The identification technology of vehicle weight based on bridge strain time-history curve

Abstract

It is the basic characteristics of bridge weigh-in-motion technology to directly identify the vehicle weight based on the bridge dynamic response. At present, bridge weigh-in-motion technology tends to be mature in identification of gross vehicle weighing, but there is no breakthrough in identification of single-axle weighing. Therefore, a new axle-weight identification method is proposed using bridge weigh-in-motion technology in this article, in which the idea of bridge weigh-in-motion technology is introduced first. The numerical expression of the single-axle weight and the identification expression of axle space and vehicle speed are presented thereafter. Furthermore, the accuracy of the presented method is further reinforced through a series of practical model experiments of simply supported and continuous beam. The experimental result indicated that the proposed method is feasible in practical application.

Keywords

axle space axle weight bridge weigh-in-motion strain time-history curve vehicle weight

Foreword

The detection of vehicle-moving load on a bridge is of great significance to bridge life and health assessment (Wang et al., 2013b). At present, there are two methods of direct and indirect identification for moving load of bridge (Wang et al., 2013a), of which the indirect identification method is to obtain the load information on bridge through the oscillation equation of car–bridge coupled system. Such method is to achieve the purpose of weight identification (Law et al., 1997; Yuan and Chen, 1997; Zhu and Law, 2001) by solving the corresponding numerical response matrix through establishing the relationship between the vehicle load and the bridge vibration response. However, such method requires system parameters and substantial complicate calculation, and the identification results are prone to the boundary conditions and roughness of pavement. The disadvantage can be overcome by the direct identification method which identify the weight, speed, and other information of vehicle directly based on the measured dynamic response data of bridge to (Ojio and Yamada, 2002;WAVE, 2001). Such method is also termed as bridge weigh-in-motion (B-WIM) technology. The B-WIM uses the feature of proportionality between the measured response curve and vehicle weight to achieve the purpose of dynamic weighing of vehicle on the bridge. For this reason, the B-WIM has received considerable attention due to its strong feasibility, low cost, and simple operation (Zhang and Duan, 2011).

Previous research has shown that, it is ideal to identify the gross vehicle weight (GVW) by the direct identification method (He, 2015; Kobayashi et al., 2004; Moses, 1979; Wang, 2013); however, there is no breakthrough in the identification of single-axle weight because of the influence by the vehicle itself and the measured curve. Based on the study of dynamic weighing system of bridge, Christopher et al. (2009) stated that the quadratic change value of bridge dynamic response that is caused by a vehicle on the bridge is proportional to the axle weight of the vehicle according to the study on dynamic weighing system of the bridge. However, there is a lack of completeness in the study. In this article, the method of vehicle axle-weight identification is systematically illustrated by investigating the relationship between the measured strain time-history curve area and its second derivative.

It is noted that the identification of multiple-vehicle presence is still one of the main challenges faced by B-WIM technology. The transverse position (TP) of each vehicle requires to be identified when multiple vehicles are present on the bridge. The novel nothing-on-the road (NOR) B-WIM algorithm method is conducted using three-dimensional vehicle and bridge models, so it is able to identify the vehicle’s TP and axle weights using only the weighing sensors and numerical simulations. Yu et al. (2016) proposed an algorithm to identify different cases of multiple-vehicle presence. The application of B-WIM algorithms can be divided into two categories: one is the static algorithms that aim at obtaining the static axle weight and the dynamic. The other one is the moving force identification (MFI) that is the dynamic B-WIM algorithm. The dynamic B-WIM has the potential to be more accurate than static algorithms. The MFI method has the distinctive drawbacks when compared to the static B-WIM algorithms (Yu et al., 2016). An alternative B-WIM method is used to measure the velocity, wheelbase, and weight of vehicles, which is merely based on a single set of long-gauge fiber Bragg grating (FBG) sensors. A vehicle–bridge interaction (VBI) system simulation was performed based on the result of an indoor experiment. In addition, an in-situ test on an expressway bridge was performed to initially verify its feasibility. Chen et al. (2018) showed that this method can achieve its function with good accuracy under various conditions, but a long-term test still require to verify the durability and reliability of FBG sensors.

B-WIM technology

The bridge dynamic weighing technology is a method to identify the vehicle weight by a direct measured bridge dynamic response. The strain response of the bridge is illustrated briefly as an example. Assuming that the measured bridge strain curve is $ε (t)$ , the time integral area of the strain time-history curve $A_{(t)}$ can be obtained by integrating $ε (t)$ over the time $Δ T$ as follows

A_{(t)} = \int ε (t) d (t)

(1)

where $Δ T$ is the time period when the vehicle enters and leaves the bridge. Using $x = v \cdot t$ , equation (1) can be changed to

v \cdot A_{(t)} = v \cdot \int ε (t) d (t) = \int ε (t) d (x) = A_{(x)}

(2)

where $A_{(x)}$ is the integral area of the strain time-history curve along the bridge span, which is called the span integral area. It should be mentioned that $A_{(x)}$ is only related to the vehicle weight on the bridge and the bridge span, but irrespective to the speed and time that the vehicle is passing over the bridge. For the bridge in the elastic working range, the load acting on the bridge is also proportional with the strain at the same point caused by that load, so

α = \frac{{GVW}_{K}}{A_{K (x)}} = \frac{{GVW}_{β}}{A_{β (x)}}

(3)

in which GVW_K is the calibrated vehicle weight, $A_{K (x)}$ is the span integral area of the measured calibrated vehicle, ${GVW}_{β}$ is the unknown vehicle weight on the bridge, $A_{β (x)}$ is the span integral area of the strain time-history curve measured from the unknown vehicle weight, and $α$ is the bridge structure coefficient, which is a constant for the same bridge at the same measured point and can be obtained by calibrated from the vehicle weight and its span integral area of time-history curve in equation (3). Therefore, the weight of an unknown vehicle on a bridge can be obtained as follows

{GVW}_{β} = α \cdot A_{β (x)} = α \cdot v \cdot A_{β (t)}

(4)

where $A_{β (t)}$ can be calculated directly, and the vehicle speed v can be obtained according to $v = (L + d) / Δ T$ , where $Δ T$ is the time period the vehicle passes through the bridge measured from the strain time-history curve, L is the bridge span, and d is the vehicle length.

It has been shown that the vehicle-weight identification method by bridge dynamic weighing technology is applicable to bridges with stress condition in elastic or elastoplastic stage (Hitchcock et al., 2012).

Research on vehicle axle-weight identification technology based on B-WIM

The theory of single-axle weight identification

A simply supported beam is taken as an example to illustrate the identification process of single-axle weight. Assuming that a single-axle weight p acts on a simply supported beam with a length of L and a stiffness of EI, then the theoretical strain time-history curve of its midspan can be given as

ε (t) = {\begin{matrix} \frac{PZvt}{2 EI} 0 < t ⩽ \frac{L}{2 v} \\ \frac{PZL}{2 EI} (1 - \frac{vt}{L}) \frac{L}{2 v} < t < \frac{L}{v} \end{matrix}

(5)

where Z is the distance between the position of the sensor and the neutral axis of the middle cross-section. The following formula can be derived from equation (5)

\frac{d ε_{c}}{dt} (t) = {\begin{matrix} \frac{PZv}{2 EI} 0 < t < \frac{L}{2 v} \\ - \frac{PZv}{2 EI} \frac{L}{2 v} < t < \frac{L}{v} \end{matrix}

(6)

where equation (6) is a discontinuous constant function and then equation (7) can be derived therefore as follows

\frac{d^{2} ε_{c}}{d t^{2}} (t) = {\begin{matrix} \frac{PZv}{2 EI Δ t} 0 < t < \frac{L}{2 v} \\ - \frac{PZv}{2 EI Δ t} \frac{L}{2 v} < t < \frac{L}{v} \end{matrix}

(7)

The function graphs of equations (5) to (7) are shown in Figure 1.

Figure 1.

Identification diagram of single axle where “ε” means strain value of the cross section, “t” means time, “dε/dt” means the first derivative value of the strain, “d²ε/dt²” means the second derivative value of the strain.

From Figure 1(a), it can be seen that the peak point of the strain curve is corresponding to the strain value of the cross-section of the midspan measuring point C when the load P is passing through. Meanwhile, the point C’s cross-section is the demarcation point of the strain time-history curve changing from rising to falling and the point that the first derivative value of the strain curve changes from a positive value to a negative value in Figure 1(b).

It can also be seen from Figure 1 that the strain value changes significantly at point C, because point load acts on the left and right sides of measured point C section is in turn. Because the theoretical assumption is that the bridge is in elastic stage, there is an elastic relationship between the strain and external force, so it can be concluded that the magnitude of strain variation is directly proportional to the load on the section.

It can also be found that the vertical coordinate value of curve in Figure 1(c) can be treated as the scale factor of the strain when the axle weight passes through the point C. Therefore, the axle weight can be determined by the second derivative of strain time-history curve, as shown in equation (8)

p_{n} = \frac{d^{2} ε}{d t^{2}} \cdot ψ

(8)

where $ψ$ is a proportional constant, which is determined by the parameters of different bridge structure.

The theory of multi-axle weight identification

The process of multi-axle weight identification is similar to that of single axle. According to the identification theory shown in section “The theory of single-axle weight identification,” the strain time-history curve of simply supported beam under multi-axle weight is shown in equation (9)

ε = \sum_{n = 1}^{N} ε_{n} (t - t_{n})

(9)

where t_n is the time for the nth-axle weight entering the bridge. In the same way, the first and second derivative of the strain curve can be expressed as the following formula, respectively

\frac{d ε}{dt} = \sum_{n = 1}^{N} \frac{d ε_{n}}{dt} (t - t_{n})

(10)

\frac{d^{2} ε}{d t^{2}} = \sum_{n = 1}^{N} \frac{d^{2} ε_{n}}{d t^{2}} (t - t_{n})

(11)

For the multi-axle weight, it can be simply assumed that the number of axle n = 4, then the weight of each axle is $P_{1} = 6 h, P_{2} = 9 h,$ $P_{3} = 9 η, and P_{4} = 11 η$ , respectively, and $η$ is the proportion coefficient. While the speed v of each axle weight acts on a simply supported beam in turn, the function graphs based on equations (9) to (11) can be shown as below.

From Figure 2(a), it can be seen that each single-axle weight P is corresponding to a complete strain time-history curve. Taking $ε_{1} (t)$ as an example, it indicates that the load $P_{1}$ is entering the bridge at the original point $t = 0$ and leaving at $t = t_{3}$ , and the corresponding length $d_{3} = v \cdot t_{3}$ is the actual bridge length L. Therefore, the total length of the measured strain time-history curve for the multi-axial weight is $(L + d_{1} + d_{2} + d_{3})$ and the measured strain $ε (t)$ is $(ε_{1} (t) + ε_{2} (t) + ε_{3} (t) + ε_{4} (t))$ in total. The total strain time-history curve is shown in Figure 2(b). The variation value (quadratic variation) of the strain change can be obtained by taking the second derivative of the total measured strain time-history curve function. It can be seen from the description in section “The theory of single-axle weight identification” that the proportional coefficient of the correlation axis load is corresponding to the second derivative of the curve, as shown in Figure 2(c). It is worth mentioned that the positive second derivative value of strain time-history curve is a result of strain changes of midspan measured point when the axle load enters or leaves the bridge, and the negative value corresponds to the strain changes when axle load passes through the cross-section of measured point.

Figure 2.

Identification of multi-axle diagrams. where “ε” means strain value of the cross section, “t” means time, “dε/dt” means the first derivative value of the strain, “d²ε/dt²” means the second derivative value of the strain.

It can be observed that when the unit axle load passes through the measured point, the second derivative of the time-history curve is a constant in a very short time $Δ t$ , which can be assumed as $λ$ , and then the equation (11) can be written as

\frac{d^{2} ε}{d t^{2}} (t_{n}) = - \frac{Zv}{EI Δ t} \cdot P_{n} = P_{n} \cdot λ

(12)

Therefore, the correlation coefficient of the total axle load can be written as

\sum_{n = 1}^{N} \frac{d^{2} ε}{d t^{2}} (t_{n}) = \sum_{n = 1}^{N} P_{n} \cdot λ = GVW \cdot λ

(13)

Comparing formulas (12) and (13), it is not difficult to find that

\frac{\frac{d^{2} ε}{d t^{2}} (t_{n})}{\sum_{n = 1}^{N} \frac{d^{2} ε}{d t^{2}} (t_{n})} = \frac{P_{n} \cdot λ}{GVW \cdot λ} = \frac{P_{n}}{GVW}

(14)

Therefore, the identification of each axle weight can be identified as follows

P_{n} = [\frac{\frac{d^{2} ε}{d t^{2}} (t_{n})}{\sum_{n = 1}^{N} \frac{d^{2} ε}{d t^{2}} (t_{n})}] \cdot GVW

(15)

The aforementioned is the basic theory of the axle-weight identification based on B-WIM, which is not only applicable to the simply supported beam bridge but also to the continuous girder bridge.

Experiment on vehicle axle-weight identification technology based on B-WIM

Overview of model experiment

For the theoretical identification technology of vehicle weight, this article studied the corresponding bridge model. The experimental objects include two bridge models of simply supported beam bridge and continuous beam bridge. In order to make the experiment practical, the experimental model bridge is based on 20:1 scale of the veritable bridge, and the span of the simply supported beam model bridge is 2000 mm. The continuous beam model bridge is based on 25:1 scale of the veritable bridge, and the span of the continuous beam model is 1300 + 1400 + 1300 mm, which are shown in Figures 3 and 4.

Figure 3.

Model of simply supported beam.

Figure 4.

Model of continuous beam.

After determining the specific size of the model, according to the similarity rule of the model experiment, a series of parameters of the experiment were determined based on the studies of Gui et al. (2014, 2015), and the model boundary and quality were corrected according to the relevant parameters to meet the experimental requirements.

The traditional symmetrical arrangement principle is adopted for the arrangement of the test points in the experiment. For the simply supported beam model, the point at the half span is chosen as the main measuring point and points at the 1/4 and 3/4 span as the two auxiliary measuring points. For the continuous beam, the point at the half span is treated as the main measuring point and the two auxiliary measuring points are set on the left and right span, respectively. The layout of the survey points is shown in Figure 5.

Figure 5.

T-beam cross-section and layout of measuring points (unit: mm).

At the same time, in order to accurately simulate the vehicle–bridge coupling situation, the fabrication of the model vehicle for the experiment is simplified, and the suspension system of vehicle is considered (Zhu and Law, 2003). As shown in Figure 6, the model vehicle is made based on the double-axle heavy truck which is more common on highways, Ao Ling GTX-3028 is chosen as a referential prototype considering the experimental vehicle working condition. Donghua DHDAS eight-channel dynamic signal acquisition is shown in Figure 7, and analysis system is adopted in this experiment.

Figure 6.

Model vehicle.

Figure 7.

Data acquisition system.

In the experiment, the servo motor and frequency converter are combined as the power traction device to pull the model vehicle to cross the bridge model at different speeds, and the strain data samples are collected at the same time. The specific value of speed, axle space used in this study is based on the common parameters of truck specifications in highway transportation. By using different values, the accuracy and reliability of the proposed method in this article can be further reinforced. The experimental group was divided into 10 working conditions by different weights, speeds, wheelbase, and axle weight. The results are summarized in Table 1.

Table 1.

Vehicle weight working conditions.

Working condition no.	Speed of vehicle (m/s)	Vehicle weight (kg)	axle space of vehicle (mm)	Axle-weight ratio (front axle/rear axle)
1	0.29	4.60	170	3:7
2	0.29	8.85	170	3:7
3	0.29	13.42	170	3:7
4	0.29	17.90	170	3:7
5	0.56	8.85	170	3:7
6	0.56	13.42	170	3:7
7	0.56	17.90	170	3:7
8	0.29	17.90	340	1:1
9	0.56	17.90	260	1:1
10	0.56	17.90	340	1:1

Experimental results and analysis

During the experiment, there is a large fluctuation to the collected data due to the influence caused by the unevenness between the bridge deck and the acceleration zone or the deceleration zone when the model vehicle passes in and out of the bridge. To avoid the large identification error, the data after the vehicle entering and before the vehicle passing the bridge is considered as the criterion of axle identification instead of taking derivative of the whole process.

The time-history curves of a simply supported beam and a continuous beam model under a working condition is shown in Figure 8(a). The measured data acquisition frequency is 20 Hz, so the time interval $Δ t$ between the two adjacent strain points on the corresponding time curve is 0.05 s. It can be seen from Figure 8(a) that there is an obvious inflection point that appears on the curve when the front and rear axles of vehicle passing the cross-section of the measuring point. Taking the corresponding inflection point as the target and the time steps $Δ t$ as a unit to intercept the corresponding curve section, as shown in Figure 8(b), the second derivative of the corresponding curve is considered as the identification of the axle weight at each point, and the time interval $Δ T$ between different “turning points” is considered as the identification of the axle space. The identification result of two vehicles with different vehicle weight, axle weight and wheelbase are shown in Tables 2 and 3, respectively.

Figure 8.

Multiple axles weight identification diagram where“ε” means strain value of the cross section,“t” means time.

Table 2.

Identification values for vehicle parameter.

Working condition number		Axle space (mm)			Vehicle weight (kg)
Working condition number		True values	Identification values	Relative error (%)	True values	Identification values	Relative error (%)
Working condition 1	Simply supported beam	170	156	−8.2	4.60	4.56	0.81
Working condition 1	Continuous beam	–	–	–	–	–	–
Working condition 2	Simply supported beam	170	144	−15.3	8.85	8.92	0.8
Working condition 2	Continuous beam	170	174	2.4	8.85	9.15	3.4
Working condition 3	Simply supported beam	170	186	9.4	13.42	13.78	2.7
Working condition 3	Continuous beam	170	165	−2.9	13.42	13.40	−0.1
Working condition 4	Simply supported beam	170	148	−12.9	17.9	17.61	−1.6
Working condition 4	Continuous beam	170	174	2.4	17.9	17.22	−3.8
Working condition 5	Simply supported beam	170	146	−14.1	8.85	8.78	−0.8
Working condition 5	Continuous beam	170	171	0.6	8.85	9.05	2.3
Working condition 6	Simply supported beam	170	149	−6.4	13.42	13.46	0.3
Working condition 6	Continuous beam	170	174	2.4	13.42	13.50	0.6
Working condition 7	Simply supported beam	170	176	3.5	17.9	17.42	−2.7
Working condition 7	Continuous beam	170	170	0.0	17.9	17.77	−0.7
Working condition 8	Simply supported beam	–	–	–	–	–	–
Working condition 8	Continuous beam	340	317	−6.7	17.9	17.69	−1.2
Working condition 9	Simply supported beam	–	–	–	–	–	–
Working condition 9	Continuous beam	260	236	−9.2	17.9	17.41	−2.7
Working condition 10	Simply supported beam	–	–	–	–	–	–
Working condition 10	Continuous beam	340	351	3.2	17.9	17.71	−1.1
Working condition 11	Simply supported beam	–	–	–	–	–	–
Working condition 11	Continuous beam	260	278	6.9	17.9	17.39	−2.8

Table 3.

Identification values for vehicle axle-weight parameter.

Working condition number		Front axle (kg)			Rear axle (kg)
Working condition number		True values	Identification values	Relative error (%)	True values	Identification values	Relative error (%)
Working condition 1	Simply supported beam	1.38	1.53	−9.8	3.22	3.06	4.9
Working condition 1	Continuous beam	–	–	–	–	–	–
Working condition 2	Simply supported beam	2.66	2.22	16.5	6.19	6.63	7.1
Working condition 2	Continuous beam	2.66	2.70	1.5	6.19	6.15	0.6
Working condition 3	Simply supported beam	4.03	4.69	16.3	9.39	8.73	7.0
Working condition 3	Continuous beam	4.03	4.77	18.9	9.39	8.63	8.1
Working condition4	Simply supported beam	5.37	5.97	11.2	12.53	11.93	4.8
Working condition4	Continuous beam	5.37	5.45	1.5	12.53	12.45	0.7
Working condition 5	Simply supported beam	2.66	3.34	25.5	6.19	5.49	11.3
Working condition 5	Continuous beam	2.66	2.65	0.4	6.19	6.20	0.2
Working condition 6	Simply supported beam	4.03	3.83	4.9	9.39	9.59	2.1
Working condition 6	Continuous beam	4.03	3.85	4.5	9.39	9.59	2.1
Working condition 7	Simply supported beam	5.37	6.50	21.0	12.53	11.40	9.0
Working condition 7	Continuous beam	5.37	5.31	1.1	12.53	12.59	0.4
Working condition 8	Simply supported beam	–	–	–	–	–	–
Working condition 8	Continuous beam	8.95	8.95	0.0	8.95	8.95	0.0
Working condition 9	Simply supported beam	–	–	–	–	–	–
Working condition 9	Continuous beam	8.95	9.63	7.6	8.95	8.26	7.7
Working condition 10	Simply supported beam	–	–	–	–	–	–
Working condition 10	Continuous beam	8.95	8.64	3.5	8.95	9.26	3.5
Working condition 11	Simply supported beam	–	–	–	–	–	–
Working condition 11	Continuous beam	8.95	8.26	7.7	8.95	9.64	7.6

Taking some of the identification values of the vehicle weight (GVW) and the axle weights from Tables 2 and 3 as X-axis and the true values as Y-axis to form Figure 9(a) and (b), in which the boundary equation is $y - x = 0$ . From Figure 9(a), it is shown that the overall weight identification effect is ideal, with a minimum error of 0.2% and a maximum error of less than 4%. The identification effect of simply supported beam is slightly better than that of continuous beam under the same vehicle weight due to the influence of bearing restlessness. As shown in Figure 9(b), the overall identification error of the axle weight is within 25%, and the identification error becomes smaller as the axle weight increase. This is due to the fact that the signal-to-noise ratio will become larger for the lighter axle weight and relatively smaller for the heavier axle weight. It is also shown that the identification error can be controlled within 10% when the vehicle axle weight rises to 8 kg. Moreover, by comparing the identification results under the same vehicle working condition, the overall identification results of continuous beam are better than that of simply supported beam, especially in the situation of lighter axle weight. For the same simply supported beam or continuous beam, higher precision in axle-weight identification can be achieved with smaller axle weight.

Figure 9.

(a) Identification result of vehicle weight and (b) identification result of axle weight.

For vehicle axle space identification, this article adopts the method by extracting the time interval $Δ T$ between the front and rear wheels peak points of the strain time-history curve and considering identified vehicle passing speed to obtain the information. From the data summarized in Table 1, it can be seen that the vehicle axle space identification is greatly influenced by the vehicle speed. At the sampling frequency (for example: 20 Hz in this article), the number of sampling point within the identification range of the peak point decreases with increasing vehicle speed (generally $2 Δ t ~ 4 Δ t$ in case of 20 Hz and 20 km/h). In addition, it can be found that the overall speed identification results of continuous beam are also better than that of the simply supported beam.

Experiment of bridge engineering test and results

To validate the proposed B-WIM identification method in identifying vehicle axle space and axle weight, the bridge engineering test was carried out on a 2 × 40 m T-beam bridge to identify the parameters of vehicle. The elevation diagram of the bridge is shown in Figure 10, and the transverse section of the T beam and the arrangement of the test points which are arranged at the bottom of the 1 # ∼3 # T beam are shown in Figure 11.

Figure 10.

Layout of test bridge elevation (unit: cm).

Figure 11.

T-beam cross-section and layout of measuring points (unit: cm).

A triaxle truck is used with a front-middle axle space of 380 cm and middle-rear axle space of 140 cm. The vehicle was loaded with gravel as additional weight, and each axle loads were obtained by static weighing. The front axle load is 8900 kg, the middle axle load and the rear axle load are 17,000 kg and 17,300 kg, respectively. The parameters of the vehicle are shown in Figure 12(a). Due to poor road traffic and safety considerations, vehicle run crossing the test bridge at different low speeds of 30,40, and 60 km/s, and the test process is shown in Figure 12(b).

Figure 12.

(a) Axle load and wheelbase parameters and (b) photo of vehicle crossing the bridge.

Strain time-history curves of 3# strain measurement point are shown in Figure 13, which are the unprocessed raw data. According to the calculation method introduced in the second section, the main identification values for vehicle parameter are summarized in Table 4. The distance between the front axle and the center of gravity of middle axle and the rear axle is summarized in Table 4 as “Identification of axle space*.”

Figure 13.

Strain time-history curve of 3# strain measurement point.

Table 4.

Identification values for vehicle parameter.

Speed (km/s)	Identification of speed		Identification of GVW		Identification of front axle		Identification of rear axle		Identification of axle space*
Speed (km/s)	Result (km/s)	Errors (%)	Result (kg)	Error (%)	Result (kg)	Error (%)	Result (kg)	Error (%)	Result (cm)	Error (%)
30	32	6.7	445	3.01	92	3.37	353	2.9	489	8.67
40	38	−5.0	423	−2.08	87	−2.25	336	−2.0	430	−4.44
60	63	5.0	452	4.63	91	2.25	361	5.2	407	−9.56

GVW: gross vehicle weight, * Identification of axle space.

It can be seen from the Table 4 that in the actual bridge engineering test, when the speed changes from 30 to 60 km/s, the relative error of speed identification results changes from −5.0% to 6.7%, the relative error of vehicle total weight and axle load identification results changes from 2.08% to 5.2%, and the relative error of wheelbase recognition results changes from −4.44% to 9.56%. The increase in error with increasing vehicle speed is mainly due to the minimal distance between the middle axle and rear axle, which cannot be identified.

Conclusion

Based on the measured bridge strain time-history curve and the dynamic weighing technology of B-WIM bridge, a new identification method of vehicle axle space and axle weight is studied in this article. The highlights of this study are shown in Appendix 1. The theoretical identification results were obtained through the corresponding theoretical methods combine with the experimental data from the actual experiments of the Plexiglas simply supported beam bridge and the continuous beam bridge model. The following conclusions are drawn and summarized as follows:

The sampling frequency should be kept between 20–50 Hz for directly extracted bridge strain time-history curve. This can increase the accuracy of speed identification and reduces the influence of support noise.

The identification accuracy of axle weight is influenced by axle weight as well as the axle-weight ratio. The greater the axle weight and the smaller the axle-weight ratio is and the higher the identification precision.

It can be concluded that by increasing the sampling frequency combined with using the relevant modified noise reduction method, the vehicle axle space identification curve obtained from the experiment can be more accurately modeled.

The overall identification result of continuous beam bridge is better than that of simply supported beam bridge; as a result, the continuous beam bridge is more appropriate for research purpose.

Footnotes

Appendix 1 Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was partly sponsored by following fund programs: (1) China Postdoctoral Science Foundation (Grant No.: 2017M612874) and (2) the Natural Science Foundation of Guangxi Province (Grant No.: 2015GXNSFBA139229).

ORCID iD

Tianzhi Hao

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