Based on the scenario of highway operation and maintenance, the resilience of highway system operation and maintenance refers to the anti-interference ability of the highway system to maintain basic traffic functions, the response ability to quickly identify faults, and the repair ability to restore normal operation after disasters in the face of sudden traffic events (such as road collapse and multi vehicle rear end collisions) and environmental disturbances (such as meteorological disasters). It is a comprehensive reflection of the combined effects of system stability, redundancy, adaptability, recovery, and external driving forces. This definition differs from traditional single-disaster resistance capabilities, emphasizing the dynamic characteristics of the entire process from interference to response and recovery, and is in line with the operational needs of continuous operation of and sudden risks in highways (Figure 1).

Based on the core connotation of resilience theory, this study constructs a five-dimensional evaluation framework for stability, redundancy, adaptability, resilience, and driving force by combining the technical characteristics of highway operation and maintenance (such as facility status and traffic flow) with the external environment (such as regional economy). The theoretical basis for each dimension is as follows: Stability: Based on the theory of infrastructure safety monitoring, it focuses on the basic ability of the system to resist interference. By quantifying indicators such as environmental equipment monitoring coverage, entrance and exit density, and facility integrity [15, 16], use of a sound monitoring system and high-quality facilities can reduce the probability of sudden failures, which is the fundamental guarantee for resilience; Redundancy: Based on the theory of system redundancy design, the risk of traffic flow fluctuations and resource shortages is evaluated through indicators such as channel congestion, per capita road area, and peak traffic volume [3, 7]. The theoretical logic is that when a certain passage fails (such as an accident occupying the road), redundant resources (such as emergency lanes and backup road networks) can replace the original functions, reduce service interruption time, and the per capita road area reflects the supporting role of redundant resources in conferring resilience. Adaptability: Based on the theory of organizational management adaptation, it emphasizes the ability of operation and maintenance entities to respond to complex scenarios, quantified through indicators such as security management system, dispatch and command efficiency, and personnel skill quality [32, 33]^. The adaptability of personnel and systems determines the flexibility of the system’s response to sudden situations, and the skill quality of dispatchers selected in this article directly affects the efficiency of on-site command after accidents. Resilience: Based on the theory of post-disaster repair efficiency, focusing on the system’s ability to recover from a fault state, evaluated through indicators such as the integrity of communication electromechanical systems, emergency response capabilities, and fire water supply systems [34, 35]. The availability of critical facilities and the completeness of emergency mechanisms determine the time taken for fault repair. Driving force: Based on the theory of economic infrastructure synergy, we innovatively incorporate regional economic factors into resilience assessment [36, 37]. Economic indicators such as regional per capita GDP and urbanization rate determine the investment of operation and maintenance funds, which are external guarantee factors for enhancing overall system resilience. Economic development has a positive driving force on operation and maintenance resilience.

ELM is a single hidden layer feedforward neural network (SLFN) learning algorithm that revolutionizes traditional neural networks. The core breakthrough of the ELM model lies in optimizing the inefficient learning mode that relies on the iterative adjustment of all parameters in traditional neural networks and establishing an efficient learning framework based on random mapping and analytical solutions. Compared with traditional methods such as backpropagation (BP) neural networks, ELM models significantly improve learning speed and generalization performance while maintaining nonlinear fitting ability [36, 38–42].

The fast learning characteristics of ELM models stem from a unique parameter determination mechanism. During network training, the weights and biases from the input layer to the hidden layer are randomly initialized and do not require iterative optimization through backpropagation [3, 43, 44]. The weights from the hidden layer to the output layer are directly determined through analytical methods for solving linear systems. This process avoids the local optimal trap and lengthy iterative process brought by traditional gradient descent methods. This mechanism exhibits the advantages of excellent efficiency on large-scale datasets, such as MNIST handwriting recognition and traffic sign recognition.

From a theoretical perspective, the ELM model breaks through the traditional neural network’s dependence on parameter iteration adjustment [45, 46]. Its mathematical essence is to construct a feature space through randomly generated hidden layer nodes and then solve for the optimal output weights through the least squares method. This method not only ensures the universal approximation ability of the model but also significantly reduces the need for human intervention. In engineering applications, the ELM model is particularly suitable for handling high-dimensional, nonlinear, and noisy data in scenarios such as highway operation and maintenance. The randomly initialized hidden layer parameters can capture complex patterns in the data, while the analytical solving process ensures stable learning performance even under small sample conditions. Compared with the BP neural network, the ELM model effectively avoids the shortcomings of slow training speed and easy to fall into local extremum. In empirical research in multiple fields such as runoff prediction and quality monitoring, it has shown better relative error and certainty coefficient [47].

The Dungeon Optimization Algorithm (DBO) is a novel swarm intelligence optimization algorithm proposed in 2022. The core innovation lies in constructing an optimization framework that balances global exploration and local development by simulating the three ecological behaviors of beetles in nature. Compared with traditional methods such as particle swarm optimization (PSO) and genetic algorithm (GA), the DBO algorithm exhibits stronger convergence ability and resolution accuracy when dealing with complex optimization problems [48].

The three behaviors of the DBO algorithm have achieved comprehensive improvement in optimization performance through dynamic collaboration. Global exploration ensures the breadth of search, local development ensures the depth of search, and diversity maintenance ensures the sustainability of search. This collaborative mechanism enables the DBO algorithm to strike a balance between convergence speed and solution quality when dealing with complex engineering problems such as ELM model parameter optimization, providing an efficient and reliable parameter optimization solution for the resilience assessment model of highway operation and maintenance [32, 33, 49, 50]^.

IAHP is used to deal with fuzzy problems under the condition of insufficient information, which can effectively reflect the uncertainty and fuzziness of things. IAHP [11] Using interval number instead of point value to describe its uncertainty can effectively weaken the subjective tendency in expert evaluation and is more suitable for the evaluation of operation and maintenance toughness of high-speed traffic projects.

The CRITIC method is a weighting method to calculate the objective weight according to the amount of information in objective data. Compared with the entropy weight method, the CRITIC method is more effective in reflecting the differences and conflicts between indicators. Assuming that there are m schemes and indicators, the steps to determine the objective weight by the CRITIC method are as follows.

In this paper, the combination weight is determined according to the principle of minimum discriminant information, and the subjective or objective limitations in the selection of index weight are overcome by narrowing the deviation between the combination weight and the subjective and objective weights of indicators [17, 56–59]. The mathematical model for determining the combination weight is as follows (Equation 13): min ⁡ W = ∑ i = 1 n ω j ⁡ ln ω j w z j + ω i ⁡ ln ω j w k j . s . t . ∑ i = 1 n ω j = 1 ,   ω j ⩾   0   i = 1 , 2 , ⋯ , n (13)

The combined weights thus obtained are as follows (Equation 14): w j = w z j w k j ∑ i = 1 n w z j w k j (14)

Aiming at the problems of low operation efficiency and poor applicability of traditional evaluation methods, and the subjective and nonlinear characteristics of multi-index, multi-factor and evaluation results in high-speed toughness efficiency evaluation, an evaluation model of expressway operation and maintenance toughness efficiency based on extreme learning machine is proposed.

ELM has good generalization performance and extremely fast learning ability. Compared with the traditional neural network algorithm, the ELM does not need iteration or manual adjustment and only needs Moore–Penrose generalized inverse to calculate the weights. The basic structure of ELM significantly reduces the computational complexity and improves the operation speed such as shown in Figures 2–4. See Formula 15 for the evaluation model. f L x = h x * β ∧ h x = G α 1 , b 1 , x , ⋯ , G α L , b L , x (15)

Where f_L is the model function; h(x) Is the response of the hidden layer about x; G(α₁, b₁, x): Is a hidden layer function; β is the least square solution of the minimum norm of the loss function. f L x : modeling functions; h x : hidden layer G α 1 , b 1 , x : hidden layer function

The selection of ELM model parameters has a great influence on the accuracy of efficiency evaluation. Based on DBO, the hidden layer activation function, number of hidden layer neurons, and regularization coefficient of ELM are optimized by simulating dung beetle behaviors (such as rolling dung balls, breeding, foraging, and stealing) [60–62]. In order to improve the convergence accuracy of the algorithm and avoid local optimization problems, piecewise chaotic mapping is used to initialize the population and control the individual distribution. At the same time, the variable spiral search strategy is introduced to improve the breeding and foraging process and enhance the global search ability; Levy flight random walk is used to optimize the stealing behavior (Table 2), increase the disturbance of the solution, and enrich the population diversity [63–65]. The formula of the DBO optimization algorithm is (Equations 16–21).

The improved DBO algorithm is used to optimize the evaluation model of the extreme learning machine’s expressway operation and maintenance toughness, and a rapid evaluation model of expressway operation and maintenance toughness safety, applicability, durability, protection, green economy, and efficiency is constructed [66–71]. The algorithm flow of the DBO-ELM model is as follows Figure 5.

Invite five experts and scholars who are familiar with expressway traffic operation and maintenance projects and have in-depth research on toughness theory, compare the identified operation and maintenance safety and toughness system sampling 1–9 scale method in the form of interval numbers, and give the judgment matrix Table 5. Take stability as an example to give the comparison result of the first expert: A 11 = α 1 T , α 2 T , α 3 T , α 4 T , α 5 T , α 6 T , α 7 T , α 8 T

Expert weight ³ ω = 0.3 , 0.15 , 0.25 , 0.1 , 0.2 According to experts, the interval judgment matrix is calculated, and the consistency matrix is as follows: = B 1 β 1 T , β 2 T , β 3 T , β 4 T , β 5 T , β 6 T , β 7 T , β 8 T .

Calculate the weight of the consistency matrix, and combine the interval judgment matrix and the consistency matrix to obtain the range matrix at both ends. The consistency matrix and the range matrix at both ends are as follows, and the interval weight is refined by SPA method, the IAHP weight and CRITIC weight are obtained, and the comprehensive weight of combination weighting is determined according to the principle of minimum discriminant information as follows:

ω = (0.171, 0.183, 0.105, 0.120, 0.100, 0.132, 0.102, 0.087), repeat the above steps, and the weight of expressway operation and maintenance safety and toughness evaluation index is as follows:

Stability: 1 (0.171, 0.183, 0.105, 0.120, 0.100, 0.132, 0.102, 0.087); redundancy: 2: (0.480, 0.104, 0.134, 0.179, 0.103).

In this paper, the qualitative indicators are mainly eight indicators of the adaptability dimension. The questionnaire survey is used as a data collection method, and the data are collected by directional questionnaire to the actual dispatchers and commanders of the expressway. The measured data are obtained through on-the-spot investigation and monitoring, and the driving indicators are Statistical Yearbook data ⁴ , and the county data near the expressway are used instead.

Based on the model algorithm of expressway operation and maintenance toughness efficiency evaluation established in this paper, the model training parameters and sample database in Table 3 are input, and the sequential relationship of discrete index eigenvalues is eliminated by using single heat coding. And standardize the sample database to eliminate the dimensions of different indicators. See Tables 3, 4 for parameters of the expressway operation and maintenance toughness efficiency evaluation model.

Type of hidden layer activation function (discrete variables are coded as integers); number of hidden layer neurons; regularization coefficient (Equations 24, 25). To minimize the mean square error (MSE): g · L ∈ Z + C ∈ R + Loss = 1 N ∑ i = 1 N   y i − y ^ i 2 (24)

y i is the true value, and y ^ i is the predicted value of ELM. Number range of neurons : ; L min ≤ L ≤ L max Regularization coefficient range : . C min ≤ C ≤ C max (25)

Iterative training for 400 times, the fitness and iteration times of expressway operation and maintenance toughness efficiency evaluation model are as follows Figure 4. In the 125th generation, it tends to be stable, and the minimum fitness is 0.65.

In this study, the safety and toughness of expressway operation and maintenance are quantitatively analyzed through the comprehensive evaluation model. The results in Table 5 show that (1) the overall operation and maintenance toughness (73.411) has been moderate, and there is room for improvement. (2) Among the indicators, the driving (89.776) evaluation result is excellent, while the adaptability, redundancy, and recoverability are in a poor evaluation level. Redundancy and recoverability become shortcomings in operation and maintenance, reflecting the shortage of emergency resource reserve (for example, the weight of per capita road area B5 is only 0.103) and accident response efficiency (the score of D6 indicator is low), which is different from the 12-h recovery time limit in the K68 section of Changsha–Zhangjiakou Expressway in 2024. The driving force is close to the excellent threshold, indicating that economic factors have a significant leverage effect on toughness improvement, and operation and maintenance management should be carried out according to local conditions.

In order to verify the validity of the model, this paper selects the XGBOOST model, Adaboost model, and other models for comparative testing. The Adaboost model trains several weak classifiers (such as decision stumps) iteratively and adjusts the sample weights according to the previous round of classification errors so that subsequent classifiers pay more attention to difficult samples and finally integrates all weak classifiers to form a strong classifier. The XGBOOST model is based on the improved version of gradient lifting tree (GBDT), which supports the regularization term and parallel computation by minimizing the negative gradient direction of loss function.

The goodness of fit refers to the fitting degree of the model algorithm to the observed values. The statistic to measure the goodness of fit is to determine the coefficient r, which belongs to the range of 0–1, and the greater the r, the better the degree of fit. The accuracy of the algorithm is measured by goodness of fit. By calculating the total sum of squares (SST), the regression sum of squares (SSR) and the residual sum of squares (SSE), the determination coefficient R2 is obtained, and the goodness of fit of each algorithm is calculated (Table 5).

By introducing the improved DBO, the model can optimize the key parameters of ELM, such as hidden layer activation function, number of hidden layer neurons, and regularization coefficient, thus further improving the efficiency and accuracy of operation (Figure 7). It can be seen that in practical application, the mean square error of the DBO-ELM model is greatly reduced compared with the traditional single ELM model, DBO-ELM improved R ² by 12.5% over ELM, showing excellent performance. Compared with XGboost, Adaboost, and SVR models, R2 is increased by 147%, 193%, and 131%, respectively. Therefore, the DBO-ELM model has strong evaluation adaptability and strong robustness.