Direct Enforcement in Belgium with High Speed Weigh-in-Motion (HS-WIM)

Abstract

Interest for high speed weigh-in-motion of vehicles, or HS-WIM keeps growing worldwide. The main purpose of such systems is checking weights of vehicles in a self manner, in order to impose a penalty to overloaded ones. Overloaded vehicles may cause several problems such as safety issues, road deterioration or unfair competition. Walloon Public Service (WPS) has dealt with the settings and approval of a HS-WIM system in Belgium. The latest resurfacing of the roadway around the prototype provides good-quality data that allows for reaching excellent results in terms of accuracy of the weight estimation. Therefore, direct weight enforcement may be activated since the system has a type approval certificate to be used in accordance with legal metrology requirements.

1. Introduction

Many issues such as deterioration of the roadway or lack of safety may arise due to overloaded vehicles on a highway (see, for example, [1]). For the moment, controlling and punishing the overloaded vehicles is a heavy work. Indeed, each vehicle must be, generally, deviated from the road to the nearest static weighing system or low-speed weigh-in-motion system (LS-WIM). This approach requires a lot of time and only a small part of the traffic can be checked. Several existing articles are dedicated to a development and an implementation of HS-WIM systems. For instance, Ref. [2] presents a network of HS-WIM stations implemented on highways and motorways. This network seeks to face two main problems in France. The first one is the increase of the total number of heavy vehicles over time. The second one is the decrease of the total number of static weighings in the last few years.

Another paper [3] presents the HS-WIM systems installed in Czech Republic. The authors show the statistical results of the initial verification for their weighing system and explain all the tests of resistance that it must pass to be certified by the legal metrology.

Alongside the presentation of statistical results, more theoretical articles as [4] develop a mathematical background for HS-WIM, especially for the multi-sensors case. One of the main problems of weighing in high speed remains the extraction of the static load from the dynamics load. To this end, the authors in the latest article figure out the most effective distance between sensors in order to estimate the static weight more accurately. This procedure aims to design the optimal space between sensors compared to the average speed range and frequency of the exciting vibration caused by the roughness of the pavement. However, the bigger the number of sensors, the higher the accuracy of the estimations. In our case, good performances with only two sensors per wheel are reached. This can be achieved by a rigorous renewal of the pavement and a decrease of the dynamic load.

The goal of the WPS is to weigh automatically the vehicles at real speed with the use of piezo-electric quartz sensors. In [5], these sensors were presented as a solution for direct enforcement and their electro-mechanical behavior obtained during several experiments were analyzed. In particular, compression and bending test of the sensors were carried to describe their electrical response. The article also reports results of experiments with suspended and moving masses to show the effect of dynamic loads.

Besides the performances of the sensors, the renewal of the roadway improves the quality of the data collections and the trust in the given results. Under some individual validity conditions for vehicles, classes A and C are reached for trucks and vans, respectively, according to OIML recommendations [6]. In this paper, we explain what has been put in place in order to reach confidence level for the accuracy of a legal HS-WIM system: i.e., a weighing system able to produce metrological weights. The whole system consists of a renewal of all the layers of the road section along 250 m and a double grid of sensors with optimized parameters for the weighing algorithms.

After giving details on the road structure and the configuration of the grids, we explain how the data set of comparative weights were obtained. We then present the results and discuss them.

2. Materials and Methods

2.1. Road and Sensors Layout Description

In July 2019, the roadway was renewed, and this makes the HS-WIM site in the class II (good) according to the COST323 criteria [7]. As it was explained in [8], “The trunk bottom of the roadway is made of sand (or clay sand) with excellent natural lift. Draining sand with a minimum thickness of 20 cm is installed on this trunk floor. On this sub-foundation, 20 cm-thick lean concrete was laid, followed by 22 cm of asphalt broken down into four layers, as follows: 7 cm Type III, 7 cm Type III, 5 cm Type I and 3 cm Type II”.

In this new configuration for the roadway, the HS-WIM system was installed according to the diagram in Figure 1. The description of the HS-WIM is represented with the piezo-quartz sensors in green, position sensors in black, temperature sensors in red and magnetic loops in blue. The arrows indicate the traffic direction.

Two independent WIM systems compute the weight of the same vehicle. The first one (A) is used to make of the weight estimate, while the second one (B) provides a second measurement for legal metrology purpose, i.e., to confirm the first measurement.

2.2. Data Collection

The data collection campaign started in September 2019 and ended in February 2020. The environmental conditions of the collection are the Full Environmental Reproducibility (III) due to seasonal effects, as explained in [7]. Since a vehicle is weighed only once and came directly from the traffic flow, the Full Reproductibility Conditions (R2) are considered. The campaign and the calibration focused on the following types of vehicles:

• T2S3: two-axle tractor with a semi-trailer on a tridem axle;
• U2: vans i.e., two-axle rigid vehicle with a maximum authorized weight of 3.5 tons.

The weights measured in motion are systematically compared to the check measurements (LS-WIM), in order to estimate the error of the weighing. The LS-WIM scale is located 6 km downstream on the same road. It is a B(1) scale according to the OIML R-134 [6].

Table 1. Number of vehicles.

Number	T2S3		U2
Validity Criterion	OFF	ON	OFF
All periods	404	180	188
September	97	40	1
October	203	87	46
November	31	15	37
December	25	15	33
January	36	17	57
February	12	6	14

shows the number of each type of vehicles for each month. Each system uses a validity criterion that can be turned ON or OFF. If it is turned ON, the correctness of the passing for each vehicle is verified before giving an estimate of the weight. In this case, an estimation is ignored if the passing does not meet each validity condition. The conditions of a correct passing are mainly constant speed or driving straight ahead. The validity criterion also checks if the weight of the T2S3 is more than a certain limit weight because the statistical parameters are optimized for the most heavy vehicles. All U2 vehicles have a OFF validity criterion meaning that no sorting was applied on that category.

The system allows control staff to see in real time which vehicles pass on the grids. They then proceed to bring them to the LS-WIM scale. Without the use of the HS-WIM, they must deviate randomly one vehicle at a time towards the LS-WIM weighing station during occasional intervention.

In Figure 2, one observes the distribution of the gross weight for the T2S3. The validity criterion does not modify the initial distribution of the gross-weights for the T2S3 above 20T. The set of T2S3 after the filtering is thus consistent with the application of weigh-in-motion.

3. Relative Errors of Measurements

The fundamentals for the assessment of the accuracy are introduced here, according to [9,10].

Let the static weight computed with a static weighing instrument $W_s$ and the weight measured in motion $W_d$ computed with the HS-WIM system, which is possibly inaccurate. The relative error of weight estimation $e_r$ is computed as follows:

$$e_r=\frac{W_d-W_s}{W_s}$$

Under the assumption that the random variables $e_r$ are independent identically distributed normal variables, $\mathsf{\Pi }$ is the probability that, for a risk $\alpha$, a single relative error falls within the confidence interval $[-\delta ,+\delta ]$. As no information about the true $e_r$’s-distribution is available, only a sample estimate $\pi$ of $\mathsf{\Pi }$ can be found. The higher the value of $\delta$, the lower the class of weight estimate for the HS-WIM will be.

4. Results

Here, the performances of the estimations are presented for several cases: gross weight (GW), group of axle (GoA), single axis (SA), and axle of a group (AoG). For our purpose, one can add the weighing of the second axle (SA2) for the T2S3. As one notices in

Table 2. Number of overloaded T2S3 according to the single axles and the gross-weight for the period of time from 5 January 2021 to 21 January 2021. The second axle is considered as overloaded above 12T. The limit weight for the other axles is 9T and 44T for the gross-weight.

	SA1	SA2	SA3	SA4	SA5	GW
Number of
detections	4	2057	544	460	506	1375

, the main part of the detected overloads comes from the SA2 and the GW. Therefore, the system installed in Louvain-la-Neuve only considers the weighting of the gross-weight and the second single-axle (as legal measure). In the following tables, these cases are separated from the AoG, SA and AoG. The last three lines are only dedicated to give additional information about the behaviour of the system.

Let N, m and s be the number of considered vehicles, the experimental mean and the sample standard deviation computed on these relative errors, respectively. According to [9], ${\pi }_0$ is equal to $93.1\%$ under the assumptions of (III) and (R2). Let ${\delta }_0$ be a particular value of $\delta$ that will be used to compute the related confident level ${\pi }_{{\delta }_0}$. Under the same assumptions and according to the class that we expected to reach, the values of ${\delta }_0$ depend on the considered case as explained above, and are expressed in %.

Table 3. Performance for all T2S3 (Class A).

Entity	N	m $(\%)$	s $(\%)$	${\mathit{\pi }}_0$	${\mathit{\delta }}_{{\mathit{\pi }}_0}$	${\mathit{\delta }}_0$	${\mathit{\pi }}_{{\mathit{\delta }}_0}$
GW	404	−0.11	4.89	93.1	9.39	5	64.46
SA2	404	0.52	4.46	93.1	8.62	8	90.71
GoA	404	0.51	5.80	93.1	11.19	7	72.99
SA	808	−0.92	5.21	93.1	10.00	8	85.05
AoG	1212	0.53	6.71	93.1	12.62	10	84.70

,

Table 4. Performance for valid T2S3 (Class A).

Entity	N	m $(\%)$	s $(\%)$	${\mathit{\pi }}_0$	${\mathit{\delta }}_{{\mathit{\pi }}_0}$	${\mathit{\delta }}_0$	${\mathit{\pi }}_{{\mathit{\delta }}_0}$
GW	180	0.53	0.98	93.1	2.16	5	99.99
SA2	180	0.73	1.59	93.1	3.43	8	99.99
GoA	180	1.17	1.50	93.1	3.64	7	99.99
SA	360	−0.43	2.10	93.1	4.13	8	99.97
AoG	540	1.19	2.18	93.1	4.68	10	99.99

and

Table 5. Performance for U2 (Class C).

Entity	N	m $(\%)$	s $(\%)$	${\mathit{\pi }}_0$	${\mathit{\delta }}_{{\mathit{\pi }}_0}$	${\mathit{\delta }}_0$	${\mathit{\pi }}_{{\mathit{\delta }}_0}$
GW	188	−4.71	2.90	93.1	9.45	15	99.96
SA	376	−4.78	3.53	93.1	10.39	20	99.99

show the results for all T2S3, all valid T2S3 and all U2, respectively.

For the T2S3, the validity conditions substantially improve the performance of the HS-WIM and it allows for situating it in class A for valid T2S3.

For the U2, the table clearly shows the belonging to class C.

Though one must pay attention to the fact that the system fulfills the requirements of OIML recommendations [6] and COST323 specifications [7] for certain types of vehicles.

In practice, what is really important is the capability to detect infractions and not to flag the too light vehicles. Such information is concentrated in the confusion matrix. It is the 2 by 2 matrix which describes the four possible cases of a classifier: the vehicle must be given a penalty or not, while the vehicle is given a penalty or not by the classifier. One wants obviously to obtain as many correct weight estimates as possible. The confusion matrix emphasizes the fact that two risks are important to consider for an estimation. The first one is the risk of over-estimate the weight estimate, which corresponds to the lower left entry of the matrix. One can see that there is no over-estimation of the weight, which leads to a wrong penalty. On the other hand, it emphasizes a second risk which is the under-estimation of the weight or the withdrawal of the estimation due to the validity criterion. One notice that this second risk stays high because of the 40 T2S3 of 56 which are not given a penalty while they are overloaded. At this time, one prefers to calibrate the system in this way in order to be sure of having the lower risk of type 1, which is much worse in the legal context. For the moment, no re-calibration is expected.

In

Table 6. Confusion matrix for valid T2S3.

		Weight estimates
		>44T	<44T
	>44T	16	40	56
Check weights
	<44T	0	348	348
		16	388	404

and

Table 7. Confusion matrix for U2.

		Weight estimates
		>4T	<4T
	>4T	72	48	120
Check weights
	<4T	0	68	68
		72	116	188

, the confusion matrices for valid T2S3 and for U2 are showed. We observe that the algorithm used by this HS-WIM system displays overloaded vehicles which are found overloaded for real (via the LS-WIM scale). No false positives are recorded. This is an essential criteria in order to use such system for direct enforcement. However, only 16 infractions of the 56 are really detected for T2S3 and only 72 of the 120 for the U2.

5. Discussion

The application of the HS-WIM opens the way of much more efficient weight estimate in Belgium and much more fining. In 2021, according to the HS-WIM, around 5,000 T2S3 were overloaded and 21,000 U2, while only a hundred fines were issued with the actual interventions of weighting with the LS-WIM scale.

The reasons for expecting the presented performances are two-fold. The first one is the renewal of the roadway that tends to reduce the dynamic disturbances. The second one is the application of validity conditions. These conditions aim to remove all the estimates that are suspicious, i.e. that does not follow a specific behaviour. For example, a condition checks if the estimation of the speed on the first grid of sensors is not too far from the estimation of the estimation on the second one. A second condition is verifying if the position of the center of the vehicle does not pass too far from the center of the grid.

For the specific cases of gross weight and weight of axle 2 for the T2S3, one can observe very good precision and belonging to a class of high accuracy.

On the down side, adding a validity filter highly decreases the number of tested vehicles and so increases the risk of not being legally weighed. Indeed, the reached classes ensure accurate estimations for only 180 of 404 T2S3, i.e., $44.55\%$ are tested and few penalties are given. In a practical sense, only a small part of the traffic flow is weighted and so is the number of given penalties.

6. Conclusions

As a conclusion, one shows that the specific road quality provided a solid base to install a double grid of sensors. This new configuration is coupled with a large data set of comparative weighings (high-speed vs. low-speed), and good parameters can be computed. One emphasizes the fact that there is no over-estimation of the weight in motion.

The system reaches very high levels of confidence (>99.8%) without any false-positive records. Such good results are a first worldwide. It meets the requirements of the Belgian regulation or in the case studied of the regional regulations in Wallonia. Therefore, a type approval certificate was delivered, and the system may now be used for direct enforcement.

The ongoing research seeks to increase the proportion of candidates to fine in order to broaden the types of vehicles treatable by the system.