THEORETICAL TESTING OF A MULTIPLE-SENSOR BRIDGE WEIGH-IN MOTION ALGORITHM

Transcription

1 7th International Svmposim on Heavv Vehicle Weights & Dimensions Delft. The Netherlands. Jne THEORETICAL TESTING OF A MULTIPLE-SENSOR BRIDGE WEIGH-IN MOTION ALGORITHM Artro Gonzalez Department of Civil Engineering, University College Dblin, Earslfort Terrace, Dblin 2, Ireland Mark F. Green Department of Civil Engineering, Qeen's University at Kingston, Ontario, Canada K7L 3N6 Egene 1. O'Brien Department of Civil Engineering, University College Dblin, Earslfort Terrace, Dblin 2, Ireland) Haiyin Xie Department of Civil Engineering, Qeen's University at Kingston, Ontario, Canada K7L 3N6 ABSTRACT A Bridge Weigh-In-Motion (B-WIM) system is based on the measrement oftheflexre in a bridge and the se of measrements to estimate the attribtes of passing traffic loads. The information provided by strain sensors and axle detectors is converted into axle weights throgh the application of an algorithm. Becase the dynamic interaction between bridge and vehicle has many parameters for which estimation is very difficlt from raw bridge strains, the traditional B- WIM algorithm consists of static eqations of eqilibrim. Hence, dynamics can be a significant sorce of inaccracy in B-WIM systems depending on the bridge and vehicle characteristics. In this papel the inflence of dynamics on B- WIM accracy is assessed nmerically by simlating the passage of a nmber of vehicles over a bridge. Then, the theoretical bridge response is sed to test a new B- WIM algorithm based on mltiple longitdinal sensor locations and the traditional algorithm based on one single location. In smooth road conditions, the mltiple sensor B-WIM achieved better reslts, while the traditional B- WIM failed to predict individal axle weights accrately. In rogh conditions, reslts were mch poorer de to high dynamic excitation and only gross vehicle weight was predicted accrately. Keywords: accracy, bridge, vehicle, dynamics, WIM. INTRODUCTION In the 197' s in the USA, the Federal Highway Administration (FHW A) started stdying Bridge WIM systems to acqire WIM data. Moses (1979) introdced an algorithm based on the assmption that a moving load will case a bridge to bend in proportion to the prodct of the load magnitde and a reference crve representative of the bridge behavior, the inflence line. In the 198's, Peters (1984) developed AXWAY in Astralia. This B-WIM system is based on the same concept of inflence line. A few years later, he derived a more effective system for weighing trcks sing clverts, known as CUL WAY (Peters 1986). Both the American and Astralian systems have been sed for commercial applications on bridges and clverts. Bridge Weighing Systems Inc. developed one of the first commercial B-WIM systems in 1989 on the basis of Moses' algorithm (Snyder 1992). In the 199's, three new independent B-WIM systems were developed in Ireland, Slovenia and Japan (O'Connor 1994, Znidaric & Bamgartner 1998, Ojio et al. 2). All of these B-WIM systems se algorithms based on static eqations of eqilibrim combined with measrements at one single longitdinal section. Becase the data being recorded is the sm of static and dynamic components, the dynamic component is generally ignored. However, bridge and trck dynamics have been proven to be one of the sorces of inaccracy of static algorithms. Traditional averaging or filtering techniqes are not sitable for the removal of dynamics in every case. The data inpt is particlarly difficlt to analyse from the dynamic response of bridges de to the wide range of trcks on bridges with different classifications and with different dynamic properties. In this paper, theoretical simlations are sed to evalate the inflence of sspension type and road profile on the accracy of a B-WIM algorithm. Additionally, the static eqations of the traditional algorithm are extended to mltiple longitdinal sensor locations along the bridge. Both one-sensor and mltiple-sensor based algorithms are tested in a highly dynamic scenario with the first natral freqency of the bridge close to trck body freqencies. 19

2 MULTIPLE SENSOR BRIDGE WEIGH IN MOTION (MS-BWIM) ALGORITHM Kealy & O'Brien (1998) first attempted to develop a weigh in motion system capable of giving a history of axle weights at each point in time as a trck crosses a bridge at normal highway speed by sing mltiple strain gage sensor locations. However, simltaneos eqations reslted dependent in some cases and a soltion was only feasible for redced nmber of axles on the bridge (eqal to the nmber of independent eqations at that instant). It has been fond that combining more sensors with a least sqares fitting techniqe allows determination of a higher nmber of axles and makes the algorithm applicable to bridges with longer spans. This instantaneos calclation along the length of the bridge reqires many sensors; well in excess of the nmber of axles. Ths, if there are a nmber of sensors, rn, eqal to or greater than the nmber of axles n, it is possible to minimise the error fnction defined in Eqation 1 at each instant t: k=m f =i)ck-,j" k ; 1 (1) where ck is the theoretical total strain de to the applied load at location k and Ek is the measred strain de to the applied load at sensor location k. By assming linearity and applying the principle of sperposition, it is possible to express the strain at each sensor as: (2) where: Ci) : vale of inflence line of strain at sensor location i de to moving load located atj Wj : applied load at location j, n : total nmber of axles on the bridge. By combining Eqations 1 and 2 at each instant t: k=m f = )CklWI +ck2w2 +",+cknw n - k)2 k=l (3) Differentiating Eqation 3 with respect to the axle weight, W i and setting it eqal to zero gives: (4) The fll set of eqations can be expressed in matrix form as: k=m k=m k=1il k=1il LCklCkl LCk2 C kl LCknCkl L kckl k=l k=1 k=1 k=l k=m k=1il k=m (:'l k=1il L C kl C k2 L C k2 C k2 LCknC k2 L k C k2 k=l k=l k=l k=l k=m k=m k=1i1 k=1ii LCklCkn L C k2 C kll LCkllCkll L kckn k=l k=1 k=l k=l (5) Finally, applied loads (weights) can be calclated from Eqation 6: (6) If the nmber of strain sensor locations is high enogh, Eqation 6 provides a soltion along most of the bridge. The static vale can be obtained from the root mean sqare of the calclated instantaneos axle forces. 11

3 THEORETICAL SIMULATIONS The bridge and trck are modelled separately and combined in an iterative procedre. The prediction of bridge response involves convoltion of the vehicle loads with modal responses of the bridge and the convoltion integral is solved by transformation to the freqency domain sing the fast Forier transform. The method is then extended by an iterative procedre to inclde dynamic interaction between the bridge and an arbitrary mathematical model of a vehicle. Green & Cebon (1994) illstrate the effectiveness of this calclation method, the convergence of the iterative procedre, and the good agreement with experimental data. The Bridge Weigh In Motion (B-WIM) system is calibrated with a two-axle flly laden linear sprng vehicle (for degrees of freedom). Then, the system is evalated with a for-axle vehicle and two different sspension systems (air and steelleao. The bridge is modelled as a beam 3 m long. Strain otpt is calclated every.1 s (1 Hz) at 5, 1, 15,2 and 25 m from the bridge spport. Figre l(a) shows the records in free vibration after the vehicle has left the bridge and Figre 1(b) the corresponding spectra for the three rns of the two-axle calibration vehicle. From these Figres,.97% damping and a 3.33 Hz first natral freqency are obtained. The vehicle models developed by Green et al. (1995) are a steel sprng for-axle articlated vehicle validated experimentally, and a similar vehicle fitted with air sspensions and hydralic dampers. The dynamic response of the 3 m beam model is obtained for crossings of each of these two vehicles. The for-axle articlated vehicle has 11 degrees of freedom as shown in Figre 2. In this Figre, elements A, Band C represent a spring with adiabatic behavior, Colomb friction, and a linear spring/damper, respectively. For the vehicle with air sspension, models of air springs with parallel viscos dampers replace the steel-spring elements on the drive axle and the two trailer axles. The sspension on the steer axle is the same for both vehicle models. Two srface profiles, three different speeds (55, 7 and 85 km/h), and three different loading conditions are chosen for the simlations. Figres 3 and 4 represent the applied dynamic forces over same length of smooth and rogh road profile respectively. It can be seen how these forces increase with speed and road roghness. Steel sspensions are clearly more sensitive to these changes, except for a singlarity localised at abot 9 m. This singlarity is de to a bmp in the road that excites the wheel-hop mode of the vehicle. A steel sspension is better damped at high excitation amplitdes than an air sspension. However, for low excitation the friction in the steel-springs is not overcome and damping is only provided by the tires. Under sch circmstances any viscos shock absorber can provide higher damping than the friction in the steel springs The load sharing between axles within the tandem of the air-sprng vehicle is less than in the steel-sprng vehicle. The amplitde of the applied dynamic wheels is higher for worse road conditions as shown in Figre 4. Ths, bridge response will increase with road roghness. Also, body bonce modes of vehicle vibration are excited by longer wavelength variations in road profile whereas axle hop are excited by short wavelength defects sch as pot-holes, road debris, a rogh repair or a mis-aligned joint in a bridge, more likely to occr in a road in poor conditions. The strain response at the bridge midspan for the flly laden for-axle vehicle on a smooth profile is represented in Figre 5. As expected, the steel sspended vehicle cases higher dynamic oscillations on strain than the airsspended vehicle. Figre 6 shows the bridge response at midspan for the flly laden vehicle on a rogh profile. The maximm dynamic response takes place at 7 km/h for the steel-sprng vehicle and 85 kmlh for the air-sprng vehicle. It can be seen that the air-sspended vehicle cases significantly lower dynamic bridge response than the steel-spring sspended vehicle and it is less sensitive to a change in speed. In comparison to the smooth profile, the dynamic response de to the steel-sprng vehicle increases by over 1%. These high dynamics sggest the occrrence of freqency matching between the steel-sprng vehicle and the bridge. Conseqently, Bridge WIM will tend to be less accrate in the cases of steel-spring sspensions, rogh road profile, and, for this bridge, for vehicle speeds near 7 km/h. Xie (1999) investigates the maximm interaction of bridges with natral freqencies close to air-sprng vehicles and vehicle axle-hop vibrations. CALIBRATION The traditional static and mltiple-sensor B-WIM algorithms are calibrated with longitdinal bending at midspan and bending at five points eqally spaced along the bridge respectively. Accracy classes are determined according 111

4 to the COST323 Eropean Specification on WIM (1999). Ths, the calibration takes place in fll repeatability conditions (rl): A two-axle vehicle passing at different speeds, one load and one lateral position on the road. Then, the following section evalates the system in limited reprodcibility conditions (RI): two 4-axle vehicles passing over the bridge at different speeds with different loads. Reslts are given for two different road profiles. Concerning calibration, the shape of the theoretical inflence line is known from beam theory and the static algorithm only reqires a calibration factor to adjst the magnitde of the strains to the theoretical model. If the exact inflence line for bending moment is sed, the calibration factor is the prodct of the modls of elasticity and the section modls. Several approaches are available for obtaining the real shape of the inflence line from an experimental record (Gonzrez 21). For this analysis, the calibration factor is obtained by dividing the real static gross vehicle weight by the predicted weight of the calibration trck. A linear sprng two axle vehicle with 4 m axle spacing, kn static weight in the front axle and kn in the rear axle is sed for calibration. Smooth Road Profile At one particlar location i, bending moment, M i, is proportional to strain, ;, throgh the elasticity, E, and section modls, Si' as shown in Eqation 7. (7) Bending moment depends on the shape of the inflence line, bridge length, static axle weights, axle spacings and position of the calibration vehicle. The reslts of the static calibration are shown in Figre 7. The calibration factor changes for each speed very slightly (2.IlxI 1o at 55 kmlh, 2.1 xl 1 at 7 kmlh and 2.8 xl 1 at 85 km/h). An average vale of2.1o xlo IO is adopted. Other sensor locations sed for MS-BWIM are calibrated in the same way. The axle forces predicted by MS BWIM are compared to the simlated applied forces in Figres 8(a) and (b). A clear correspondence between predicted and simlated instantaneos wheel forces is not evident, bt the average vale is very similar in both cases. Dynamic wheel forces are strongly excited by a bmp located at abot 5 m from the bridge end. Vales tend towards infinity at both ends of the instantaneos calclation (very small vale of the determinant in Eqation 6) and they are not taken into accont in the determination of the static weight. Figre 9 illstrates the reslts in static weights for the calibration vehicle. The front axle is the lightest and the percentage error tends to be higher than in the rear axle as shown in Figres 9(b) and (c). MS-BWIM is slightly worse than B-WIM for predicting gross vehicle weight, bt the improvement in individal axle weights is very significant. Rogh Road Profile The calibration of the static algorithm is shown in Figre 1. The scale factor between real and predicted gross weight is 2.12xI 1o at 55 kmih, 2. 12xlO lo at 7 kmih and 2.8xlO 1 at 85 kmlh. An average vale of 2.9x1 1 is adopted as the calibration factor. Figre 11 shows the instantaneos axle forces from the simlation rn at 55 kmih and the corresponding prediction by MS-BWIM. As in the smooth road profile, the forces increase enormosly at abot 5 m from the bridge end and the instantaneos soltion from here to the end of the record is ignored. There is a large increase in oscillations over the smooth case. Figre 12 shows the variation of axle forces at 7 kmlh. The prediction of the static answer proves more difficlt at higher speeds, especially in the case of a rogh profile. Figre 13 shows the calclation at 85 kmlh. The front axle is overweighed. MS-BWIM is not able to distingish which is the force applied by each axle de to the strong dynamics and the limitation in the nmber of sensors. Ths, Figres 13(a) and (b) show how the prediction of the front axle follows a pattern similar to the simlated rear axle. The errors in individal axle weights for the test vehicle are given in Figre 14. Calibration reslts are mch poorer than in the case of a smooth profile (Figre 9). Reslts in individal axle weights at 85 kmlh are very inaccrate, bt static B-WIM can predict gross weight with less than 2% error. 112

5 CHECK OF ACCURACY A for-axle vehicle (axle spacings 3.49, 6.76 and 2 m) is chosen for assessment of the calibration carried ot in the previos section (inflence line and calibration factors obtained with the two-axle calibration vehicle do not sffer any frther maniplation). The static weights of this vehicle were nknown to the first athor prior to the calclations. Two types of sspensions are investigated: air and steel leaf sprng. These two vehicles are driven at three different speeds (55, 7 and 85 km/h) and three loading conditions (nloaded, half and flly laden). Smooth Road Profile Figre 15 shows the approximation by the static B-WIM algorithm to the response cased by a flly laden 4-axle trck at 7 km/h. The reslts illstrated in Figre 15 are based on the concept of an inflence line. The contribtion of each axle separately and all axles to the expected static strain are represented. The strain record cased by a steel leaf sspension exhibits a higher deviation from the fitted response than air sspension. Hence, predictions of individal axle weights are expected to be more accrate for air sspensions. Figre 16 shows the simlated load history and the prediction by MS-BWlM for the case of a flly laden 4-axle trck with air sspension travelling at 7 km/h. Figres 16(c) and (d) show that the third and forth axles allow for an instantaneos soltion only when the first axle is located between 17 and 25 m from the bridge start (as reslt of the nmber of trck axles, their spacings and the nmber of sensors, their locations and inflence lines). Figre 17 shows the reslts of MS-BWIM when sing the same trck and speed as Figre 16, bt with a steel sspension. From Figres 16(c), 9.16(d), 9.l7(c) and 9.l7(d), the prediction of the third and forth axles can be seen to be more difficlt for the leaf sprng than for the air sprng vehicle. Tables 1 and 2 give accracy classes according to the COST323 WIM Eropean Specification (1999) for each criterion and algorithm. MS-BWIM is very accrate for all single criteria, even axles of a grop in class B(lO). The static B-WIM algorithm can predict gross weight accrately (A(5)), bt fails to predict single axles (E(45)). All reslts are represented in Figre 18. Rogh Road Profile Reslts for a rogh road profile are very poor and only gross weight give sensible levels of accracy. The poor accracy of a B-WIM algorithm on a rogh profile can be explained by Figre 19. Figre 19 represents the approximation by the static algorithm to the total strain generated by a flly laden trck at 7 km/h. The total response is far from this static response de to the high dynamic oscillations. The static algorithm is very inaccrate and their approximations (by minimising difference between total response and expected static response) can lead to negative vales for individal axle weights: For instance, the second and forth axles in Figres 19(a) and (b) (thin line representing bending moment diagram de to a single axle is over the x-axis). As in the case of a smooth profile, steel leaf sspensions give worse reslts than air sspensions. If the road is in a poor condition, algorithms based on linearity and sperposition do not appear to offer a valid soltion. MS-BWIM is also extremely inaccrate becase it minimises the instantaneos soltion by sing inflence lines at many locations. Figre 2 shows the reslts for the same rn as Figre 19(a). The static vale can be estimated from instantaneos vales when the first axle is located between 18 and 25 m from the bridge start. However, the third axle and forth axles are strongly overweighed and nderweighed respectively (Figres 2(c) and (d)). According to Tables 3 and 4, gross weight is the only criterion which gives reasonable levels of accracy. The static B-WIM gives the best reslt - C(l5) for gross weight (Table 3). The poor reslts in individal axles are de to the failre of the static algorithm to estimate the static component cased by each axle from the total bending response (illstrated in Figre 19). Figre 21 illstrates the estimation of every identity in the sample. However, if the test took place in extended repeatability conditions (r2) taking into accont only the rns of the air sspension trck, the accracy class for gross weight wold be raised to A(5) and C(15) for the static B-WIM and MS-WIM algorithms respectively. 113

6 CONCLUSIONS A B-WIM system has been theoretically tested in very adverse dynamic circmstances. A two-axle linear sprng vehicle model has been sed for calibration and accracy has been assessed with a for-axle non-linear sprng vehicle 1 degrees of freedom). Air and steel sspensions on both smooth and rogh pavements were considered. In smooth road conditions, MS-BWIM achieved the most accrate overall class BOO) (corresponding to the criterion of axle weights within an axle grop, bt B+(7) for the criterion of individal axle weights). The traditional static B-WIM had the same accracy class, A(5), for gross vehicle weight as MS-BWIM, bt it failed to predict individal axle weights accrately (E(45)). The 3 m span length made it difficlt to identify individal axles from strain at only one location, and MS-BWIM derived a more accrate vale from the load history. B-WIM accracy decreased for steel sspensions becase bridge dynamic response was more important than for air sspensions. The poorest reslts were obtained with steel sspensions on rogh profiles. Bridge strains oscillated with higher amplitdes when crossed by the steel sspension trck de to the proximity of the freqencies of the trck and the bridge, which reslted in hge errors in any B-WIM algorithm. In these conditions, the estimation of individal axle weights is very inaccrate (class E), bt the traditional static B-WIM algorithm can still provide reasonable vales for gross vehicle weight (COS)). In order to deal with high dynamic bridge excitation, the se of dynamic models and the soltion of the dynamic inverse problem in B-WIM practice need to be analysed in the near ftre. In the interim, bridges selected as B-WIM sites shold have natral freqencies that do not coincide with the dominant natral freqencies of heavy vehicles. COST323 (999), Eropean Specification on Weigh-In-Motion of Road Vehicles, version 3, EUCO_COST/323/8/99, LCPC, Paris, Agst, 66 pp. Gonzalez, A. (21), 'Development of Accrate Methods of Weighing Trcks in Motion', Ph.D. Thesis, Department of Civil Engineering, Trinity College Dblin, Ireland. Green, M.F. & Cebon, D. (994), 'Dynamic Response of Highway Bridges to Heavy Vehicle Loads: Theory and Experimental Validation', Jornal of Strctral Engineering, ASCE, Vol. 121, No. 2, Febrary, pp Green, M.F., Cebon, D. & Cole, DJ. (1995), 'Effects of Vehicle Sspension Design on Dynamics of Highway Bridges', Jornal of Strctral Engineering, ASCE, Vol. 121, No. 2, Febrary, pp , (995). Xie, H. (999), 'The Effects of Srface Roghness and Vehicle Sspension Type on Highway Bridge dynamics', M.Sc. Thesis, Department of Civil Engineering, Qeen's University at Kingston, Ontario, Canada. Kealy, N.I. & O'Brien, E l. (998), 'The Development of a Mlti-sensor Bridge Weigh-In-Motion System', 5th International Symposim on Heavy Vehicle Weights and Dimensions, Maroochydore, Astralia, March/April, pp Moses, F. (1979), 'Weigh-in-motion System sing Instrmented Bridges', Transportation Engineering Jornal of ASCE, Proceedings of the American Society of Civil Engineers, Vol. 15, No. TE3, May, pp O'Connor, J.M. (1994), 'The Development of a Weigh In Motion System in Ireland', M.Sc. Thesis, Trinity College Dblin, Ireland. Ojio, R., Yamada, K. & Shinkai, H. (2), 'BWIM Systems sing Trss Bridges', Bridge Management For, Edited by M.J. Ryall, G.A.R. Parker and J.E. Harding, Thomas Telford, University of Srrey, UK, pp Peters, RJ. (1984), 'AXWAY - A System to Obtain Vehicle Axle Weights', in Proceedings 12th ARRB Conference, 12(1), pp Peters, R.J. (1986), 'An Unmanned and Undetectable Highway Speed Vehicle Weighing System', in Proceedings 13 th ARRB Conference, 13(6), pp Snyder, R.E. (992), 'Field Trials of Low-Cost Bridge WIM', in Pblication FHWA-SA-92-14, Washington DC. Znidaric, A. & Bamgftner, W. (1998), 'Bridge Weigh-In-Motion Systems - An Overview', in Preproceedings of the 2 nd Eropean Conference on Weigh-In-Motion, eds. E.J. O'Brien & B. lacob, Lisbon, Portgal, pp

7 Table 1- Accracy classification for static B-WIM algorithm (smooth profile) (R 1) (n: Total nmber of vehicles; m: mean; s: Standard deviation; no: level of confidence; B: tolerance of the retained accracy class; Bmin: minimm width of the confidence interval for no; n: Level of confidence of the interval [-B,B] ) Relative error statistics Accracy calclation Criterion n m s no Class B Bmin 1t Class (%) (%) (%) (%) (%) (%) Retained Single axle E(45) Grop of axles C(15) E(45) Gross Weight A(5) Table 2- Accracy classification for static MS-BWIM algorithm (smooth profile) (RI) (n: Total nmber of vehicles; m: mean; s: Standard deviation; no: level of confidence; B: tolerance of the retained accracy class; Bmin: minimm width of the confidence interval for no; n: Level of confidence of the interval [-B,B] ) Relative error statistics Accracy calclation Criterion n m s no Class B Bmin 1t Class (%) (%) (%) (%) (%) (%) Retained Single axle B+(7) Axle of grop B(1) Grop of axles A(5) BOO) Gross Weight A(5) Table 3- Accracy classification for static B-WIM algorithm (rogh profile) (RI) (n: Total nmber of vehicles; m: mean; s: Standard deviation; no: level of confidence; B: tolerance of the retained accracy class; Bmin: minimm width of the confidence interval for no; n: Level of confidence of the interval [-B,B] ) Relative error statistics Accracy calclation Criterion n m s no Class B Bmin 1t Class (%) (%) (%) (%) (%) (%) Retained Single axle E(3) Grop of axles E(1) E(3) Gross Weight C(5) Table 4- Accracy classification for static MS-BWIM algorithm (rogh profile) (RI) (n: Total nmber of vehicles; m: mean; s: Standard deviation; no: level of confidence; B: tolerance of the retained accracy class; Bmin: minimm width of the confidence interval for no; n: Level of confidence of the interval [-B,B] ) Relative error statistics Accracy calclation Criterion n m s no Class B Bmin 1t Class (%) (%) (%) (%) (%) (%) Retained Single axle E(3) Grop of axles E(5) E(5) Gross Weight E(3)

8 - 55kmlh - 7kmlh - 85 kmlh VJ c:: '@ b VJ ;... (.) , ' (a) Time Domain Time (s) : [:- - - = - : : : : -: : : : : : : : - - : i : t:::.::::::::: : ::::: O,..-- o Freqency (Hz) (b) Freqency Domain Figre 1 - Bridge response in free vibration de to 2-axle calibration trck (smooth profile) A A I Figre 2 - Two dimensional tractor and trailer vehicle model with steel-spring sspensions (11 degrees of freedom) 116

9 -Axle3 I Distance along the road (m) Z 4 Q) 35 I- [.I Distance along the road (m) 1 (a) Air sspension at 55 kmlh (b) Steel sspension at 55 kmih z Q) U I o [.I.. o (b) Air sspension at 85 kmlh Distance along the road (m) (c) Steel sspension at 85 kmlh Distance along the road (m) Figre 3 - Applied forces by air- and steel-sprng flly laden tandem (smooth profile) 117

10 - Axle Z 8 Cl) 6 Co) Z 8 6 Cl) Co)... & o Distance along the road (m) Distance along the road Cm) Ca) Air sspension at 55 kmlh 12 1 Z 8 Cl) Cb) Steel sspension at 55 kmlh Distance along the road (m) 1 o Distance along the road Cm) 1 Cb) Air sspension at 85 kmlh Cc) Steel sspension at 85 kmlh Figre 4 - Applied forces by air- and steel-sprng flly laden tandem (rogh profile) 118

11 - Air sspension Steel sspension -5 (a) 55 kmlh o er. c::. -1 er o o (b) 7 kmlh (c) 85 kmfh Figre 5 - EffeCt of vehicle speed and sspension on bridge response (smooth profile) 119

12 r : -: :;l- " 'j}tfrj _i o Air sspension Steel sspension (a) 55 kmlh (b) 7 kmfh o =: ",,=-----i --- '; '-- ; 'ii_; o r./) 25 c:..t:: r./) o (c) 85 kmlh 4 Figre 6 - Effect of vehicle speed and sspension on bridge response (rogh profile) 12

13 5 o --,--,---- "" "-1O : 11 :: = _ - : : : = " Static strain de to first axle -- Static strain de to second axle Total static approximation " o Simlated strain (a) 55 kmlh 5 '" -5 "C; 1= -1 '" 2-15 " t:: o T o I (b) 7 kmlh (c) 85 kmlh Figre 7 - Calibration of a static B-WIM algorithm (smooth profile) -- From MS-BWIM algorithm - From Simlation 8 7 Z 6 C 5 Q) Co)... 4 Q :.- L _ Z C & I I o L (a) Front axle (b) Rear axle Figre 8 - History of axle forces for 2-axle calibration trck at 55 kmlh (smooth profile) 121

14 11.5% 11.% 1.5% : 1.% "-' 99.5% 99.% 98.5% 98.% (a) Gross Weight Sp eed (krn/h) o B-WIM El] MS-BWlM 125% 15% 12% 13%. : 115% "-' 11% 15%. 1% 98% 95% 1% 93% 95% 9% Sp eed (kmlh) Sp eed (kmlh) (b) Front axle (c) Rear axle Figre 9 - WIM/static weight verss speed for 2-axle calibration trck (smooth profile) 122

15 1 o --,--,---,---, IZl c:::. -1 IZl e ,- - - I '- - -, : -5 1_ -----: : o Static strain de to first axle -- Static strain de to second axle -- Total static approximation - Simlated strain (a) 55 kmlh IZl 1 c:::. -1 1::: IZl l-< -2 U o ,---,--- o IZl c:::. IZl ; I _ ' o Cb) 7 kmlh Cc) 85 kmlh Figre 1 - Calibration of a static B-WIM algorithm (rogh profile) - From M S-BWIM algorithm - From Simlation 9 T,,_ 6 I , Z 6 3 C 3 Q) o ,- I , I ' ' o U l-< Ca) Front axle (b) Rear axle Figre 11 - History of axle forces for vehicle at 55 kmlh (rogh profile) 123

16 Z - From MS-BWIM algorithm - From Simlation a) a) 4 4 Cs Z (a) Front axle (b) Rear axle Figre 12 - History of axle forces for vehicle at 7 kmlh (rogh profile) - From M S-BWIM algorithm - From Simlation Z 12 Z a) 4 Cs 4 a) (a) Front axle (b) Rear axle Figre 13 - History of axle forces for vehicle at 85 kmlh (rogh profile) 124

17 11% 18% 16% o 14% en 12% 1% 98% 96% 94% 55 7 Sp eed (kmlh) 85 D B-WIM le) MS-BWIM (a) Gross Weight 3% 275% 25% o 225% en 2% 175% 15% 125% 1% 75% 55 7 Sp eed (kmlh) % 9% fl 7% en 5% 3% 1% -1% 55 7 Speed (krnlh) 85 (a) Front axle (b) Rear axle Figre 14 - WIM/static weight verss speed for 2-axle calibration trck (rogh profile) - Approx. total static strain - Total strain -- Approx. strain de to one axle en I: ce.b en -1 ; I I I I o (a) Approximation for air sspension o,---,--,, ' I I I T - -! j o (b) Approximation for steel sspension Figre 15 - Inflence of sspension on static B-WIM (smooth profile) 125

18 Z - From M S-BWIM algorithm - From Simlation Q) Q) ; (a) First axle Z Z ; : L (b) Second axle Q) Q) Z First axle position I First axle position First axle position (c) Third axle (d) Forth axle Figre 16 - Instantaneos calclation for a leaf-sprng 4-axle trck (smooth profile) 126

19 - From M S-BWIM algorithm - From Simlation 12 1 Z 8 ) 6 ;... 4 (a) First axle Z ) ( Z 8 ) ; (b) Second axle Z ) ; (c) Third axle (d) Forth axle Figre 17 - Instantaneos calclation for a steel sprng 4-axle trck (smooth profile) 127

20 13%.c 12% 1) 3 11 %. 1% rz) 99% 98% 97% 96% B-WIM o MS-BWIM Static weight (kn) (a) Gross vehicle weight 11% 16%.c on 14% 3 12%.c 15% 1) 3 1%. 95% rz) 9% 85% 8% 75% 4%. 1% rz) 8% 6% Static weight (kn) Static weight (kn) (b) Axle grop (c) Individal axle weights Figre 18 - WIM/Static verss real static weights for 4-axle trck (smooth profile) -- Approx. total static strain - Total strain -- Approx. strain de to one axle </) s:::.c;:j b </) I ;- - - l I.!... 1 ' ' _ I o (a) Approximation for air sspension 3 i 1"tIlliiiftJIiIJ;ir"" , I I _ o : -' - (b) Approximation for steel sspension Figre 19 - Inflence of sspension type on static B-WIM (rogh profile) 128

21 ... From M S-BWIM algorithm - From Simlation Z 1 C 75 Cl) ; Z 1 C 75 Cl) ; (a) First axle Z 1 C 75 Cl) ; (c) Third axle (b) Second axle Z 1 C 75 Cl) (d) Forth axle o , r o Figre 2 - Instantaneos calclation for a 4-axle trck (rogh profile) 129

22 13% :c 12% 1) v 11%. 1% Cil ci5 9% 8% 7% 6% D- O_ Static weight (kn) 4> B-WIM o M S-BWIM (a) Gross vehicle weight 2% 4% :c 175% 1) v 15% 125%. Cil ]% ci5 75% 5% 25% % Static weight (kn) :c 3% 1) v 2%. 1% Cil ci5 % -1% -2% -3% Static weight (kn) (b) Axle grop (c) Individal axle weights Figre 21 - WIMlStatic verss real static weights (rogh profile) 13