1. Introduction
In order to alleviate the water shortage in some economically developed areas and meet the increasing demand for economic development, a large number of long-distance water transfer projects have been built all over the world [
1]. With the rapid development of deep underground tunnel construction technology, in order to reduce damage to the production processes, life, and ecological environment of the cities along the project, a deep-buried long-distance water transmission tunnel is utilized as the main water transport buildings in many water diversion projects, some of which are combined with open channels, aqueducts, and other water transport structures for water distribution. According to the literature reports, the hot and humid climate in some areas is suitable for the growth of shellfish and other aquatic organisms, which often invade water transmission tunnels, resulting in reduced water transmission efficiency [
2,
3]. Therefore, in order to ensure the normal operation of long-distance water transmission projects, it is necessary to carry out regular maintenance.
A number of working shafts are arranged along deep-buried long-distance water transmission tunnels, and water stop valves are arranged in the working shafts. During operation, the water stop valves are closed, and the pipeline is in a state of full pressure flow and isolated from the external natural environment. During maintenance, the water stop valves in the working shaft along the tunnel will be opened to drain water, and the ventilation equipment will be arranged in the working shaft for ventilation during maintenance [
4]. The working shafts along the tunnel form a complete ventilation circuit with the main body of tunnels to provide fresh air for maintenance workers, and exhaust the harmful gases released by the biological death and decay in the tunnel and the exhaust fumes from the maintenance machinery, so as to improve the maintenance working environment in the tunnel. Therefore, it is of great significance to scientifically and reasonably design ventilation schemes for long-distance water transmission tunnels during maintenance to ensure the safety of maintenance work. The combined tee structure composed of multiple air ducts in the working shaft and the main body of the tunnel is quite different from the local tee structure in traffic tunnels, mine roadways, and other underground structures. After the high-speed airflow from the air ducts in the working shafts enters the tunnel, the air particles collide with each other in the local area due to the sudden change in the flow direction and the overflow section, resulting in a large local resistance loss. Therefore, the local resistance characteristics and an accurate calculation of the local resistance coefficient of the combined tee structure are the key problems to be solved in the design of maintenance ventilation schemes for long-distance water transmission tunnels.
The essence of local resistance loss is that due to the change in the flow direction and cross-section, fluid particles collide and friction in the local area, forming local eddy currents, resulting in local resistance loss. In hydraulics, the water flow has a large local head loss at the bend, reducer, and tee structures in pipelines, and many scholars have carried out significant amounts of research on local head loss [
5,
6]. In order to ensure the ventilation effect and reduce energy consumption, scholars have carried out a lot of research on the resistance characteristics of local components in urban traffic tunnels, mine laneways, utility tunnels, and other underground structures and air-conditioning ventilation systems. Wang et al. [
7] analyzed the influence of the area ratio, bifurcation angle, flow ratio, and bending radius on the local resistance coefficient of highway tunnel components such as the tee, variable diameter, and bending structure using a numerical simulation method. Wang et al. [
8] established a 1:50 bifurcated tunnel scale model based on the prototype of Xiamen Haicang Submarine Tunnel, carried out model experiments to analyze and study the airflow characteristics, and obtained the influence law of the split ratio and the length-to-height ratio of the bifurcation structure on the local loss coefficient. Liang et al. [
9] analyzed the influence rules of five traffic parameters, including the distribution of lanes, vehicle distance, blockage ratio, vehicle speed, and proportion of large-scale vehicles, on the vehicle air-resistance coefficient, targeting the influence rules of traffic conditions on the ventilation and pollutant discharge effect of urban traffic tunnels. Wang et al. [
10] used a numerical simulation to analyze the local flow field characteristics of a louvered windshield in mine roadways at different opening angles, and derived the local resistance coefficient relation of a louvered windshield. Li et al. [
11] established a 1:5 utility tunnel scale model and conducted model experiments under different conditions of the air volume, pipe diameter, and pipe layout to obtain the variation rule of the local resistance at the inlet and outlet of an integrated corridor ventilation system. A two-factor analysis of variance was used to analyze the significance of the influence of the Reynolds number, air volume, and the proportion of the pipeline area ratio. Wang et al. [
12] studied the law of influence of the guide vane on the local pressure loss of an air duct elbow through a model experiment and numerical simulation and carried out optimization research on an elbow guide vane.
It can be seen from the above studies that numerical simulations and model experiments are the main methods used to study the ventilation local resistance. However, numerical simulations and model experiments have disadvantages such as a low calculation accuracy, low efficiency, and high cost of human and material resources, and numerical simulation methods also largely depend on grid division, the selection of the turbulence model, and governing equation-solving methods. Moreover, measurement and human operation errors are unavoidable in the model experiment. Therefore, there are many scholars in the field of fluid mechanics using machine-learning methods to carry out relevant research [
13,
14,
15], using the black box model of machine learning to replace complex physical mechanisms in fluid mechanics, to overcome the shortcomings of numerical simulations and model-testing methods. Li et al. [
16] used ridge regression, decision tree, random forest, gradient boosting regression tree, and other machine-learning methods to predict the average wind pressure and fluctuating wind pressure of high-rise buildings. Zhu et al. [
17] conducted research on the surface wind pressure of low-rise buildings, obtained the surface wind pressure under different wind forces by using numerical simulation methods, established a surrogate model based on machine learning, and applied it to optimize the placement of building surface pressure sensors. Hu et al. [
18] used adaptive neural-fuzzy inference system, support vector machine, M5 model tree, least-squares support vector machine, and other intelligent prediction models to predict the overflow coefficient of curved pipelines, establishing the mapping relationship between the upstream water head, overflow ratio, curvature, and overflow coefficient. Wakes et al. [
19] used machine-learning algorithms to predict dune movement patterns under different wind conditions, providing a technical reference for predicting sediment migration paths. Rushd et al. [
20] used artificial neural networks to predict the pressure loss of crude oil transport pipelines, taking the pipe diameter, average flow rate, oil–water density, oil–water viscosity, and water content as the input parameters. In the field of mine roadways, some scholars have also carried out research on ventilation resistance coefficient prediction. Liu et al. [
21] established a BP neural network prediction model for the roadway ventilation resistance coefficient and applied the prediction results to the mine ventilation network model. Based on the least-square method, Gao et al. [
22] proposed a mathematical model to determine the ventilation resistance coefficient of mines using the inversion of the air volume and node pressure data, and adopted a genetic algorithm and particle swarm algorithm to solve the ventilation resistance coefficient inversion optimization problem.
The main idea of the application of machine learning in the field of fluid mechanics is to establish a high-dimensional mapping relationship between the input parameters and output targets through machine-learning algorithms, replacing the complex physical mechanism of fluid mechanics. The most critical part is obtaining the training sample set. In order to ensure the accuracy and efficiency of the prediction, accurate predictions of the ventilation local resistance coefficient should be obtained by using as few numerical simulation or model test results as possible. In addition, the ventilation local resistance coefficient is related to complex turbulent motion in the local area and has strong nonlinear fluctuation characteristics due to the comprehensive influence of both structural and ventilation parameters. Therefore, the prediction of the ventilation local resistance coefficient is a typical small sample nonlinear prediction problem. Relevance vector machine (RVM) is a sparse kernel method based on the Bayesian framework proposed by Tipping [
23]. Its structure is similar to that of support vector machine (SVM), but its training speed is faster, and it has a strong advantage in nonlinear small sample prediction problems. Therefore, the RVM model has been widely used in engineering fields such as mechanical service-life prediction [
24], slope deformation probability prediction [
25], short-term power coincidence prediction [
26], industrial fault classification [
27], and pollutant concentration prediction [
28]. However, a single-kernel RVM model cannot accurately excavate the deep nonlinear fluctuation characteristics of engineering data. Therefore, the hybrid kernel function is introduced into the RVM model to balance the global generalization ability and local learning ability and improve the prediction accuracy and generalization performance of the model. At the same time, the choice of kernel parameters for the HKRVM model will affect the prediction accuracy of the model. Scholars use swarm intelligent optimization algorithms such as the grey wolf optimization algorithm [
29], grasshopper optimization algorithm [
30,
31], particle swarm optimization algorithm [
32], whale optimization algorithm [
33], and bat optimization algorithm [
34] to optimize the kernel function of the HKRVM model. The artificial jellyfish search algorithm (AJS) [
35], as a swarm intelligent optimization algorithm proposed in recent years, has fewer adjustment parameters and a simple search process. It has been successfully applied in the fields of power grid energy scheduling [
36,
37], medical image segmentation [
38], civil structure engineering [
39], and construction engineering image recognition [
40]. The application results show that the AJS algorithm has a better optimization accuracy and optimization efficiency than other swarm intelligent optimization algorithms, but the AJS algorithm suffers from premature convergence and can easily fall into local optimal problems when solving high-dimensional nonlinear optimization problems.
In summary, the local resistance coefficient of water transmission tunnel maintenance ventilation is one of the key parameters to be considered in the design of ventilation schemes, and it is related to the complex turbulent movement of fluid. In order to achieve the efficient and accurate prediction of the ventilation local resistance coefficient, this paper proposes a hybrid prediction model for the local resistance coefficient of water transmission tunnel maintenance ventilation, and establishes a mapping relationship between the structural parameters, ventilation parameters, and ventilation local resistance coefficient, in place of a complex fluid mechanics mechanism. It also provides a theoretical basis and technical reference for the optimization of long-distance water transmission tunnel maintenance ventilation schemes.
The remainder of this paper is organized as follows: In
Section 2, the research framework of this paper is put forward. In
Section 3, a detailed description of the hybrid prediction model for the local resistance coefficient of water transmission tunnel maintenance ventilation based on machine learning is presented. In
Section 4, combined with a water transmission project, a case study is presented to verify the applicability of the method proposed in this paper. In
Section 5, the effectiveness and superiority of the proposed method are verified by a comparison of the model prediction performance. In
Section 6, the conclusion and prospects of the research results in this paper are presented.
2. Research Framework
In this work, a hybrid prediction model for the local resistance coefficient of water transmission tunnel maintenance ventilation based on machine learning is proposed. The research framework is composed of three steps: the construction of a training sample set, building the IAJS-HKRVM prediction model, and a case study, as shown in
Figure 1.
Step 1: Construction of training sample set. Sample points are selected in the input parameter design space, and the cross-section mean speed and pressure under different working conditions are calculated based on the three-dimensional numerical model of the local resistance of water transmission tunnel maintenance ventilation, and then, the local resistance coefficient of maintenance ventilation under different working conditions is obtained. The numerical simulation results are verified to construct the training sample set of the prediction model for the local resistance coefficient of water transmission tunnel maintenance ventilation.
Step 2: IAJS-HKRVM prediction model build. Firstly, a Gaussian kernel function with excellent local learning ability and Sigmoid kernel function with excellent global generalization ability are combined by the weighted method and are introduced into the RVM model to establish the HKRVM model, to accurately excavate the deep nonlinear characteristics of the local resistance coefficient of maintenance ventilation. Secondly, in order to determine the optimal kernel parameters of the HKRVM model, the IAJS algorithm is used to optimize the kernel parameters. Fuch chaotic mapping, lens-imaging reverse learning, and adaptive hybrid mutation strategies are introduced to improve the population initialization and location update methods of the AJS algorithm, so as to overcome the shortcomings of local optimal and premature convergence, to improve the optimization accuracy and efficiency of the algorithm. The performance of the IAJS algorithm is compared with other swarm intelligent optimization algorithms on the benchmark test function. Finally, the hybrid prediction model for the local resistance coefficient of the combined tee structure of water transmission tunnel maintenance ventilation based on machine learning is established.
Step 3: Case study. The method proposed in this paper is applied to a long-distance water transmission project and a case study is carried out. Firstly, the results of the numerical simulation and prediction are compared to verify the applicability of the proposed method in this paper. Then, the error indexes such as the relative coefficient square (R2), mean absolute error (MAE), and root mean square error (RMSE) are selected to compare the prediction performance of the proposed method in this paper with different kernel RVM models and different prediction models to verify the superiority of the proposed method.
6. Conclusions
The local resistance characteristics of water transmission tunnel maintenance ventilation are complicated, which is related to the complex nonlinear turbulent motion in the local region. In order to calculate the efficiency and accuracy of the ventilation local resistance coefficient, this paper proposed a hybrid prediction model for the local resistance coefficient of water transmission tunnel maintenance ventilation based on an intelligent optimization algorithm and a small-sample machine-learning method, and established the nonlinear mapping relationship between the structural parameters, ventilation parameters, and local resistance coefficient, so as to replace the complex physical mechanism of fluid mechanics. The main research achievements are as follows:
(1) Research on numerical simulations of the local resistance characteristics of the combined tee structure of water transmission tunnel maintenance ventilation was carried out. As a result, the local resistance characteristics of the combined tee structure were analyzed, determining that the local resistance is mainly caused by the collision and friction of the airflow in the local area and the formation of multiple local eddy currents due to the sudden change in the cross-section and flow direction.
(2) The IAJS-HKRVM hybrid model was proposed. The IAJS algorithm was used to automatically optimize the kernel parameters of the HKRVM model, which effectively improved the prediction accuracy and generalization performance, and the optimization performance of the IAJS algorithm was verified based on the benchmark test function.
(3) Combined with an actual project, the local resistance coefficient of the combined tee structure of water transmission tunnel maintenance was predicted. The results showed that the IAJS-HKRVM model has a good prediction performance and can better excavate the deep nonlinear fluctuation characteristics of the ventilation local resistance coefficient.
(4) The effectiveness and superiority of the proposed method in the prediction of the ventilation local resistance coefficient were verified by comparing and analyzing the prediction performance of different models. In terms of the prediction accuracy, the IAJS-HKRVM model has the highest improvement of 36.3% compared with different kernel RVM models, and the highest improvement of 18.8% compared with other conventional models. In terms of the prediction efficiency, it has improved by about 17.4% compared with the AJS-HKRVM.
In future studies, the local resistance coefficient prediction method for water transmission tunnel maintenance ventilation proposed in this paper will be combined with a multi-objective optimization study of the maintenance ventilation scheme of a long-distance water transmission tunnel, to provide a theoretical basis and technical parameters for the design and optimization of the maintenance ventilation scheme of a long-distance water transmission tunnel.