Velocity Update Research Articles

Multistrategy Fusion Particle Swarm for Dynamic Economic Dispatch Optimization of Renewable Energy Sources

This paper presents a multistrategy fusion particle swarm optimization model for dynamic economic dispatching of renewable energy in distribution networks. The objective is to minimize active network losses and system voltage deviation while considering the integration of distributed energy sources and static reactive power compensators. The algorithm incorporates specific strategies, including a particle position change strategy based on the midpipeline convergence approach, a strategy for generating exploding particles near the optimal particles, and a particle velocity update strategy relying on the global optimal particle position. The inertia weights and particle position update methods of the simplified particle swarm optimization algorithm are also utilized. Simulation experiments are conducted on an IEEE 33 bus radial distribution system, demonstrating the effective optimization of system losses while ensuring system voltage stability. This research contributes to the scientific understanding of renewable energy integration in distribution networks and its economic dispatching.

Stationary Detection for Zero Velocity Update of IMU Based on the Vibrational FFT Feature of Land Vehicle

Stationary Detection for Zero Velocity Update of IMU Based on the Vibrational FFT Feature of Land Vehicle

A Large-Scale Multiobjective Particle Swarm Optimizer With Enhanced Balance of Convergence and Diversity.

Large-scale multiobjective optimization problems (LSMOPs) continue to be challenging for existing multiobjective evolutionary algorithms (MOEAs). The main difficulties are that: 1) the diversity preservation in both the objective space and the decision space needs to be taken into account when solving LSMOPs and 2) the existing learning structures in current MOEAs usually make the learning operators only coincidentally serve convergence and diversity, leading to difficulties in balancing these two factors. Therefore, balancing convergence and diversity in current MOEAs is difficult. To address these issues, this article proposes a multiobjective particle swarm optimizer with enhanced balance of convergence and diversity (MPSO-EBCD). In MPSO-EBCD, a novel velocity update structure for multiobjective particle swarm optimization is put forward, dividing the convergence, and diversity preservation operations into independent components. Following the proposed update structure, a weighted convergence factor is introduced to serve the convergence strategy, whilst a diversity preservation strategy is built to uniformly distribute the particles in the searched space based on a proposed multidimensional local sparseness degree indicator. By this means, MPSO-EBCD is able to balance convergence and diversity with specific parameters in independent operators. Experimental results on LSMOP benchmarks and a voltage transformer optimization problem demonstrate the competitiveness of the proposed algorithm compared to several state-of-the-art MOEAs.

Investigating Hessian-based inversion velocity analysis

Inversion velocity analysis (IVA) is an image-domain method built upon the spatial scale separation of the model. Accordingly, the IVA method is performed with an iterative process composed of two minimization steps consisting of migration (inner loop) and tomography (outer loop), respectively, with each step accounting for its Hessian or not. The migration part provides the common-image gathers (CIGs) with extension in the horizontal subsurface offset. Then, the differential semblance optimization (DSO) misfit measures the focusing of the events in the CIGs, which indicates the quality of the velocity model. Commonly, the velocity updates are obtained from the DSO gradient. IVA is a modified version in which the approximate inverse replaces the adjoint of the inner loop process; in that case, the migration Hessian is approximately diagonal in the high-frequency regime. In this work, we report on implementation of the tomographic Hessian (i.e., the second derivative of the DSO misfit with respect to the background model) for the estimation of the background velocity model. We apply the second-order adjoint-state method to obtain the application of the tomographic Hessian on a vector. Then, we use the truncated-Newton (TN) method to obtain the update directions by computing approximately the application of the inverse of the tomographic Hessian on the descent direction. We also make a theoretical comparison between tomography in the IVA and full-waveform inversion contexts. Two numerical examples are used to compare, in terms of geophysical results and computational costs, the TN method with different gradient-based optimization methods applied to the IVA. A small model allows us to evaluate the eigenvalues of the tomographic Hessian, which explains the large damping needed in the TN case.

Structure preserving and energy dissipative contact approaches for implicit dynamics

AbstractIn this work, several structure preserving and energy dissipative contact approaches are proposed and evaluated. The time integration schemes considered are general with regard to the version of constraint type, but here the emphasis was on mortar contact. The proposed mortar contact approach conserves both linear and angular momentum for mortar contact in a novel way. The proposed time integration scheme can conserve energy or provide strict contact dissipation. In addition, the proposed scheme enforces both gap constraints and gap velocity constraints (i.e., persistency). Using a midstep time integrator often causes energy dissipation during initial impact, here this energy can be recovered in a novel way. Enforcing the gap velocity constraint mitigates the contact chatter of the contact pressure and nodes in many problems. Whereas some approaches enforce the persistency condition and gap constraints simultaneously during the solution of the equations of motion (EOM) requiring multipliers for both constraints included in the equation set, here the gap constraint is solved through the equations of motion and the persistency condition is satisfied in the time integration scheme by the velocity update after the equations of motion. It is shown that this approach is strictly dissipative in that a plastic contact condition can be achieved. Analogous to a coefficient of restitution for rigid bodies, any dissipated energy can then be returned upon release if energy conservation is desired. Structure preserving methods are good for long‐time dynamics simulations and energy conserving and strictly dissipative methods can overcome stability issues associated with standard time integration algorithms such as the Newmark method.

A novel stabilized nodal integration formulation using particle finite element method for incompressible flow analysis

AbstractIn simulations using the particle finite element method (PFEM) with node‐based strain smoothing technique (NS‐PFEM) to simulate the incompressible flow, spatial and temporal instabilities have been identified as crucial problems. Accordingly, this study presents a stabilized NS‐PFEM‐FIC formulation to simulate an incompressible fluid with free‐surface flow. In the proposed approach, (1) stabilization is achieved by implementing the gradient strain field in place of the constant strain field over the smoothing domains, handling spatial and temporal instabilities in direct nodal integration; (2) the finite increment calculus (FIC) stabilization terms are added using nodal integration, and a three‐step fractional step method is adopted to update pressures and velocities; and (3) a novel slip boundary with the predictor–corrector algorithm is developed to deal with the interaction between the free‐surface flow with rigid walls, avoiding the pressure concentration induced by standard no‐slip condition. The proposed stabilized NS‐PFEM‐FIC is validated via several classical numerical cases (hydrostatic test, water jet impinging, water dam break, and water dam break on a rigid obstacle). Comparisons of all simulations to the experimental results and other numerical solutions reveal good agreement, demonstrating the strong ability of the proposed stabilized NS‐PFEM‐FIC to solve incompressible free‐surface flow with high accuracy and promising application prospects.

Fluid Structure Interaction Using Modal Superposition and Lagrangian CFD

This study investigates the impact of fluid loads on the elastic deformation and dynamic response of linear structures. A weakly coupled modal solver is presented, which involves the solution of a dynamic equation of motion with external loads. The mode superposition method is used to find the dynamic response, utilizing predetermined mode shapes and natural frequencies associated with the structure. These essential parameters are pre-calculated and provided as input for the simulation. Integration of the weakly coupled modal solver is accomplished with the Lagrangian Differencing Dynamics (LDD) method. This method can directly use surface mesh as boundary conditions, so it is much more convenient than other meshless CFD methods. It employs Lagrangian finite differences, utilizing a strong formulation of the Navier–Stokes equations to model an incompressible free-surface flow. The elastic deformation of the structure, induced by fluid forces obtained from the flow solver, is computed within the modal coupling algorithm through direct numerical integration. Subsequently, this deformation is introduced into the flow solver to account for changes in geometry, resulting in updated flow pressure and velocity fields. The flow particles and vertices of the structure are advected in Lagrangian coordinates, resulting in Lagrangian–Lagrangian coupling in spaces with weak or explicit coupling in time. The two-way coupling between fluid and structure is successfully validated through various FSI benchmark cases. The efficiency of the LDD method is highlighted as it operates directly on surface meshes, streamlining the simulation setup. Direct coupling of structural deformation eliminates the conventional step of mapping fluid results onto the structural mesh and vice versa.

Data Fusion of Dual Foot-Mounted INS Based on Human Step Length Model.

Pedestrian navigation methods based on inertial sensors are commonly used to solve navigation and positioning problems when satellite signals are unavailable. To address the issue of heading angle errors accumulating over time in pedestrian navigation systems that rely solely on the Zero Velocity Update (ZUPT) algorithm, it is feasible to use the pedestrian's motion constraints to constrain the errors. Firstly, a human step length model is built using human kinematic data collected by the motion capture system. Secondly, we propose the bipedal constraint algorithm based on the established human step length model. Real field experiments demonstrate that, by introducing the bipedal constraint algorithm, the mean biped radial errors of the experiments are reduced by 68.16% and 50.61%, respectively. The experimental results show that the proposed algorithm effectively reduces the radial error of the navigation results and improves the accuracy of the navigation.

A Particle Swarm and Smell Agent-Based Hybrid Algorithm for Enhanced Optimization

The particle swarm optimization (PSO) algorithm is widely used for optimization purposes across various domains, such as in precision agriculture, vehicular ad hoc networks, path planning, and for the assessment of mathematical test functions towards benchmarking different optimization algorithms. However, because of the inherent limitations in the velocity update mechanism of the algorithm, PSO often converges to suboptimal solutions. Thus, this paper aims to enhance the convergence rate and accuracy of the PSO algorithm by introducing a modified variant, which is based on a hybrid of the PSO and the smell agent optimization (SAO), termed the PSO-SAO algorithm. Our specific objective involves the incorporation of the trailing mode of the SAO algorithm into the PSO framework, with the goal of effectively regulating the velocity updates of the original PSO, thus improving its overall performance. By using the trailing mode, agents are continuously introduced to track molecules with higher concentrations, thus guiding the PSO’s particles towards optimal fitness locations. We evaluated the performance of the PSO-SAO, PSO, and SAO algorithms using a set of 37 benchmark functions categorized into unimodal and non-separable (UN), multimodal and non-separable (MS), and unimodal and separable (US) classes. The PSO-SAO achieved better convergence towards global solutions, performing better than the original PSO in 76% of the assessed functions. Specifically, it achieved a faster convergence rate and achieved a maximum fitness value of −2.02180678324 when tested on the Adjiman test function at a hopping frequency of 9. Consequently, these results underscore the potential of PSO-SAO for solving engineering problems effectively, such as in vehicle routing, network design, and energy system optimization. These findings serve as an initial stride towards the formulation of a robust hyperparameter tuning strategy applicable to supervised machine learning and deep learning models, particularly in the domains of natural language processing and path-loss modeling.

An updated 3D crustal velocity model in Cyprus by non-linear traveltime tomography

We have used >6000 regional earthquakes in the broader Cyprus island area, with 100,000+ P and S-phases recorded by 26 local seismological stations to obtain a 3D velocity model for the Cyprus area using a non-linear seismic tomography approach. Due to the limited aperture of the recording network, the tomographic model mainly recovers the dominant geophysical features of the upper crust of the Cyprus island. The obtained results reveal new information on the 3D structure of the Troodos ophiolithic complex, identifying a high velocity anomaly that coincides with the NW-SE trending ophiolitic units of the Troodos mountain. Furthermore, they clearly show that the anomaly associated with the ophiolite zone of Troodos is well preserved up to a depth of at least 10 Km, dipping towards the Northeast. The Mesaoria basin in central Cyprus is recognized as a large low-velocity feature, with the results suggesting a significant thickness of the basin, exceeding 5 km. A similar low-velocity pattern can be observed for the Circum Troodos formations (Pakhna and Lefkara) to the southwest of the Troodos mountain, while the Kyrenia range is not associated with a crustal velocity anomaly. To assess the reliability of the results we have conducted checkerboard resolution tests, which suggest that the uppermost crustal features are well reconstructed, while for larger depths (>10 km) we cannot recover mid-crustal anomalies due to the insufficient traveltime data coverage and quality (e.g., traveltime picking errors).

Mechanization of a Robust Navigation Scheme for Land Applications Employing GNSS/INS Augmented with Zero Velocity Update

Mechanization of a Robust Navigation Scheme for Land Applications Employing GNSS/INS Augmented with Zero Velocity Update

Zero-Velocity Update-Based GNSS/IMU Tightly Coupled Algorithm with the Constraint of the Earth's Rotation Angular Velocity for Cableway Bracket Deformation Monitoring.

Cableways have been widely used in industrial areas, cities, and scenic spots due to their advantages, such as being a convenient mode of transportation, time-saving, labor-saving, and low cost, as well as offering environmental protection. To ensure the safe operation of a cableway, based on the characteristic that the velocity of the cableway bracket is approximately zero in a static deformation monitoring environment, a deformation monitoring method called zero velocity update (ZUPT)-based GNSS/IMU tightly coupled algorithm with the constraint of the Earth's rotation angular velocity was proposed. The proposed method can effectively solve the problem of a single GNSS being unable to output attitude, which is directly related to the status of wire ropes and cable cars. Meanwhile, ZUPT is used to restrain the Kalman filter's divergence when IMU is stationary. However, the improvements of ZUPT on attitude are not obvious, so the constraint of the Earth's rotation angular velocity was applied. The performance of the proposed method was evaluated through monitoring the cableway bracket of the Yimeng Mountain Tourism area in Shandong. Compared with the ZUPT-based GNSS/IMU tightly coupled algorithm (ZUPT-TC), the proposed method can further constrain the error accumulation of IMU while stationary and, therefore, it can provide reliable position and attitude information on cableway brackets.

THE DEVELOPMENT AND VALIDATION OF A TACTICAL GRADE EGI SYSTEM FOR LAND VEHICULAR NAVIGATION APPLICATIONS

Abstract. Over recent years, the utilization of commercially available integrated navigation systems for the development of navigation algorithms has become increasingly commonplace. Nevertheless, the wide range of sensor quality on the market complicates system customization and restricts the evolution of navigation algorithms. This study aims to address these issues by creating an affordable, tactical-grade, real-time integrated navigation system, EGI-500 (Embedded GNSS and INS), encompassing both hardware and software components. EGI-500 incorporates a tactical-grade IMU500 and a Septentrio Mosaic-X5 GNSS receiver module. The integration process is segmented into three distinct stages. The first involves hardware integration, with an illustrative architecture diagram of the real-time navigation system. Second, we focus on data preprocessing, where a cross-correlation approach is proposed to tackle multi-sensor time synchronization issues, specifically to determine potential time lags in IMU data. The final phase covers the fusion of multi-sensor data and motion constraints. The Extended Kalman Filter (EKF) forms the backbone of this part, with Zero Velocity Update (ZUPT) and Non-Holonomic Constraints (NHC) being integrated into the Loosely Coupled (LC) scheme. Furthermore, the IMU calibration process is performed to ascertain necessary algorithmic parameters. Experimental results, conducted in diverse environments (open sky, GNSS challenging, and GNSS denied), will be presented in this paper. Comparisons with reference data indicate that the navigation accuracy of the developed integrated system, both in terms of hardware and navigation algorithm, achieves expected meter-level accuracy, fulfilling the "Which Lane" and "Which Road" level criteria in varied environments. Furthermore, outcomes from the GNSS denied environment align with predictions based on propagation error theory, demonstrating the feasibility of our navigation algorithm for tactical integrated navigation systems.

A lightweight odometry network for GNSS/INS integration during GNSS outages

In challenging environments like urban canyons and tunnels, the Global Navigation Satellite System (GNSS) signal can be interrupted. When this happens, the integrated Global Navigation Satellite System/Inertial Navigation System (GNSS/INS) navigation system relies solely on INS, resulting in rapid dispersion of positioning accuracy over time. Incorporating odometer information into a filter algorithm is one potential solution for correcting INS errors and improving navigation accuracy. However, this approach increases the cost and power consumption of the system. To implement an odometer-assisted integrated navigation system without inflating cost and power consumption, we propose a lightweight odometer network, LONet. This network can emulate a wheeled odometer, determine the carrier’s forward velocity using Inertial Measurement Unit (IMU) output data, and utilize non-holonomic constraint (NHC) and zero velocity update (ZUPT) to maintain the system’s positioning accuracy. To evaluate the performance of our network, we conducted velocity estimate experiments across different velocity intervals. The results demonstrated that our network requires fewer parameters and produces lower errors in estimated velocity compared to state-of-the-art networks. Furthermore, we integrated LONet into the navigation system to mitigate the effects of GNSS signal outages. The results show that the LONet-assisted integrated navigation system achieved horizontal errors comparable to, and sometimes lower than, those obtained using a real wheeled odometer.

Present-day crustal movement and seismic moment balance on major active faults around the easternmost segment of the Kunlun fault, Tibetan Plateau, China

After the 2021 Ms 7.4 Madoi, China earthquake located south of the eastern Kunlun fault, the coseismic Coulomb stress changes show that the earthquake potential is enhanced towards the easternmost segment of the Kunlun fault. Before the 2008 Mw 7.9 Wenchuan, China earthquake, the easternmost segment of the Kunlun fault is considered to being a region with the highest frequency occurrence of moderate-to-strong earthquakes in mainland China, where there are still at least three seismic gaps at present, indicating an urgent earthquake hazard. The tectonic deformation pattern is closely related to the development and occurrence of earthquakes. In this study, we collect all the available GPS data to obtain a crustal movement velocity field with high precision and high resolution by removing nontectonic effects within the study area. The GPS velocity profile and two-dimensional strain rates are then derived from the updated GPS velocities to analysis the characteristics of crustal deformation. Our results demonstrate that the Longriba fault zone slips predominantly right-laterally with the rate of 5.2 ± 0.5 mm/yr and the crustal shortening rate is ∼0.5 mm/yr across the Longriba and Longmenshan faults. Along with notable crustal extension and contraction, the principal strain rate field is distributed in a wide area on the northwest part of the Longmenshan fault, and decreases southwestward along the Longmenshan fault zone. In addition, we provide the time series of 8 campaign GPS stations which have never been published before. Moreover, the moment deficit estimate is a well-established way of assessing the earthquake hazard at a specific fault. Accompanying with the inverted slip rates and locking depth, we estimate the rates of moment accumulation on major faults and compare them with the seismic moment released on each fault derived from the Chinese historical earthquake catalog which extends for more than 2000 years in many regions. We find that the moment deficit is mainly concentrated on the Longriba fault with a value of 4.18 × 1017 Nm/yr. The Longriba fault have accumulated enough seismic energy to generate one Mw > 7.7 earthquake on it, or two Mw > 7.5 earthquakes on its two branches in the future. This study is an essential indicator for understanding the present-day tectonic deformation pattern in the Tibetan Plateau and is also helpful for seismic hazard assessment.

Reverse time migration surface offset gathers by attribute migration and constrained least-squares inversion

Abstract Surface offset gathers (SOGs) are crucial for velocity updating in seismic data migration and muting the stretched waveform in shallow parts of migrated seismic data. Kirchhoff-based migration methods can output SOGs because they take every seismic trace as the input. As a result, the imaging results can be rearranged according to the offset value of the input data to obtain SOGs. However, regarding more accurate wave equation methods (such as reverse time migration, RTM), the SOGs cannot be obtained directly with a single migration calculation. Attribute migration is an easy-to-implement method to output SOGs of wave equation migration methods. It calculates the offset value of each imaging point by dividing the migration result modulated by the offset attribute with the conventional migration result. However, the division error may cause the calculation result outside the given offset value. This paper proposes a constrained least-squares inversion method for stable calculation of the RTM offset range. The method ensures that the calculated results are within the given offset range. We tested the method against the direct division and least-squares methods without constraints using the Marmousi model and a real 3D dataset. We show that the SOGs obtained by the constrained least-squares inversion attribute migration method had the same characteristics as those derived using the division-based attribute migration method, but they also had higher vertical resolution, better energy distribution, and improved lateral continuity. In a further study, we expect to develop a stable and direct method to efficiently calculate SOGs for RTM and an iterative closed loop for RTM velocity updating.

Frequency Stability Enhancement of Microgrid Using Optimization Techniques-Based Adaptive Virtual Inertia Control

In recent years, a sharp increase in integration of renewable energy sources (RESs) in power system network has been observed. High penetration of RES interfaced with power electronics converters-inverters with reduced or no inherent inertia compromises modern power system’s overall stability. Due to low inertia, voltage and frequency deviations far off the allowable threshold occur. To overcome this challenge, an adaptive inertia control strategy based on optimization technique is proposed. The improved particle swarm optimization (PSO) and genetic algorithm (GA) optimization techniques-based PID controller has been used to generate the appropriate virtual inertia coefficient for effective emulation of inertia in the presence of energy storage system. The conventional PSO suffers local optima stagnation, resulting in premature convergence during searching process in order to achieve global and local position. To address this issue, the velocity update equation was modified on inertia weight (w) using an additional exponential term with linear decreasing inertia weight PSO (LDIW-PSO). In this paper, exponential power is taken strategically instead of squaring it in order to reduce the number of iterations for faster convergence. Finally, a microgrid based on wind and solar energy is simulated using MATLAB/Simulink where three cases, 2% disturbance, 3% disturbance, and 4% disturbance, have been considered. Here, the evaluation of proposed system is carried out based on four main performance indices (ITAE, IAE, ISE, and ITSE). Furthermore, validation was done through hardware prototype to get experimental results in real time. The results from MATLAB simulation and experimental setup are in sync.

Multiscale ultra‐short‐term wind power prediction model based on GD‐IFEM‐PSO and VMD‐BP

AbstractWind power prediction enables advance prediction of the future capacity of wind farms to improve production, increase capacity and reduce costs, however, wind power generation data are highly unstable, making it difficult to achieve high‐precision prediction. Signal decomposition methods and optimization algorithms allow for data smoothing and optimization of parameter settings, but the limitations of parameter dependency and the slow optimization search process prevent existing research from being applied in a practical setting. To address these issues, this article proposes a multiscale ultra‐short‐term wind power prediction model based on particle swarm optimization based on greedy dynamic and integrated fitness evaluation method (GD‐IFEM‐PSO) and variational mode decomposition and back propagation network (VMD‐BP). First, this article improves the velocity update formula in the particle swarm optimization algorithm by the proposed GD weight and sets up a fitness function using multiple evaluation metrics by the proposed integrated fitness evaluation method (IFEM), so that the improved particle swarm optimization algorithm achieves high efficiency in the optimization search while ensuring the comprehensiveness of the evaluation. Second, the variable mode decomposition (VMD) decomposition algorithm is used to decompose the historical wind power data to achieve smoothing of the wind power data, and the improved particle swarm optimization algorithm is used to optimize the K and ⍺ values in the VMD decomposition algorithm to improve the comprehensive performance of the decomposition. Then, to achieve data reduction and fast model training, the components are divided into trend components, low‐frequency vibration components, high‐frequency vibration components, and random noise components according to the central frequency, so that the model can better grasp the data trend while reducing the number of components and achieving high prediction accuracy. Finally, the different components are predicted by the BP neural network and the predicted values of the different categories of components are reconstructed into the final wind power prediction values. To demonstrate the rationality and progressiveness of the proposed model, several models are compared on several data sets, and the results show that the proposed model has faster prediction speed and higher prediction performance, and is more suitable for application in real‐world environments.

GPS data analysis and geodetic velocity field investigation in Greece, 2001–2016

In this study, an updated crustal velocity field for the Greece area was estimated using a time series analysis that covers a duration of 16 years (2001–2016) from 227 Global Navigation Satellite System (GNSS) permanent stations. The GPS processing was carried out using GNSS Analysis software at MIT (GAMIT) and the velocity field expressed with respect to Eurasian plate. For the time series analysis, we applied a robust Median Interannual Difference Adjusted for Skewness trend estimator to mitigate the effects of discontinuities due to geophysical phenomena on the estimation of geodetic velocities and their uncertainties. The main earthquake events that occurred in the GPS time series analysis in the study area are analyzed, providing the co-seismic displacements in the permanent GNSS stations. We also compare our geodetic velocities with five previous publications, where we found consistency at the mm/year level, leading to reliable results for the geodynamic behavior of the Greek area, providing a dense velocity field.

Analyzing the Stability of Rock Surrounding Deep Cross-Tunnels Using a Dynamic Velocity Field

With the increasing number of deep rock engineering projects, many different types of tunnels have emerged, such as cross-tunnels. These tunnels intersect with each other in rock, which causes potential safety hazards. We must analyze the stability of the surrounding rock, to ensure worker safety. This article presents a method for dynamically assessing the stability of the surrounding rock in deep-buried cross-tunnels. The method consists of two main analysis steps: (1) P-wave velocity field inversion; and (2) Stability analysis of the surrounding rock. The P-wave velocity field inversion involves inverting the S-wave velocity field by Rayleigh wave and inverting the P-wave velocity field by adjoint state traveltime tomography. Then, a method of stability analysis is proposed which is used to update the mechanical properties of the rock (based on the continuously updated wave velocity field). The elastic modulus of the surrounding rock is approximated throughout the excavation process. CASRock V1.0 (Cellular Automation Software for engineering Rockmass fracturing processes) is used to assess rock damage via the equivalent plastic shear strain and local energy release rate. The new method is used to analyze the stability of a new tunnel excavated in Jinping (in China). The results reveal the severity and spatial distribution of the damage caused. The yield depth is concentrated near the sidewalls, while the top and bottom of the tunnel exhibit a smaller depth. The yield depths present a particular pattern of change (high–low–high–low) with increasing distance from tunnel #2. Finally, this research enriches our understanding of excavating deep cross-tunnels and makes an important contribution to improving worker safety in deep cross-tunnels.