High-speed Rail System Research Articles

Influence of cork-rubber gasket on the circular propagation of train-induced vibration waves in high-speed railway shield tunnels

Shield tunnels are constructed by assembling segment, and this construction method will produce a large number of joints. As the component with the largest contact area in the joints of the shield tunnel, the cork-rubber gasket has a significant effect on the transmission of train-induced vibration waves between the segments. In order to study the influence of cork-rubber gasket on the transmission of train-induced vibration waves in the circumferential direction, based on the hammering test of high-speed railway shield tunnel, a dynamic calculation model for high-speed railway shield tunnel was constructed, and the influence of elasticity modulus of cork-rubber gasket on the propagation of train-induced vibration waves was investigated. The results show that: (1) the longitudinal joints of high-speed railway shield tunnels can weaken high-frequency vibration waves more than low-frequency vibration waves; (2) the lower the modulus of elasticity of cork-rubber gasket is, the greater the attenuation of the peak of the temporal range of vibration acceleration of train-induced vibration waves after they pass through the longitudinal joints; (3) compared with the cork-rubber gasket of high elasticity, the cork-rubber gasket with low elasticity can improve the damping effect of the longitudinal joints on low-frequency bands (0–500 Hz) effectively. This research offers new methodologies for optimising vibration isolation in shield tunnels and contributes to the advancement of tunnel design for high-speed rail systems.

Metaheuristics-based multistage iterative optimization framework for decomposed high-speed rail systems planning problem

High-speed rail (HSR) systems planning and decision-making is a large-scale, multistage, intricate problem, where each stage represents a complex sub-problem. The solution approach to the multistage problem needs information exchange across the stages. A non-optimal planning and decision at any stage could yield a sub-optimal HSR system. This study proposes a novel multistage iterative HSR station location and alignment optimization framework (HSLAOF) to solve the main problem by decomposing it into the identification of (a) HSR potential regions and corridor, (b) station location, (c) shortest sequence/corridor of stations, and (d) collision-free alignment (horizontal and vertical) sub-problems. It integrates these sub-problems, which are solved separately using customized artificial intelligence- and motion planning-based metaheuristics such as particle swarm optimization for station location, ant colony optimization for shortest sequence of stations, path planner method for horizontal alignment and exploration, and exploitation-based ant colony optimization for vertical profile. In HSLAOF, the information from the upper and lower stages of the optimization process are exchanged and combined for a holistic optimized HSR system. Application of HSLAOF in the Mumbai-Ahmedabad HSR project yielded a solution that has 14.24 % lower total system cost, no environmental impact, 5.82 % better socio-economic impact, 21.14 % lesser noise and vibration impacted population, and 2.79 % higher station location utility than the one proposed by the experts. For predefined station location, the HSLAOF yielded alignment with 13.90 % lower total system cost and 24.00 % less noise and vibration impacted population than the one developed by experts. It required about 150 min to obtain a solution for each iteration.

Empowering super-stars or rising-stars? Dynamics of the high-speed rail network planning in China

ABSTRACT The development of high-speed rail (HSR) systems as a critical component of the global 'infrastructure turn' is deeply embedded in regional socioeconomic contexts. Drawing on advances in actor-oriented network modelling and longitudinal inter-city HSR data in China during 2008-2022, this study explores how the evolution of the HSR network is dynamically and differentially underpinned by attribute-based effects of socioeconomic scale and growth rate to balance the short-term efficiency and long-term equity of nationwide development. After controlling for structure-based effects (transitive triads and balance) as well as attribute-based effects related to geographic, natural and cultural contexts, the results provide evidence that while the scale and the growth rate of economy and population both positively impact HSR link formation, the impacts of scale-related effects significantly diminish over time whereas the impacts of growth-rate-related effects exhibit a significant strengthening trend. The results further illustrate that while the scale-related and growth-rate-related effects of economy function as substitutes in driving HSR link formation, the two corresponding effects of population complement each other, providing evidence for the heterogeneous roles of economic and social contexts in underpinning HSR network planning. The findings provide implications for more effective and equitable regional socioeconomic development through strategic HSR network planning.

Rapid design method for composite emergency steel piers with thin-walled steel tube framework and discussion on "temporary-permanent" transition

To address the conflict between the reserve of repair materials for existing bridge piers and the demands for emergency repairs, as well as the challenge of converting temporary emergency structures into permanent ones without significant disassembly, a novel composite emergency steel pier has been developed. This pier utilizes commonly available thin-walled steel tube sections as the framework, I-beams as the connecting elements, and incorporates a "temporary-permanent" transition function. Taking the emergency steel pier for medium-height bridge piers in high-speed rail systems as an example, this study introduces three evaluation metrics—security coefficient (n), stability coefficient k), and variation coefficient (V)—analyzing the factors influencing the design and application thresholds of the emergency steel piers from perspectives of strength, stability, and load distribution uniformity. Based on this, a rapid design method for composite emergency steel piers with thin-walled steel tube frameworks that does not require numerical simulation has been developed and experimentally validated. Research findings indicate that when used for the emergency repair of medium-height or lower bridge piers in high-speed railways, the column line stiffness of the thin-walled steel tube framework composite emergency steel piers should range between 0.34 × 10 exp7 kN/mm to 4.15 × 10 exp7 kN/mm. The transverse and longitudinal spacing of the columns should be 1 m to 3 m and 1.5 m to 3 m respectively. The line stiffness of the plinth beams I and II should be greater than 0.69 kN/mm and 1.01 kN/mm respectively. Within these parameter ranges, the emergency steel pier will not experience strength failure or instability, and the load distribution among the columns remains uniformly favorable. In applications to other scenarios, the rapid generation of composite emergency steel piers with thin-walled steel tube frameworks can be achieved by following three steps: parameter selection and structural configuration determination, calculation of the pier-beam linear stiffness ratio, and criterion-based result verification. The rapid design and implementation of composite emergency steel piers help alleviate the contradiction between material stockpiling and repair demands. Furthermore, the pre-designed "temporary-permanent" transition functionality facilitates integrated operations for emergency repairs and permanent restorations.

A review on research regarding HSR interactions with air transport and outlook for future research challenges

The interactions between high-speed rail (HSR) and air transportation systems constitute a complex, evolving integral component of our modern transportation landscape. Over recent decades, changes in travel patterns and growing environmental concerns, spurred by advancements in railway technology, have significantly influenced the dynamics of these two transportation modes. While previous reviews on this subject have provided seminal insights, there is a necessity for a novel synthesis of research findings in recent years, given that extant reviews have covered the evolving landscape until the year 2018 only. This review critically evaluates the latest literature to analyze five aspects regarding air/HSR interactions: Modal integration/modal competition, bi-directional impacts, emission aspects, robustness/resilience perspectives, and some other related work. In addition, we propose a set of ten challenging research questions, highlighting the need for concerted research efforts, considerations of more practical decision factors, and evidence-based policy making to foster a sustainable and resilient integration of air/HSR systems in the 21st century.

A Simulation Approach for Analysis of the Regenerative Potential of High-Speed Train Suspensions

This study primarily investigates the adaptability and performance of hydraulic–electric regenerative dampers for high-speed trains by substituting conventional primary dampers with hydraulic–electric regenerative dampers. The primary objectives are to develop a detailed model of primary suspension regenerative damper (PSRD) energy conversion that incorporates factors such as oil pressure loss, motor efficiency, and overall system efficiency, and to perform a comprehensive comparative analysis of vibration responses, wheel wear, comfort indices, and power generation using an integrated MATLAB and SIMPACK co-simulation platform. The results reveal that at an operational speed of 350 km/h, the dynamic responses of the carbody, bogie, wheelset, and dampers equipped with the proposed PSRD systems closely align with those of conventional primary vertical damper systems. The detailed PSRDs’ hydraulic–mechanical–electrical model effectively captures the subtleties of oil pressure fluctuations and their impacts. The wear distribution and magnitude across the vehicle remain consistent during acceleration, constant, and deceleration speeds, ensuring uniform wear characteristics. Under real-world railway operational conditions, the ride comfort metrics of vehicles fitted with regenerative dampers are comparable to those with conventional primary vertical dampers. Furthermore, each regenerative damper can generate up to 21.72 W of electrical power, achieving a generation efficiency of 45.28%. Finally, a test rig was designed and fabricated to validate the primary suspension regenerative damper (PSRD) model, showing good agreement between predicted and actual damping force and power regeneration, with results indicating a peak damping force of 12.5 kN and approximately 230 W of regenerated power. This research provides a theoretical foundation and experimental validation for implementing power regeneration mechanisms in railway transportation, demonstrating that the hydraulic–mechanical–electrical PSRD model can fulfil the performance criteria of conventional dampers while offering substantial energy harvesting capabilities. This advancement not only enhances energy efficiency but also contributes to the sustainable development of high-speed rail systems.

Design and Implementation of Electrochromic Smart Windows with Self-Driven Thermoelectric Power Generation.

Electrochromic smart windows can achieve controllable modulation of color and transmittance under an external electric field with active light and thermal control capabilities, which helps reduce energy consumption caused by building cooling and heating. However, electrochromic smart windows often rely on external power circuits, which greatly affects the independence and portability of smart windows. Based on this, an electrochromic smart window driven by temperature-difference power generation was designed and implemented. This smart window provides automatic and manual control of the reversible cycle of electrochromic glass from light blue to dark blue according to user requirements and changes in the surrounding environment, achieving adaptive adjustment of visual comfort and reducing energy consumption. The infrared radiation rejection (from 780 to 2500 nm) of the electrochromic smart window is as high as 77.3%, and its transmittance (from 380 to 780 nm) fluctuates between 39.2% and 56.4% with changes in working state. Furthermore, the temperature in the indoor simulation device with electrochromic glass as the window was 15 °C lower than that with ordinary glass as the window after heating with a 250 W Philips infrared lamp for ten minutes. After 2000 cycles of testing, the performance of the smart window was basically maintained at its initial values, and it has broad application prospects in buildings, vehicles, and high-speed rail systems.

Transient Analysis on the Crosswind Effect to the Aerodynamics of High-speed Train Travelled on the Bridge Between Two Tunnels at Jakarta -Bandung Track

The rapid evolution of global transportation technology is exemplified by Indonesia's innovative high-speed train initiative, linking Jakarta and Bandung in an impressive 45 minutes. Operating at 350 km/h, the HST CR400AF underscores the importance of aerodynamics in high-speed rail systems. This study delves into the significant impact of crosswind on key aerodynamic factors (drag, lift, rolling moment) within the tunnel-bridge-tunnel configuration. Leveraging Computational Fluid Dynamics (CFD) through ANSYS FLUENT, the analysis explores crosswind variations at 0 m/s, 10 m/s, and 25 m/s. Results reveal a proportional increase in aerodynamic load with higher crosswind intensities: 1.67 times for drag, 58.8 times for lift, and 29.8 times for rolling moment. Notable observations include pronounced aerodynamic load fluctuations during the "OUT" process, with the head section bearing the greatest load, followed by the tail and middle sections. These findings contribute valuable insights to the global discourse on enhancing safety and efficiency in high-speed rail systems

Research on mobilization and effective utilization of capital for high-speed rail system development in countries: Some issues for Vietnam

The construction project of the high-speed rail (HSR) line on the North-South axis has extremely immense scale, with complex technical-technological standards, deeply and long-term impacting the country's economic and social development. This marks the first implementation of such project in Vietnam, thus requiring thorough and comprehensive research and evaluation. The selection of an appropriate financial mechanism is crucial to the project's success. The Vietnamese government is currently implementing a socialization policy in the transportation sector in general, and the North-South HSR project is proposed to be executed through a public-private partnership (PPP) model. In this framework, the state budget plays a leading and decisive role; external resources are deemed vital for breakthroughs. However, aspects such as how to mobilize funds, how the private sector participates, how it is managed, how the capital is repaid, whether to opt for limited-term transfers or lease of asset exploitation rights, over how many years... have yet to be addressed. Researching the mobilization and utilization of financial resources in countries with developed HSR systems, the authors observe varying investment and operational methods in each nation. Even within a single country, different financial models are applied in distinct phases. Alongside the successes achieved, there are instances of failed projects resulting in substantial losses. Hence, in addition to analyzing experiences in mobilizing and using funds for construction investment of HSR systems in other countries, the article also assesses the advantages and challenges for Vietnam. These are vital suggestions to aid the Vietnamese government in drawing lessons and selecting appropriate forms of mobilization and use of capital in line with the country's actual resources, exploiting the potential and advantages of the country.

Research on Public-Private Partnership (PPP) Investment under Build - Operate - Transfer (BOT) and Build-Lease-Transfer (BLT) Contract Types in the High-Speed North-South Rail Project (HSR), the Hanoi - Vinh Line

Introduction The North-South high-speed rail development is a completely new field in Vietnam. Calculations show that Vietnam's high-speed rail system will attract a significant amount of investment, which is 4-5 times higher than developing highways, and the annual operation and maintenance costs are three times higher. Methods Public-Private Partnership (PPP) investment is effective and required to ease the strain on the state budget. This research aims to build a database for calculating the financial efficiency of the high-speed rail project (Hanoi -Vinh line), thereby establishing a mechanism for sharing benefits and risks between the state and investors through financial scenarios: applying Build - Operate - Transfer (BOT) contracts with state participation rates of 50% and 80%, respectively. Results The qualitative research method is used to determine the indicators influencing the project's benefits and costs, assume and adjust economic, financial, and fare parameters based on Vietnam's actual conditions, and investigate and survey the affected areas to assess passenger transport demand. Conclusion Furthermore, the financial efficiency of the project is calculated, and various participation options for the parties involved are proposed to attract investors.

BAYESIAN NETWORKS AND STRUCTURAL EQUATION MODELLING TO INVESTIGATE THE PASSENGERS’ PERCEPTIONS IN HIGH-SPEED RAIL SYSTEMS

Ensuring sustainability in the global world today depends on perception management as well as financial management. In order to manage the perceptions, which are inherently latent variables as they are measured indirectly through their indicators, they must be accurately handled and modelled comprehensively. In the present study, a hybrid technique combining Bayesian Networks (BN) and Structural Equation Modelling (SEM), which are regarded as causal models, was used to investigate the perceptions of High-Speed Rail System (HSRS) passengers. In order to provide insight into the customer retention strategy for HSRS, the analyses were performed on the survey data gathered from the frequent users of HSRS operating between 2 cities of Turkey. After the measurement model of the perception variables through SEM was established, the relationships between the variables were learned using BN knowledge extraction algorithms. As a result, relationships from image to trust and loyalty, from trust to perceived value, from perceived value to satisfaction, and from satisfaction to loyalty were determined. Final interpretations were made in terms of risk management with the help of the probabilistic predictive ability of the BN by setting evidence on the satisfaction levels of the perceptions.

Numerical study of dynamic amplification factor and characteristic wind curves of high-speed train in tornado-like vortices

Tornado-induced railway accidents occurred globally and the risk analysis of high-speed train in tornado-like wind fields is required, particularly in the context of the ongoing development of high-speed rail systems. To study the applicability of Burgers-Rott and Sullivan tornado models, CFD simulations are firstly carried out. It reveals that the Burgers-Rott model can effectively simulate the tangential velocity characteristics of tornado-like vortices up to the two-celled turbulent vortex stage while the Sullivan model is a suitable choice for vortices in the multi-vortex stage. Subsequent analyses delve into the behavior of the dynamic amplification factor (DAF) in tornado-like vortices. The Burgers-Rott model exhibits a higher DAF value when the passing time exceeds 1.5s whereas the dominance of the Sullivan model is evident when the passing time is less than 1.5s. Finally, a linear relationship between characteristic wind curve (CWC) and train speed is noted. This relationship manifests as the characteristic wind speed reaches approximately 30 m/s as the train speed is 150 km/h. It is also noteworthy that the CWC exhibits an upward trajectory as the translational speed of the tornado intensifies. In conclusion, this study serves as a valuable reference for assessing the operational safety of high-speed trains in tornado-like vortices.

Research on capacity optimization of new energy hybrid energy storage system of high-speed railway

With the fast expansion of electrified railways, the need for energy is growing. Thus, improving railway coupling and interconnection, new energy, and energy storage is critical to support low-carbon and green railway development. Therefore, this paper proposes an optimal configuration method for the access capacity of wind power generation system (WPGS), photovoltaic power system (PVPS), and hybrid energy storage system (HESS) in the traction power supply system (TPSS) of high-speed railways. Firstly, the HESS’s mathematical model is developed, then the high-speed railway TPSS’s economic optimization operating model is built, and a HESS energy management approach is presented, taking the energy management strategy parameters and model capacity configuration parameters as the optimization variables. The mixed integer linear programming approach is used to resolve the actual example with the least daily operational cost of the high-speed rail system as the optimization goal, and the optimal capacity of WPGS, PVPS, and HESS is obtained. Finally, through comparison and analysis, it is verified that the economic benefit is the highest when the distributed complementary energy system covering WPGS, PVPS, and HESS is connected to the traction substation, and 10.47% of the daily expenditure is saved.

Application of Variational Graph Autoencoder in Traction Control of Energy-Saving Driving for High-Speed Train

In a high-speed rail system, the driver repeatedly adjusts the train’s speed and traction while driving, causing a high level of energy consumption. This also leads to the instability of the train’s operation, affecting passengers’ experiences and the operational efficiency of the system. To solve this problem, we propose a variational graph auto-encoder (VGAE) model using a neural network to learn the posterior distribution. This model can effectively capture the correlation between the components of a high-speed rail system and simulate drivers’ operating state accurately. The specific traction control is divided into two parts. The first part employs an algorithm based on the K-Nearest Neighbors (KNN) algorithm and undersampling to address the negative impact of imbalanced quantities in the training dataset. The second part utilizes a variational graph autoencoder to derive the initial traction control of drivers, thereby predicting the energy performance of the drivers’ operation. An 83,786 m long high-speed train driving section is used as an example for verification. By using a confusion matrix for our comparative analysis, it was concluded that the energy consumption is approximately 18.78% less than that of manual traction control. This shows the potential and effect of the variational graph autoencoder model for optimizing energy consumption in high-speed rail systems.

Agent-based modelling of high-speed railway interdependent critical infrastructures facing physical and cyber threats

Globally, high-speed rail systems serve nearly 2 billion passenger-km daily. By virtue, they are a critical infrastructure like telecommunication and power networks. Accordingly, they become a catalyst for societal and economic growth stemming from the mobility business. The highspeed rail operations are very complex and interdependent, owing to the escalated demands for long-distance interconnected transportation. In recent years, there have been unreasonable delays for passengers as a new norm due to unfortunate train cancellations and relaxation of mobility performance requirements. Therefore, accurate measurements, monitoring and prediction of disruptive impacts and service performance metrices are indispensable. Within the scope of high-speed rail services, this paper examines how agent-based and multi-agent-based models are utilized to address such the challenges. Our findings reveal that the current use of agents or multi-agent models has some limitations for practical applications. Previous studies showed that mathematical methods to assess the resilience of critical infrastructures, railway scheduling, and vehicle dispatching can yield more satisfactory outcomes, although the approaches can be relatively time-consuming. In contrast, agent-based and multi-agent-based models can shorten processing time and uncover disruptive events more promptly. The paper thus showcases several emerging concepts, including i) the utilization of big data for crisis management, ii) interconnectivity analysis of high-speed rail infrastructures, and iii) enhancement of transport resilience. In addition, our findings identify the most influential agents and their possible applications to enhance systems resilience of highspeed rail networks when dealing with unforeseen physical and cyber threats.

Postearthquake train operation safety assessment model based on machine learning

Abstract Assessing the seismic risk to high-speed rail systems with limited structural damage data is a challenging task. This study employs machine learning algorithms to predict the wheel–rail forces of high-speed trains operating under postearthquake conditions, particularly when infrastructure along the railway is damaged. By developing a postearthquake train operation safety assessment model, this article effectively predicts the impact of track irregularities induced by different earthquake intensities on wheel–rail interactions. The results obtained through feature selection and regression analysis using the Random Forest algorithm provide valuable insights into key safety indicators for postearthquake train operations. Compared to traditional multibody dynamic models, this approach significantly improves the efficiency of analysis and computation. An analysis of the results across multiple speed levels reveals that trains operating at 250 km/h face derailment risks when subjected to high-intensity earthquakes (PGA > 0.6 g). The proposed predictive safety assessment model demonstrates that adjusting train speeds according to seismic intensity can effectively enhance operational safety, offering critical support for postearthquake emergency recovery efforts.

Automated Monitoring and Emergency Response System for Sensitive Areas Along High-Speed Railway Lines

The safety of high-speed railroads is an important indicator of travelers’ trust, and it is also an important factor in determining whether or not the operation volume can reach the expected goal. Therefore, high-speed railroad companies in Europe, the United States, and Japan have invested heavily in establishing safety monitoring systems in order to avoid the occurrence of disasters and to strengthen the mechanism of crisis response and emergency treatment. High-speed railroad operation may occur in a variety of accidents, different disaster warning, emergency response and rescue, need to have different equipment, contingency measures, and well-trained personnel to deal with. Therefore, the safety standards for high-speed rail systems in advanced countries around the world are much higher than those for traditional train systems. The theories and technologies of disaster prevention and relief have matured both at home and abroad. This study combines the theories and technologies of disaster prevention with GIS, such as monitoring instruments, satellite positioning, remote sensing detection, radio transmission, the Internet, database management, and information management, to provide effective support for decision-making and analysis of commanders, to rapidly assist in crisis management, and to strengthen the mechanism of emergency response.

Power and the politics of infrastructure planning: a case study of the proposed construction of a high-speed rail system in Texas.

The proposed construction of a high-speed rail system in Texas has faced significant political and social challenges, in this paper we examine the power dynamics and political implications of infrastructure planning. The purpose of the article is to provide insights into the decision-making processes, stakeholder roles, and the influence of political and economic factors on infrastructure planning. Drawing on a qualitative research method, this study utilizes secondary data including News articles, media coverage, and Academic literature in which we explore the power dynamics and political landscape surrounding the high-speed rail system in Texas. The findings reveal that private companies, such as the Texas Central Partners, hold significant power and influence in driving the high-speed rail project. The study highlights the complex relationships and power struggles between different stakeholders including private companies, state governments, interest groups, and local communities in the infrastructure planning process. This study provides several recommendations for infrastructure planning practice. Overall, this study contributes to the understanding of power dynamics and political factors in infrastructure planning, specifically focusing on the proposed high-speed rail system in Texas. The insights and recommendations presented have implications for policymakers, practitioners, and researchers involved in infrastructure planning and development. By addressing the complexities of power dynamics, this study aims to inform more equitable and sustainable infrastructure planning practices.

A line planning approach based on time-varying demand for high-speed rail under the combined operation of periodic and aperiodic services

Passenger demand for high-speed rail systems is highly fluctuating in temporal and spatial throughout the day. In order to effectively improve passenger satisfaction and service level for high-speed rail, the formulation of line plan must make the distribution of the trains’ capacities be meet with the time-varying demand of passengers. The aperiodic line plan can well meet this demand since it is more flexible with different stop patterns and various headways. However, the irregular arrival/departure times are not convenient for travel planning. We propose a new type of line plan that would combine both the regularity of the periodic line plan and the flexibility of the aperiodic ones. An optimization method of high-speed railway line plan based on a combination of periodic and aperiodic operation is structured, which can well satisfy the temporal-spatial distributions of passenger demands in different time periods. The main challenge is to coordinate the numbers of periodic and aperiodic trains, and their temporal-spatial distributions on the rail network considering the passengers’ train-choice decisions. Based on generating a set of candidate routes and constructing a passenger travel network, we propose a model to optimize the numbers of both periodic and aperiodic trains, and their paths, stops, approximate arrival and departure times at each visited stations for minimizing the total operation cost of trains and the total generalized travel cost of passengers. Then, a simulated annealing algorithm is designed to efficiently solve our proposed optimization model. Finally, numerical experiments based on the Shanghai-Nanjing intercity railway in China verify the effectiveness and practicability of the optimization method.

An Energy-Efficient Optimization Method for High-Speed Rail Communication Systems Assisted by Intelligent Reflecting Surfaces (IRS)

This paper proposes an intelligent reflecting surface (IRS)-assisted energy efficiency optimization algorithm to address the problem of energy efficiency (EE) degradation in high-speed rail communication systems caused by line-of-sight link blockages between base stations and trains. The joint optimization of base station beamforming and IRS phase shifts is formulated as a variable-coupled energy efficiency maximization problem, subject to the base station’s transmission power and the IRS unit’s modulus constraints. This is known to be an NP-hard problem, making it challenging to obtain the global optimal solution. To tackle the issue of optimization variable coupling, an alternating optimization is employed to decompose the original problem into two sub-problems: base station beamforming and IRS phase-shift optimization. The Dinkelbach method is utilized to convert the fractional objective function into a difference form; then, the successive convex approximation (SCA) algorithm is applied to transform non-convex constraints into convex ones, which are solved using CVX. The Riemann conjugate gradient (RCG) algorithm can effectively solve the difficult unit module constraint. Finally, an alternating iterative strategy is employed to converge to a suboptimal solution. Our simulation results demonstrate that the proposed algorithm significantly enhances system efficiency with low computational complexity. Specifically, when the number of IRS reflecting elements is 64, the system’s EE is improved by approximately 12.41%, 35.26%, and 37.96% compared to the semi-definite relaxation algorithm, the random phase shift approach, and no IRS scheme, respectively.