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TRANSPORT AND ROAD RESEARCH LABORATORY Department of Transport
RESEARCH REPORT 307
EVALUATION OF A MULTIPLE-SENSOR WEIGH-IN-MOTION SYSTEM
by M H Glover and W H Newton
The views expressed in this report are not necessarily those of the Department of Transport
Vehicles and Environment Division Vehicles Group Transport and Road Research Laboratory Crowthorne, Berkshire, RG 11 6AU 1991
ISSN 0266-5247
Ownership of the Transport Research Laboratory was transferred from the Department of Transport to a subsidiary of the Transport Research Foundation on I st April 1996.
This report has been reproduced by permission of the Controller of HMSO. Extracts from the text may be reproduced, except for commercial purposes, provided the source is acknowledged.
CONTENTS
Abstract
1. Introduction
2. Types of WIM sensor
2.1 Area sensors
2.2 Strip sensors
3. Sources of error in WlM systems
3.1 Equipment errors
3.2 Errors due to the motion of the vehicle
3.2.1 Vehicle bounce
3.2.2 Load transfer between parts of the vehicle
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4
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5
3.3 Calibration errors 5
4. The weigh-in-motion system used in the trials 6
4.1 The sensors 6
4.2 The array of sensors 7
4.2.1 Number of sensors 7
4.2.2 Length of sensor array 7
4.2.3 The sensor spacings 7
5. The test programme 7
5.1 Vehicles used in the tests 8
5.2 Test procedure 8
5.3 Calibrating the sensors 8
6. Results 8
6.1 Results for individual sensors 10
6.2 Results for the array of sensors 10
6.2.1 Simple processing methods 12
6.2.2 Using different numbers of sensors 13
6.2.3 Curve fitting techniques 13
6.3 Drift
7. Discussion
7.1 Evaluating the accuracy of weigh- in-motion systems 17
7.2 Results for the multiple-sensor array 18
7.3 Further work 19
8. Conclusions 19
9. Acknowledgements 19
10. References 19
Appendix A: Curve f i t t ing algorithm 20
© CROWN COPYRIGHT 1991 Extracts from the text may be reproduced,
except for commerc ia l purposes, provided the source is acknowledged
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17
EVALUATION OF A MULTIPLE-SENSOR WEIGH-IN- MOTION SYSTEM
ABSTRACT
Weigh-in-motion (WIM) systems are devices which measure the loads imposed by the axles of vehicles travelling at normal highway speeds. Their main limitation is their poor accuracy in determining static axle and gross vehicle weights. A major reason for this is that vehicles bounce on their tyres and suspensions as they travel at speed. The accuracy of WIM systems may be improved by the use of multiple-sensors. An array of 9 weigh-in- motion sensors was installed in the TRRL research track and tested using a variety of vehicles travelling at a range of speeds. The tests showed that the use of the array reduced the coefficient of variation (CoV) of the gross weight impact factor (gross weight measured using the WlM divided by gross weight measured using an enforcement weighbridge) from, on average, 8.8 per cent using only one sensor to 3.6 per cent using the average from 9 sensors.
1 INTRODUCTION
Weigh-in-motion (WIM) systems are devices which measure the loads imposed by the axles of vehicles travelling at normal highway speeds. Potential uses of WIM systems include:
- - predicting road wear (Robinson, 1988);
-- selecting goods vehicles for enforcement weighing (Sommerville and Tarry, 1990);
-- monitoring the overloading of goods vehicles (Newton, 1989);
-- as an input to automatic systems for enforcing lorry bans (a system which used axle spacing is reported in Tarry, 1989);
-- as an input to a toll charging system; and
- - preventing dangerous overloading of bridges or roll-on roll-off ferries.
For some of these uses, estimates of static axle and gross vehicle weights are required (for example, monitoring overloading), whilst for others (for example, monitoring road wear), data on axle weights may be sufficient.
At present the main shortcoming of WIM systems is their limited accuracy. (The accuracy of WIM systems is expressed in terms of the impact
factor- - the weight measured_using the WIM system divided by the weight measured using an enforcement weighbridge.) For example, results from limited trials at TRRL (Moore, Stoneman and Prudhoe, 1989) showed Coefficients of Variation (CoV--the standard deviation divided by the mean value) of the axle weight impact factor of between 12 and 29 per cent. In contrast, the equipment used by enforcement officers to weigh the axles of vehicles which are stationary or moving slowly has a CoV of less than 0.3 per cent. There are three main sources of error. Firstly, errors arise from imperfections in the WIM sensors (drift, non- uniform output, etc). Secondly, at speed all vehicles bounce on their tyres and suspensions (the imposed load tends to vary cyclically, at typical ly 2 to 4 Hz ) and load is transferred between axles when, for example, vehicles accelerate or decelerate. Thirdly, errors are introduced by the calibration procedure-- these systems are dif f icult to calibrate--and these errors wil l lead to systematic over or under estimation of the weights.
To some extent, the second type of error can be overcome by using several sensors arranged in a linear array on a level site where vehicles are not accelerating or decelerating. With this arrangement, the axle passes over several similar sensors in succession and its static weight is determined by processing the outputs (by calculating the average value, f i t t ing an analytic function to the sensor outputs or by other processing methods). The use of an appropriate combination of sensor spacings and processing method should make it possible to compensate for the axle bounce and thus calculate the static axle weight. To assess the accuracy of a multiple-sensor WlM system, 9 sensors were installed in one lane of the TRRL research track and tests conducted using a number of goods vehicles over a period of nearly 7 months.
This report f i rst considers the main types of WIM sensor (Section 2) and various sources of error in WlM systems (Section 3). It then describes the multiple-sensor weigh-in-motion system installed at TRRL (Section 4), gives details of how it was tested (Section 5) and summarises the results of the tests (Section 6)
2 TYPES OF WlIVI SENSOR
There are two types of weigh-in-motion sensors. These are area sensors and strip sensors.
2.1 AREA SENSORS Area sensors are of suff icient size to support the whole area of the tyre(s) and therefore bear the whole weight on the wheel for a short period. They have been available for many years. For example, the TRRL Weighscale system has been in use for over 20 years (Trott and Grainger, 1968) (see Plate 1). These sensors are relat ively accurate weighing devices (they normally measure the loads using strain gauges or load cells), can easily be calibrated using stat ical ly applied loads and the calibration settings tend to remain stable. However, they are expensive to install (Plate 2 shows the excavation necessary to install a Weighscale unit) and may disturb the profile of the road (which may cause axles to impose loads on the sensors which are untypical of normal loads).
2.2 STRIP SENSORS Strip sensors are narrow strips laid across the road and so only part of the weight on the wheel or axle is on the sensor at any instant (see Plate 3). The wheel/axle weight is calculated by integrating the output over the length of the tyre contact patch. (In practice, it is calculated by integrating the output over t ime and then mult iplying by the speed of the vehicle.) Compared with area sensors, they are much cheaper to install (requiring a narrow slot in the road rather than major excavation) and have little effect on the profile of the road. Strip sensors
are, however, less s t ra ight forward to cal ibrate since it is d i f f icul t to devise a sat is fac tory arrangement for applying defined test loads to the strip. Also, the most common strip sensors consist of piezo electric cables which respond to changes in load rather than the load itself. Thus the only ef fect ive calibration procedure is to run axles of known weight over the str ip sensor, der ive f igures for the axle weights using the above procedure and then compare averages of the t w o sets of f igures (see Section 3.3). Because the axle is bouncing as it passes over the sensor, the load it applies during its passage wil l normal ly not be its s tat ic weight .
3 SOURCES OF ERROR IN W l M SYSTEMS
The errors in WlM systems are of three types:
-- equipment er rors- - inaccurac ies in the measuring and recording equipment, including dr i f t in the ins t rument 's zero or gain;
-- errors due to the mot ion of the veh ic le- - uncertaint ies caused by the var iabi l i ty of loads imposed by moving axles;
-- cal ibrat ion errors.
Each type of error is considered in turn in the next three sections.
- • . 0 e . e ~ e
CR 679/77/6
Plate 1 Area sensors (TRRL Weighscale units ready to be instal led)
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Plate 2 Pit for area sensors (TRRL Weighscale units) during installation
R 878/74/7
. . . . = . . . . . i i i • i
CR 152,,88,9
Plate 3 Strip sensors (short 'off-track" and main sensors)
3
3 . 1 E Q U I P M E N T E R R O R S
All types of weigh- in-mot ion sensor can be expected to exhibi t errors due to changes in temperature, excessive stresses caused by except ional ly high loads, fat igue or work-hardening of the sensor elements. In addit ion, errors can be caused by faul ts in electronic or recording systems used to process the outputs of the sensors.
Wi th strip sensors (for example, piezo-electr ic cables) the sens i t iv i ty of the sensor may vary along the length of the str ip (ie: across the road). This is due to variat ion in the electr ical propert ies of the cable, in the mechanical dimensions of the strip and its mount ing (which may be compounded by the presence of ruts and other imperfect ions in the road) and non-uni formi t ies in the composi t ion of the sensor. Since str ip sensors calculate the instantaneous axle we igh t by mul t ip ly ing the integrated sensor output by the vehicle speed, it is important that the vehicle speed is determined correct ly.
Equipment errors wi l l occur whether systems employ single or mult ip le sensors, al though it might be possible to design mult ip le sensor systems wh ich automat ica l ly check and correct for individual sensors which produce abnormal outputs.
3 . 2 E R R O R S D U E T O T H E M O T I O N O F T H E V E H I C L E
There are t w o main reasons why the axle weights measured using a WIM system wi l l not be the same as those measured using an enforcement weighbr idge. These are:
-- vehicle bounce;
-- load t ransfer between parts of the moving vehicle.
On an enforcement weighbr idge both these ef fects are negligible since at the t ime of weigh ing the vehic le is ei ther s tat ionary or moving at a very s low speed over a special ly constructed smooth surface.
3 . 2 . 1 Veh ic le bounce
The vert ical load imposed by a moving axle varies cyc l ica l ly during mot ion, typ ica l l y at between 2 and 4 Hz (cycles per second) w i th a superimposed random component . This is a result of osci l lat ions of the vehicle on its suspension sys tem and tyres. For a vehicle t ravel l ing at 40 mi le/h (64 km/h) along a re la t ive ly smooth pavement surface, the standard deviat ion of the instantaneous load is typ ica l ly 10 to 20 per cent of the stat ic load (Mi tchel l , 1987). On rough roads, there is a second osci l lat ion at 10 to 15 Hz wh ich involves the axles moving ver t ica l ly re lat ive to the chassis (called wheel hop or axle t ramp). This mode appears to a greater extent in
the response of suspensions which have l i t t le coulomb fr ict ion, for example, air suspensions. Oscil lat ions at similar frequencies can also occur because of pitching of 2-axle bogies and because of the f lexib i l i ty of the structure of the vehicle.
The loads on an axle are i l lustrated in Figure 1, which shows the variation of the offside rear wheel load of a 2-axle rigid vehicle measured using sensors mounted on the vehicle. The pattern is approximated by the function:
IL = W + co. s in~ + RN(/~,~)
where: IL = the instantaneous load W = the axle's static weight co = the amplitude of the sinusoidal
variation q~ = the phase of the axle~s bounce cycle
RN(/~,~) = a function returning a random variate from a Normal distribution wi th mean value/~ and Standard Deviation ~.
A sensor placed in the path of an axle produces an output representing the instantaneous axle load at the t ime of contact. In most cases this wi l l be a poor representation of the axle's static weight.
If the system is being used to record the cumulat ive loading on a road, it is usually assumed that the phase of the instantaneous loads from individual axles will be random. If this were so there would then be no systemat ic difference between the
10
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I I I
5 10 15 Distance (m)
20
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o , , " 0 5 10 15 20
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Fig.1 Loads on the offside rear wheel of a 2-axle rigid vehicle measured using instruments on the vehicle
4
average axle weight recorded by the weigh-in- motion sensor and the average axle loading at any other point along the section of road traversed by the same group of vehicles. Thus, even though individual axle weights would not be recorded accurately, the overall pavement loading would be. However, there is some evidence that there are points on roads where the axle loading is frequently abnormally high, a series of such spots probably being caused by a single abrupt change in the pavement's profile. If the sensor is positioned at such a location it would indicate an untypically high average axle load (this applies particularly if static calibration is used--see Section 3.3).
The effects of motion are more troublesome when the static weights of individual axles are required-- for example when targetting a particular vehicle for check-weighing. The uncertainty about the phase of the axle's load pattern at the sensor can give rise to large errors.
If the outputs from several sensors are averaged, the error should be reduced. From statistical theory, the standard deviation of the mean value of outputs from several sensors is the standard deviation of the output from a single sensor divided by the square root of the number of sensors (provided that the outputs are independent). For example, the standard deviation of the mean value from 9 sensors would be expected to be one third (square root of 9) of the standard deviation of the output of one sensor. However, the sensor outputs are not independent because the wheel loading oscillates as it travels from one sensor to the next, and so the loads measured at the sensors are correlated by a generally sinusoidal function. Also the sensors are fixed relative to the local profile of the road pavement (see Section 3.2.2).
With two sensors, the sinusoidal components at the two sensor positions cancel when the oscillations are exactly out of phase at the two sensors (ie: the sensor spacing is half the wavelength of the oscillation) and errors will be small. When they are exactly in phase, at some other bounce frequency or vehicle speed perhaps, maximum errors will O c c u r .
If more than two sensors are used, it should be possible to fit a function of the same form as the equation given above to each of the set of sensor outputs (which are samples of the axle's load pattern) and hence reduce the error in the estimate of the axle's static weight.
3.2.2 Load transfer between parts of the vehicle
The load on individual axles of mechanically linked compensating bogies can depend on the relative heights of the axles. This effect occurs when the vehicle is either moving or stationary and
potentially applies to enforcement weighbridges as well as WlM systems. Tests have shown (Prudhoe, 1988) that if the axle that is being weighed is on ground that is higher or lower than that under the other axles of the bogie, load transfers of up to 100 kg per mill imetre of height difference can occur. Thus, if the weigh-in-motion system is installed in a slightly raised position relative to the surrounding road, the measured weight of each bogie axle is likely to be greater than the weight measured by weighing equipment installed at the same level as the surrounding road surface. This weight transfer is a quasi-static effect that occurs whatever the speed of the vehicle. It affects the measured gross vehicle weight whenever this is obtained by summing axle weights that are not themselves measured simultaneously. Even for axles which are not part of a linked bogie set, systematic weight transfers between axles can occur if vehicles are weighed on longitudinal slopes, when travell ing at speed (due to aerodynamic drag and drag from non-driven axles) or when accelerating or braking.
These load transfers wil l affect the accuracy of measuring individual axle weight but may not affect the accuracy of measuring the gross weight of the vehicle (for example, load transfers due to the vehicle travell ing at speed might be partially cancelled as axle weights are summed to calculate the gross weight). The errors depend on the vehicle's axle configuration since, for example, 2-axle rigid vehicles are obviously not affected by weight transfers between bogie axles.
Load transfer effects may be minimised by making the road profile as smooth and level as possible, by avoiding sites where vehicles are likely to be braking or accelerating and by using several sensors at different positions rather than a single sensor (thus averaging any effects).
3 .3 C A L I B R A T I O N ERRORS Three methods are used to calibrate weigh-in- motion systems:
- - static calibration;
-- dynamic calibration;
- - self-calibration.
Static calibration involves setting the calibration factor so that the output from the WIM sensor is the same as the 'true' static load applied to the sensor. (A hydraulic test rig is used to apply the load to the TRRL Weighscale sensors.) This method is normally used to calibrate area sensors but cannot be used to calibrate piezo-electric strip sensors because they respond to changes in load rather than to the load itself; also a strip sensor responds only to part of a wheel 's load at any instant. Static calibration may lead (paradoxically)
to s ign i f icant over- or under-est imat ion of actual s tat ic axle loads. The sensor may measure the true instantaneous load, but if it is at a point on the road which exper iences an abnormal range of loads (possibly because the sensor has altered the road profi le) its output may not be typical of the loads imposed by the same axle or axles on the road pavement as a whole. For example, tests wi th the TRRL Weighscale system (which is calibrated stat ical ly) have shown that the mean impact factor (dynamic load divided by true load) can vary f rom 0.89 to 1.05 between sites (Hodge, 1989).
Dynamic cal ibrat ion involves sett ing the cal ibrat ion factor so tha t the average output f rom the WlM sensor is equal to the average stat ic axle (or gross) we ights of a number of vehic les travel l ing at normal h ighway speeds. (These could be a number of passes of each of a l imited number of vehicles or, bet ter sti l l , a single pass of each of a large number of d i f fe rent vehicles.) This method is normal ly used for str ip sensors. There are problems wi th this method. First ly, at these speeds, the axle loads contain large dynamic componen ts - -wh i ch means that a large number of vehic le /ax le passes are required to establ ish the cal ibrat ion. Secondly, there is ev idence that if the same vehicle passes along the same length of road at the same speed a number of t imes, the peak dynamic loads wi l l repeatedly occur at the same points on the road. This means that a var iety of vehicles and speeds is required to establ ish the cal ibrat ion and, as a result, dynamic cal ibrat ion is general ly more expensive than stat ic cal ibrat ion though stat ic cal ibrat ion requires the road or lane to be closed for short periods, wh ich can be expensive on Moto rways .
The stat ic and dynamic cal ibrat ions should be identical if the sensor is posit ioned on a section of road which has a profile w i thou t large discrete i rregular i t ies close to or upstream of the sensor; a representat ive combinat ion of vehicles and speeds needs to be used for the dynamic cal ibrat ion.
The third method is self-cal ibrat ion. This relies on some we igh t character ist ic in t ra f f ic remaining constant over t ime. For example, observat ions
made over the last decade indicate that the average load on the f irst axle of 5-axle artics with 2-axle tract ive-units is fair ly constant at about 5.7 t o n n e s - t h e precise figure depends on the traf f ic and may need to be established for the road where the sensor is installed. The system's calibration can be automatical ly adjusted to equalize the system's est imate of this weight wi th the expected figure.
4 THE WEIGH-IN-MOTION SYSTEM USED IN THE TRIALS
In October 1988, a multiple-sensor weigh-in-motion system consisting of 9 axle weighing strip sensors was installed in a lane of the TRRL research track. In this section, the sensors and the array of sensors are described. It should be noted that prototype sensors and sensor mountings were used in the evaluation.
4.1 THE SENSORS Golden River WIMSTRIP sensors were used in the mult iple-sensor weigh-in-motion system. These are a new design of capacit ive strip sensor. Each sensor consists of a hol low alluminium al loy extrusion wi th a cross section about 9 mm high and 30 mm wide. An electrical capacitor is formed between the top surface of the extrusion and a copper electrode inside the extrusion. As a wheel passes over the sensor, the distance between the top surface of the extrusion and the inner electrode decreases, increasing the capacitance. Tests conducted by Cambridge Universi ty have shown that this type of sensor has a low sensi t iv i ty to changes in temperature and that the variat ion in sensi t iv i ty (capacitance change for a given load) along the length of each sensor is typical ly less than ± 2 per cent (Cebon and Winkler, 1990).
The sensors were linked to a Golden River Marksman 600 control box. This continual ly monitored the output from each sensor. As an axle passed over a sensor, the Marksman calculated the
0 1 2 3 4 5 6 7 8
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9 10 11 12 13 ! 15 16 17
A B C D E F G H I
N o t e : 0 - 1 7 = w h e e l s e n s o r s
A - I = a x l e s e n s o r s
Scale 0 1 2m
Fig.2 Sensor positions
total load applied to it. This value was mult ipl ied by the speed of the vehicle (calculated from the t ime taken for the axle to pass between two given sensors) and a calibration constant, to give the axle load over the sensor.
Each sensor was sealed to prevent the ingress of moisture, encapsulated and f i t ted into a pre-formed channel which had already been installed in a slot in the road. (This system was used in the prototype array to allow the sensors to be replaced if necessary-- i t would not be used on a public road.) The top surface of the encapsulation was flush with the road surface. Each sensor was 1.5 metres long--about half the width of a normal traff ic lane. In order to weigh complete axles rather than just the wheels on one side of the vehicle, the 18 sensors (wheel sensors) were arranged as 9 pairs (labelled A to I in Figure 2), each pair forming an axle sensor extending across the whole t raf f ic lane. The combined output from each pair represents the load imposed by an axle.
4 . 2 THE A R R A Y OF S E N S O R S Three factors were considered when designing the multiple-sensor weigh-in-motion system:
-- how many sensors to use;
-- the length of the array of sensors; and
-- the sensor spacings (these could be uniform or varied).
4.2.1 Number of sensors
If the outputs from sensors are independent, the standard deviation of the mean value from several sensors is the standard deviation from the ind iv idual sensors divided by the square root of the number of sensors. An array of 9 sensors was installed in the TRRL research track. This was expected to provide a three-fold improvement over the use of one sensor. This number of sensors is suff ic ient to allow curve f i t t ing techniques to be tested and analysis based on a smaller number of sensors and a variety of sensor spacings to be conducted.
4 .2 .2 Length of sensor array The overall length of the array of 9 sensors was designed to be longer than the wavelength of the axle bounce oscil lat ions for the fastest vehicles that were expected to pass over it (the wavelength is proportional to the vehicle speed). If the array was shorter than this wavelength, the results could be biassed towards a particular part of the waveform.
The wavelength (w) (in metres) of the oscil lation is:
w = 1.609 s
3 . 6 f
where s is the speed (mile/h) and f the bounce frequency (Hz).
Thus, for a speed of 75 mile/h (120 km/h) and a f requency of 3 Hz, the wave length is 11.2 metres. Computer simulat ion indicated that the performance of the mult ip le-sensor array would not be s igni f icant ly degraded provided the array was longer than this wavelength and so the overal l length of the array on the TRRL research track was set at 15.96 metres.
4 . 2 . 3 The sensor spacings The sensor array was designed to make it possible to determine the stat ic axle load by using an algori thm which relies on f i t t ing a curve to the sensor outputs. Nyqu is t 's Theorem requires that, if a repeating wavefo rm is being examined to determine its f requency, the sampl ing rate should be at least tw ice the f requency (ie: tw i ce per wavelength) . With 9 equal ly spaced sensors occupying a total length of 15.96 metres, the lowest speed for which two adjacent sensors are half a wavelength apart is 27 mi le/h assuming a bounce f requency of 3 Hz (18 mile/h at 2 Hz). A t lower speeds, the sensor spacing would be greater than half a wavelength and so the outputs f rom the sensors would be insuf f ic ient to map out the wave pattern. It was considered that some improvement of performance at low speeds might be obtained, at the expense of that at higher speeds, by reducing the spacing between some of the sensors. The sensor array is shown in Figure 2 and the spacings are listed in Table 1.
Ax le sensor
A B C D E F G H I
Wheel sensors
0 + 9 1 + 1 0 2 + 1 1 3 + 1 2 4 + 1 3 5 + 1 4 6 + 1 5 7 + 1 6 8 + 1 7
TABLE 1
Sensor spacin! s
Distance f rom Distance between sensor A (m) sensors (m)
3.84 6.39 7.15 7.98 8.81 9.57
12.12 15.96
3.84 2.55 0.76 0.83 0.83 0.76 2.55 3 .84
5 THE TEST P R O G R A M M E
The performance of the mul t ip le-sensor weigh- in- motion system was assessed by compar ing axle and gross weights recorded by the WlM sensors w i th the ' t rue' stat ic weights .
5.1 VEHICLES USED IN THE TESTS The fol lowing seven goods vehicles were used in the tests (their approximate gross vehicle weights are shown in brackets):
A: 2-axle rigid (6.9 tonnes); B: 2-axle rigid (16.1 tonnes); C: 3-axle rigid (10.5 tonnes); D: 4-axle attic (12.7 tonnes); E: 4-axle artic (31.7 tonnes); F: 5-axle artic with 2-axle tractive-unit and
3-axle semi-trailer (37.0 tonnes); G: 5-axle artic with 2-axle tractive-unit and
3-axle semi-trailer (37.7 tonnes).
These vehicles were chosen to ensure a wide range of axle configurations, gross weights and axle weights. The axle weights ranged between 1.87 tonnes (the third axle of vehicle D) and 10.04 tonnes (the second axle of vehicle G). Details of the axle and gross weights are given in Table 2.
The tests were conducted in two sessions. The first of these was in March 1989 and the second was in September 1989. Two of the seven vehicles were used in March (vehicles B and F) and six were used in September (all the vehicles except vehicle F).
5 .2 TEST PROCEDURE The WIM system was tested by passing each vehicle over the sensors a number of t imes at each of a range "of speeds and comparing the outputs from the WIM sensors wi th the 'true' static axle and gross weights. The number of passes over the sensors of these vehicles are shown in Table 3. These range from 7 passes for vehicle G (all at the same speed) to 80 passes for vehicle F (at four di f ferent speeds). (It was intended to record about 20 passes for each vehicle at each speed but problems with the power supply to the sensors curtailed some tests.) In total, 358 vehicle passes (1137 axle passes) were recorded for each sensor. Of these, 146 vehicle passes (467 axle passes) were at about 50 mile/h.
The speeds were usually chosen to be multiples of 10 mile/h, reflecting the current speed l imits for heavy goods vehicles in the United Kingdom (60 mile/h on Motorways, 50 mile/h on other dual- carr iageways, 30 mile/h on most urban roads, and 40 mile/h on other roads). Most of the test vehicles were unable to achieve 60 mile/h over the array of sensors because of the layout of the research track.
During the tests, the ' true' static axle and gross weight (sum of axle weights) of each vehicle were measured at least 4 t imes on level ground and the results averaged. For the tests in March, these weights were established using a slow speed dynamic axle weigher. (This is the standard type of enforcement axle weigher.) With this equipment, each axle is weighed in turn as the vehicle is driven at a slow and steady speed (less than 4 km/h) over
a weighbeam set in a precision-laid concrete apron (see Prudhoe, 1988). In September, a set of portable weighpads were used (Eastman, 1988). These were used to weigh all the wheels of the vehicle simultaneously whilst it was stationary on the pads.
5.3 CALIBRATING THE SENSORS It was necessary to determine a separate calibration factor for each of the 18 wheel sensors. These were based on 25 passes of vehicle B over the sensors at 8 mile/h. At this slow speed the amount of vehicle bounce should be small (Figure 1 shows vehicle bounce at 5 mile/h and 50 mile/h) and the wheel weight recorded by the sensors should be close to the static weights. The calibration factors established using this method should be similar to static calibration factors.
The calibration factor for each of the nearside wheel sensors was set so that the average of the sum of the nearside wheel weights of the calibration vehicle, as recorded by the sensor, was the same as the equivalent value determined using either a slow-speed 'dynamic' axle weigher (March) or portable weighpads (September). The same method was used for the offside sensors.
The data used to establish the calibration factors are included in the data used for the main analysis. Thus validation is not totally independent of calibration since, for example, the mean impact factor for runs with vehicle B at 8 mile/h in March wil l be, by definition rather than measurement, 1.0, but the effect on the overall results is small because the data used to calibrate the sensors only account for a small proportion (7 per cent) of the overall data.
Four of the wheel sensors failed between March and September (sensors 1,3, 6 and 17). These were replaced with new units and recalibrated for the September trials. The calibration of the remaining sensors was not changed.
6 RESULTS In this report, four main measures of the accuracy of weigh-in-motion equipment are used. These are:
MIF - - the mean impact factor;
CoV - - the coefficent of variation of the impact factor;
P5 -- the proportion (per cent) of weights within 5 per cent of the 'true' weight; and
P10 -- the proportion (per cent) of weights within 10 per cent of the 'true' weight.
The impact factor is defined as the weight indicated by the weigh-in-motion sensor divided by the 'true'
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p~
~ l~ ° I°~ ° I~ ° I
ffl
° E "~ ~- ~ - ~ o I I I I t I ~ J
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e--
m "~ I 1 1 1 1 IN r
. m
r-
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X X X X X X ~ X ~
o
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static weight. The mean impact factor (MIF) provides an indication of systematic error or bias. Thus, if the MIF is 1.05, the WlM system, on average, indicates weights which are 5 per cent greater than the 'true' static weights.
The Coefficient of Variation (CoV) indicates the variabil i ty of the results. For a set of axle or vehicle passes:
CoV = (standard deviation of the impact factors)x 100
mean impact factor
For an ideal weigh-in-motion system, the MIF would be 1.00 (ie: there would be no systematic error), the CoY would be small (ie: there would be little random variabil ity) and the values of P5 and PIO would be near 100 per cent (ie: most or all individual axle or gross weight readings would be within 5 per cent / lO per cent of the true values).
6.1 RESULTS FOR I N D I V I D U A L r SENSORS
The results for each of the 9 axle sensors used separately are shown in Table 4. The mean impact factors for measurements of gross vehicle weights varied between 0.91 for sensor G (0.92 when determining axle weights) and 1.10 for sensor H (1.11 when determining axle weights). On average, the coefficients of variation (CoV) of the impact factors determined using only one axle sensor were 13.2 per cent for axle weights and 8.8 per cent for gross weights (the sum of axle weights on a vehicle). The values for individual sensors ranged from 11.5 per cent for axle weights and 6.3 per cent for gross weights (sensor B) to 15.7 per cent for axle weights and 11.8 per cent for gross weights (sensor F). This variation between sensors may be partly explained by difference in the profile of the pavement at the different sensor locations (at each location there will be a different spectrum of axle loading). It may also be partly dependent on the sensit iv i ty and repeatabil ity of the outputs from individual sensors.
Table 5 shows detailed results for axle sensor C. For some combinations of vehicle and speed the coeff icient of variation of the output from a single sensor was relatively small. For example, for vehicle B at 50 mile/h on the 26th of September, sensor C had a CoY of 2.4 per cent for gross weights compared with 7.2 per cent over all test vehicles and speeds. The low value of CoV for one vehicle at one speed is because, when a vehicle is repeatedly driven along the same length of road at the same speed, the pattern of dynamic loads along the road repeats quite accurately. However, since the mean impact factors varied between vehicles and speeds (the gross weight MIFs for sensor C varied between 0.98 and 1.16) the CoV over all vehicles and speeds (7.2 per cent) was greater than most of the CoVs for individual combinations of vehicle and speed. For example, Figure 3 shows the
TABLE 4
Outputs for individual axle sensors
Axle sensor MIF CoV P5 PIO
Axle weights: A 1.06 12.1 30.2 55.9 B 1.08 11.5 27.4 52.2 C 1.05 11.9 33.1 57.5 D 0.96 14.5 27.4 53.9 E 0.93 14.5 23.7 48.0 F 1.02 15.7 23.7 47.9 G 0.92 11.9 31.7 53.8 H 1.11 12.1 27.2 49.1
1.04 14.2 32.9 59.4 Average for single sensor -- 13.2 28.6 53.1
Gross weights: A 1.06 8.4 39.9 62.6 B 1.07 6.3 39.9 69.6 C 1.05 7.2 43.6 72.6 D 0.95 10.7 44.7 71.2 E 0.92 9.8 36.6 60.1 F 0.99 11.8 31.6 59.5 G 0.91 8.0 33.0 52.8 H 1.10 7.2 25.4 49.2 I 1.04 9.9 39.7 68.2 Average for single sensor -- 8.8 37.2 62.9
Notes: MIF =
CoV = Mean Impact Factor Coefficient of variation of impact factors (per cent)
P5 = Proportion of weights (per cent) within 5 per cent of true value
P10 = Proportion of weights (per cent) within 10 per cent of true value
Axle sensor A consists of wheel sensors 0 and 9, axle sensor B consists of wheel sensors 1 and 10, etc (see Table 1)
distribution of gross weight impact factors for vehicle B passing over sensor C at three different speeds. Whilst the range of values of impact factor at each speed is relatively small (CoV 2.4 to 3.6 per cent), they are centred about different mean values (MIF 0.98 to 1.16) and so, when the output for all speeds is examined, an uneven distribution with a higher CoV results. The apparent dependence of MIF on speed shown in Figure 3 is discussed in Section 7.1.
6 .2 RESULTS FOR THE A R R A Y OF SENSORS
A number of different ways of combining the outputs from the multiple-sensor array have been examined. These form two main groups. The first are simple methods of averaging the outputs and the second are methods using curve fitting techniques.
10
C
"5
- O
E
z
8 mile/h
0.9 1.0
M I F = 0 .98
CoV = 3.6
1.1 1 2 1.3
Gross weight impact fac to r
"O
"5
E z
50 mile/h 6
4
2
0 o~9
IF] 17, .0 1.1
Gross weight impact fac to r
M I F = 1.02
CoY = 2.4
i
'2 1. 1.3
C
"5 $
- O
E
z
60 mile/h
0:9
M I F = 1.16
CoY = 3.3
I
I i0 1.1 1.2 1.3 Gross weight impact factor
C
"5
- O
E
z
10
8
6
4
2
0
AIIspeeds
|
0.9 1.0
Gross weight impact fac to r
M I F = 1.05
CoY = 8.0
! !
1.1 1.2 I
1.3
Fig.3 Distr ibut ion of gross weight impact factors for vehicle B passing over sensor C (September tests)
N o t e : M I F = M e a n I m p a c t F a c t o r C o V = C o e f f i c i e n t o f V a r i a t i o n o f i m p a c t
f a c t o r s (per c e n t )
11
TABLE 5
Detailed results for axle sensor C
Vehicle
A 2-axle rigid
B 2-axle rigid
C 3-axle rigid
D 4-axle artic
E 4-axle artic
F 5-axle artic ( 2+3 )
G 5-axle artic ( 2+3 )
Date
27 Sept. 1989
9 March 1989
26 Sept. 1989
26 Sept. 1989
27 Sept. 1989
26 Sept. 1989
7 March 1989
27 Sept. 1989
Speed
Mean gross weight impact factors (coefficients of variation in
brackets)
1.09 (5.9) 1.10 (4.9) 1.10 (5.4)
1.00 (4.9) 1.01 (4.1) 1.01 (5.1) 1.00 (4.8)
0.98 (3.6) 1.02 (2.4) 1.16 (3.3) 1.05 (8.0)
1.14 (4.8) 1.09 (5.4) 1.12 (5.5)
1.04 (8.4) 1.06 (8.5) 1.05 (8.5)
1.08 (2.5)
50 mile/h 60 mile/h
All
8 mile/h 40 mile/h 50 mile/h
All
8 mile/h 50 mile/h 60 mile/h
All
40 mile/h 50 mile/h
All
40 mile/h 50 mile/h
All
50 mile/h (All)
20 mile/h 30 mile/h 40 mile/h 50 mile/h
All
50 mile/h (All)
1.07 (4.3) 1.01 (4.4) 0.98 (4.5) 1.03 (4.1) 1.02 (5.4)
1.08 (12.3)
Overall 1.05 (7.2)
Note: Axle sensor C consists of wheel sensors 2 and 11.
6.2.1 Simple processing methods Four simple methods of averaging the weight of each axle have been tested. These are:
-- using the mean value from the 9 sensors (mean);
-- using the median value from the 9 sensors (median);
-- using the average of the highest and lowest values from the 9 sensors (max/rain);
-- calculating the mean and standard deviation from the 9 sensors and then recalculating the mean, excluding any values greater than 2 standard deviations away from the original mean (mean exc 2SD)-- th is method wil l exclude any abnormal readings.
For each averaging method, the gross weight of a vehicle was calculated as the sum of its axle weights. These weights were then used to calculate the mean impact factors, coefficients of variation and values of P5 and P10.
The results using each of these methods are summarised in Table 6. The mean impact factors (MIF) were similar for the different methods of averaging (1.019 to 1.025 for axle weights and 1.008 to 1.013 for gross weights). The lowest coefficients of variation (CoV) were for the mean value (5.60 per cent for axle weights and 3.62 per cent for gross weights) and the highest were for the median value (6.89 per cent for axle weights and 4.23 per cent for gross weights). As might be expected from the MIF close to unity and the small CoV, the values of P5 and P10 were high (P10 was
12
T A B L E 6
Different methods of calculating average values from array of 9 sensors
MIF CoV P5 P10
Axle weights: Mean Median Max/Min Mean exc 2SD
Gross weights: Mean Median Max/Min Mean exc 2SD
1.020 5.60 62.4 1.019 6.89 54.3 1.025 6.43 58.0 1.019 5.83 60.3
89.1 85.0 83.3 89.5
1.009 3.62 78.5 100.0 1.008 4.23 70.1 99.2 1.013 3.92 71.8 99.2 1.008 3.75 78.5 100.0
Notes: Methods of c~lculating averages are defined in Section 6.2.1. MIF = Mean Impact Factor CoV = Coeff ic ient of variation of impact
factors (per cent) P5 = Proportion of weights (per cent)
wi th in 5 per cent of true value P10 = Proportion of weights (per cent)
wi th in 10 per cent of true value
89 per cent for axle weights and 100 per cent for gross weights when the mean value from the 9 sensors was used).
6 . 2 . 2 Using d i f fe ren t n u m b e r s of sensors
Mean values were also calculated for the outputs from different sets of sensors. (See Table 7 which, for simplicity, l ists only some of the sets containing symmetrical arrays of sensors.) Generally the coefficient of variat ion decreased and the values of P5 and PIO increased as more sensors were taken into account (see Figure 4). There were exceptions to this pattern. For example:
-- low CoV for 2 sensor combination C and G (4.2 per cent for gross weights);
-- lowest CoV for 7 sensor combination excluding sensors D and F (3.0 per cent for gross weights). This combination provided the best results of all those listed in Table 7.
The results for the two sensors C and G are part ly explained by the close matching between their sensitivit ies and relat ive distance apart. Sensors C and G were two of the four sensors (B, C, G and H) with the smallest individual sensor gross weight coefficients of variat ion (see Table 4). The results for all combinat ions of these four sensors are shown in Table 8. The lowest gross weight CoY for these combinations was 2.9 per cent (sensors B, C and G). This value is lower than that for any of the combinations listed in Table 7. In comparison, the
lowest axle we ight CoV for a combinat ion of sensors B, C, G and H was 5.6 per cent (either sensors B, C and G or all four sensors), compared wi th the lowest value in Table 7 which was 5.1 per cent (mean of 7 sensors).
The CoVs for the mean value from 7 sensors were lower than those for the mean of 9 sensors (see Table 7). This may be due to a combinat ion of t w o di f ferent ef fects. Firstly, the gross we igh t CoVs for the t w o sensors omit ted f rom the 9 sensor array (sensors D and F) were the highest individual sensor values (see Table 4). Secondly, the 9 sensor array included a group of 5 closely spaced sensors (sensors C to G- -see Figure 2). The average inter- sensor spacing between sensors C and G was 0 .8 metres for the 9 sensor array compared w i th 1.6 metres for the 7 sensor array (which omi t ted sensors D and F). Thus, part of the axle osci l lat ion wavefo rm may be over-represented in the 9 sensor array leading to a bias in the results.
Detailed results for the 7 sensor array (excluding sensors D and F) are shown in Table 9. The overal l MIF for gross weights was 1.02 and the values for individual combinat ions of vehicle and speed ranged between 0.98 (vehicle B in September at 50 mile/h) and 1.06 (vehicle A at 50 mile/h). This table shows that the MIFs were not dependent on the vehicle speed in any consistent way . For example, for runs using vehicle F a t 20, 30, 40 and 50 mi le/h the axle we igh t MIFs varied between 1.03 and 1.04. Simi lar ly, for runs in September using vehic le B at 8, 50 and 60 mile/h, the axle weight MIFs varied between 0.98 (at 50 mile/h) and 1.01 (at 8 mile/h).
Figure 5 shows the distr ibut ion of gross we igh t impact factors using the mean value f rom 7 sensors, the mean from 3 sensors (B, C and G),and the output f rom sensor C.
6 . 2 . 3 C u r v e f i t t ing t e c h n i q u e s
It was expected that the performance of the array could be improved by using curve f i t t ing techniques to process the sensor outputs. Results f rom computer model l ing indicated that the most promising approach would be to f i t a s imple mathemat ica l funct ion to the pattern of sensor outputs for each axle and solve for the stat ic we igh t component. The funct ion has the same form as the equation in Section 3.2.1:
where:
IL, = W + w.sin(2.Tr.f.t i + ~) + E
IL, = the output of the i-th sensor (in tonnes);
W = the stat ic we igh t (in tonnes); w = the ampl i tude of the osc i l la tory com-
ponent of the axle load (in tonnes); f = the f requency of the osc i l la tory com-
ponent of the axle load (in Hz); t, = (the t ime at which the axle passes
over the ith sensor) = A, x 3.6 / s;
13
T A B L E 7
Average (mean) results for different numbers of sensors
Number of sensors averaged
Gross weights:
1
2
3
4
6
7
8
9
Axle sensors used
average*
A I B H C G
D F
A E I B E H C E G
DEF
A C G I AB HI
A C E G I AB E HI
ABC GHI AB D F HI
ABC E GHI
ABCD FGHI
ABCDEFGHI
MIF
1.05 1.08 0.98 0.97
1.01 1.03 0.96 0.95
1.01 1.07
1.00 1.04
1.04 1.03
1.02
1.02
1.01
CoV
8.8
7.9 6.0 4.2 9.9
5.4 5.5 4.5 9.2
5.0 4.4
4.1 3.8
3.3 4.3
3.0
3.4
3.6
P5
37.2
36.3 31.3 69.0 41.3
64.2 51.7 58.7 49.4
67.9 38.3
74.3 62.0
70.9 60.6
81.0
75.4
78.5
P10
62.9
64.6 60.1 97.5 64.0
91.9 89.7 91.6 66.2
93.6 74.9
100.0 93.6
94.1 94.7
99.7
100.0
100.0
Notes: MIF = Mean Impact Factor CoV = Coefficient of variation of impact factors (per cent) P5 = Proportion of weights (per cent) within 5 per cent of true value P10 = Proportion of weights (per cent) within 10 per cent of true value * see Table 4
T A B L E 8 Average (mean) results for combinations of sensors B, C, G and H
Number of sensors averaged
Gross weights:
2
3
4
Axle sensors used
BC GH
C G B G
C H B H
BC G C GH
BC H B GH
BC GH
Sensor spacing (metres)
2.55 2.55 3.18 5.73 5.73 8.28
2.55/3.18 3.18/2.55 2.55/5.73 5.73/2.55
2.55/3.18
MIF
1.06 1.00 0.98 0.99 1.07 1.08
1.01 1.02 1.07 1.03
1.03
CoY
4.2 5.0 4.2 4.7 4.9 6.0
2.9 3.3 4.3 4.5
3.2
P5
40.2 73.5 69.0 72.9 28.2 31.3
89.4 80.4 24.9 60.6
66.2
P10
79.6 95.0 97.5 95.3 71.5 60.1
99.7 99.2 72.6 93.9
99.2
Notes: MIF = CoV = P5 = PIO =
Mean Impact Factor Coeff icient of variation of impact factors (per cent) Proportion of weights (per cent) within 5 per cent of true value Proportion of weights (per cent) within 10 per cent of true value
14
E
CL
'C
"6 E co
.o "4--
O
Q.
.c
{3 . £
Q.
15
10
100
75
50
25
Fig.4
Coefficient of Variation "°
". Axle weights
• %°• /
% ° o .
Gross weights "'- . . . . . . . . . . .
I I I I I I I I I
1 2 3 4 5 6 7 8 9
Number of sensors
P5 and P10 s" . . . . . . . . . .
s S s S • ° ° ' ° ° ° ° ' ° * * ° ° ° ° "
.... ,,,',°,.,o°,"
i I I e l i I s • •
I I I i I - i t • I
• • • • . ° . • . . • • • °
• • • • • " • I • " • • ° "
° ° • • ~ - . ~ l ° • °
I ° • "
s ~ ° . • s SS . • •
s S . . °
• • ° "
• " P10 Gross weights
~ P l 0 Axle weights
~.-- P5 Gross weights
~ - - P 5 Axle weights I I I I I l I I I
1 2 3 4 5 6 7 8 9
Number of sensors
Results for calculating mean values using different numbers of sensors (averages for combinations of sensors listed in Table 7)
40 E
a.l
~ 20 e~ E
z 0
40 E
Co
"6 20 e~ E z 0
E ~5
"6
.(3 E
z
6 0
40
20
Sensor C
0 .9 1.0 1.1 1.2
Gross weight impact factor
M IF = 1.05
C o Y = 7.2
m
1:3 1:4
Mean of 3 sensors (B C G)
i I m ,
0.9 1.0 1.1 1.2
Gross weight impact factor
Mean of 7 sensors (excludes D and F)
0 .9 1.0 1.1 1.2
Gross weight impact factor
M IF = 1.01
CoY = 2.9
113
M I F = 1.02
CoY = 3.0 o
114
Fig.5 Distribution of gross weight impact factors for three different processing methods
Note: M IF = Mean Impact Factor CoV = Coefficient of variation of impact
factors (per cent)
15
T A B L E 9
Detailed results for average (mean) of 7 axle sensors (excludes axle sensors D and F)
Vehicle
A 2-axle rigid
B 2-axle rigid
C 3-axle rigid
D 4-axle artic
E 4-axle artic
F 5-axle artic
( 2+3 )
G 5-axle artic
( 2+3 )
Date
27 Sept. 1989
9 March 1989
26 Sept. 1989
26 Sept. 1989
27 Sept. 1989
26 Sept. 1989
7 M a : ~ , 9 8 9 -
27 Sept. 1989
Overall
Speed
Mean gross weight impact factors (coefficients of variation in
brackets)
1.06 (2.3) 1.04 (3.4) 1.05 (3.1)
1.00 (2.4) 1.02 (1.2) 1.01 (1.4) 1.01 (1.9)
1.00 (1.2) 0.98 (1.1) 0.99 (1.6) 0.99 (1.7)
1.05 (2.2) 1.01 (2.6) 1.03 (3.4)
1.05 (2.1) 1.05 (3.0) 1.05 (2.5)
1.00 (1.1)
, 103 i16) -1 .04 (1.9)
1.02 (1.7) 1.02 (1.6) 1.03 (1.9)
1.00 (2.3)
50 mile/h 60 mile/h
All
8 mile/h 40 mile/h 50 mile/h
All
8 mile/h 50 mile/h 60 mile/h
All
40 mile/h 50 mile/h
All
40 mile/h 50 mile/h
All
50 mile/h (All)
20 mi~le/h ,, ........ 30 mile/h 40 mile/h 50 mile/h
All '
50 mile/h , - (All)
1.02 (3.0)
A, = the distance of the i-th sensor from a fixed datum (in metres);
s = the speed (in km/hour); q~ = the phase of the oscillation at the
instant of contact between the axle and the f irst sensor; and
E = the residual random component rep- resenting all sources of error.
Appendix A shows that 3 simultaneous equations can be defined in terms of the 9 sensor outputs and the known constants of the system (such as the sensor spacings). These equations can then be solved to derive a value for W, the axle's static weight.
There is a di f f icul ty with this method. There is no independent information about the axle bounce
frequency (f). In theory, this can be overcome by introducing a fourth equation, but an explicit algebraic solution procedure could lead to harmonic solutions for the frequency, since the sine function is many-valued. It was therefore decided to use an empirical method using assumed values for the frequency. The method was tested using assumed values of 2.0 to 4.0 Hz varied at 0.25 Hz increments.
The results using this method and the 7 sensor array are shown in Table 10. The lowest CoVs were achieved using an assumed frequency of 3.25 Hz (4.97 per cent for axle weights and 2.93 per cent for gross weights). These values were slightly lower than the equivalent figures when the mean output of 7 sensors was used (0.16 and 0.12 percentage points respectively).
16
T A B L E 1 0
Output f rom curve f i t t ing procedure (7 axle sensor array -- excludes D and F)
Assumed frequency MIF CoY P5 P10
Gross weights:
2.00 Hz 2.25 Hz 2.50 Hz 2.75 Hz 3.00 Hz 3.25 Hz 3.50 Hz 3.75 Hz 4.00 Hz
Notes: MIF =
CoV =
P5 =
P10 =
1.027 3.12 75.7 99.2 1.031 3.03 72.9 98.6 1.031 3.20 71.2 98.9 1.029 3.05 74.0 99.2 1.024 2.95 79.6 99.2 1.021 2.93 80.4 99.4 1.019 3°05 83.0 99.7 1.015 3.32 82.4 99.7 1.013 3.63 80.4 98.9
Mean Impact Factor Coeff ic ient of variation of impact factors (per cent) Proportion of weights (per cent) wi th in 5 per cent of true value Proportion of weights (per cent) wi th in 10 per cent of true value
6.3 DRIFT Tests using vehicle B were conducted in both March and September 1989, enabling the dri f t of the sensor outputs to be examined. Several types of drif t in WIM sensor outputs may occur:
- - t ime drift: a simple ageing process depending only on the passage of time;
- - wear drift: a process depending on the number and weight of axles passing over the sensor;
-- temperature drift: the sensi t iv i ty of the sensor depending on the temperature (with both an annual cycle and a diurnal cycle).
It can be dif f icult to distinguish between the sources of drift because all three are t ime dependent. A variation between results recorded in Summer and Winter could be due to any of the three processes or a combination of the three.
The sensors in the research track were not subject to signif icant wear as the track was only l ight ly traff icked between the two sets of tests. However, they were subject to ageing and temperature changes. It was colder in March (maximum temperatures 8 .7°C on the 7th and 11.3°C on the 9th) than in September (maximum temperatures 18.8°C on the 26th and 17.2°C on the 27th).
In order to measure the drift, calibration factors were calculated for both March and September for the array excluding the four wheel sensors which
were replaced between March and September. The changes in these factors over this period are shown in Table 11. Whi ls t the indicated dr i f t was greater than 5 per cent for 2 of the wheel sensors (sensors 9 and 14), the overal l dr i f t was negligible ( - 0 . 5 per cent) and the number of sensors wi th indicated posi t ive drift was equal to the number w i th indicated negat ive dri f t .
T A B L E 1 1
Change in cal ibrat ion factors of wheel sensors between March and September 1989
Change in cal ibrat ion factor Wheel sensor (per cent)
0 2 4 5 7 8
9 10 11 12 13 14 15 16
- 1 . 6 + 2 . 0 + 4 . 6 + 2 . 4 + 3 . 5 - 3 . 0
- 8 . 3 - 4 . 5 + 2 . 0 + 4 . 6 - 2 . 8 - 6 . 6 - 0 . 1 + 0 . 2
Overall - 0 . 5
Notes: Wheel sensors 1, 3, 6 and 17 were replaced between March and September. See Sect ion 5.3 for method of calculat ing cal ibration factors.
7 D I S C U S S I O N
7.1 EVALUATING THE ACCURACY OF WEIGH-IN-MOTION SYSTEMS
The accuracy of WIM systems is usual ly evaluated by comparing the WIM outputs wi th the true (static) weights ei ther for a few goods vehicles, each of which is dr iven over the sensors several t imes, or for a larger select ion of goods vehicles, each of which passes over the sensors only once, which are check-weighed separately in the normal enforcement programme. The results of these evaluations wi l l depend on the accuracy w i th which the WlM sensor(s) measures instantaneous loads, the spacing between the sensors (if there is more than one sensor), the mix of test vehic les, the speeds of the tes t vehic les, the local road profi le,
17
the method of calibration, etc. For the sensors installed in the TRRL research track, the mix of test vehicles, ' their speeds and the method of calibration was the same for each sensor. The factors which varied between sensors were the accuracy and repeatabil i ty of each sensor, which depended on manufacturing and installation, and the local road profile. The effect of these factors was expected to be small. Nevertheless the mean gross weight impact factors ranged between 0.91 and 1.10 and the equivalent coefficients of variation ranged between 6.3 and 11.8 per cent.
The results also highlight the diff icult ies in assessing the effect on WlM accuracy of individual factors such as vehicle speed. For example, considering the results from sensor C, the mean gross weight impact factor for vehicle B in September was 0.98 at 8 mile/h, 1.02 at 50 mile/h and 1.16 at 60 mile/h, apparently indicating a speed effect. However, when the average from 7 sensors is examined, the equivalent mean impact factors were 1.00 at 8 mile/h, 0.98 at 50 mile/h and 0.99 at 60 mile/h, indicating no systematic speed effect overall. Figure 3 suggests that, for the particular case of vehicle B and sensor C, there is some regular relationship between MIF and speed. This is dispelled by inspection of Table 5, showing MIFs for other vehicles, which shows no obvious correlation. It is unfortunate that, for individual vehicles, the effect can be so large. It seems likely to arise through some interaction between the characteristics of the vehicle (its axle spacing and dynamic properties) and the profile of the ground containing the sensor. As was found by Prudhoe (Prudhoe, 1988), it is probable that the best results would be obtained using a specially contructed, level, f lat and smooth pavement.
7.2 RESULTS FOR THE MULTIPLE- SENSOR ARRAY
The use of the multiple-sensor weigh-in-motion system led to a large improvement in the accuracy of determining static axle and gross weights from the sensor outputs. The coefficients of variation were reduced from, on average, 13.2 per cent for axle weights and 8.8 per cent for gross weights using a single sensor to 5.1 per cent and 3.0 per cent respectively, using the mean of 7 sensors. With this array, 90.2 per cent of axles and 99.7 per cent of gross weights were within 10 per cent of the true static values determined using an enforcement weighbridge. (The figures for a single sensor were, on average, 53.1 per cent and 62.9 per cent respectively.) The coeff icients of variation for the mean output from 7 sensors were lower than those for the mean output from 9 sensors. Generally at 9 sensor array should be more accurate than a 7 sensor array, and this better performance from 7 sensors is partly due to the sensor spacing used in the 9 sensor array: by removing sensors D and F from the non-uniform array, a more uniform 7
sensor array is left (see Figure 2). The reduction in the gross weight CoV from 3.6 per cent to 3.0 per cent is consistent with the hypothesis that uniform spacings are better than non-uniform spacings, although further work needs to be done before firm conclusions can be drawn.
A low gross weight CoV was also obtained (2.9 per cent) when one particular combination of three sensors (B, C and G) was used. (The axle weight CoV for this combination was 5.6 per cent.) The increased accuracy for this combination may be partly due to the accuracy of the three individual sensors and partly due to their spacing. (These results should be treated with care because the particular combination of sensors was identified during the analysis--the results may be due to random effects.) Theoretical work by Dr Cebon of the Cambridge University Engineering Department (Cebon and Winkler, 1990) recommended that the spacing between evenly spaced WlM sensors should be:
spacing= 2 ( n - 1) s f n 2
where: n = the number of sensors in a multiple- sensor array;
s = the average traffic speed (m/s); and f = average frequency of dynamic axle
loads (Hz).
For a three sensor array, an average traffic speed of 40 mile/h (18 re~s, the average value for the test vehicles) and an average frequency of 3 Hz, the spacing would be 2.7 metres. This is similar to the average spacing for the three sensor array consisting of axle sensors B, C and G (spacings of 2.55 and 3.18 metres = average of 2.86 metres).
Further improvements in accuracy may be possible with longer arrays based on similar spacings. Arrays with larger numbers of sensors also permit the system to check for faulty sensors by automatically comparing the results from individual sensors with the average value. (This was possible with the 9 sensor array used during the trials.)
The accuracy of the results obtained using the curve fitting algorithm and the outputs from 7 sensors was a slight improvement on the accuracy obtained using the mean value from the same 7 sensors. The small improvement probably does not justi fy the extra computation involved. The effectiveness of the curve fitting algorithm depends on the precision of the calibration procedure, on the amplitude of the dominant bounce component of the axles' imposed loads and onthe dominant bounce component having a relatively constant frequency with few (or small) superimposed higher frequency components. Nevertheless, it would be surprising if the known fixed spacings between sensors could not be harnessed in order to reduce CoVs.
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7.3 FURTHER WORK The work with the 9 sensor array has shown that significant improvements in the accuracy of WIM systems can be achieved by using a multiple-sensor array. Further work is desirable to improve the design of the array and to test its accuracy in operational use.
Both the modelling work and the results from the tests have indicated that the design of the array of sensors can be improved. In particular, the number of sensors and their spacing need to be reconsidered. Some further modelling work is needed. In particular, the model needs to be extended to represent imperfections in sensors and the quasi-static effects on axles' imposed loads due to variations in road pavement profiles.
At a later stage, operational tests on the public highway will also be required. The tests described in this report used only a limited number of vehicles. To evaluate the accuracy of a WlM system more fully, tests using a large number and variety of vehicles should be conducted. This can only be done on the public highway. Such trials would also test the durability of the sensors and the long term drift, and would enable inaccuracies associated with particular types of vehicle, types of suspension, weather conditions, etc to be investigated.
8 CONCLUSIONS
Trials on the TRRL research track of a prototype multiple-sensor weigh-in-motion system have led to the following conclusions:
1. The coefficients of variation of the impact factors calculated for individual sensors were, on average, 13.2 per cent for axle weights and 8.8 per cent for gross weights.
2. The coefficients of variation calculated from the mean outputs of 9 sensors were 5.6 per cent for axle weights and 3.6 per cent for gross weights.
3. The variation of the measurements depends on the relative positions of the sensors and on differences in accuracy between individual sensors. Because of this, the coefficients of variation obtained with a particular arrangement of only 7 sensors (5.1 per cent for axle weights and 3.0 per cent for gross weights) were lower than those for the full array of 9 sensors.
4. The coefficients of variation obtained when a curve-fitting algorithm was used to process the outputs from 7 sensors were slightly lower than those calculated using the mean value of the sensor outputs.
5. A low gross weight coeff icient of variation was obtained (2.9 per cent) when the average output of a particular combination of 3 sensors was used. However, the axle weight coeff icient of variation (5.6 per cent) was greater than the equivalent value for the mean from 7 sensors. This may not be a repeatable result and further trials are needed to confirm this result.
6. The overall drift in the calibration of the sensors between March and September 1989 was less than 1 per cent.
9 ACKNOWLEDGEMENTS
The work described in this report was carried out in the Vehicles and Environment Division of the Vehicles Group of TRRL as part of the Director's Discretionary Research Programme.
10 REFERENCES
CEBON, D and WlNKLER, C B (1990). A study of road damage due to dynamic wheel loads using a load measuring mat--exper imental programme, multiple-sensor weigh-in-motion. Strategic H ighway Research programme, National Research Council, Washington D C.
EASTMAN, C R (1988). Evaluation of portable weighpads. Department of Transport TRRL Report CR114, Transport and Road Research Laboratory, Crowthorne.
HODGE, A R (1989). An evaluation of TRRL weighscale measurement accuracy. Department of Transport TRRL Report RR214, Transport and Road Research Laboratory, Crowthorne.
MITCHELL, C G B (1987). The effect of the design of goods vehicle suspensions on loads on roads and bridges. Department of Transport TRRL Report RR115 Transport and Road Research Laboratory, Crowthorne.
MOORE, R C, STONEMAN, B G and PRUDHOE, J (1989). Dynamic axle and vehicle weight measurements: weigh-in-motion equipment trials. Traffic Engineering and Control, Jan 1989, pp 10-18.
NEWTON, W H (1989). Methods of monitoring the overloading of goods vehicles. Department of Transport TRRL Report RR 193, Transport and Road Research Laboratory, Crowthorne.
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PRUDHOE, J (1988). Slow speed 'dynamic ' axle we ighers : e f fec ts of surface irregular i t ies. Department of Transport TRRL Report RR 134, Transpor t and Road Research Laboratory, Crowthorne .
ROBINSON, R G (1988). Trends in axle loading and thei r e f fec t on design of road pavements. Department of Transport TRRL Report RR 138, Transpor t and Road Research Laboratory, Crowthorne .
SOMMERVlLLE, F K and TARRY, S (1990). Evaluat ion of a we igh - in -mo t ion pre-selector sys tem for en fo rcemen t we igh ing . Department of Transport TRRL Report CR 198, Transpor t and Road Research Laboratory, Crowthorne .
TARRY, S (1989). Deve lopment of a lorry mon i to r ing and ident i f i ca t ion system. Department of Transport TRRL Report CR165, Transpor t and Road Research Laboratory, Crowthorne .
TROTT, J J and GRAINGER, J W (1968). Design of a dynamic we ighbr idge for recording vehic le whee l loads. Department of Transport TRRL Report LR219, Transpor t and Road Research Labor~itory, C rowtho rne .
APPENDIX A:
CURVE FITTING ALGORITHM This Append i x descr ibes an a lgor i thm w h i c h solves for W, f, w and ¢ (See Sect ion 6 .2 .3 . ) .
Using the symbo ls def ined in Sect ion 6 .2 .3 , the expec ted value of an axle 's w e i g h t at the i-th sensor is g iven b y : - -
IL, = W + w.sin(E), + ¢ ) + E, . . . . . . . . . A1 where
E), = 2.Tr . f .A, .3 .6/s . . . . . . . . . . . . . . . . . . . . . A2 a n d i = 1, 2 . . . . n (the number of sensors in the array)
Here, IL,, A,, s are all known; thus O, is also k n o w n apart f rom the bounce f requency , f. If we have prior know ledge of f, for example if it can be assumed to be close to 3 Hz, equat ions can be set up w h i c h can be so lved for the unknowns , W, w and ¢ . The
method, based on minimising least square residual error, is out l ined below.
Af ter re-arranging equat ion A1, the residual error is given b y : -
E, = W + w.sinE),.cos¢ + w . c o s O , . s i n ¢ - I L , . A3
Define the fo l low ing var iables:- -
X = W; Y = w.cos¢ ; Z = w.s in¢ ; s, = sinE),, c, = cosO,; and equat ion A3 b e c o m e s : -
E, = X + Y.s, + Z . c , - I L ,
squaring: --
E, 2 = (X + Y.s, + Z . c , - I L , ) 2
. . . . . . . . . . . . A4
Values of X, Y and Z are required wh ich minimise F,(E,2), the sum of the squares of the residuals over all n sensors.
Sett ing each of the partial derivat ives of ]C(E, 2) w i th respect to X, Y and Z equal to zero yields the fo l lowing Normal Equations after some manipulat ion: --
X.n + Y.S + Z.C = P = ElL, X.S + Y.E + Z.D = G = Es,.IL, X.C + Y.D + Z.F = H = Ec,.IL,
where: --
S = E s j C = Ec,; D = Es,.c,; E = E(s,) 2 F = E(c,) 2 n = E,; Q = E(IL,)2;
. . . . . . . . . . . A5 . . . . . . . . A6 . . . . . . . . A7
The values of X, Y and Z wh ich sat isfy these equat ions minimise the least square residual error (]C(EL2)). We are concerned pr incipal ly w i th X, the steady state value of the axle we igh t and this is" obtained by el iminat ing Y and Z between equations A5 to A7 w i th the fo l low ing resul t : - -
(H .D - G.F).(C.D - F.S) - (H.C - F.P).(O 2 - E.F) X = (C.D - F.S) 2 - (C 2 - n.F).(D 2 - E.F)
back-subst i tut ing yields Y and Z: - -
( H . D - F.G) - X . ( C . D - F.S) Y =
( D 2 - E.F)
Z = ( P - Y . S - n . X ) / C
The residual is given by : - - ]~(E, 2) = P.(P.S + 2.Y.S + 2 . Z . C - 2 . P ) +
Y.(Y.E + 2 . Z . D - 2.G) + Z . ( Z . F - 2.H) + 2.Q
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