Evaluation of road condition based on BA-BP algorithm

Abstract

BP (Back Propagation) neural network has been widely applied for classification tasks including road condition evaluation, however, BP model has the problem of lower accuracy and slow convergence rate. A novel road condition evaluation method based on BA-BP (Bat-Back Propagation) algorithm is proposed for the unstructured small road condition evaluation, which filled the vacancy of specific small road scenes. Firstly, five kinds of road condition features including roughness, curvature, obstacle width to height ratio, obstacle effective area ratio, obstacle coefficient are defined and extracted. Then obstacles from region of interest (ROI) in front of the vehicle are analyzed. Finally, Bat algorithm is used to optimize the searching of initial network weights and thresholds, which obtained a higher accuracy of 95.15% and efficient training process. Comparison experiments showed that the proposed approach improved the accuracy with 5.31%, 3.32%, 3.17% than the BP, GA-BP and FA-BP model, respectively. As for the processing time of collected road data, BA-BP network consumed less time of 2 s and 3.9 s compared with GA-BP and FA-BP. Proposed method also outperformed than most of the state-of-the-art approaches with higher accuracy and simpler hardware environments, which proved its potential of being popularized in large scale real-time systems.

Keywords

Road condition evaluation BP neural network Bat algorithm adjustment factor

1 Introduction

Problems of road accident and traffic jam have been rising in recent years due to the rapid development of automobile industry and urban construction, which seriously affect people’s travel safety and efficiency [1]. Frequent information exchange including road condition, car data and drivers have brought heavy pressure to the traditional vehicle technologies, ensuring a safe, efficient and unblocked traffic has become the hot spot in both engineering and academic field around the world [2]. Road condition evaluation serves as a key role in traffic management, accident prevention and vehicle maintenance, which is also the foundation of traffic regulation and control [3].

Current studies of road condition evaluation based on traffic information extraction usually aimed at typical road structures including highways, winter or asphalt roads. There are few researches on unstructured small roads like city alley and unknown staggered small streets. Therefore, studies on these specific road conditions are even less. Most of the road evaluation approaches applied the machine learning methods or deep learning models, which obtained general classification performance and complex computation [4 –6]. Traditional BP (Back Propagation) Neural Network has the problem of lower accuracy and slow convergence rate [7]. A novel BP network improved by the Bat algorithm (BA-BP) is proposed to evaluate the unstructured small road conditions using five surface features including road roughness, road curvature, obstacle width to height ratio, obstacle effective area ratio and obstacle coefficient. BA-BP model in this paper overcame the random defects of weights and threshold selection in BP neural network, bringing of adjustment factor also helped to obtain a more reasonable and efficient training process. Optimal accuracy of the proposed method achieved 95.15% on the collected road segment dataset.

2 Literature review

Various modeling and evaluation methods based on neural network and machine learning have been widely applied in the fields like transportation [8, 9] and industrial engineering [10 –12], however, there are few road condition evaluation approaches for the unstructured small roads. Most of the existing methods are applied for common road condition detection, which can be roughly divided into two categories including deep learning and traditional machine learning approaches. Szankin et al. [13] proposed the deep learning based system dedicated for resource constrained environments to classify road conditions including possible hazards, which obtained the precision and recall above 70% in most cases. Pre-trained CNN was used by Pan [14] for the winter road surface condition monitoring, which filled the snow scene of road condition assessment. Abdić et al. [15] introduced a recurrent neural network for automated road surface wetness detection from audio of tire surface, which achieved the average recall of 93.2%. Zhang [16] trained a supervised deep convolutional neural network to detect the road crack and outperformed than the existing hand-craft methods. Maeda et al. [17] used a convolutional neural networks to train the damage detection model with the proposed dataset, which relied heavily on the hardware. Other deep learning models like transfer learning [18], Faster and SSD model [19], GPU based CNN [20], YOLO [6], classical CNN [14], and SqueezeNet [13] are also widely applied for road condition detection. These methods obtained better classification performance while requiring deeply on the hardware and balance of datasets, which still need to be improved before their wide promotion in market.

As for the machine learning based methods, Sandamal et al. [3] explored the applicability of smartphone-based roughness data to assess the pavement condition of rural roads. New pavement condition indicators using a machine learning algorithm named regularized regression with lasso was proposed by Marcelino et al. [21], which improved the classification accuracy of pavement condition when less data are available. While the accuracy of Marcelino is not satisfied. Guha [22] applied the Multi-Criteria Analysis (MCA) model to classify the grades of collected data, 243 Chernoff faces were used for the classification this problem, which added to the computation complexity. Sharma et al. [23] applied the combining method of image processing and ultrasonic sensors for the road surface evaluation. Their approach relied deeply on the ultrasonic sensors. Other machine learning methods based on SVM (Support Vector Machine) [24], RF (Random Forest), KNN (K-Nearest Neighbor) [25, 26], ANN (Artificial Neural Network) [27] are also used for road condition classification or damage detection, however, their accuracy are not satisfied. Therefore, improved light weight models based on BP neural network are considered for the road condition evaluation.

BP neural network [7] does not require the same complex environment as deep learning models, which also achieved similar accuracy as neural networks. Machine learning algorithms like SVM decides the final result with a small number of vectors, which depend largely on the precision of feature engineering and have worse robustness as well as generalization ability than neural network. Detection accuracy of machine learning models is also not satisfied. BP algorithm [28 –30] has been commonly applied as the base model for relevant road condition evaluation or experiments, which still has the weak points [31] like slow convergence speed and falling into local minimum. Problem of hard to converge and poor prediction performance are especially serious when the initial weights and threshold of BP neural network are not appropriate [29]. BP network combined with Bat algorithm [32] is proposed in order to fix these problems, which could set initial weights and thresholds better in order to compensate for the random defects in BP parameter configuration [33]. Adjustment factors are also added to emphasize the major influence of obstacles features in road conditions aiming at achieving the target of improving the algorithm stability as well as the global value searching ability, which behaved well in the proposed experiments.

Main contribution of this paper is to establish the unstructured small road condition evaluation model based on BA-BP algorithm, which improved the efficiency and accuracy of the traditional BP network. Vacancy of small road condition assessment has also been filled. Rest of the paper is organized as follows: road condition features are given in Section 3, Section 4 talked about the road condition evaluation model based on BA-BP. Experimental results and discussion are conducted in Section 5. Remarks are provided in Section 6 for the conclusion of paper.

3 Proposed road condition features

Evaluation of road condition based on vision considers various factors including roads, obstacles and evaluation indexes. This section applies digital image processing method to select several most suitable features for road condition evaluation, definition of features and corresponding specific characteristics are studied respectively.

3.1 Road roughness

Roughness refers to the longitudinal deviation value of a road surface, which is a significant index for the road condition evaluation. As one of the key features for the analysis of road condition, it directly determines the driving comfort, road safety and state of use. Road can be difficult for driving and decrease the safety when the pavement is crude or bumpy; a moderately smooth pavement would bring pleasant driving experience; when the road is too smooth like icy, it would not be suitable for safe driving. Proper roughness of road contributes largely to the driving safety and experience. Figure 1 shows two kinds of common road conditions, which bring different driving experience. Left part of Fig. 1 is a flat narrow road with brick structure, and the asphalt pavement on the right is broken and has protrusions in middle, whose comparison shows the change of roughness.

Fig. 1

Samples of different road roughness.

Texture are the local irregular while macroscopic regular features of the image, which reflects certain changes in grayscale and color from the object surface. Analysis of road texture helps to correctly understand and interpret the current condition of pavement. Grey-level co-occurrence matrices (GLCM) is applied to obtain the statistical texture vectors including energy, entropy, contrast, correlation and inverse difference moment [34], which represents the texture uniformity, complexity, clarity, linear relationship and gray value uniformity. These five features constitute the vector A = (a1, a2, a3, a4, a5). Image acquisition cycle is T, change rate of pavement texture is given as follows: $Δ_{s} = \frac{{∥ A_{t + T} - A_{t} ∥}_{2}}{{∥ A_{t} ∥}_{2}}$ (1)

Where A_t is the image texture feature vector collected at time t, A_t+T is the texture feature acquired the next time. Too smooth or rough roads can lead to larger Δ_s, while roads with proper roughness will generate smaller Δ_s. In addition, uneven roads can be regarded as curved surfaces. Treat the number and amplitude of ups-and-downs shapes in regions of interest as the parameters of Brown’s motion, road surface roughness model is as follows: $F = \sum_{i = 1}^{n} f (u, v, u_{i}, v_{i}, P_{i})$ (2)

Where F is the curve fluctuation function, f (u, v, u_i, v_i, P_i) represents the fluctuation shapes. Positive integer n represents the number of undulating shapes on road surface, which obeys the normal random distribution. Set the starting point as the origin point, u is the coordinate along the direction of road, v is the coordinate from the road width direction. u_i and v_i are center points of the i-th undulating shape. Then the hemispherical sign function is as follows: $f = sign (R_{i}) \sqrt{R_{i}^{2} - {(u - u_{i})}^{2} - {(v - v_{i})}^{2}}$ (3)

The value of R_i obeys normal distribution, which determines the direction of pavement fluctuation. Negative R_i represents that this part of the road is a dent compared to the baseline, positive R_i means that this part is a hump. $P_{i} \subseteq {(u, v) | {(u - u_{i})}^{2} + {(v - v_{i})}^{2} = R_{i}^{2}}$ (4)

P_i is the range of fluctuation, which starts from u_i and v_i. Its coordinate points are uniformly distributed along the road surface direction.

F and Δ_s are not independent to each other considering the impact of pavement texture change rate as well as the fluctuation degree. Pavement texture change rate will increase if the road undulates with bumps and hollows. Considering the correlation between Δ_s and F:

$\begin{matrix} I (Δ_{s}, F) = & \sum_{i} \sum_{j} P_{Δ_{s} F} (Δ_{si}, F_{j}) \log \\ [\frac{P_{Δ_{s} F} (Δ_{si}, F_{j})}{P_{Δ_{s}} (Δ_{si}) P_{F} (F_{j})}] \end{matrix}$ (5)

I (Δ_s, F) represents the quantitative value for the correlation of two variables, P_{Δ
_{s
F}} (Δ_si, F_j) is the probability for the two factors reaching the state of poor or good simultaneously. Road roughness L are described as follows considering the road situation of excessive smoothness and flawed:

$L = {\begin{matrix} \frac{1}{(1 - Δs)Δs / 2 + F2 / 2∥F2 ∥ - I (Δ, F) \cdot Δ_{s} \cdot F}, Δ_{s} \in [0, 0.2) \\ \frac{1}{Δs2 / 2 + F2 / 2∥F2 ∥ - I (Δ_{s}, F) \cdot Δ_{s} \cdot F}, Δ_{s} \in [0.2, 1] \end{matrix}$ (6)

3.2 Road curvature

Accident rate at the bend is eight times higher than that in other road conditions, which shows that correct evaluation of road curve impact has become an important factor for road condition assess. Collected images are segmented firstly, then the results are processed by Hough transform to obtain the pure road surface. Finally, boundary and area of road are extracted. When the valid road boundary is not able to obtain due to various environmental factors such as shadow and water stain, road edge of both sides would be identified after removing the noise and smoothing the edge line. The edge above represents the road contour, and the area of feasibility are constructed by the ground hump and line.

Curvature is a quantity that describes the local properties of a curve, which demonstrates of the curve bending degree [35]. Curve M corresponds to the arc s, stands for the arc s + Δs, $| \overset{⌢}{MM} | = | Δ s |$ . Tangent angle of M → M′ is |Δα|. Mean curvature $\bar{K}$ of arc $\overset{⌢}{MM}$ and curvature K at point M are as follows: $\bar{K} = | \frac{Δ α}{Δ s} |, K = lim_{Δ s \to 0} | \frac{Δ α}{Δ s} | = \frac{d α}{ds}$ (7)

The larger the incircle is, the smaller the bending degree of curve will be, which brings smaller curvature and bigger curvature radius. Proposed road curvature can be characterized by the curvature of bending part as shown in Fig. 2. Curvature radius of the corresponding bending segment is calculated as r = 1/ k.

Fig. 2

Bending road segment.

3.3 Dynamic obstacle

Obstacles on the road are the main factors that affect the driving quality according to the research of road information [36], therefore, dynamic obstacles are mainly defined and analyzed the in this part. Research object of this paper is small smart car in complex small roads, region of interest I in front of the car are selected and defined, the size of the car body is m * n. Domain of I is a rectangular area in front of the car with length of 4 m and width of 1.25 m (set by the intelligent vehicle speed parameters, ensuring that the original straight route of car is not affected). All the bumps on both sides in front of the vehicle are avoided using the image processing, then the driving area is selected. Region of interest for the vehicle will be re-established according to the environment changes in the driving process.

Dynamic obstacle is judged by the change of suspected objects in front of the running vehicle, then the object is decided that whether it is a dynamic obstacle. Only the salient objects in area of interest need to be identified during the obstacle detection process, as shown in Figs. 3 and 4, vehicles from the road sides can be ignored. Pedestrians in front of the car are the suspected obstacles, distance from them to the intelligent car is recorded as d, which will continue being updated during the running process. There are multiple obstacles in area of interest as shown in Fig. 4 (b), different pedestrians or obstacles will be separated by the clustering algorithm [5]. Then distances d1 and d2 of pedestrians A and B will be calculated and combined according to the weight based on ratio of area. Finally, the combined obstacle ratio is input into the BA-BP algorithm for road condition evaluation.

Fig. 3

The region of interest I.

Fig. 4

Single and multiple dynamic obstacles determination.

Initial height and width values of the front collected objects are respectively h₀ and w₀, the distance between the vehicle and suspected obstacle is d₀. Set the dynamic obstacle decision coefficient as γ. Collected image information of the suspected obstacles should obey the following expression: $γ = {\begin{matrix} 0, h \leq h_{0} or w \leq w_{0} \\ 1, h > h_{0} or w > w_{0} \end{matrix}$ (8)

If the contour size of the suspected obstacle within the region of interest keeps unchanged or smaller, it indicates that the distance between the vehicle body and the suspected obstacle are constant or bigger, then it can be excluded from the obstacles, where d ⩾ d₀, γ = 0; on the contrary, bigger contour size of the suspected obstacle indicates d < d₀, γ = 1, which makes it as the dynamic obstacle.

3.3.1 Width to height ratio

Suspected obstacle in region of interest is firstly handled by the edge detection, then the shape features are extracted. Different contours of obstacles can be divided to rectangular, oval, round (round-like), polygon shapes and so on. Circular contour detection is conducted as a sample. Hough transform can be applied to connect the discontinuous edge pixels to form a closed border curve. Figure 5. is an example of common trash can on the road in front of vehicle. h and w are set as the height and width of the minimum enclosing rectangle for edge extraction.

Fig. 5

Edge detection of sample obstacle.

Height h and width w of the locked suspected obstacle within the region of interest will vary when the car is moving forward, but the overall shape of the object remains unchanged in short time. So, the width to height ratio c of the obstacle remains the same, which is given as follows: $\frac{w}{h} = c$ (9)

3.3.2 Effective area ratio

Pre-detect is conducted on the collected video or image in order to find the suspected obstacles, contour size change of suspected obstacle in region of interest determines the dynamic obstacle coefficient γ, which indicates that γ depends on the width w and height h of the object. Change of the object’s outline size also indicates the variation of the area ratio for the object in image, because the camera placed on the vehicle has a fixed range of view. If vehicles and the objects ahead are in the similar speed, their distance will keep within bounds, and the proportion of the object from whole image will just fluctuate in a tiny range; if they have a relative velocity, proportion of the object in whole image will change obviously. Whether a certain object in the region of interest can be decided as a dynamic obstacle depends on the effective area ratio R of the suspected obstacle, for R greater than the threshold T, it will be judged as a suspected obstacle. The proposed threshold T is a fixed value, which is determined according to the intrinsic parameters of vehicle and camera. The effective area ratio is given as follows: $R = \frac{S_{o}}{S_{r}}$ (10)

S_o is the number of valid pixels in suspected obstacle from the region of interest after binary process. Previous S_r is set as the total pixels in whole image, proposed S_r is defined as the total number of pixels in region of interest for less computation. Select the region of interest as the boundary, the area of the child as the suspected obstacle, S_r and S_o are as shown in Fig. 6.

Fig. 6

Effective area ratio of the sample image.

3.3.3 Obstacle coefficient

This paper concentrates on the influence degree of the obstacle features in driving, which can be concluded as obstacle coefficient q through the comprehensive analysis using the shape, width and height characteristics. As for the experimental smart car, whose wheel radius is r, r/4 is the raised critical point that the smart car can pass, then the definition of q is as follows: $q = exp (- \frac{4 h_{t}}{r}) \cdot | ln w_{t} |$ (11)

Where, h_t and w_t are the actual height and weight of obstacle, q ∈ (0, 1). The method of calculating the obstacle width and height is referred to the principle of reverse image for car, then features of obstacle are speculated based on basic principles of camera modeling and photographic geometry [37]. Besides, new area of interest will be determined each time the smart car faces barriers hindering the original route, then the circulation of analysis is conducted.

4 Road condition evaluation model based on BA-BP

BP neural network has been widely used for classification task, while there still exist some problems like slow convergence speed and falling into local minimum in the actual model construction. Therefore, BP network optimized by the Bat algorithm is applied to conduct the road condition evaluation, which achieved better results compared with traditional BP network and other baselines [33].

4.1 Bat algorithm

Bat algorithm is a novel swarm intelligence method proposed by Yang in University of Cambridge by simulating the bat echolocation, which belongs to stochastic optimization algorithms [38]. Process of Bat is described as follows:

Set a D-dimensional searching space, $v_{i}^{t}$ and $x_{t}^{i}$ are the i-th bat’s velocity and position at time t. Then the new velocity and position of the i-th bat in prey process can be generated by the equations below: $f_{i} = f_{min} + (f_{max} - f_{min}) β$ (12) $v_{i}^{t} = v_{i}^{t - 1} + (x_{i}^{t} - x^{*}) f_{i}$ (13) $x_{i}^{t} = x_{i}^{t - 1} + v_{i}^{t}$ (14)

Where f_i is the pulse frequency applied by the i-th bat at the present time, f_i ∈ [f_min, f_max].β is a random number and β ∈ [0, 1], x^* is the current global best location (or solution). If a solution (bat) needs to be selected from the current optimal results in local searching, new position of the bat can be obtained by the random disturbance Equation (15): $x_{new} (i) = x_{old} + ɛ A^{t}$ (15)

ɛ is a D-dimensional random vector, which randomly ranges in [- 1, 1]. x_old stands for the random solution selected in the current optimal set. A^t is the average loudness of all the bats at current time t. Then the new solution can be generated from the neighborhood regions around the selected solution based on the local searching.

Prey and tracking of bats can be mainly divided into two processes: (1) transmit pulse with larger loudness and lower frequency to expand searching area in the early process of prey, which helps to search in a broader space; (2) gradually decrease the loudness and increase the frequency of pulse according to the distance between the bat and prey, which aims to monitor the movement and latest position of prey. The loudness A (i) and emission frequency r (i) are updated with the iteration as shown follows: $r^{t + 1} (i) = r^{0} (i) \times [1 - exp (- γ \times t)]$ (16) $A^{t + 1} (i) = α A^{t} (i)$ (17)

Where r⁰ (i) represents the maximum pulse frequency, r^t+1 (i) is the frequency at time t + 1, A^t+1 (i) is the loudness at the same time t + 1. γ is the growth coefficient of pulse frequency, α is the attenuation coefficient of pulse loudness, they are all constants. γ > 0, 0 < α < 1.

4.2 BA-BP algorithm

BP neural network consists of three layers: input layer with n nodes, hidden layer with p nodes, output layer with q nodes. Set the input mode vector A_k = (a₁, a₂, ⋯ , a_n), desired output vector Y_k = (y₁, y₂, ⋯ , y_q); middle layer unit input vector S_k = (s₁, s₂, ⋯ , s_p), output vector B_k = (b₁, b₂, ⋯ , b_p); Output layer unit input vector L_k = (l₁, l₂, ⋯ , l_q), output vector C_k = (c₁, c₂, ⋯ , c_q); Connection weights {W_ji } , i = 1, 2, ⋯ , n, j = 1, 2, ⋯ , p; connected weights from middle layer to output layer {V_tj } , j = 1, 2, ⋯ , p, t = 1, 2, ⋯ , q; unit output threshold in middle layers {θ_j } , j = 1, 2, ⋯ , p; unit output threshold in output layer {γ_t } , t = 1, 2, ⋯ , q, above k = 1, 2, ⋯ , m.

Training process of BP network closely relates to the error function curve, improper parameter selection may lead to local minimum, which largely depends on insufficient implicit nodes and inappropriate initial weights. Therefore, it is mainly caused by the selection of initial weights where there are sufficient hidden nodes. Distribution of network weights are strictly related to their contribution to outputs in cases of small noise.

Main idea of optimizing the weights of BP neural network using Bat algorithm is as follows: firstly, apply the Bat algorithm to optimize the distribution of initial weights and obtain a better searching space; then use the obtained optimal set of weights and thresholds as the initial parameters to carry out the training process, iterate the training until the precision requirements are met.

Indexes which affect the evaluation results of road conditions includes L, K, c, R and q given in section 3, the effects of factors for evaluation are different. Distribution of initial weights should be biased aiming at highlighting the difference between indexes, so that latter training process can be more reasonable and efficient. Simple weighting method for road evaluation model is proposed, by which the weight coefficients closest to the desired values are obtained: w_L = 0.1156, w_K = 0.0893, w_c = 0.1744, w_R = 0.3915, w_q = 0.2292. Coefficients above shows that the most significant factor on road condition evaluation is the effective obstacle area ratio, the second is obstacle factor. Roughness and curvature contribute least for the results, which also confirms that road evaluation is mainly based on dynamic obstacles.

$\bar{w_{i}}$ is the spectral value of the input variable a_i referred to the weight spectrum formula. Set the adjustment factor ς₁ and ς₂ in BA-BP algorithm: $\bar{w_{i}} = \frac{1}{p} (\sum_{p} | W_{ji} |) \sqrt{n + p}$ (18) $ς_{1} = \frac{\bar{w_{4}}}{\sum_{i = 1}^{5} \bar{w_{i}}}$ (19) $ς_{2} = \frac{\bar{w_{5}}}{\sum_{i = 1}^{5} \bar{w_{i}}}$ (20)

Influence degree of inputs on the outputs can be analyzed according to the spectrum value. Partial initial weights of BP neural network need to satisfy the condition: ς₁ ⩾ 0.35, ς₂ ⩾ 0.20 in order to highlight the function of obstacle features, then the constraints are obtained and verified by the weighted model experiment, by which a more ideal searching space is obtained.

Flow of BA-BP algorithm are as shown in Fig. 7 and follows:

Fig. 7

Flow chart of BA-BP algorithm.

BA-BP algorithm

Step 1: Use the real number to code for the individual of Bat algorithm, treat the parameters W_ji, V_tj, θ_j, γ_t of BP neural network as a whole part for coding. Each individual contains all the BP weights and thresholds, which also represents a complete BP neural network.

Step 2: Generate n bats randomly and form the initial bat population. Randomly initialize the bat position xi, speed vi, loudness Ai and pulse frequency ri in searching space.

Step 3: Associate the bat location of each individual with the adaptation degree f(x). The fitness function is as follows:

$f (x_{i}) = \frac{1}{l} \sum_{m = 1}^{l} {(T_{im} - {\hat{T}}_{im})}^{2}$ (21) Where T_im and ${\hat{T}}_{im}$ represent the actual output and the expected output from the network, which is determined by the weights and thresholds of the i-th bat among the m-th training samples. l is the total number of the training sample.

Step 4: Determine whether the algorithm reaches the maximum number of iterations, if the condition is satisfied, terminate the algorithm, output the optimal solution; otherwise, go to Step 5.

Step 5: Update the speed and position of the bats according to formula (12), (13) and (14).

Step 6: Generate a random number rand1, if rand1 > r_i (r_i is the pulse frequency of the i-th bat), obtain x_new by formula (15).

Step 7: Evaluate the location: good or bad?

Step 8: Generate a random number rand2, if rand2 < Ai (A_i is the pulse loudness of the i-th bat), when f (x_i) < f (x^*), update bat individuals, decrease Ai through the formula (17), increase r_i with the formula (16).

Step 9: If the termination condition is met, output the target value and terminate the algorithm, otherwise; turn to Step 3.

Step 10: Decode the individuals after BA optimization, apply the results as the initial connection weights and thresholds of BP neural network.

Step 11: Adjust the factor ς₁ and ς₂ based on the pre-selected values by Step 10, if the condition ς₁ ⩾ 0.35 or ς₂ ⩾ 0.20 cannot be satisfied, turn to Step 5.

Step 12: If ς₁ ⩾ 0.35 and ς₂ ⩾ 0.20 are both satisfied, use the pre-selected values as the initial parameters of BP neural network.

4.3 Road condition evaluation model

Five subindexes of the extracted road features including L, K, c, R and q are obtained according to the modeling analysis above, which refer to the road roughness, curvature, obstacle width to height ratio, obstacle effective area ratio, and obstacle coefficient, respectively. All the features are specifically defined in section 3. A general evaluation index E is obtained finally, basic network structure diagram is shown in Fig. 8. Specific steps of the improved BA-BP neural network are as follows: (1) establish the initial BP neural network, use the encoding method to generate the initial parameters including maximum number of training, training accuracy, learning rate, while obtaining the optimal weights and thresholds by the Bat algorithm. (2) optimize the BP neural network with the optimal weights and threshold obtained by the BA-BP algorithm, get the best BP neural network structure which can meet the performance requirements through training.

Fig. 8

Road condition evaluation model based on BA-BP network.

The input layer contains five neurons which correspond to five subindexes, hidden layer has 16 neurons, whose associated node number is also 16, the output layer contains one neuron. Transfer function from input layer to hidden layer is tan-sigmoid, and that from hidden layer to output layer adopts the logarithm S transfer function, namely log-sigmoid function. $g (x) = \frac{e^{x} - e^{- x}}{e^{x} + e^{- x}}, f (x) = \frac{1}{1 + e^{- x}} .$ (22)

Early stop as a regularized approach is applied in the training of the model, because all the neural networks are learned through gradient descent. Use this approach to update the model so that it better fits the training set in each iteration. This approach could improve the performance of model on the testing set and avoid the problem of over fitting to some extent. MSE (mean-square error) function with L2 regularization are used to reduce the complexity of the proposed BA-BP model, which achieved better results and learn the inherent patterns due to the intricate road condition data. Overall, the evaluation model based on BA-BP algorithm is: $y = f (\sum_{j = 1}^{16} V_{j} g (\sum_{i = 1}^{5} W_{ji} a_{i} + θ_{j}) + γ)$ (23)

5 Experimental results and discussion

5.1 Data description and preprocessing

200 road segments including alleys, campus and communities in Dongcheng District, Beijing are collected as the experimental data in this paper, a sample image for illustration is given in Fig. 9, which contains a relatively smooth cement road between two rows of buildings. Then the features of images are extracted and applied for performance evaluation of the proposed model. Corresponding analysis are conducted as follows.

Fig. 9

Original sample image for test.

Proposed road image pre-processing method includes: gray scale, image filter, edge enhancement, binarization. Filtering is applied to eliminate the noise mixed in the image and better extract features for image recognition, filtering result of the proposed image is as shown in Fig. 10. Edge detection helps to greatly reduce the amount of data, meanwhile removing the irrelevant information, and retains the important structural attributes, like the edge of road and building in Fig. 11. Figure 12 shows the binarization result, which highlighted the outline of sample image. Then the final optimal edge of road in sample is obtained by the method of region growing, as is shown in Fig. 13.

Fig. 10

Filtering result.

Fig. 11

Edge detection result.

Fig. 12

Binarization outputs.

Fig. 13

Optimal edge of road in sample.

Theoretically, region of interest is in rectangular, while that of the proposed method is trapezoidal due to the certain light and angle of camera on car. Left and right sides of trapezoid are respectively parallel to edges of road sides, trapezoidal bottom and height are equal to theoretical values. Then the obstacle distribution is detected. Method of multi-threshold segmentation is used to segment, calibrate obstacles and extract features. Part of the experimental results are as follows: the extracted region of interest can be seen in Figs. 14 and 15, which is marked by the green box. Detection of obstacles is subjected to in the area of interest, obstacles exist outside of the area will not be considered.

Fig. 14

Region of interest in sample.

Fig. 15

Road obstacle detection of sample.

5.2 Road feature extraction of samples

Selected features and corresponding evaluation value of the road condition for each path are listed below. Features of 10 roads are listed in following tables for concision.

Road roughness are obtained using the data in Tables 1 and 2 based on the formula (6), which is as shown in Table 3.

Table 1
Change rate of pavement texture

1 2 3 4 5 6 7 8 9 10

Δ_s 0.0804 0.0664 0.2006 0.1744 0.2808 0.1613 0.4008 0.1437 0.2476 0.3250

	1	2	3	4	5	6	7	8	9	10
Δ_s	0.0804	0.0664	0.2006	0.1744	0.2808	0.1613	0.4008	0.1437	0.2476	0.3250

Table 2

Fluctuate data of road surface

	1	2	3	4	5	6	7	8	9	10
F	0.0414	0.0821	0.1865	0.2016	0.2958	0.2053	0.4325	0.1809	0.1988	0.4052

Table 3

Pavement roughness data

	1	2	3	4	5	6	7	8	9	10
L	0.0660	0.0864	0.2221	0.3744	0.3808	0.2791	0.4553	0.1937	0.2530	0.3980

Proposed curvature of the pavement can be characterized by the road bending, which of 10 roads are shown in Table 4.

Table 4

Road curvature data

	1	2	3	4	5	6	7	8	9	10
K	0.0035	0.0040	0.0225	0.0062	0.0000	0.0024	0.0052	0.0055	0.0094	0.0126

Width to height ratio of the dynamic obstacles in area of interest in front of the intelligent vehicle is shown in Table 5 according to the definition above:

Table 5

Obstacle width to height ratio data

	1	2	3	4	5	6	7	8	9	10
c	0.2850	0.9873	1.5677	4.2275	1.3095	5.7552	1.0056	6.3552	5.7558	2.3180

Width to height ratio data of obstacles at the next time is collected for comparison as shown in Table 6:

Table 6

Obstacle width to height ratio data at the next time of Table 5

	1	2	3	4	5	6	7	8	9	10
c	0.2851	0.8956	1.2566	3.0028	1.3095	0.9582	0.0169	7.8994	5.7558	2.2516

Effective area ratio of obstacles is calculated after processing, as shown follows in Table 7:

Table 7

Obstacle effective area ratio data

	1	2	3	4	5	6	7	8	9	10
R	0.154	0.397	0.773	0.836	0.797	0.815	0.252	0.623	0.105	0.388

According to the obstacle coefficient defined in section 3, coefficients from the collected sample images are as follows in Table 8:

Table 8

Obstacles coefficient

	1	2	3	4	5	6	7	8	9	10
q	1.1038	0.3117	0.8664	1.6943	2.7932	0.3223	4.3536	0.5632	2.1205	1.8186

Therefore, multi-dimensional feature structure system is established using the extracted information data from road condition. Later they are input into the BA-BP model for road condition evaluation.

5.3 Comparison with baselines

In this paper, 200 road segments including alleys, campus and communities in Dong Cheng District, Beijing are used to carry on the simulation experiment, 100 sets of data are used as training set, and the other 100 sets are the test set. In the previous section, five characteristics from the data that can reflect the characteristics of the road condition are extracted, then the evaluation factors of road condition are normalized to 0∼1, noted as: e1∼e5.

Relevant parameters of Bat algorithm used in the experiment are set as follows: the number of population is 40, the maximum pulse loudness A = 0.25, pulse frequency range is [0, 2], pulse frequency enhancement coefficient γ = 0.05, pulse loudness attenuation coefficient α = 0.95. The maximum iteration number is 500, when the number of iterations exceeds 500, terminate the program forcibly and output the results.

Manual evaluation of the selected road is determined as the grade of the road before training. In the experiment, 10 drivers who have excellent driving skill and 10 road constructors who work more than 5 years are chosen to judge the level of road conditions using their driving and work experience, aiming at laying the foundation of sample for next step. Roads are divided into five levels including excellent, good, medium, sub, poor, such a classification is convenient to define the status of different road conditions.

Figure 16 shows the training curves of BA-BP, GA-BP, and FA-BP models. Adaptive learning rate is set as 0. 001, it is concluded from the curve that FA-BP reached higher decreasing speed at the start of training with error rate of 0.6. While the converging efficiency of GA-BP is higher than BA-BP before training times of 15. The error rate of three models kept decreasing with the increase of training times, while the error rate of GA-BP changed little and finally remained at the level of 0.0817 when the iteration time reached 90. BA-BP model passed the FA-BP model on the metric of accuracy after the 20 iteration times, whose classification performance of road condition kept promoting and reached 95.15% when the training process got over 100 times. The proposed BA-BP network outperformed than the methods of GA-BP and FA-BP in accuracy and convergence speed, which meets the requirements of real-time and speediness, it could also be applied for the traffic condition evaluation and auto-driving after further improved. Comparison of training curves between baselines proved the advantages of proposed BA-BP method in accuracy and speed.

Fig. 16

Comparison of training curves with baselines.

Accuracy of the evaluation model based on BA-BP neural network using the collected dataset is shown in Table 9.

Table 9

Accuracy of the proposed evaluation model based on BA-BP algorithm

Actual grade	Experiment results
	Excellent	Good	Medium	Sub	Poor	Sum	Accuracy1
Excellent	16	0	0	0	0	16	100%
Good	0	26	1	0	0	27	96.30%
Medium	0	1	23	1	0	25	92.00%
Sub	0	0	0	14	1	15	93.33%
Poor	0	0	0	1	16	17	94.12%
	Total accuracy = 95.15%

BP neural network and particle swarm optimization method are used to conduct the evaluation model for comparison in order to further verify the performance of the proposed approach, which are trained and tested with the same data. Accuracy of them are shown below.

It is concluded from the tables above that accuracy of evaluation model based on the BP neural network is 89.84%, which is the lowest. That of the evaluation model based on GA-BP and FA-BP algorithm is 91.83% and 91.98%, respectively. The accuracy of the proposed method is 95.15%. Experimental results show that reliability of the proposed evaluation model based on the multi-parameters reached the highest, which gives reasonable classification results about the road condition intuitively and rapidly. And the evaluation results are similar to the experienced drivers and road constructors, which can satisfy the travel demand of road condition evaluation and have good potential for further promotion.

Table 13 talks about the classification performance of models on metrics of accuracy, RMSE, and MAPE. It is concluded that the proposed BA-BP model outperformed than other approaches on all metrics, which obtained the increase of 5.31% on accuracy compared with the classical BP network. Bat algorithm increased the predictive ability of the BP and addressed the over-fitting problem, which made up for the shortcomings of traditional BP neural network. Lower indicators of RMSE and MAPE denotes that the proposed approach has relatively good prediction and classification performance, which obtained the foundation of further research and promotion.

Table 10

Accuracy of the evaluation model based on BP neural network

Actual grade	Experiment results
	excellent	Good	Medium	Sub	Poor	Sum	Accuracy2
Excellent	14	2	0	0	0	16	87.50%
Good	1	24	2	0	0	27	88.59%
Medium	0	1	23	1	0	25	92.00%
Sub	0	0	1	13	1	15	86.67%
Poor	0	0	0	1	16	17	94.12%
	Total accuracy = 89.84%

Table 11

Accuracy of the evaluation model based on GA-BP algorithm

Actual grade	Experiment results
	Excellent	Good	Medium	Sub	Poor	Sum	Accuracy3
Excellent	15	1	0	0	0	16	93.75%
Good	0	25	2	0	0	27	92.59%
Medium	0	1	23	1	0	25	92.00%
Sub	0	0	1	13	1	15	86.67%
Poor	0	0	0	1	16	17	94.12%
	Total accuracy = 91.83%

Table 12

Accuracy of the evaluation model based on FA-BP model

Actual grade	Experiment results
	Excellent	Good	Medium	Sub	Poor	Sum	Accuracy4
Excellent	15	1	0	0	0	16	93.75%
Good	1	25	1	0	0	27	92.59%
Medium	0	1	23	1	0	25	92.00%
Sub	0	0	0	14	1	15	93.33%
Poor	0	0	0	2	15	17	88.24%
	Total accuracy = 91.98%

Table 13

Performance comparison on metrics of accuracy, RMSE (Root Mean Squared Error) and MAPE (Mean Absolute Error)

Metric	BP	BA-BP	GA-BP	FA-BP
Accuracy	89.84%	95.15%	91.83%	91.98%
RMSE	0.7832	0.3475	0.4911	0.4509
MAPE	0.9348	0.3162	0.4436	0.4174

10-fold cross-validation was also conducted to test the generalization ability of the proposed BA-BP algorithm. Another road segment dataset for validation with 80 pictures are added and divided into 10 groups where 9 of them are trained and 1 of them was tested by turns, then the mean value of the results of 10 times are applied as the estimation of the accuracy. Overall accuracy is obtained by the mean average value as follows. Other parameters of Bat algorithm are kept the same as the baseline experiment above. Results of experiments including accuracy of total set and subsets are as shown in Fig. 17.

Fig. 17

10-fold cross-validation results for the BA-BP algorithm.

Figure 17 shows the detection accuracy of subsets in 10-fold cross-validation, excellent, medium, poor and sum accuracy are reserved for better illustration. It is concluded from the Fig. 17 that the proposed model has a relatively stable classification performance, and its total accuracy kept at a higher level of around 95% in the validation experiment. Detection accuracy of medium class is lower than that of other categories, but its lowest value reached 86%, which also has certain advantages compared with other existing road condition classification algorithms. As for the excellent and poor categories, their corresponding accuracy are higher due to the explicit features. Cross-validation proves the stability and accuracy of the proposed road condition evaluation model, which further explains its generalization performance and will be suitable for extension to more complex road scenarios.

Processing time of different models including BP, BA-BP and baselines using validation dataset are as shown in Fig. 18. The average processing time of the BA-BP model reached 33.4 s, which is the lowest of all the approaches. It is concluded that the traditional BP neural network had the worst processing efficiency of over 40 s, which is due to the slower convergence rate caused by network structure. Improved versions of BP network like BA-BP, GA-BP and FA-BP speeded up the convergence efficiency of the network significantly, the proposed BA-BP consumed less time of 2 s and 3.9 s compared with GA-BP and FA-BP, respectively.

Fig. 18

Comparison of processing time between BA-BP and baselines.

5.4 Comparison with state-of-the-art algorithms

Performance evaluation between the proposed model and state-of-the-art algorithms are conducted using the metrics of accuracy and F1-score. Proposed method is tested on the private dataset with road pictures collected from Dongcheng District, Beijing. Other results come from the publicly available literatures, which are as shown in Table 14. Performances of different algorithms are analyzed and compared from multiple perspectives.

Table 14
Comparison between proposed model and state-of-the-art approaches

Ref Approach Data Result (%)

[23] Road surface monitoring method using ultrasonic sensors and image processing techniques Ultrasonic data and graphic features Accuracy: 95.50

[39] Object-based image analysis method using feature selection, support vector machine (SVM), and random forest (RF) algorithm WorldView-2 dataset Accuracy: 83.19

[4] Multiple deep learning models of DenseNet and NASNet Road pictures collected from 40 stations connected to Ontario Road Weather Information System (RWIS) F1-score: 91.80 Accuracy: 91

[6] You Only Look Once (YOLO) network BigData Cup Challenge pictures of urban streets F1-score: 62.0

[14] Pretrained convolutional neural network (CNN) Highway 6 dataset in Southwestern Ontario Accuracy: 93.51

[13] SqueezeNet with optimized number of parameters Private dataset collected using smartphones Accuracy: over 95

Proposed Improved BP neural network based on Bat algorithm Pictures collected from the urban roads Accuracy: 95.15

Ref	Approach	Data	Result (%)
[23]	Road surface monitoring method using ultrasonic sensors and image processing techniques	Ultrasonic data and graphic features	Accuracy: 95.50
[39]	Object-based image analysis method using feature selection, support vector machine (SVM), and random forest (RF) algorithm	WorldView-2 dataset	Accuracy: 83.19
[4]	Multiple deep learning models of DenseNet and NASNet	Road pictures collected from 40 stations connected to Ontario Road Weather Information System (RWIS)	F1-score: 91.80 Accuracy: 91
[6]	You Only Look Once (YOLO) network	BigData Cup Challenge pictures of urban streets	F1-score: 62.0
[14]	Pretrained convolutional neural network (CNN)	Highway 6 dataset in Southwestern Ontario	Accuracy: 93.51
[13]	SqueezeNet with optimized number of parameters	Private dataset collected using smartphones	Accuracy: over 95
Proposed	Improved BP neural network based on Bat algorithm	Pictures collected from the urban roads	Accuracy: 95.15

As is shown in Table 14, the proposed method obtained the highest accuracy on the evaluation of small road images, which also has lower hardware requirements and space complexity compared with the state-of-the-art models. Sharma et al. [23] designed a novel system using ultrasonic sensors with GPS and Dynamic time warping (DTW) technique to improve the classification accuracy of road surface, which obtained a slightly higher accuracy of 95.50% than the proposed method. While their system operates with the hardware of ultrasonic sensors and a GPS, which has a hash working environment and lacks robustness, its system is also not easy to be updated and extended. The proposed method works only relies on pictures, which has good expansibility. Image analysis method based on feature selection, SVM and RF are proposed by Shahi et al. [39] and conducted on the dataset of WorldView-2. The overall accuracy of [39] is 83.19% due to the subtle variations in texture and spectrum of roads, which is 11.96 percent points lower than the proposed method. Deep learning models like DenseNet and NASNet are applied for the road condition evaluation in [4], with an accuracy of 91% and F1-score of 91.80%. The proposed method outperformed than the deep learning models using a lightweight constructure with a higher accuracy, which achieved better results without the need of complex networks and hardware environments. Alfarrarjeh et al. [6] used the novel YOLO network to detect the road damage from smartphone pictures, which obtained the F1-score of 62%. There still exists room for improvement in the road damage information provided by the detection box, the dataset images concentrate on larger roads, whose detection effect on urban roads targeted by the proposed method is rather general. Method [13, 14] applied pretrained CNN and optimized squeezeNet to evaluate the road condition from various environments using the highway and private dataset, respectively. Accuracy of them are 93.51% and over 95%, which are slightly lower than the proposed method due to the complex image backgrounds. Deep networks help to extract the high dimensional features of road images, which will also lead to the dependence on hardware devices. The proposed method can be further improved by enlarging the training dataset and fine turning of the network structure.

6 Conclusion

A novel road condition evaluation model based on BA-BP algorithm aimed at unstructured small scenes is introduced in this paper. Our main contribution is addressing the slow convergence speed and falling into local minimum problem of traditional BP network by optimizing the initial network weights and thresholds with Bat algorithm. Besides, adding of adjustment factor demonstrated the major influence of dynamic obstacles in road condition evaluation. Vacancy of small unstructured road condition evaluation has also been filled by the proposed model. Overall accuracy of BA-BP method was improved with 5.31%, 3.32%, 3.17% from the BP, GA-BP and FA-BP model, whose time consuming was also 2 s and 3.9 s less compared with the latter two. BA-BP model also outperformed than most of the state-of-the-art model in accuracy with simpler hardware environments. In the future, the proposed BA-BP model will be further optimized in terms of lightweight and dynamic aiming at being deployed in large-scale industrial scenarios.

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Evaluation of road condition based on BA-BP algorithm

Abstract

Keywords

1 Introduction

2 Literature review

3 Proposed road condition features

3.1 Road roughness

4.1 Bat algorithm

5.1 Data description and preprocessing

Table 1 Change rate of pavement texture 1 2 3 4 5 6 7 8 9 10 Δ s 0.0804 0.0664 0.2006 0.1744 0.2808 0.1613 0.4008 0.1437 0.2476 0.3250

References

Table 1
Change rate of pavement texture

1 2 3 4 5 6 7 8 9 10

Δ_s 0.0804 0.0664 0.2006 0.1744 0.2808 0.1613 0.4008 0.1437 0.2476 0.3250