procedures for adjusting calibration factors. The first example is to increase or decrease the Axle-1 weights and the GVW, if the right and left sensors are in balance by simply increasing or decreasing all the weight calibration factors by the percentage corresponding to the increase or decrease in weight outputs. The second example is to balance the right and left sensor weight outputs while maintaining the same axle weight and GVW outputs. The last example is to weight outputs of only the right or left sensor back to historical weight outputs, or to assign temporary factors to a sensor that has been replaced or repaired.
Figure 88. Procedure. Procedures and examples for adjusting calibration factors based upon traffic stream data statistics.

5.5.3. Axle Spacings (and thereby speed)

If the average Axle 2-3 spacing for the sample of the Class 9's Type 3S2 is not 4.3 feet, adjust the system's sensor-to-sensor or loop-to-loop parameter value to bring the average spacing to 4.3 feet (refer to Figure 89).

Note that a vast majority of the Type 3S2 vehicles in the U.S. has Axle 2-3 (drive tandem) spacings, which, for a large sample, average 4.3 feet. However, for locations that have Canadian truck traffic or "specialty" truck types, 4.3 feet may not be a valid constant. Consideration needs to be given to observed axle spacing configurations and the percentage of such atypical vehicles. The parameter values for determining axle spacing and speed should be initially determined based upon test truck data.

Figure 89. Procedure. Procedure and example for adjusting axle spacing lengths (and thereby speeds).  The majority of the Type 3S2 vehicles in the U.S. have an Axle 2-3 (drive tandem) spacing of 4.3 ft. However, for locations that have Canadian truck traffic or specialty truck types, 4.3 feet may not be a valid constant. Consideration needs to be given to observed axle spacing configurations and the percentage of such atypical vehicles. The parameter values for determining axle spacing and speed should be initially determined based upon test truck data. This figure presents a procedure and sample calculations to increase or decrease the Axle 2-3 spacing for sample of where the Class 9's Type 3S2 Axle 2-3 spacing is not 4.3 feet by adjusting the system's sensor-to-sensor or loop-to-loop parameter value.
Figure 89. Procedure. Procedure and example for adjusting axle spacing lengths (and thereby speeds).

5.5.4. Overall Vehicle Length

If the average Overall Vehicle Length is not five to seven feet longer than the average Axle 1 to 5 wheelbase for a sample of Class 11's Type 2S12 vehicles (or the average Axle 1 to 6 wheelbase for Class 12's 3S12 vehicles), adjust the loop length parameter values (see Figure 90).

Note that the procedure described in Figure 90 assumes that the particular system calculates Overall Vehicle Length based upon the time of a vehicle's inductance for either or both loops.

Figure 90. Procedure. Procedure and example for adjusting overall vehicle lengths. This figure presents a procedure and sample calculations to increase the accuracy of the WIM overall vehicle lengths based upon sampling of traffic stream data. This procedure is typically performed if the average Overall Vehicle Length is not five to seven feet longer than the average Axle 1 to 5 wheelbase for a sample of Class 11's Type 2S12 vehicles (or the average Axle 1 to 6 wheelbase for Class 12's 3S12 vehicles) by adjusting the loop length parameter values. This procedure assumes that the particular system calculates Overall Vehicle Length based upon the time of a vehicle's inductance for either or both loops.
Figure 90. Procedure. Procedure and example for adjusting overall vehicle lengths.

As stated previously, the procedures for using traffic stream data to make calibration factor adjustments presented in this section are temporary, short-term measures and not a replacement for using data from on-site test truck sessions. On-site validations with test trucks should be performed at least on an annual basis for systems with no operational problems. Test truck validations should be performed as soon as possible when one or more sensors are replaced or other modifications made which might affect a system's calibration or when calibration monitoring by use of traffic stream data indicates calibration drift. Furthermore, these procedures should be performed by experienced data analysts and need to be documented (why, how, which method).

5.6. MAKING BEST USE OF AVAILABLE RESOURCES

One of the many benefits in performing calibration monitoring is the ability to best allocate available resources for performing onsite calibrations/validations with test trucks. Few agencies, if any, have the resources to run test trucks at every WIM site every six months on a routine basis, and also every time a system's maintenance of calibration is questionable.

If the monitoring of a particular system indicates very consistent truck traffic stream operating characteristics with little if any seasonal variation after a couple years of monitoring, there is little need to routinely validate calibration with test trucks every six months. If calibration factors are adjusted based upon truck traffic stream monitoring for more than one site, validation of the sites' calibrations with test trucks should be scheduled in the order of not only the importance of each site's data but also in the analyst's confidence of the factor adjustments based upon monitoring.

For sites with inconsistent truck traffic stream operating characteristics, factor adjustments based upon traffic stream statistics are not dependable, and any such adjustments should be validated with test trucks as soon as possible.

Contact

Mike Moravec
Office of Transportation Performance Management
202-366-3982
E-mail Mike

 
 
Updated: 01/04/2013
 

FHWA
United States Department of Transportation - Federal Highway Administration