Fusion of RF algorithm and logistic regression model for high-speed illegal toll evasion vehicle inspection

The primary goal of data standardization is to reduce the issues caused by unit differences between different attributes and large numerical spans between the same attributes.To reduce significant biases in the data, it is necessary to limit the data to a narrow interval when building a model, with the goal of improving the accuracy of the Euclidean distance calculation algorithm. In the process of in-depth analysis of highway traffic data, the inconsistency of data units and the wide range of attribute values may have a significant impact on the accuracy of constructing TEV detection models. It is particularly important to standardize abnormal charging data to ensure that the model can accurately identify TEB.Firstly, this study requires data preprocessing, including data cleaning, handling missing values, and outlier detection.During the data cleansing process, this study will identify and correct any erroneous or inconsistent data records, or delete them entirely.Next, this study will standardize the data to eliminate significant differences in attribute value ranges. The basic idea of using the Min-Max-S is to use a specific algorithm to compress the numerical range of data attributes into the range of 0 to 1. The maximum value of the data is set to 1, and the minimum is set to 0. This method is easy to operate and can adjust attribute data through linear transformation to adapt to the characteristics of non-normal distribution data [15-16]. The specific calculation is shown in equation (1).

In equation (1), x_new is the standardized data value. x is the original data. x_max and x_min are the maximum and minimum of x. The error value in the data refers to the situation where the data identified by the charging system does not match the actual situation. To improve the accuracy of data, it is necessary to analyze these error values, identify their causes, and take corresponding corrective or deletion measures to ensure the validity of the data and enhance its practicality. In the original dataset, multiple numerical attributes that are incorrect can be observed. The most common of these is license plate number recognition errors, in addition to errors in recording passing times. Dealing with error values is a crucial step in data mining work, and it is equally important in the big data environment.By removing these error values, the accuracy of the original dataset can be significantly improved, creating a strong data foundation for establishing TEV detection models and improving the accuracy of prediction results. Given the high inaccuracy rate of license plate recognition in the dataset, this study will focus on demonstrating how to correct the inaccuracy of license plate recognition. Other types of data errors are handled by deleting these data. The proposed method involves calculating the error rate of the data, labeling the error values, and ultimately deleting them [17-18]. The formula for error rate is shown in equation (2).

In equation (2), k_i and n_i are the number of erroneous data entries and data entries on day i. x_i is the proportion of k_i. Figure 1 shows the data cleaning process.

Figure 1.

Flowchart of data cleaning

Figure 1 depicts an automated method for cleaning license plate numbers that are incorrect. It starts by reading data records, extracting license plate number strings, and checking if their length meets the standard. Records that do not match will be marked. Next, records that meet the length requirements will be further checked to see if the first character of the license plate number meets the prescribed standards, while those that do not will also be marked. After processing all records, the total number of marked records is counted and the data error rate is calculated. All marked records are ultimately deleted to guarantee the accuracy and quality of the data.

After processing the data of abnormal toll vehicles on highways, this study uses big data technology to screen key information from a large dataset, and uses machine learning technology to establish and analyze models to assist in decision-making. The aim of the research is to identify abnormal toll behavior and develop a efficient TEV recognition system by sorting out toll data on highways. The period of establishing the TEV recognition model is displayed in Figure 2.

Figure 2.

Architecture diagram of vehicle recognition model for toll evasion

In Figure 2, the core steps of the constructed TEV recognition model involve data collection, data preprocessing, feature extraction, and TEB prediction. Firstly, an in-depth analysis is carried out on the toll system of highways, including data acquisition, transmission paths, and billing rules. The avoidance of toll operations was classified into different categories. Subsequently, in the data preparation stage, advanced data analysis techniques are utilized to clean and standardize the payment data format. An in-depth analysis of the features of TEV is conducted and their criticality in identifying TEB is evaluated to ensure the accuracy of data input. Subsequently, in the feature extraction stage, this study utilizes machine learning algorithms to extract key fee evasion features from a large amount of billing data, and optimizes the traditional TEV detection model to establish a more accurate recognition system. Finally, in the prediction phase, the established model is utilized to predict the likelihood of TEV and perform precise TEB identification to determine the specific type of fare evasion. To enhance the objectivity and accuracy of TEV feature extraction, an RF algorithm is introduced for feature selection.RF is an ensemble learning method that constructs multiple datasets for classification or regression, and votes or averages the results to improve prediction accuracy [19-20]. The mathematical expression of RF is shown in equation (3).

In equation (3), RF(X) is the input feature vector. T_b(X) is the prediction result of the feature vector X by the b-th DT. B is the total number of DTs. Through training on the cost avoidance information set, this study can identify the factors that have the most significant impact on TEB, thereby improving the accuracy and constructing algorithms that are more closely related to practical applications. This study uses LR to predict the probability of vehicles evading tolls on highways. The LR model predicts the probability of an event occurring by using logical functions. The expression of LR is equation (4).

In equation (4), P(y=1|x) is the conditional probability that the sample belongs to the positive class, i.e. TEV, given the feature vector x. β₀ is the intercept term of the model. β₁,…,β_n are the model parameter, corresponding to the coefficients of feature x₁,…,x_n· e is the base of the natural logarithm. Figure 3 shows the TEV recognition process based on the RF-logit model.

Figure 3.

Flowchart of vehicle identification for toll evasion based on RF-logit model

In Figure 3, the evasion target dataset is first determined and split from the networked charging data, and then the data are extracted and cleaned, including normalization and virtualization of type variables. Next, the RF algorithm is used to identify key features that affect TEB. Subsequently, these features are applied to the training and prediction process of the LR model to estimate the likelihood of vehicles evading tolls.

On the basis of constructing a TEV recognition model based on RF-logit, to deeply identify TEVs and analyze and evaluate their prediction results, TEB classification is defined as a multi class prediction problem. Given the outstanding performance of neural networks in handling such problems, this study selects BPNN to identify different evasion patterns of TEVs, in order to establish an accurate recognition model.BPNN is made up of numerous units that are interconnected through a complex network of connections, which simulates the storage function of the human brain. Each connection has a specific weight value, and the unit uses an activation function to determine the output result [21]. Figure 4 shows the structure of the neural unit.

Figure 4.

Details of the construction of the neuron

Figure 4 illustrates the input-output relationship of artificial neurons, as shown in equation (5).

In equation (5), a_i is the output of the i-th neuron. φ(·) is an activation function used to convert linear inputs into nonlinear outputs. w_ij is the weight that connects the j-th input neuron to the i-th output neuron. w_ij is the output value of the j-th input neuron. The BPNN used includes the layers of an input, multiple hidden, and an output. After the data are received by the input layer, it will be sequentially passed to the units of each hidden layer. After being analyzed and processed by the hidden layer, and transformed by the function, the data are finally sent to the output layer. This process is a complete forward propagation.If there is a significant deviation between the output and the expected result, the network will adjust the weights between neurons in each layer through error backpropagation until the expected accuracy is achieved.When training, the network continuously iterates and propagates, optimizing the weights through gradient descent. Figure 5 shows the BPNN structure.

Figure 5.

BPNN structure

In Figure 5, during the training and propagation process of BPNN, each layer’s nodes are learned and adjusted through the model. The output function of the hidden layer is given by equation (6).

In equation (6), o_j and q_j are the output and threshold of the j-th neuron. f is an activation function used to convert linear inputs into nonlinear outputs. w_ij is the weight that connects the i-th input neuron to the j-th output neuron. X_i is the output of the i-th input neuron. The output function of the output layer is expressed in equation (7).

In equation (7), Y_k is the output of the k-th unit. T_jk is the weight connecting the j-th and k-th units. q_k means the activation threshold for the _k-th unit.

This study first constructs a TEV dataset, performs preliminary cleaning and processing on the data, and then selects and organizes the data built on the data characteristics and the cases of fare evasion recorded at toll stations, based on previous analysis of TEB on highways. Python programming language is used for model construction and data analysis. This study first normalizes the raw data by using the Min-Max-S scheme to scale it to the [0, 1] interval, and virtualizes the type variables to eliminate their impact.The LR’s parameters are optimized using the maximum likelihood estimation method. The BPNN model is trained using gradient descent. The learning rate is 0.1 after 20,000 iterations. Table 1 displays the data specifics of various TEBs.

In Table 1, by analyzing the toll data, twelve types of vehicle information violations are selected and integrated into the TEV dataset, including inconsistent license plates, U-shaped driving, no pass card, gear shifting behavior, abnormal weight measurement data, overtime parking, overloading and exceeding limits, no readings from weighing equipment, forced card punching, abnormal exit axle load, abnormal entrance axle load, and failure to weigh. To verify the performance of the RF-logit-BPNN, it is compared with RF-logit, RF-BPNN, RF+SVM [22], and Gradient Boosting Machine (GBM) [23]. Figure 6 illustrates the accuracy and recall of the five algorithm models.

Figure 6.

Comparison of accuracy and recall

Figure 6 (a) shows that the RF-logit-BPNN has a higher accuracy rate than other models, ultimately reaching 99%.This indicates that the model can significantly reduce the misclassification of non-TEVs as TEVs when predicting TEVs, thereby effectively improving the accuracy of the prediction.The research model’s advantage in recall rate was demonstrated in Figure 6 (b), with a final recall rate of 92%. This means that the model can successfully identify 92% of actual TEVs, while other models have relatively low recall rates, resulting in more TEVs being missed. The high recall rate of the research model indicates that it is more comprehensive and effective in identifying TEVs, and can minimize misjudgments of TEBs to the greatest extent possible. The error fitting curve between the RF-logit-BPNN model and RF+SVM is shown in Figure 7.

Figure 7.

Comparison of error fitting curves

In Figure 7 (a), the fitting degree of the RF-logit-BPNN model reaches over 99%. This high degree of fit means that the model can predict TEV very accurately, and the predicted results are very close to the actual data. This reflects the strong recognition ability of the model for TEB. This indicates that the RF-logit-BPNN can effectively capture relevant patterns and trends when handling TEV inspection tasks on highways. In contrast, in Figure 7 (b), the fitting degree of the RF+SVM is only about 50%, indicating lower accuracy in predicting TEV and an obvious deviation between the predicted results and the real cost evasion situation. RF-logit-BPNN outperforms RF+SVM in fitting, demonstrating its practical application potential in TEV inspection. The high performance of the research model is attributed to its combination of RF feature selection ability, LR classification ability, and BPNN non-linear modeling ability, making it more advantageous in handling complex evasion detection tasks.

to comprehensively evaluate the effectiveness of the RF-logit-BPNN model in detecting high-speed illegal TEVs, it is compared with RF-logit, RF-BPNN, RF+SVM, and GBM. Comparative indicators include prediction accuracy, classification accuracy, inspection time, Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and stability. The final result of normalizing all indicators can be found in Table 2.

In Table 2, the RF-logit-BPNN model shows the optimal performance, with scores above 0.9, significantly better than other models. This indicates that RF-logit-BPNN has high accuracy, efficiency, and stability in TEV inspection tasks, and can be used as an effective tool for highway toll evasion inspection. The Receiver Operating Characteristic (ROC) curves of the RF-logit-BPNN and RF+SVM models for predicting TEV probabilities are shown in Figure 8.

Figure 8.

Comparison of ROC curves

In Figure 8 (a), the AUC of the RF-logit-BPNN reaches 0.9, indicating excellent performance in TEV prediction. The research model has demonstrated efficient and reliable predictive ability in TEV recognition. In Figure 8 (b), the AUC of the RF+SVM is only 0.6, indicating its limited performance in predicting TEV. The predictive performance of this model is comparable to random guessing and fails to distinguish between toll evasion and non-TEV. The RF+SVM has certain limitations in capturing data complexity or patterns when dealing with TEV recognition problems.