High Computational Efficiency Research Articles

Elastic reverse time migration based on nested triangular mesh in 2D isotropic media

Abstract Reverse time migration (RTM) based on two-way wave equation is an important imaging tool, which has been widely used in exploration geophysics. It offers distinct advantages in handling complex geological structures. Moreover, elastic reverse time migration (ERTM) can produce more physically meaningful images for subsurface and has received increasing attention in recent years. However, rugged topography presents challenges in the reconstruction of subsurface structures for ERTM. To overcome this problem, we introduce the grid method for topography ERTM, which is an unstructured mesh based algorithm. However, the conventional gird method for RTM is implementing by discretizing model into small meshes, leading to high computational cost. To address this problem, we introduce the grid method based on nested unstructured meshes to implement ERTM with complex surface topography. Low-order small meshes, due to their fine scale, can accurately depict complex surface topography. However, their generation process is relatively time-consuming. In contrast, high-order large meshes contain many similar small meshes internally, which can be processed in parallel, resulting in higher computational efficiency. Therefore, we propose the following strategy: for the receiver wavefield, several layers on surface discreted by the small meshes are used to place receivers and remaining layers discreted by the large meshes to improve computational efficiency. For the source wavefield, only the large meshes are used because the spacing of shot is relatively large. In this way, we ensure the accurate description of complex surface topography for the implementation of ERTM with high computational efficiency. Finally, the effectiveness of our method is validated through experiments on three models with complex topography.

A shortest‐path‐aided fast‐sweeping method to improve the accuracy of traveltime calculation in vertically transverse isotropic media

AbstractThe high accuracy and efficiency of traveltime calculation are critical in seismic tomography, migration, static corrections, source locations and anisotropic parameter estimation. The fast‐sweeping method is an efficient upwind finite‐difference approach for solving the eikonal equation. However, the fast‐sweeping method is accurate only along the axis directions. In two‐dimensional or higher dimensional cases, the accuracy is severely decreased in the diagonal directions due to the numerical errors in these directions. These similar numerical errors also arose in higher order fast‐sweeping method and anisotropic fast‐sweeping method. To improve the accuracy of traveltime calculation in two‐dimensional or higher dimensional space, a shortest‐path‐aided fast‐sweeping method is proposed. The shortest‐path‐aided solution is embedded into the sweeping process of the standard fast‐sweeping method to improve the traveltime accuracy in the diagonal directions. Shortest‐path‐aided fast‐sweeping method is very easy to implement nearly without additional computational cost and memory consumption. Furthermore, this method is easy to extend from two‐dimensional to higher dimensional, from low‐order to higher‐order and from isotropic to anisotropic cases.

Chemical Gas Source Localization with Synthetic Time Series Diffusion Data Using Video Vision Transformer

Gas source localization is vital in emergency scenarios to enable swift and effective responses. In this study, we introduce a gas source localization model leveraging the video vision transformer (ViViT). Utilizing synthetic time series diffusion data, the source grid is predicted by classifying the grid with the highest probability of gas occurrence within the diffusion data coverage. Through extensive experimentation using the NBC-RAMS simulator, we generate large datasets of gas diffusion under varied experimental conditions and meteorological environments, enabling comprehensive model training and evaluation. Our findings demonstrate that the ViViT outperforms other deep learning models in processing time series gas data, showcasing a superior estimation performance. Leveraging a transformer architecture, the ViViT exhibits a robust classification performance even in scenarios influenced by weather conditions or incomplete observations. Furthermore, we conduct an analysis of accuracy and parameter count across various input sequence lengths, revealing the ability of the ViViT to maintain high computational efficiency while achieving accurate source localization. These results underscore the effectiveness of the ViViT as a model for gas source localization, particularly in situations demanding a rapid response in real-world environments, such as gas leaks or attacks.

A computational efficient approach for distributionally robust unit commitment with enhanced disjointed layered ambiguity set

AbstractTo achieve the sustainable development of the society, renewable energy dominated power systems are gradually formed. However, the uncertainty of renewable power poses challenges for power system operations, such as balancing the load and generation in day‐ahead unit commitment problems. To address this issue, an enhanced disjointed layered ambiguity set is proposed in this paper to effectively capture the uncertainty of renewable generation forecast errors. On this basis, a two‐stage distributionally robust unit commitment optimization problem is formulated, which is computational challenge. To this end, a novel reformation approach and a worst‐case support set identification method are proposed to derive the optimal solution in a computationally efficient way. Simulation results demonstrate that the proposed ambiguity set brings lower operation costs of unit commitment while maintaining similar reliability compared to existing methods. In detail, the proposed ambiguity set achieves a reduction in operating costs of approximately 10.01%. The proposed novel reformation approach and solution method are also shown to have higher computation efficiency than the existing Benders decomposition method, resulting in a reduction in computation time to less than 3.78% of the original duration.

Analytical solution for forced vibration response of rectangular thin plates attached by straight and curved acoustic black hole beams based on symplectic and impedance method

In recent years, due to the excellent vibration reduction performance of the acoustic black hole (ABH), its application in engineering has become increasingly widespread. This paper proposes an analytical method which combines the symplectic method with the impedance method, for solving the forced response of the rectangular thin plates attached by the straight and curved ABH beams. The ABH beams and plate are connected by a short bar. Firstly, the impedance method is used to obtain the dynamic stiffness of the coupling end of the ABH beam. Secondly, the symplectic method is used to obtain analytical waves of the plates. By utilizing the relationship between force and displacement at plate-beam junction, the dynamic stiffness of the plate at the coupling point can be obtained. Finally, based on wave propagation analysis, the forced vibration response of the hybrid system are obtained. The numerical examples compared the calculation results of this method with the finite element method. The results show that the proposed method can effectively predict the forced response of the hybrid system considered in this paper. Then, the influence of the relative position between the coupling point and the excitation point on the vibration reduction effect was analyzed. This method is analytical, with accurate results and high computational efficiency.

A user-friendly software package for modelling gravimetric geoid by the classical Stokes-Helmert method

AbstractWith the progress in Global Navigation Satellite Systems (GNSS) technology, accurate geoid modelling has started to play an essential role in geodetic applications such as establishing height datum as a continuous surface model and related vertical control for infrastructure projects. Thus, numerous geoid modelling methods have been offered since 1990’s, each of them has its own algorithm and approximation theories. Classical Stokes-Helmert is one of the most well-known methods all over the world by geodetic communities. However, a user-friendly software package of the method is not publicly accessible on the Internet. Therefore, a compact and user-friendly software package “CSHSOFT” is developed and presented for scholars in this field. A fractionated programming strategy has been treated to build individual components striving high accuracy and computational efficiency for geoid heights. Subsequently, the CSHSOFT is simply tested to construct a geoid model in the mountainous area in Auvergne test-bed where several geoid modelling techniques are implemented. Afterward, the new geoid model of the region is externally evaluated by GNSS-levelling data in terms of rigorous orthometric heights. The fitting statistics of 2.75 cm and 0.36 ppm in absolute and relative height differences fairly indicate that the CSHSOFT is a vigorous tool for gravimetric geoid modelling, and can be comfortably employed for geoscientific and technical studies.

Dynamic phase-differencing profilometry with number-theoretical phase unwrapping and interleaved projection

High-speed 3D measurement is receiving increasing attention. However, simultaneously achieving high computational efficiency, algorithmic robustness, and reconstructing ratio is challenging. Therefore, a dynamic phase-differencing profilometry (DPDP) is proposed. By capturing the minimum three phase-shifting sinusoidal deformed patterns and establishing a brand-new model, the phase difference between the object on the reference plane and the reference plane is directly resolved to effectively improve computational efficiency. Although it is wrapped, by using only two auxiliary complementary gratings with a purposely designed lower frequency, a DPDP-based number-theoretical temporal phase unwrapping (NT-TPU) algorithm is also proposed to unwrap the wrapped phase difference rather than the phase itself with high robustness. Furthermore, compared to existing PSP-based NT-TPU, the proposed NT-TPU can normally work under more relaxed restrictions. In order to accomplish a high reconstructing ratio, a pentabasic interleaved projection (PIP) strategy based on time division multiplexing is proposed. It can improve the reconstructing ratio from one reconstruction per every five patterns to an equivalent of one reconstruction per every 1.67 patterns. Experimental results demonstrate that the proposed method achieves high computational efficiency, high algorithmic robustness, and high reconstructing ratio simultaneously and has prospective application in high-speed 3D measurement.

A novel method for rapid estimation of active bone marrow dose for radiotherapy patients in epidemiological studies.

In a dedicated effort to improve the assessment of clonal hematopoiesis (CH) and study leukemia risk following radiotherapy, we are developing a large-scale cohort study among cancer patients who received radiation. To that end, it will be critical to analyze dosimetric parameters of red bone marrow (ABM) exposure in relation to CH and its progression to myeloid neoplasms, requiring reconstruction method for ABM doses of a large-scale patients rapidly and accurately. To support a large-scale cohort study on the assessment of clonal hematopoiesis and leukemia risk following radiotherapy, we present a new method for the rapid reconstruction of ABM doses of radiotherapy among cancer patients. The key idea of the presented method is to segment patient bones rapidly and automatically by matching a whole-body computational human phantom, in which the skeletal system is divided into 34 bone sites, to patient CT images via 3D skeletal registration. The automatic approach was used to segment site-specific bones for 40 radiotherapy patients. Also, we segmented the bones manually. The bones segmented both manually and automatically were then combined with the patient dose matrix calculated by the treatment planning system (TPS) to derive patient ABM dose. We evaluated the performance of the automatic method in geometric and dosimetric accuracy by comparison with the manual approach. The pelvis showed the best geometric performance [volume overlap fraction (VOF): 52% (mean) with 23% (σ) and average distance (AD): 0.8cm (mean) with 0.5cm (σ)]. The pelvis also showed the best dosimetry performance [absorbed dose difference (ADD): 0.7Gy (mean) with 1.0Gy (σ)]. Some bones showed unsatisfactory performances such as the cervical vertebrae [ADD: 5.2Gy (mean) with 10.8Gy (σ)]. This impact on the total ABM dose, however, was not significant. An excellent agreement for the total ABM dose was indeed observed [ADD: 0.4Gy (mean) with 0.4Gy (σ)]. The computation time required for dose calculation using our method was robust (about one minute per patient). We confirmed that our method estimates ABM doses across treatment sites accurately, while providing high computational efficiency. The method will be used to reconstruct patient-specific ABM doses for dose-response assessment in a large cohort study. The method can also be applied to prospective dose calculation within a clinical TPS to support clinical decision making at the point of care.

Optimization of BLDC-based electric vehicles: Vehicle dynamics modelling through dual-motor approach and designing a novel augmented TLBO algorithm for PID control

The work primarily focuses on increasing the efficiency of EV drive in electric two-wheeler by working on several aspects, such as modulating the vehicle’s design, optimizing the control strategy, and increasing the speed range using a dual-motor approach. The dynamics of electric two-wheeler have been discussed with a mathematical vehicle model and further tuning of several aspects. Besides, this paper also introduces a novel Augmented Teaching and Learning based Optimization (ATLBO) technique designed exclusively to control BLDC motors for the electric two-wheeler vehicle. Besides, the designed technique has been implemented for the widely used commercial e-bike of Hero Company. Most two-wheeler electric motors are mounted on the rear side of the wheel, which has a limited speed range. Therefore, an analysis has been performed to increase the vehicle’s speed range using a dual motor, from 45 km hr−1 to 62 km hr−1, proving to be a viable alternative to a single motor generally used in an electric bike. ATLBO technique has been designed against a conventional TLBO to optimize the proportional-integral-derivative (PID) controller for the speed control of a linear brushless DC (BLDC) motor. The proposed method has several advantages, including ease of implementation, a consistent convergence characteristic, and high computational efficiency. Furthermore, the literature has validated the merits of the presented novel control technique. The only disadvantage of using a dual motor is the initial cost, but the overall cost is moderated in the long-term usage for its augmented performance parameters. The performance parameters of the above technique are analyzed against other optimization techniques like conventional Teaching and Learning based optimization (TLBO), Particle Swarm Optimization (PSO). MATLAB/Simulink models the brushless DC motor and implements ATLBO, TLBO, and PSO algorithms. It has been found that the response obtained from ATLBO is comparatively much faster than other optimization techniques, which supports the motor for quick acceleration as well as more efficient in improving the step response characteristics such as rise time, settling time, and steady-state error in the speed control of a linear BLDC motor.

MocapMe: DeepLabCut-Enhanced Neural Network for Enhanced Markerless Stability in Sit-to-Stand Motion Capture.

This study examined the efficacy of an optimized DeepLabCut (DLC) model in motion capture, with a particular focus on the sit-to-stand (STS) movement, which is crucial for assessing the functional capacity in elderly and postoperative patients. This research uniquely compared the performance of this optimized DLC model, which was trained using 'filtered' estimates from the widely used OpenPose (OP) model, thereby emphasizing computational effectiveness, motion-tracking precision, and enhanced stability in data capture. Utilizing a combination of smartphone-captured videos and specifically curated datasets, our methodological approach included data preparation, keypoint annotation, and extensive model training, with an emphasis on the flow of the optimized model. The findings demonstrate the superiority of the optimized DLC model in various aspects. It exhibited not only higher computational efficiency, with reduced processing times, but also greater precision and consistency in motion tracking thanks to the stability brought about by the meticulous selection of the OP data. This precision is vital for developing accurate biomechanical models for clinical interventions. Moreover, this study revealed that the optimized DLC maintained higher average confidence levels across datasets, indicating more reliable and accurate detection capabilities compared with standalone OP. The clinical relevance of these findings is profound. The optimized DLC model's efficiency and enhanced point estimation stability make it an invaluable tool in rehabilitation monitoring and patient assessments, potentially streamlining clinical workflows. This study suggests future research directions, including integrating the optimized DLC model with virtual reality environments for enhanced patient engagement and leveraging its improved data quality for predictive analytics in healthcare. Overall, the optimized DLC model emerged as a transformative tool for biomechanical analysis and physical rehabilitation, promising to enhance the quality of patient care and healthcare delivery efficiency.

Cell deformability drives fluid-to-fluid phase transition in active cell monolayers.

Cell deformability is an essential determinant for tissue-scale mechanical nature, such as fluidity and rigidity, and is thus crucial for tissue homeostasis and stable developmental processes. However, large-scale simulations of deformable cells have been restricted to those of polygonal-shaped cells, limiting our understanding of populations of arbitrarily deformable cells, such as mesenchymal, amoeboid cells, and nonconfluent epithelial cells. Here, we present an efficient approach for simulating large populations of nonpolygonally deformable cells with considerably higher computational efficiency than existing methods. Using the method, we demonstrate that the densely packed active cell population interacting via excluded volume interactions exhibits a fluid-to-fluid transition. An experimentally measurable index of topological defects, defined using the number of neighboring cells, is also proposed to characterize this transition. This study provides a flexible approach to tissue-scale cell population and a broader perspective on the biological fluid phases.

Efficient pulse sequence design framework for high-dimensional MR fingerprinting scans using systematic error index.

For effective optimization of MR fingerprinting (MRF) pulse sequences, estimating and minimizing errors from actual scan conditions are crucial. Although virtual-scan simulations offer an approximation to these errors, their computational demands become expensive for high-dimensional MRF frameworks, where interactions between more than two tissue properties are considered. This complexity makes sequence optimization impractical. We introduce a new mathematical model, the systematic error index (SEI), to address the scalability challenges for high-dimensional MRF sequence design. By eliminating the need to perform dictionary matching, the SEI model approximates quantification errors with low computational costs. The SEI model was validated in comparison with virtual-scan simulations. The SEI model was further applied to optimize three high-dimensional MRF sequences that quantify two to four tissue properties. The optimized scans were examined in simulations and healthy subjects. The proposed SEI model closely approximated the virtual-scan simulation outcomes while achieving hundred- to thousand-times acceleration in the computational speed. In both simulation and in vivo experiments, the optimized MRF sequences yield higher measurement accuracy with fewer undersampling artifacts at shorter scan times than the heuristically designed sequences. We developed an efficient method for estimating real-world errors in MRF scans with high computational efficiency. Our results illustrate that the SEI model could approximate errors both qualitatively and quantitatively. We also proved the practicality of the SEI model of optimizing sequences for high-dimensional MRF frameworks with manageable computational power. The optimized high-dimensional MRF scans exhibited enhanced robustness against undersampling and system imperfections with faster scan times.

Modelling of high-speed engine flows using a space-marching method

A computationally efficient mathematical model was developed to analyze high-speed engine flows. The inlet and nozzle flows were modelled using the space-marching method to automatically solve the shock reflection and nozzle plume flow. The combustor flow was treated using a quasi-one-dimensional model that considered the rise in pressure of the isolator owing to the shock train. The resulting model was compared with the experimental results. Three test cases were used to validate the model's accuracy: 1) a hydrogen-fuelled combustor experiment, 2) an integrated inlet/combustor configuration experiment, and 3) a single-expansion-ramp nozzle flow experiment. The results showed that the space-marching method predicted the pressure profiles of the inlet flow and nozzle plume flow with reasonable accuracy. The computational time for the inlet and nozzle flows merely takes several minutes on a CPU with 3.6 GHz. The quasi-one-dimensional model calculated the fuel ignition and pressure rise in the combustor with a high computational efficiency of several seconds. The integration of the space-marching method and quasi-one-dimensional method can be developed as a powerful tool for fast evaluations of high-speed engine performance.

RGB‐D road segmentation based on cross‐modality feature maintenance and encouragement

AbstractDeep images can provide rich spatial structure information, which can effectively exclude the interference of illumination and road texture in road scene segmentation and make better use of the prior knowledge of road area. This paper first proposes a new cross‐modal feature maintenance and encouragement network. It includes a quantization statistics module as well as a maintenance and encouragement module for effective fusion between multimodal data. Meanwhile, for the problem that if the road segmentation is performed directly using a segmentation network, there will be a lack of supervised guidance with clear physical meaningful information and poor interpretability of learning features, this paper proposes two road segmentation models based on prior knowledge of deep image: disparity information and surface normal vector information. Then, a two‐branch neural network is used to process the colour image and the processed depth image separately, to achieve the full utilization of the complementary features of the two modalities. The experimental results on the KITTI road dataset and Cityscapes dataset show that the method in this paper has good road segmentation performance and high computational efficiency.

Ultrasensitive textile strain sensors redefine wearable silent speech interfaces with high machine learning efficiency

This work introduces a silent speech interface (SSI), proposing a few-layer graphene (FLG) strain sensing mechanism based on thorough cracks and AI-based self-adaptation capabilities that overcome the limitations of state-of-the-art technologies by simultaneously achieving high accuracy, high computational efficiency, and fast decoding speed while maintaining excellent user comfort. We demonstrate its application in a biocompatible textile-integrated ultrasensitive strain sensor embedded into a smart choker, which conforms to the user’s throat. Thanks to the structure of ordered through cracks in the graphene-coated textile, the proposed strain gauge achieves a gauge factor of 317 with <5% strain, corresponding to a 420% improvement over existing textile strain sensors fabricated by printing and coating technologies reported to date. Its high sensitivity allows it to capture subtle throat movements, simplifying signal processing and enabling the use of a computationally efficient neural network. The resulting neural network, based on a one-dimensional convolutional model, reduces computational load by 90% while maintaining a remarkable 95.25% accuracy in speech decoding. The synergy in sensor design and neural network optimization offers a promising solution for practical, wearable SSI systems, paving the way for seamless, natural silent communication in diverse settings.

Distributed identification based partially-coupled recursive generalized extended least squares algorithm for multivariate input–output-error systems with colored noises from observation data

System identification determines the model of the plant from the measurement data and has been widely used in the prediction and control. In this paper, the parameter estimation problem is studied for multivariate equation-error systems with autoregressive moving average noises. Since the considered system is high-dimensional, the distributed identification is considered in this paper. The subsystems are obtained by decomposing the original system in accordance with the number of the outputs. However, the subsystems contain the same parameter vector, resulting in many redundant estimates. By taking the average of the parameter estimation vectors, we develop a partially-coupled subsystem recursive generalized extended least squares (PC-S-RGELS) algorithm to cut down the redundant parameter estimates. In consideration of the information communication between the subsystems and the convergence of the estimation algorithm, a partially-coupled RGELS (PC-RGELS) algorithm is presented by means of the coupling identification concept. Compared with the multivariate RGELS algorithm, the two algorithms have higher computational efficiencies. Finally, an illustrative example is provided to demonstrate the effectiveness of the two proposed algorithms.

Dynamic Analysis of an FGM Beam Undergoing Large Overall Motion in Temperature Field

The dynamic analysis of a functionally gradient material (FGM) beam undergoing large overall motion based on meshless methods is studied in the variable temperature field environment. Considering the high-order terms of nonlinear coupling deformation which were often ignored in previous studies, the high-order rigid–flexible coupled (HOC) dynamic model of a rotating FGM beam with a lumped mass in a temperature field is established by employing Lagrange’s equations of the second kind. Compared with the first-order approximate coupled (FOAC) dynamic model, the HOC dynamic model is more accurate and has a wider scope of application. The validity of the point interpolation (PIM) method and radial point interpolation method (RPIM) in this paper is verified by comparison with simulation results of the assumed mode method (AMM) and the finite element method (FEM). On this basis, the factors affecting the dynamic characteristics of the FGM beam such as the form of temperature field, the functionally gradient index, and the location of added lumped mass are discussed. In this paper, the meshless method with higher computational efficiency and the HOC dynamic model with more accurate results are adopted. This study will provide guidance and reference for dealing with problems in engineering, machinery, aerospace, and other fields in complex environment.

A new highly accurate and efficient pure visco‐acoustic wave equation for tilted transversely isotropic attenuating media

AbstractThe propagation of seismic waves in attenuating anisotropic media exhibits amplitude dissipation and phase dispersion. To describe its effects, the fractional Laplacian pure visco‐acoustic wave equations capable of producing stable and noise‐free wavefields have been derived. However, except for acoustic approximation, previous wave equations utilize the approximations with lower accuracy in simplifying the denominator of the approximate complex‐valued dispersion relation, resulting in reduced accuracy. To address this concern, we use a combination of complex stiffness coefficients to replace the denominator term of the approximate complex‐valued dispersion relation. This approximation effectively reduces the loss of accuracy caused by ignoring the influence of the velocity anisotropy parameter ε and the attenuation anisotropy parameter εQ in the denominator term, leading to a wave equation with high accuracy in media with large anisotropic parameters ε and δ. In addition, the new wave equation only contains two high‐order spatial partial derivatives and has high computational efficiency. Theoretical analysis and numerical examples demonstrate that the proposed pure visco‐acoustic tilted transversely isotropic wave equation outperforms the previous pure visco‐acoustic wave equation in terms of simulation accuracy. The newly developed wave equation is well suited for the application of Q‐compensated reverse time migration and full waveform inversion in attenuating anisotropic media.

High-order residual moveout correction with global optimization in local time windows

Residual moveout (RMO) correction is significant for optimizing the common image gathers (CIGs) and migration stacked sections, which is a vital step in seismic data processing. The conventional RMO correction methods flatten the migrated gathers by inverse normal moveout and then pick up the velocity parameters, which require high labor of manual picking with low efficiency. The existing high-order RMO correction methods by scanning technology need a bispectral picking process. To address these issues, we propose a novel high-order RMO correction method based on a crosscorrelation-based objective function with global optimization in local time windows. The selected time windows covering the reflected events in the stacked section are used for parameter estimation. Then the very fast simulated annealing (VFSA) algorithm is used to simultaneously invert the two effective parameters (migration velocity and anellipticity anisotropic parameter) with the local CIGs in the time window, which has relatively high computational efficiency. The Hess model example test results show that the proposed method can effectively deal with the RMO problem in the case of anisotropic media, and the developed high-order RMO correction based on anisotropic assumption significantly improved the imaging performance compared to the conventional isotropic RMO correction methods, especially for steep structures. The application to a real 3D land data set further confirms the effectiveness and practicability of the proposed method.

Composite continuum robots: Accurate modeling and model reduction

Models of continuum robots often trade off accuracy and speed. The constant curvature assumption model can perform fast calculations but with poor accuracy. Static models can obtain good calculation accuracy but with slower computation speed. In this paper, a precise and efficient method for establishing a non-constant curvature kinematic model for composite continuum robots is proposed. First, an algorithm based on the Beam Constraint Model is proposed to establish the static model of the continuum robot. The situation in which friction changes gradually in continuum robots is considered in the static model. Then, the Kepler elliptic curve is used to simplify the static model to build a non-constant curvature kinematic model of the continuum robot. Then, complex inverse kinematics solutions are transformed into explicit sets of equations by mathematical transformation. Finally, simulations and experiments are designed to demonstrate the algorithm proposed in this paper. The simulation results show that the proposed algorithm is 1572 times faster than the Levenberg–Marquardt algorithm. The experimental results show that the average error of the static model is 0.065 mm, accounting for 0.13% of its length. The maximum error is 0.309 mm, accounting for 0.618% of its length. The positioning accuracy of the non-constant curvature model proposed in this paper is 2.02 times that of the constant curvature model. The results show that the simplified kinematic model algorithm based on the static model has high accuracy and computational efficiency. This research is crucial for the practical application of continuum robots in engineering.