Influence of Trajectory and Dynamics of Vehicle Motion on Signal Patterns in the WIM System

This paper presents the analyses of the signals recorded by the main sensors of a WIM test station in the cases of abnormal runs (i.e., runs with the changes of trajectory or the dynamics of vehicle motion). The research involved strain gauges which are used for measuring the weight of vehicles, inductive loops, as well as piezoelectric sensors used, inter alia, to detect twin wheels and to determine where a vehicle passes through a station. Since the designers intend the station to be able to implement the direct enforcement function, the selection of runs deviating from the normative ones constitutes an important issue for the assessment of the measurement reliability. The study considered the location of the trajectory of the runs, the dynamics (acceleration/braking) and the trajectory changes. The change in the amplitude and the value of the signal recorded by the strain gauges as a function of the location (position) of the contact between sensor and tires is a noteworthy observation which indicates the need to monitor this parameter in automatic WIM systems. Other tests also demonstrated the influence of the analysed driving parameters on the recorded results. However, by equipping the WIM station with a set of duplicate strain gauges, the measurement errors of the gross weight and axle loads are normally within the accuracy limits of class A(5) stations. Only in the case of accelerating/decelerating, does the error in measuring the load of a single axle reach several per cent.


Introduction
Weigh-In-Motion (WIM) systems are in many countries the primary source of information about overloaded vehicles on the road. They allow to select such vehicles quickly while providing a range of other relevant traffic data. The data recorded by the system of sensors and measuring devices included in the WIM station are also a source of data on key traffic parameters such as the volume, density, and traffic speed. This information enables complex analyses and the construction of predictive models [1,2]. WIM systems can also find application in assessing the environmental impact of road transport [3], or the occupancy level of public transport vehicles [4]. The increasing requirements placed on them have resulted in a great deal of research and development work being carried out all over the world both in terms of the concept of WIM systems themselves and their individual components. A relatively new issue is the development of WIM systems adapted for direct enforcement (i.e., systems directly delivering penalties) [5].
High-speed WIM systems use sensors based on different technologies. The design and performance characteristics of the most used are reported, among others, in the article [6]. These include piezo-polymer, piezo-quartz, bending plate, and single load cell sensors. In addition, sensor readings are affected by various environmental factors. In [7], the dependence of weighing results on pavement temperature and vehicle speed for polymer, part of the study. The signals generated by strain gauges, piezoelectric sensors, and inductive loops were analysed. The waveforms of the recorded signals and selected measures characterising the obtained signals are presented. Reference is also made to quantities, such as total weight, vehicle length, and axle loads. The influence of the conditions of the tested runs on the waveforms of the recorded measurement signals was assessed, in particular, by comparing the values of the measures characterising the signal with the measures obtained for the waveforms of these signals recorded for runs considered by the authors as normative.

Location
The WIM test station is located in Poland on the DK44 single carriageway national road in the Silesia region ( Figure 1). Information on annual average daily traffic (ADDT), the proportion of heavy goods vehicles (HVs) and lane widths is shown in Table 1.  Prior to the commencement of the tests, the technical condition of the pavement was assessed in terms of the requirements for the operation of the WIM station. This assessment was based on the recommendations of COST 323 [21] regarding the suitability of the section for the operation of a pre-selective vehicle weighing system in pavement quality site class I (WIM site I Excellent) for class A(5) and B+(7) measurement systems ( Table 2). The assessment involved pavement deflection measurements, longitudinal evenness measurements, and rut depth measurements.  Prior to the commencement of the tests, the technical condition of the pavement was assessed in terms of the requirements for the operation of the WIM station. This assessment was based on the recommendations of COST 323 [21] regarding the suitability of the section for the operation of a pre-selective vehicle weighing system in pavement quality site class I (WIM site I Excellent) for class A(5) and B+(7) measurement systems ( Table 2). The assessment involved pavement deflection measurements, longitudinal evenness measurements, and rut depth measurements. Table 2. WIM accuracy classes. Data from [21].

Criteria
Accuracy  I  I  II  III  III  III The DK44 road in the section in question, i.e., 50 m before and 25 m after the location of the WIM station, is a straight section. The values of the longitudinal and transverse gradients of the road and the evenness of the pavement are shown in Table 3. The presented measurement results confirm that the section in question meets the requirements of COST 323 for site I Excellent. In the next step, the dynamic deflection of the pavement was measured using Dynatest 8002 type Falling Weight Deflectometer (FWD) (Dynatest, Ballerup, Denmark) ( Figure 2).
The tests were carried out in August, with a mineral and asphalt layer temperature of +23 • C. The results obtained are demonstrated in Figure 3. Table 2. WIM accuracy classes. Data from [21].

Criteria
Accuracy Classes: Confidence Interval Width δ (%) A(5) B+(7) B(10) C(15) D+(20) Gross weight > 3 .5 t  5  7  10  15  20  Axle load of group of axles > 1 t  7  10  13  18  23  Axle load of single of axles > 1 t  8  11  15  20  25  Axle load of axle of a group > 1 t  10  14  20  25  30  Minimum WIM site class  I  I  II  III  III The DK44 road in the section in question, i.e., 50 m before and 25 m after the of the WIM station, is a straight section. The values of the longitudinal and tra gradients of the road and the evenness of the pavement are shown in Table 3. T sented measurement results confirm that the section in question meets the requi of COST 323 for site I Excellent.  Figure 3.   The calculated mean deflection values of 165 μm and 200 μm for the left and right wheel tracks, respectively, are values that classify the pavement as site I Excellent according to COST 323 for so-called "Flexible pavements." The pavement response to quasi-static loading was evaluated based on the results of the FWD deflectometer tests using a correlation coefficient between the FWD test and the Benkelman beam test (quasi-static loading) as reported by [22]. The test results are shown in Figure 4. Under quasi-static loading conditions, the deflection of the pavement is less than 300 μm, whereas the difference in deflection for the left and right wheel tracks is less than 70 μm, which means that the pavement meets the requirements for flexible pavements and site I Excellent according to COST 323. The calculated mean deflection values of 165 µm and 200 µm for the left and right wheel tracks, respectively, are values that classify the pavement as site I Excellent according to COST 323 for so-called "Flexible pavements".
The pavement response to quasi-static loading was evaluated based on the results of the FWD deflectometer tests using a correlation coefficient between the FWD test and the Benkelman beam test (quasi-static loading) as reported by [22]. The test results are shown in Figure 4.  The calculated mean deflection values of 165 μm and 200 μm for the left and right wheel tracks, respectively, are values that classify the pavement as site I Excellent according to COST 323 for so-called "Flexible pavements." The pavement response to quasi-static loading was evaluated based on the results of the FWD deflectometer tests using a correlation coefficient between the FWD test and the Benkelman beam test (quasi-static loading) as reported by [22]. The test results are shown in Figure 4. Under quasi-static loading conditions, the deflection of the pavement is less than 300 μm, whereas the difference in deflection for the left and right wheel tracks is less than 70 μm, which means that the pavement meets the requirements for flexible pavements and site I Excellent according to COST 323. Under quasi-static loading conditions, the deflection of the pavement is less than 300 µm, whereas the difference in deflection for the left and right wheel tracks is less than 70 µm, which means that the pavement meets the requirements for flexible pavements and site I Excellent according to COST 323.

Sensors and Components
The WIM station where the research was conducted consists of the following equipment ( Figure 5): • a set of strain gauges to measure the contact load on the right and left wheels of a given vehicle axle; • a set of piezoelectric sensors to detect the tyre width, the tyre-sensor contact point and thus the lane position of the vehicle; and • a set of inductive loops to trigger the reading of data from strain gauges and the determination of vehicle lengths.

Sensors and Components
The WIM station where the research was conducted consists of the following equipment ( Figure 5): • a set of strain gauges to measure the contact load on the right and left wheels of a given vehicle axle; • a set of piezoelectric sensors to detect the tyre width, the tyre-sensor contact point and thus the lane position of the vehicle; and • a set of inductive loops to trigger the reading of data from strain gauges and the determination of vehicle lengths.   Linear strain gauge sensors constitute the main component of the weighing station. The installation used strain gauge load cell sensors (Intercomp, Medina, MN, USA) ( Figure 6). They are constructed using resistance strain gauges that change their resistance due to strain. They have the following technical parameters [

Sensors and Components
The WIM station where the research was conducted consists of the following equip ment ( Figure 5): • a set of strain gauges to measure the contact load on the right and left wheels of given vehicle axle; • a set of piezoelectric sensors to detect the tyre width, the tyre-sensor contact poin and thus the lane position of the vehicle; and • a set of inductive loops to trigger the reading of data from strain gauges and the de termination of vehicle lengths.      The key component of the WIM system is a data logging device using analogue-todigital tracks, FPGA (field-programmable gate array), NIOS (configurable embedded processor), and a datalogger built using an ARM controller ( Figure 9). Using the FPGA-based architecture allows high performance in the processing, integration, and synchronization of signals from strain gauge load sensors, inductive loops, and additional piezoelectric sensors within a single device. The sampling frequency of WIM system is 31,250 Hz for strain gauge and piezoelectric sensors and 3125 Hz for inductive loops.    The key component of the WIM system is a data logging device using analogue-todigital tracks, FPGA (field-programmable gate array), NIOS (configurable embedded processor), and a datalogger built using an ARM controller ( Figure 9). Using the FPGA-based architecture allows high performance in the processing, integration, and synchronization of signals from strain gauge load sensors, inductive loops, and additional piezoelectric sensors within a single device. The sampling frequency of WIM system is 31,250 Hz for strain gauge and piezoelectric sensors and 3125 Hz for inductive loops. The key component of the WIM system is a data logging device using analogue-todigital tracks, FPGA (field-programmable gate array), NIOS (configurable embedded processor), and a datalogger built using an ARM controller ( Figure 9). Using the FPGA-based architecture allows high performance in the processing, integration, and synchronization of signals from strain gauge load sensors, inductive loops, and additional piezoelectric sensors within a single device. The sampling frequency of WIM system is 31,250 Hz for strain gauge and piezoelectric sensors and 3125 Hz for inductive loops.
Each time, before starting a series of test runs, static loads were measured by means of a dedicated measuring station equipped with portable IRD SAW III scales of OIML R76 class (static accuracy ± 25 kg for weight up to 2.5 Mg; ± 50 kg for weight from 2.5 to 10 Mg). Each time, before starting a series of test runs, static loads were measured by means of a dedicated measuring station equipped with portable IRD SAW III scales of OIML R76 class (static accuracy ± 25 kg for weight up to 2.5 Mg; ± 50 kg for weight from 2.5 to 10 Mg).

System Calibration
The system calibration was performed using a two-axle vehicle with a total weight of 18 Mg and a five-axle vehicle with a weight of 38 Mg ( Figure 10). In the first stage, a number of test runs were conducted to select calibration coefficients separately for each strain gauge sensor. A series of 10 verification runs were then carried out to confirm the expected accuracy class of the measurement system. On each occasion, the vehicles were moving at the speed of approximately 50 km/h in the axis of the lane.

System Calibration
The system calibration was performed using a two-axle vehicle with a total weight of 18 Mg and a five-axle vehicle with a weight of 38 Mg ( Figure 10). In the first stage, a number of test runs were conducted to select calibration coefficients separately for each strain gauge sensor. A series of 10 verification runs were then carried out to confirm the expected accuracy class of the measurement system. On each occasion, the vehicles were moving at the speed of approximately 50 km/h in the axis of the lane. Each time, before starting a series of test runs, static loads were measured by means of a dedicated measuring station equipped with portable IRD SAW III scales of OIML R76 class (static accuracy ± 25 kg for weight up to 2.5 Mg; ± 50 kg for weight from 2.5 to 10 Mg).

System Calibration
The system calibration was performed using a two-axle vehicle with a total weight of 18 Mg and a five-axle vehicle with a weight of 38 Mg ( Figure 10). In the first stage, a number of test runs were conducted to select calibration coefficients separately for each strain gauge sensor. A series of 10 verification runs were then carried out to confirm the expected accuracy class of the measurement system. On each occasion, the vehicles were moving at the speed of approximately 50 km/h in the axis of the lane.    Figure 11 shows the measurement error statistics obtained for each vehicle. As can be observed, for the five-axle vehicle, the maximum gross weight measurement error did not exceed 1%, while for the two-axle vehicle it was 2%. The largest errors were recorded for the single axle measurement of the five-axle vehicle, with an error rate of 7% during a single pass. These quantities indicate that the system at the location in question meets the requirements of class A(5) according to COST 323. As can be observed, for the five-axle vehicle, the maximum gross weight measurement error did not exceed 1%, while for the two-axle vehicle it was 2%. The largest errors were recorded for the single axle measurement of the five-axle vehicle, with an error rate of 7% during a single pass. These quantities indicate that the system at the location in question meets the requirements of class A(5) according to COST 323.

Influence of the Trajectory on the Measurement Results
In the first series of tests, 14 runs each were made with a five-axle vehicle and a twoaxle vehicle ( Figure 12). The study involved the following three types of runs:

Influence of the Trajectory on the Measurement Results
In the first series of tests, 14 runs each were made with a five-axle vehicle and a two-axle vehicle ( Figure 12). The study involved the following three types of runs: As can be observed, for the five-axle vehicle, the maximum gross weight measurement error did not exceed 1%, while for the two-axle vehicle it was 2%. The largest errors were recorded for the single axle measurement of the five-axle vehicle, with an error rate of 7% during a single pass. These quantities indicate that the system at the location in question meets the requirements of class A(5) according to COST 323.

Influence of the Trajectory on the Measurement Results
In the first series of tests, 14 runs each were made with a five-axle vehicle and a twoaxle vehicle ( Figure 12). The study involved the following three types of runs:    The obtained results show that, in particular, the right side runs resulted in a measurement error that slightly exceeded the permissible values for A(5) class for both gross weight in the case of five-axle and two-axle vehicle and single axle load for five-axle vehicle. For the left-side runs, this error was comparable to the central runs.
The following section presents example patterns of signals for a five-axle vehicle recorded during the tests. The signal patterns from the strain gauge sensors (W1P and W1L) are demonstrated in Figure 15. The characteristics of the recorded signals with respect to the amplitude and calculated load of individual vehicle wheels are presented in Tables 4  and 5. The coefficient R² between the signal amplitude and the wheel load was 0.79 for sensor W1P and 0.85 for W1L.   The obtained results show that, in particular, the right side runs resulted in a measurement error that slightly exceeded the permissible values for A(5) class for both gross weight in the case of five-axle and two-axle vehicle and single axle load for five-axle vehicle. For the left-side runs, this error was comparable to the central runs.
The following section presents example patterns of signals for a five-axle vehicle recorded during the tests. The signal patterns from the strain gauge sensors (W1P and W1L) are demonstrated in Figure 15. The characteristics of the recorded signals with respect to the amplitude and calculated load of individual vehicle wheels are presented in Tables 4  and 5. The coefficient R² between the signal amplitude and the wheel load was 0.79 for sensor W1P and 0.85 for W1L. The obtained results show that, in particular, the right side runs resulted in a measurement error that slightly exceeded the permissible values for A(5) class for both gross weight in the case of five-axle and two-axle vehicle and single axle load for five-axle vehicle. For the left-side runs, this error was comparable to the central runs.
The following section presents example patterns of signals for a five-axle vehicle recorded during the tests. The signal patterns from the strain gauge sensors (W1P and W1L) are demonstrated in Figure 15. The characteristics of the recorded signals with respect to the amplitude and calculated load of individual vehicle wheels are presented in Tables 4 and 5. The coefficient R 2 between the signal amplitude and the wheel load was 0.79 for sensor W1P and 0.85 for W1L.   The analysis of the presented characteristics and signal patterns indicates a change in the amplitude and load recorded for each wheel by strain gauges W1P and W1L in the case of passing on the right side of the lane. In the case of axle 3, 4, and 5, the error exceeded 10%. Importantly, laboratory tests of sensor linearity performed in previous work did not indicate significant changes in signal values depending on the load position [26].
The driving trajectory, in the case of piezoelectric sensors P45P and P45L, has also a slight impact on the signal corresponding to the recording of the load from the twin wheel. The signal patterns for the twin wheel at different passing modes are shown in Figure 16 and their characteristics in Table 6.  The analysis of the presented characteristics and signal patterns indicates a change in the amplitude and load recorded for each wheel by strain gauges W1P and W1L in the case of passing on the right side of the lane. In the case of axle 3, 4, and 5, the error exceeded 10%. Importantly, laboratory tests of sensor linearity performed in previous work did not indicate significant changes in signal values depending on the load position [26].
The driving trajectory, in the case of piezoelectric sensors P45P and P45L, has also a slight impact on the signal corresponding to the recording of the load from the twin wheel. The signal patterns for the twin wheel at different passing modes are shown in Figure 16 and their characteristics in Table 6.  The analysis of the waveform and characteristics of the signal recorded by the P45P sensor for the right-side lane run indicates a comparable amplitude value and a correct response of the sensor to the load from the twin wheel. Only for the left-side run is the Peak-Peak distance slightly higher. However, in all the cases, the identification of the twin wheel is possible.
Changing the trajectory also causes some differences in the signals recorded by the induction loops. Example signals from induction loops for right-and left-side passing and in lane alignment for a five-axle vehicle are presented in Figure 17. The characteristics of the signal from the induction loops are given in Table 7.  The analysis of the waveform and characteristics of the signal recorded by the P45P sensor for the right-side lane run indicates a comparable amplitude value and a correct response of the sensor to the load from the twin wheel. Only for the left-side run is the Peak-Peak distance slightly higher. However, in all the cases, the identification of the twin wheel is possible.
Changing the trajectory also causes some differences in the signals recorded by the induction loops. Example signals from induction loops for right-and left-side passing and in lane alignment for a five-axle vehicle are presented in Figure 17. The characteristics of the signal from the induction loops are given in Table 7.   For the analysed trajectories, both loop L1 and loop L2 generated a qualitatively similar signal to ensure that the measurement path of the WIM station was properly activated and the vehicle length was correctly calculated. However, the passing trajectory affected the peak value and the mean signal level which reach the highest values when passing in the lane centreline (normative) and the lowest when passing on the right side of the lane.
The analysis of the measurement errors for the different trajectories indicates that passing on the right side of the lane could result in an increase in the measurement error exceeding the acceptable level. In the authors' opinion, especially in WIM systems with a direct enforcement function, it is worth considering monitoring the trajectories, e.g., by determining the tyre-sensor contact point using piezoelectric sensors mounted at 45 degrees.

Effects of Acceleration/Deceleration on Measurement Results
As part of the research on the influence of the runs' dynamics on the sensor signals at the WIM station, 12 runs were made with a five-axle vehicle and 12 runs with a twoaxle vehicle. Three types of runs were included in the study:  For the analysed trajectories, both loop L1 and loop L2 generated a qualitatively similar signal to ensure that the measurement path of the WIM station was properly activated and the vehicle length was correctly calculated. However, the passing trajectory affected the peak value and the mean signal level which reach the highest values when passing in the lane centreline (normative) and the lowest when passing on the right side of the lane.
The analysis of the measurement errors for the different trajectories indicates that passing on the right side of the lane could result in an increase in the measurement error exceeding the acceptable level. In the authors' opinion, especially in WIM systems with a direct enforcement function, it is worth considering monitoring the trajectories, e.g., by determining the tyre-sensor contact point using piezoelectric sensors mounted at 45 degrees.

Effects of Acceleration/Deceleration on Measurement Results
As part of the research on the influence of the runs' dynamics on the sensor signals at the WIM station, 12 runs were made with a five-axle vehicle and 12 runs with a two-axle vehicle. Three types of runs were included in the study:    The results obtained indicated a fairly significant scatter of values for the single axle load measurement of a five-axle vehicle ( Figure 18). For the two-axle vehicle, significant errors (>10%) were recorded for the passage with braking ( Figure 19).
Example waveforms of signals from strain gauges concerning the passage of a fiveaxle vehicle are shown in Figure 20. Tables 8 and 9 summarise the signal characteristics in relation to the signal amplitude and the calculated load of the individual vehicle wheels. Table 9 also contains information on the static wheel loads. For this type of run, due to the dynamics, it was decided to present the signals from two sensor lines measuring the wheel load of the right side of the vehicle (signal W1P and W2P).   Figures 18 and 19 show the measurement errors obtained for the gross weight and axle loads for constant speed, acceleration, and braking runs.  The results obtained indicated a fairly significant scatter of values for the single axle load measurement of a five-axle vehicle ( Figure 18). For the two-axle vehicle, significant errors (>10%) were recorded for the passage with braking ( Figure 19).
Example waveforms of signals from strain gauges concerning the passage of a fiveaxle vehicle are shown in Figure 20. Tables 8 and 9 summarise the signal characteristics in relation to the signal amplitude and the calculated load of the individual vehicle wheels. Table 9 also contains information on the static wheel loads. For this type of run, due to the dynamics, it was decided to present the signals from two sensor lines measuring the wheel load of the right side of the vehicle (signal W1P and W2P). The results obtained indicated a fairly significant scatter of values for the single axle load measurement of a five-axle vehicle ( Figure 18). For the two-axle vehicle, significant errors (>10%) were recorded for the passage with braking ( Figure 19).
Example waveforms of signals from strain gauges concerning the passage of a fiveaxle vehicle are shown in Figure 20. Tables 8 and 9 summarise the signal characteristics in relation to the signal amplitude and the calculated load of the individual vehicle wheels. Table 9 also contains information on the static wheel loads. For this type of run, due to the dynamics, it was decided to present the signals from two sensor lines measuring the wheel load of the right side of the vehicle (signal W1P and W2P).
The analysis of the values of signal amplitudes obtained during the run with acceleration or braking in the WIM station area indicates an average difference of more than 6% in the values of amplitudes in relation to the run with constant speed. In the vast majority of cases, a dynamic run results in a higher amplitude signal being recorded for individual vehicle wheels. When analysing the load values for the wheel of the first axle in the case of a run with deceleration, it can be easily observed that it is overloaded compared to a constant-speed run and that it is under-loaded in the case of an accelerated run. These variations are within ±15%.
The signal patterns for the twin wheel during the variable speed run are shown in Figure 21 and their characteristics in Table 10.  The change of speed when passing through piezoelectric sensors causes, in most cases, an increase of several per cent in the signal amplitude value. The average difference in amplitude values was almost 12%. It is worth noting, however, that variable speed runs lead to the effect of a specific stretching of the signal in the vicinity of the maximum value, which causes problems in the unambiguous determination of the Peak-Peak distance and, consequently, may cause problems in the identification of the twin wheel.
Example signals from induction loops for a variable speed run for a five-axle vehicle are presented in Figure 22. The characteristics of the signal from the induction loops are given in Table 11.  The change of speed when passing through piezoelectric sensors causes, in most cases, an increase of several per cent in the signal amplitude value. The average difference in amplitude values was almost 12%. It is worth noting, however, that variable speed runs lead to the effect of a specific stretching of the signal in the vicinity of the maximum value, which causes problems in the unambiguous determination of the Peak-Peak distance and, consequently, may cause problems in the identification of the twin wheel.
Example signals from induction loops for a variable speed run for a five-axle vehicle are presented in Figure 22. The characteristics of the signal from the induction loops are given in Table 11. Table 11. Signal characteristics from inductive loops-amplitude and mean signal value (ADU).   The signal recorded by the induction loop during variable speed runs is qualitatively consistent with the signal for a constant speed run. However, during such runs the maximum value of the signal is on average more than 9% higher. Also, the mean value of the recorded signal for runs with a variable speed is several per cent higher on average. Nevertheless, this does not have a major impact on the correctness of the determined vehicle length. For this parameter, the maximum error reaches 2%.

Run\Loop L1 Max Mean
The analysis of measurement errors for variable speed runs shows that accelerating or braking while passing through the measurement system can result in an increase in axle load measurement error beyond the acceptable level. However, the system consisting of duplicate sensors allows the gross weight to be determined correctly.

Influence of Trajectory Changes on the Measurement Results
The last element of the study was to perform runs with a change of trajectory. In this case, the vehicles initially travelled on the left side of the lane and then, when passing the sensor set, made a change of trajectory towards its right side ( Figure 23).  The signal recorded by the induction loop during variable speed runs is qualitatively consistent with the signal for a constant speed run. However, during such runs the maximum value of the signal is on average more than 9% higher. Also, the mean value of the recorded signal for runs with a variable speed is several per cent higher on average. Nevertheless, this does not have a major impact on the correctness of the determined vehicle length. For this parameter, the maximum error reaches 2%.
The analysis of measurement errors for variable speed runs shows that accelerating or braking while passing through the measurement system can result in an increase in axle load measurement error beyond the acceptable level. However, the system consisting of duplicate sensors allows the gross weight to be determined correctly.

Influence of Trajectory Changes on the Measurement Results
The last element of the study was to perform runs with a change of trajectory. In this case, the vehicles initially travelled on the left side of the lane and then, when passing the sensor set, made a change of trajectory towards its right side ( Figure 23).  The signal recorded by the induction loop during variable speed runs is qualitatively consistent with the signal for a constant speed run. However, during such runs the maximum value of the signal is on average more than 9% higher. Also, the mean value of the recorded signal for runs with a variable speed is several per cent higher on average. Nevertheless, this does not have a major impact on the correctness of the determined vehicle length. For this parameter, the maximum error reaches 2%.
The analysis of measurement errors for variable speed runs shows that accelerating or braking while passing through the measurement system can result in an increase in axle load measurement error beyond the acceptable level. However, the system consisting of duplicate sensors allows the gross weight to be determined correctly.

Influence of Trajectory Changes on the Measurement Results
The last element of the study was to perform runs with a change of trajectory. In this case, the vehicles initially travelled on the left side of the lane and then, when passing the sensor set, made a change of trajectory towards its right side ( Figure 23).  Taking into account the results obtained for all trajectory-changing runs performed, the average error in determining the gross weight, the individual axle load and the group of axles was estimated. The results are summarised in Table 12. The analysis of the data presented in Table 12 allows us to conclude that a change of trajectory when a WIM station is equipped with a set of duplicate sensors does not cause the exceedance of the permissible error for a class A(5) station. However, it is noteworthy that in this case the error in axle load may be several times greater than the error in determining the gross weight.
Examples of signal patterns from strain gauge sensors are shown in Figure 24. In this case, the signals for the left and right sides of the first (W1P, W1L) and second lines (W2P, W2L) are collated. The analysis of the data presented in Table 12 allows us to conclude that a change of trajectory when a WIM station is equipped with a set of duplicate sensors does not cause the exceedance of the permissible error for a class A(5) station. However, it is noteworthy that in this case the error in axle load may be several times greater than the error in determining the gross weight.
Examples of signal patterns from strain gauge sensors are shown in Figure 24. In this case, the signals for the left and right sides of the first (W1P, W1L) and second lines (W2P, W2L) are collated.     The analysis of the signal amplitude values from sensors recording the same vehicle wheel passage (i.e., W1P and W2P, and W1L and W2L, respectively) reveals that higher amplitude values are obtained for sensors located on the right side. Also, when comparing the loads for individual wheels on the left and right side of the vehicle, the values for the wheels on the right side of the vehicle were several per cent higher. While analysing the test's video recordings, it was found that drivers started the manoeuvre of changing their lane clearly before the WIM station. In the measuring area, the manoeuvre was in its final phase, i.e., the vehicle was making a left turn. According to the principles of dynamics, it is the right wheels that are under greater strain at this time. Furthermore, by analysing the amplitude shifts of the signals for the left and right wheels of the vehicle, respectively, it is possible to infer a change in the path of the vehicle passing through the measuring station.
The signal waveforms for the twin wheel for the trajectory change are shown in Figure 25 and their characteristics in Table 15.
wheel passage (i.e., W1P and W2P, and W1L and W2L, respectively) reveals that higher amplitude values are obtained for sensors located on the right side. Also, when comparing the loads for individual wheels on the left and right side of the vehicle, the values for the wheels on the right side of the vehicle were several per cent higher. While analysing the test's video recordings, it was found that drivers started the manoeuvre of changing their lane clearly before the WIM station. In the measuring area, the manoeuvre was in its final phase, i.e., the vehicle was making a left turn. According to the principles of dynamics, it is the right wheels that are under greater strain at this time. Furthermore, by analysing the amplitude shifts of the signals for the left and right wheels of the vehicle, respectively, it is possible to infer a change in the path of the vehicle passing through the measuring station.
The signal waveforms for the twin wheel for the trajectory change are shown in Figure 25 and their characteristics in Table 15.  Changing the trajectory when passing through the piezoelectric sensors resulted in a change in the value of the signal amplitude which was greater for sensor P45L, thus located on the left side. The change in trajectory also affected the Peak-Peak distance, but to an extent that did not cause major problems in identifying the twin wheel.
An example of induction loop signals for a variable path run is presented in Figure  26. The characteristics of the signal from the induction loops are given in Table 16.  Changing the trajectory when passing through the piezoelectric sensors resulted in a change in the value of the signal amplitude which was greater for sensor P45L, thus located on the left side. The change in trajectory also affected the Peak-Peak distance, but to an extent that did not cause major problems in identifying the twin wheel.
An example of induction loop signals for a variable path run is presented in Figure 26. The characteristics of the signal from the induction loops are given in Table 16.   Trajectory changing has an effect on the variation of the signal recorded by the induction loops. The signals recorded by both loops are qualitatively consistent, but a significantly weaker signal was recorded by the second loop L2. However, this does not increase the error in determining the vehicle length. The average relative error is still in the range of 3-4%.

Conclusions
The practical use of WIM systems for direct enforcement will require them to be highly reliable in terms of the data they record. It is worth noting that currently even the most modern WIM stations do not achieve 100% efficiency [27]. In this paper, attention has been paid to the influence of both the trajectory and the dynamics of driving through a WIM station on the signals generated by the sensors. The patterns that caused errors exceeding the acceptable accuracy for WIM class A(5) stations or signal deformations that prevented proper interpretation were recorded.
Based on the research presented in this paper, the following conclusions have been drawn: • passing on the right side of the lane (i.e., close to the road end) could result in an increase in the measurement error exceeding the acceptable level; • accelerating or braking while passing through the measurement system can result in an increase in axle load measurement error beyond the acceptable level; • changing the trajectory when a WIM station is equipped with a set of duplicate sensors does not cause the exceedance of the permissible error for a class A(5) station; and • for the study conducted, there were no above-normal errors associated with the determination of vehicle length by means of induction loops.
In addition, attention should be paid to non-central runs, i.e., those where the tyre could only partially overlap the load cell. Such cases may occur at most locations, as it is very rare that solutions delineating the correct trajectory, such as the use of traffic separators, are implemented in the WIM station area. It is obvious that such runs must be detected by the direct enforcement system as abnormal runs and consequently rejected. Trajectory changing has an effect on the variation of the signal recorded by the induction loops. The signals recorded by both loops are qualitatively consistent, but a significantly weaker signal was recorded by the second loop L2. However, this does not increase the error in determining the vehicle length. The average relative error is still in the range of 3-4%.

Conclusions
The practical use of WIM systems for direct enforcement will require them to be highly reliable in terms of the data they record. It is worth noting that currently even the most modern WIM stations do not achieve 100% efficiency [27]. In this paper, attention has been paid to the influence of both the trajectory and the dynamics of driving through a WIM station on the signals generated by the sensors. The patterns that caused errors exceeding the acceptable accuracy for WIM class A(5) stations or signal deformations that prevented proper interpretation were recorded.
Based on the research presented in this paper, the following conclusions have been drawn: • passing on the right side of the lane (i.e., close to the road end) could result in an increase in the measurement error exceeding the acceptable level; • accelerating or braking while passing through the measurement system can result in an increase in axle load measurement error beyond the acceptable level; • changing the trajectory when a WIM station is equipped with a set of duplicate sensors does not cause the exceedance of the permissible error for a class A(5) station; and • for the study conducted, there were no above-normal errors associated with the determination of vehicle length by means of induction loops.
In addition, attention should be paid to non-central runs, i.e., those where the tyre could only partially overlap the load cell. Such cases may occur at most locations, as it is very rare that solutions delineating the correct trajectory, such as the use of traffic separators, are implemented in the WIM station area. It is obvious that such runs must be detected by the direct enforcement system as abnormal runs and consequently rejected.
The manner and dynamics of driving through a WIM station are not the only factors that may disqualify a given measurement as a basis for direct enforcement. The paper also presents the measurements of pavement quality which are necessary to be able to assign a WIM station to the appropriate accuracy class. Such measurements shall be repeated periodically to confirm that the pavement meets the requirements of COST 323 despite natural deterioration. The failure of the road pavement to meet the quality requirements is tantamount to excluding the WIM station from operation.
Other factors that can discredit a measurement for direct enforcement are meteorological factors. This includes the temperature of the roadway and its base, the condition of the roadway (dry, ice, or snow) as well as the direction and the speed of wind. Assessing