Journal of Shandong University(Engineering Science)

Research overview on the mechanism of deformation induced by excavation dewatering and countermeasures in soft soil stratum in Tianjin

ZHENG Gang, CHENG Xuesong, LI Qinghan, QIU Jun, CHENG Wenlong, ZHOU Shilong

Journal of Shandong University(Engineering Science). 2026, 56(3): 1-14. doi:10.6040/j.issn.1672-3961.0.2024.278

Abstract ( 12 )

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In view of the characteristics of obvious aquifer leakage and low permeability of aquifers in Tianjin, the study investigated the deformation mechanism and control methods caused by excavation dewatering based on actual engineering projects. The different mechanisms of retaining structure deformation, soil settlement, and adjacent tunnel deformation induced by two types of excavation dewatering, drainage dewatering and pressure relief dewatering, were comparatively analysed. The significant influences of aquifer leakage on deformation and its mechanism were revealed. The control strategies for deformation caused by dewatering were divided into two major categories, “optimization for excavation dewatering system” and “active control with groundwater recharge”. The first strut and segmented dewatering proved effective in controlling dewatering-induced deformation of retaining structures in different strata. The deep-shallow-well scheme significantly reduced settlement outside excavations with leaky aquifers compared to the traditional mixed-well scheme. Field tests and engineering applications indicated that groundwater recharge also demonstrates effective for water level control in silt and silty sand aquifers in regions like Tianjin. Moreover, the studies revealed distinctions between dewatering and recharge theories, such as recharge cones and well losses, and proposed efficient recharge technologies for settlement control, including pressurized recharge and interlayer recharge. To address the plugging issues during groundwater recharge in silt and silty sand aquifers, the mechanisms of plugging, such as particle migration, had been elucidated. Moreover, the anti-plugging recharge technologies, including combined recharge, optimization of well spacing, and pressurization of neighboring wells combined with redevelopment were proposed. This paper summarized the mechanisms of deformation induced by excavation dewatering, the optimization of dewatering system, and theories and applications of groundwater recharge. The aim of this paper was to provide references for controlling the environmental influences caused by excavation dewatering in soft soil, thereby contributing to urban construction safety and the protection of water resources.

Research progress of stability analysis methods for excavations in clay

HUANG Maosong, TAN Tingzhen, FU Chenzhi, LIU Yihui

Journal of Shandong University(Engineering Science). 2026, 56(3): 15-24. doi:10.6040/j.issn.1672-3961.0.2024.201

Abstract ( 14 )

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Focusing on key issues in the stability analysis of excavations in clay, numerical simulations and theoretical methods for basal heave stability were briefly reviewed, and recent advances in upper-bound limit analysis and limit-equilibrium methods were introduced. Considering the fact that the embedded wall could be rigid or flexible in engineering, two series of upper-bound mechanisms were proposed and verified by comparison with numerical simulation methods. In addition, this paper systematically clarified the problems existing in the circular sliding method adopted by domestic codes and proposed an improved circular sliding method. The proposed circular sliding method considered the circular radius and ultimate bending moment. The shortcomings of the checking method for stability against inrush in domestic codes were explained in detail, and corresponding improved checking methods were introduced. These methods could provide theoretical references for the revision of current excavation stability codes.

Design method and deformation control techniques for large-scale deep excavation group in soft soils

WANG Weidong, XU Zhonghua, ZONG Ludan, SHEN Jian

Journal of Shandong University(Engineering Science). 2026, 56(3): 25-36. doi:10.6040/j.issn.1672-3961.0.2024.188

Abstract ( 7 )

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The construction of large-scale foundation pit systems in soft soil strata necessitated the implementation of comprehensive design approaches and advanced construction control techniques to ensure structural safety, timely project completion, and effective deformation management, while minimizing cumulative environmental impacts on surrounding areas. Effectively controlled deformation and reduced the superimposed impact on the surrounding environment. Combined with the practical experience of super-large scale foundation pit in soft soil area, the design method and deformation control technologies of foundation pit group engineering were systematically expounded. It included setting single partition wall skip excavation method, setting buffer-zone symmetrical excavation method, micro-deformation control method of foundation pit group considering sensitive environmental protection. Through the setting of partition walls or buffer zones for zoned excavation, while meeting the development progress requirements of different plots, the influence degree of the space-time effect and the mutual influence between the divided zones could be effectively controlled. When a large-scale group of foundation pits was adjacent to a sensitive environment, according to the size of the adjacent zoned foundation pits, the dynamic adjustment of foundation pit deformation could be achieved by adopting steel strut with automatic axial force compensation system and concrete strut with servo system. Combined with typical engineering cases, it was proved that the above design method could achieve good economical and technological effect of deep excavation group.

Calculation theory and design method for hanging foot piles in soil-rock dualistic foundation pits with stable rock mass

ZHAO Jing, ZHANG Shangru, LI Lianxiang, DAI Changshun, CHEN Cheng, WANG Peiyan

Journal of Shandong University(Engineering Science). 2026, 56(3): 37-48. doi:10.6040/j.issn.1672-3961.0.2025.184

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Aiming at the problems of the wide application of foot-hanging piles in soil-rock dualistic foundation pits with stable rock masses, yet the lack of consensus on their working mechanism and insufficient analytical calculation methods, this paper conducted an in-depth analysis of the mechanical mechanisms of four failure modes(circular arc, circular arc-plane, cutting plane, and sliding-shearing)and their variation laws with soil depth, derived a calculation formula for rock-embedded depth based on static equilibrium equations, and determined the quantitative criterion of the overall failure coefficient S considering the respective failures of soil and rock as well as the combined failure modes with different paths. Combined with engineering cases in Qingdao and Jinan, a design method was proposed, which included failure mode judgment, support type selection, rock-embedded depth calculation, and overall stability checking. The fully recoverable foot-hanging piles were applied in soil-rock dualistic foundation pits, and the fully recoverable support structure was optimized to promote the high-quality development of soil-rock dualistic foundation pits.

Modelling of multi-vertical bar cell correction for segmental replacement of shear walls

YIN Chenglei, ZHANG Yu, ZHANG Yueran, ZHANG Bo, REN Zongfu, SUN Jiandong

Journal of Shandong University(Engineering Science). 2026, 56(3): 49-61. doi:10.6040/j.issn.1672-3961.0.2025.019

Abstract ( 9 )

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Aiming at the problem that it was difficult to accurately simulate the local shear stiffness adjustment in the segmental replacement process of shear walls using the traditional multi-vertical rod unit model, this paper proposed a multi-vertical rod unit correction model based on an improved shear spring. Through the coupled modelling of independent shear springs and vertical rods, a refined characterization of axial stiffness and shear stiffness in the segmental replacement process of shear walls was achieved. The unit stiffness matrix of the model was reconstructed based on discretization theory, and a nonlinear numerical analysis program was developed using MATLAB and was solved by the modified Newton-Raphson method. Validation through calculation examples showed that the maximum relative error between the modified model and the solid element model was only 0.833%, while the computation time was significantly reduced. Furthermore, combined with real engineering cases, the error between the simulated strain values and the monitored values was less than 1%, which indicated that the modified model could accurately reflect the stress redistribution pattern of the replaced shear wall. The results demonstrated that the proposed multi-vertical rod unit correction model greatly improved computational efficiency while ensuring accuracy, and provided a reliable theoretical tool for mechanical analysis and construction optimization of segmental replacement in shear wall reinforcement.

Advances and prospects in computerized adaptive testing

CUI Chaoran, DONG Xiaolin, ZHANG Chunyun, XI Muzhi

Journal of Shandong University(Engineering Science). 2026, 56(3): 62-72. doi:10.6040/j.issn.1672-3961.0.2024.240

Abstract ( 15 )

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With the development of the internet and online education, limitations of time and space were overcome, allowing people to learn anytime and anywhere. A vast amount of learning records was generated through various online learning and competition platforms. By effectively utilizing these records, computerized adaptive testing(CAT)enabled the customization of personalized assessments for examinees, achieving the goal of "tailored instruction". This paper aimed to comprehensively review the current development and state-of-the-art work in CAT, provide an outlook on future directions, and help future researchers and practitioners gain a systematic understanding of CAT. First, the background and theoretical foundations of CAT were introduced, followed by a formal description of CAT. Then, from a technical perspective, existing CAT methods were categorized into two types: CAT methods for selection process and CAT methods for ability estimation. A detailed overview of these two types of CAT methods was provided. Next, commonly used public datasets and evaluation metrics in CAT were compiled, with each dataset's source and relevant information described. Finally, the future research directions of CAT were discussed, and conclusions were drawn.

Improved RRT-Connect and AFSA fusion algorithm for mobile robot path planning

CHEN Zhilan, GU Chunxiang

Journal of Shandong University(Engineering Science). 2026, 56(3): 73-83. doi:10.6040/j.issn.1672-3961.0.2025.051

Abstract ( 11 )

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Aiming at the problems of the RRT-Connect algorithm in path planning, such as low search efficiency, weak target orientation, redundant path nodes, and poor smoothness, the ARRT-Connect fusion algorithm was proposed based on the improvement of the RRT-Connect algorithm and the artificial fish swarm algorithm.The algorithm introduced intermediate nodes, adopted a target bias strategy, gravitational potential field guidance, adaptive step size adjustment and pruning optimization, and combined B-spline curves to smooth the path. It improved the step size and visual range of the artificial fish swarm algorithm to enhance the global search capability. Experiments showed that compared with the RRT-Connect algorithm, the ARRT-Connect algorithm reduced the average time consumption by 82.22% and 76.92% in simple and complex environments respectively, shortened the average path length by 17.41% and 19.38%, and decreased the average number of nodes by 79.21% and 77.84%. When applied to real-world scenarios, the path length and time consumption of mobile robots were significantly shortened, and path transitions became gentler, which verified the effectiveness, superiority and feasibility of the algorithm.

Spatio-temporal series prediction based on frequency domain graph convolution network

WANG Qian, ZHANG Ruimin, LI Mingjin, MENG Xianjing, GENG Leilei

Journal of Shandong University(Engineering Science). 2026, 56(3): 84-92. doi:10.6040/j.issn.1672-3961.0.2025.134

Abstract ( 9 )

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To address the difficulties in modeling nonlinear multi-scale spatio-temporal coupling dependencies in multi-scale spatio-temporal series prediction, the challenges faced by traditional methods in capturing cross-scale interactions due to separate processing of spatio-temporal features, and the issues with existing deep learning methods such as interference from Gibbs noise and insufficient fusion of local-global features, a frequency domain graph convolution network(FDGCN)was proposed, and multi-scale spatio-temporal unified modeling was achieved through a three-stage collaborative framework. A hypervariable graph was constructed to jointly encode multi-scale temporal dimensions and spatial topology as graph nodes, and an adaptive adjacency matrix was used to explicitly model cross-scale dependencies. A discrete cosine transform-discrete Fourier transform(DCT-DFT)collaborative noise reduction mechanism was designed, which suppressed the Gibbs phenomenon in DFT through even-symmetric extension in DCT, combined with a scale-aware frequency domain filter to separate low-frequency trends and high-frequency noise. An exponential smoothing attention mechanism was introduced to dynamically fuse multi-scale features, balancing local fluctuations and long-term trends. Based on validation across multiple domains, FDGCN could achieve spatio-temporal unified modeling at multiple scales, effectively capturing complex spatio-temporal dependencies, reducing high-frequency noise, and improving training efficiency. FDGCN achieved excellent prediction performance on datasets in multiple fields such as transportation and power, which demonstrated comprehensive advantages including high prediction accuracy, superior computational efficiency, and strong cross-domain generalization ability, providing an efficient solution for spatio-temporal prediction.

Intelligent detection method for subgrade disease based on deep learning

REN Hongwei, MENG Fei, WANG Jikai, TIAN Weiyang, WEI Mingzhao, CHENG Zhiheng, DU Cong, WU Jianqing

Journal of Shandong University(Engineering Science). 2026, 56(3): 93-105. doi:10.6040/j.issn.1672-3961.0.2024.309

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A novel intelligent method for identifying subgrade distress was proposed to address the challenges associated with the concealed nature of subgrade defects and the scarcity of available data. The proposed framework consisted of a prediction module based on an attention-enhanced long short-term memory network(iTransformer-LSTM)and a regression module based on an elastic neural network. Mechanical response data were generated through dynamic loading tests on pavement model specimens, which effectively mitigated the problem of inadequate distress data. These data were subsequently used to predict the mechanical performance of the subgrade structure, and the distress types were identified accordingly. To verify the effectiveness of the proposed method, a scaled subgrade model was established using the material proportions of a real subgrade structure. Defective specimens representing looseness, differential settlement, cracks, and pipeline leakage were designed to reproduce realistic subgrade distress conditions. Strain-gauge earth pressure cells were embedded at different layers and positions within the model to monitor mechanical responses under dynamic loading. The measured earth pressure data were then collected, analyzed, and validated. The results demonstrated that the proposed model could accurately predict the distribution and evolution of earth pressure in the subgrade structure based on load and displacement data, thereby enabling rapid and accurate identification of distress types. The proposed method offered a new perspective for the nondestructive detection of subgrade distress.

Algorithm for two-sided collaborative filtering multimodal contrastive representation enhancement recommender

CHEN Yu, MENG Guangting, ZONG Chen, YUAN Weihua, WANG Jiening, WANG Xing

Journal of Shandong University(Engineering Science). 2026, 56(3): 106-117. doi:10.6040/j.issn.1672-3961.0.2024.284

Abstract ( 13 )

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The existing multimodal recommenders had three main problems: the potential relevance between multimodal data and interaction data had not been fully explored, leading to the weakening of key features; the accidentally caused noise unrelated to user interests was ignored; the static multimodal fusion method provided the same weight to each modality and could not dynamically perceive the change of user interests, resulting in insufficient discrimination of the learned representations. Therefore, a user and item two-sided collaborative filtering multimodal contrastive representation enhancement(TCFCRE)recommender was proposed. To address the shortcomings in combining multimodal and interaction data, TCFCRE used contrastive learning to enhance key features and mine the potential associations. Meanwhile, to reduce the impact of noise, a cross-modal user representation alignment module was designed to discover the consistency of user features and extract users' true interests. A mask matrix based on the user-item multimodal relationship was also constructed to generate an augmented view, and contrastive learning was adopted to reduce the noise impact in implicit feedback. To alleviate the problem that traditional methods ignored the importance of modalities and could not adapt to dynamic changes, a multimodal dynamic fusion module that calculated fusion weights for each representation was designed. Experiments on three public datasets demonstrated that TCFCRE had achieved significant improvements over existing solutions.

Enhanced Graph Transformer with node and edge feature fusion

LI Junliang, JIANG Yuan, WU Longxue, LIU Yu

Journal of Shandong University(Engineering Science). 2026, 56(3): 118-126. doi:10.6040/j.issn.1672-3961.0.2024.310

Abstract ( 9 )

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To address the problems that the neighborhood aggregation Graph Transformer(NAGphormer)lacked an effective mechanism for utilizing edge features and that the eigenvectors of the graph Laplacian matrix were only applicable to undirected graphs, this paper proposed a novel model, namely enhanced Graph Transformer with node and edge feature fusion(EGT-NEF). A dummy node was used to solve the problem that directed graphs could be converted into line graphs; the line graph mapping matrix was introduced to enable the model to learn edge features from neighborhoods; position encodings were generated through the singular value decomposition(SVD)of the graph adjacency matrix to extend the model to directed graphs. The experimental results showed that the proposed model achieved certain improvements in performance compared with the baseline.

Feature subset selection for fuzzy multi-scale multi-label data

WANG Chengzhi, LIN Guoping, JIANG Liang, LIN Yidong, QIN Yujie

Journal of Shandong University(Engineering Science). 2026, 56(3): 127-136. doi:10.6040/j.issn.1672-3961.0.2024.322

Abstract ( 13 )

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Multi-scale rough sets became one of the research hotspots in the field of granular computing. The classical Wu-Leung model performed well in handling discrete single-label data; However, it was limited in dealing with fuzzy multi-label data. To address this issue, this study drew on the theory of multi-label learning to construct a corresponding information system for fuzzy multi-scale multi-label data, and designed an algorithm that simultaneously achieved optimal scale selection and feature subset selection. Finally, experiments were conducted on seven standard multi-label datasets, and the results demonstrated the effectiveness of the proposed algorithm in feature dimensionality reduction and its stability feasibility.

Graph node classification algorithm based on multi-level core aggregation GNN

TANG Kai, WANG Fang, LIU Jianxia

Journal of Shandong University(Engineering Science). 2026, 56(3): 137-143. doi:10.6040/j.issn.1672-3961.0.2025.034

Abstract ( 16 )

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To address the problems of insufficient utilization of neighbor structure information and feature blurring caused by multi-layer propagation in node classification tasks, a multi-level core aggregation graph neural network(MCAG)model was proposed. The MCAG model divided the graph data into two-node and multi-node connected components. A custom core node selection mechanism was used to construct a total core node set, from which a core node subgraph was then extended. These subgraphs were combined to form a core node aggregation layer, which was fused with a GraphSAGE layer and a group normalization layer to obtain the final node representations. Experimental results showed that the MCAG model improved the node classification accuracy by an average of 3.28% on six datasets, including Cora. On the Amap dataset, the model performed comparably to baseline models, demonstrated stable overall performance.The training time was reduced by an average of 50% compared to the original architecture, and the performance of the core node set sampling method was superior to that of random walk sampling. These findings verified the effectiveness and superiority of the MCAG model.

A few-shot imitation learning method by improving generalization with meta-learning

WEI Long, FENG Xiang, YU Huiqun

Journal of Shandong University(Engineering Science). 2026, 56(3): 144-155. doi:10.6040/j.issn.1672-3961.0.2025.105

Abstract ( 12 )

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To address the issues of poor training performance and insufficient generalization capability of most classical imitation learning methods in few-shot scenarios due to data scarcity, a meta-learning based generative adversarial imitation learning(Meta-GAIL)method was proposed. Through the introduction of meta-learning mechanisms, the policy network pre-accumulated experiential knowledge from diverse tasks with similar characteristics to the target task. The generative adversarial imitation learning(GAIL)algorithm was utilized to fine-tune the network using the limited demonstration data provided by the target task, achieving rapid adaptive transfer to new tasks. To validate the effectiveness of the method, systematic experiments were conducted on the MuJoCo physics simulation platform, where Meta-GAIL method was compared and evaluated against baseline algorithms. Experimental results demonstrated that Meta-GAIL method exhibited stronger rapid adaptability in unseen similar task scenarios by effectively integrating cross-task knowledge representations acquired during the meta-learning phase, and its performance consistently outperformed baseline algorithms under few-shot settings.

Model-data hybrid driven estimation method of the state of charge for the lithium battery

LI Wei, REN Qiwen, CAO Yongji, YU Sen, LI Changgang, KAN Rui, LIU Ziqi

Journal of Shandong University(Engineering Science). 2026, 56(3): 156-165. doi:10.6040/j.issn.1672-3961.0.2025.089

Abstract ( 9 )

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To address the issues of insufficient estimation accuracy in model-driven methods and susceptibility of data-driven methods to the quality of training data, a model-data hybrid driven estimation method of the state of charge(SOC)for the lithium battery was proposed, which improved the estimation accuracy of SOC by combining the prior knowledge of physical models with the nonlinear fitting capabilities of data-driven methods. Considering the dynamic characteristics of the lithium battery, a second-order resistor-capacitance(RC)equivalent circuit model was used to establish the state-space equations of the battery system. The extended Kalman filter(EKF)was employed to preliminarily estimate the SOC of the lithium battery. The estimation results from the EKF, along with the terminal current and terminal voltage of the lithium battery, were used as inputs to an improved Transformer encoder to achieve a refined estimation of the SOC. The results of the case study showed that the proposed method achieved a mean absolute error of less than 0.7% under various operating conditions and temperatures, which could effectively improve the accuracy and robustness of the SOC identification method.

Identification method of transient voltage instability in case of renewable generation supply

ZOU Xin, MENG Jian, FU Shiqi, LIU Junyu, WANG Haifeng, DANG Chongyang

Journal of Shandong University(Engineering Science). 2026, 56(3): 166-176. doi:10.6040/j.issn.1672-3961.0.2025.145

Abstract ( 9 )

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To address the issue of reduced identification accuracy in the conventional positive-feedback-based transient voltage stability identification method under renewable generation integration scenarios, an improved strategy incorporating additional criteria was proposed on the basics of the original method. Voltage dynamic characteristics during the post-disturbance recovery stage were examined according to renewable generation unit control strategies, and the factors responsible for the degraded accuracy of the original method under renewable integration were identified. The conventional positive-feedback-based voltage instability criterion was modified by introducing the criterion activation-duration threshold and the voltage safety threshold. Simulation-based validation was conducted on the IEEE 39-bus system and the CEPRI-TAVC benchmark system. The results showed that appropriately prolonging the criterion activation-duration threshold and reducing the voltage safety threshold improved the identification accuracy of transient voltage stability.

Method for constructing multi-level chains of trust for distributed energy resources in virtual power plants

ZHANG Xiao, CHENG Sijin, WANG Yi, LI Xinyi, XU Yuzhang, HU Zhouyue, ZHANG Hengxu

Journal of Shandong University(Engineering Science). 2026, 56(3): 177-186. doi:10.6040/j.issn.1672-3961.0.2025.067

Abstract ( 11 )

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Aiming at the problems that existing researches predominantly focused on trust assurance in single segments of virtual power plants(VPPs)and lacked the construction of the end-to-end chains of trust, a method for constructing multi-level chains of trust for distributed energy resources in VPPs was proposed to enhance data security and operational reliability. The theoretical foundation, model algorithms, construction mechanisms for chains of trust, as well as the compatibility between chains of trust technologies and VPPs' management and control requirements, were analyzed in detail. The diverse information transmission demands and challenges in typical segments of VPPs' aggregation and operation were dissected, clarifying the necessity of introducing chains of trust into VPPs' construction to enhance data control quality. Grounded in big data, cloud computing, and blockchain technologies, a distributed collaborative framework for constructing multi-level chains of trust for VPPs' resources was proposed. The theoretical foundation, model algorithms, and construction mechanisms of the framework were systematically expounded. A simulation model encompassing data quality assessment, response delay calculation, attack defense mechanisms, and cost-benefit comparison was established for validation. Simulation results showed that, compared to traditional VPPs, the proposed framework significantly improved data accuracy, substantially reduced average response time, effectively increased attack defense success rate, and lowered total operating costs. The framework effectively addressed the lack of trust across all VPPs' operational segments through a three-level collaborative mechanism for chains of trust, providing the reliable technical support for large-scale VPPs' applications.

Multi-objective optimization design of gas-liquid two-phase centrifugal pump parameters

ZHOU Mingxu, HU Youcai, WANG Yanwei

Journal of Shandong University(Engineering Science). 2026, 56(3): 187-192. doi:10.6040/j.issn.1672-3961.0.2024.314

Abstract ( 21 )

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Under the condition of gas-liquid two-phase, the high-speed centrifugal pump of model Q5H26 was studied to improve its head and efficiency. After the three-dimensional solid modeling of the main components of the centrifugal pump, the feasibility of the numerical simulation was verified by experiments. For the condition of 10% gas content, the sensitivity analysis of impeller parameters of centrifugal pump was carried out based on multi-objective programming model, and the optimization design was carried out by genetic algorithm. The optimized model was numerically simulated, and the operating efficiency and head of centrifugal pump before and after optimization were calculated and compared to evaluate the optimization effect. When the gas content was 10%, the four key structural parameters of impeller outlet width, impeller diameter, blade trailing edge outlet angle and impeller inlet diameter significantly affected the performance of the pump. Under the rated condition, when the air content was 10%, the efficiency of the model pump designed by optimizing the impeller structure parameters was increased by 11.2% and the head was increased by 1.45 m. In this way, the stability and reliability of high-speed centrifugal pumps in dealing with liquids containing gas were enhanced.

A game study on the evolution of carbon reduction behavior of energy- consuming enterprises considering dynamic rewards and penalties

CHEN Xi, ZHANG Huan, TIAN Hongli, DAI Chunyan, JIANG Tianyan, BI Maoqiang

Journal of Shandong University(Engineering Science). 2026, 56(3): 193-203. doi:10.6040/j.issn.1672-3961.0.2024.197

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In order to explore the impact of different factors on the carbon reduction behavior of high-energy-consuming enterprises, this paper researched the carbon reduction behavior of these enterprises under government regulation, considering their participation in both the electricity and carbon markets. A game theory model of the government's and high-energy-consuming enterprises' carbon reduction behavior in the joint electricity-carbon market was constructed. The evolutionarily stable strategies were examined under two scenarios: static rewards and penalties, and dynamic rewards and penalties. The effects of parameters such as the government's electricity price incentive coefficient, regulatory costs, regulatory intensity, and the upper and lower limits of penalties on the carbon reduction behavior of high-energy-consuming enterprises and the stability speed of the system under dynamic reward and penalty mechanisms were discussed. The analysis of numerical examples showed that: under a dynamic reward and penalty mechanism, there existed a unique evolved stable strategy for both parties; during different carbon reduction periods, the government should balance the upper limit of rewards and electricity price incentives to improve the probability of high-energy-consuming enterprises choosing carbon reduction behavior; the regulatory intensity of the government had a greater impact on the carbon reduction behavior of high-energy-consuming enterprises than regulatory costs, and it was recommended that the government strictly regulate these enterprises during carbon reduction periods.

Research on the collaborative path of ecological protection and high-quality development in the Shandong section of the Yellow River Basin

DONG Yunlong, WANG Qingsong, ZHANG Yujie

Journal of Shandong University(Engineering Science). 2026, 56(3): 204-212. doi:10.6040/j.issn.1672-3961.0.2025.247

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Based on the "point-line-plane" theoretical framework, the development quality of nodes was evaluated by taking the city as the "point". The function ties of industries as the "line" were analyzed to reveal the collaborative pattern formed by them as the connecting elements. The regional "plane" was used to reveal the regionalized collaborative effects and spillover paths formed by various cities through the spatial association network. The research findings showed that at the "point" level, the comprehensive index of ecological protection and high-quality development in the Shandong section of the Yellow River Basin increased from 0.427 8 in 2013 to 0.621 8 in 2022. The number of invention patents per thousand people and per capita GDP were the common core obstacles restricting the development of each city. At the "line" level, the coupling coordination degree of each city showed significant regional heterogeneity. The innovation-active areas and regions with higher economic development levels had a stronger promoting effect on industrial coordination, while regions with a higher proportion of traditional industries had a limited promoting effect. At the "plane" level, the overall network density was 0.36, and innovation momentum, economic foundation, and industrial scale were the core positive factors driving the spatial association. The collaborative path of "strong points-smooth lines-excellent surfaces" was proposed. Through strategies such as precise empowerment of node functions, unblocking of industrial blockages, and optimization of spatial governance structures, a new regional development pattern of "complementary functions-smooth circulation-optimized efficiency" was constructed, providing theoretical basis and practical paths for solving the collaborative problems of ecological protection and high-quality development in the Yellow River Basin.

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