Displacement Error Research Articles

A novel biaxial shaking table and its performance when investigating seismic actions

AbstractThe design of a new type of biaxial shaking table is presented. The shaking table is able to apply horizontal and vertical movements to models using two actuators. It is novel in that the two actuators are horizontally aligned, through its use of a scissor mechanism, and because of its compact design which permits simple anchorage to a laboratory strong floor. The scissor mechanism translates the movement of one of the actuators to a purely vertical movement at the table. The other actuator, which moves horizontally the scissor mechanism and its supports, causes the horizontal movement of the table. The horizontal and vertical movements are applied and controlled independently, individually or simultaneously. The capability of the shaking table to control and replicate a variety of uniaxial and biaxial movements is verified by conducting several shaking table experiments. This is done when the table is naked and when it supports a payload having a nonlinear dynamic response. Very good agreements between achieved and desired uniaxial and biaxial movements are attained. Rigidity of the scissor arm mechanism and connections, and preloaded roller bearings and rail blocks, are central to its success. Displacement errors, rolling, pitching and yawing of the table's top plate are negligible. The new table type is slightly more expensive than a uniaxial system, and substantially less expensive than a six degrees‐of freedom system, meaning biaxial vertical and horizontal shaking capability can now be achieved in a laboratory at reasonable cost.

Topology optimization of link mechanisms for comprehensive synthesis of component arrangement and structure using micropolar elasticity model

AbstractThis paper proposes a method for topology optimization of link mechanisms with multiple outputs, using a multi-material micropolar elasticity model. This approach allows for comprehensive optimization of both the arrangement and structure of the link mechanism components. By utilizing a continuum model that incorporates micropolar elasticity, we can specify bending stiffness independently from tensile stiffness, resulting in deformation characteristics that approximate a link mechanism. The optimization problem of designing link mechanisms for multiple outputs is reformulated as a boundary value problem within this model framework. The design goal is to synthesize a link mechanism that not only follows a desired path but also possesses the required degrees of freedom. To achieve this, the objective function is defined by the displacement error under external force and the strain energy in the links. The multi-material micropolar elasticity model is then optimized through a gradient-based optimization method, focusing on this objective function. The effectiveness and applicability of our methodology are demonstrated through several numerical case studies.

A New Model for Steam Cavity Expansion in Vertical Wells of Heavy Oil Reservoirs

Summary Steamflooding is one of the most effective and mature methods for developing heavy oil. However, existing research has not fully explained the phenomena of steam overburden and heat loss, particularly overlooking the steam velocity loss at the steam cavity front. Therefore, the condensation heat transfer coefficient (CHTC) was introduced to describe the decrease in steam velocity at the steam cavity front. A steam cavity front expansion model, considering shape factor, pseudofluidity ratio, and CHTC ratio (CHTCR), was established and validated by using mine monitoring data. The research results show that the steam cavity of the revised model is in the shape of a “funnel,” and the steam overburden phenomenon is more pronounced at the steam cavity front. Through comparison with the field data of the P6 and P612-1 well groups, it is observed that the average displacement error of the steam cavity front of the two is only 6.58%. As steam injection progresses, the steam cavity is more degraded, and the steam overburden phenomenon is more intensified compared with the initial stage. Taking into account the phenomenon of kinetic energy loss, a higher formation heat loss rate is calculated during the middle and late stages of steam injection in the modified model. The pressure gradient at the steam cavity front is analyzed to determine an optimal displacement radius of 40 m for vertical well steamflooding in heavy oil reservoirs. When parameters such as shape factor, steam injection rate, and CHTC are increased, the development shape of the steam cavity is more ideal, but the convexity of the steam cavity front is increasingly pronounced as the pseudomobility ratio increases. The CHTC was incorporated into the steam cavity expansion model, elucidating the steam overburden phenomenon and advancing the theoretical understanding of steamflooding. By improving the existing model, the analytical formula can be used to rapidly predict the position of the steam cavity front and estimate of the steam-saturated zone, even in the absence of some field data or numerical models. Practical guidance for optimizing steam injection strategies is provided, with the potential to significantly enhance the recovery of heavy oil reservoirs.

Feasibility of augmented reality using dental arch-based registration applied to navigation in mandibular distraction osteogenesis: a phantom experiment

ObjectiveDistraction osteogenesis is a primary treatment for severe mandibular hypoplasia. Achieving the ideal mandible movement direction through precise distraction vector control is still a challenge in this surgery. Therefore, the aim of this study was to apply Optical See-Through (OST) Augmented Reality (AR) technology for intraoperative navigation during mandibular distractor installation and analyze the feasibility to evaluate the effectiveness of AR in a phantom experiment.MethodsPhantom was made of 3D-printed mandibular models based on preoperative CT scans and dental arch scans of real patients. Ten sets of 3D-printed mandible models were included in this study, with each set consisting of two identical mandible models assigned to the AR group and free-hand group. 10 sets of mandibular distraction osteogenesis surgical plans were designed using software, and the same set of plans was shared between the AR and free-hand groups. Surgeons performed bilateral mandibular distraction osteogenesis tasks under the guidance of AR navigation, or the reference of the preoperative surgical plan displayed on the computer screen. The differences in angular errors of distraction vectors and the distance errors of distractor positions under the guidance of the two methods were analyzed and compared.Results40 distractors were implanted in both groups, with 20 cases in each. In intra-group comparisons between the left and right sides, the AR group exhibited a three-dimensional spatial angle error of 1.88 (0.59, 2.48) on the left and 2.71 (1.33, 3.55) on the right, with P = 0.085, indicating no significant bias in guiding surgery on both sides of the mandible. In comparisons between the AR group and the traditional free-hand (FH) group, the average angle error was 1.94 (1.30, 2.93) in the AR group and 5.06 (3.61, 9.22) in the free-hand group, with P < 0.0001, resulting in a 61.6% improvement in accuracy. The average displacement error was 1.53 ± 0.54 mm in the AR group and 3.56 ± 1.89 mm in the free-hand group, with P < 0.0001, indicating a 57% improvement in accuracy.ConclusionAugmented Reality technology for intraoperative navigation in mandibular distraction osteogenesis is accurate and feasible. A large randomized controlled trial with long-term follow-up is needed to confirm these findings.Trial RegistrationThe project has been registered with the Chinese Clinical Trial Registry, with registration number ChiCTR2300068417. Date of Registration: 17 February 2023.

STIA-DJANet: Spatial–Temporal Intention-Aware vessel trajectory prediction based on Dual-Joint Attention Network for e-navigation

Harnessing high-precision vessel trajectory prediction holds great promise for enhancing autonomous and safe navigation towards e-navigation. However, many technical researchers and maritime managers realize that only accurate prediction of vessel trajectory is insufficient, extraction and recognition of navigation intentions from vessel around is still crucial issue and gap in current prediction models. In response to solve this shortcoming, we propose an intention-aware model for vessel trajectory prediction, which leverages both of spatial–temporal intentions and dual joint attentions network, namely STIA-DJANet. First, the double intentions of spatial–temporal aware is designed to extract the social relationships between the own vessel trajectory and neighboring trajectories at each timestamp, effectively capturing dynamic changes in their interactions. Second, feature fusion of dual joint attentions for double intentions is proposed to extract navigation features from the intention-aware module, which can be integrated into trajectory prediction. In experiments, numerical results and comparisons on three real-world datasets demonstrate that our framework outperforms state-of-the-art models in terms of the average displacement error (ADE) and final displacement error (FDE) metrics. The average improvements were 42.852% and 44.726%, respectively. Reliable prediction results can significantly advance the development of e-navigation systems development.

STAFGCN:A spatial-temporal attention-based fusion graph convolution network for pedestrian trajectory prediction

Pedestrian trajectory prediction provides crucial data support for the development of smart cities. Existing pedestrian trajectory prediction methods often overlook the different types of pedestrian interactions and the micro-level spatial-temporal relationships when handling the interaction information in spatial dimension and temporal dimension. The model employs a spatial-temporal attention-based fusion graph convolutional framework to predict future pedestrian trajectories. For the different types of local and global relationships between pedestrians, it first employs spatial-temporal attention mechanisms to capture dependencies in pedestrian sequence data, obtaining the social interactions of pedestrians in spatial contexts and the movement trends of pedestrians over time. Subsequently, a fusion graph convolutional module merges the temporal weight matrix and the spatial weight matrix into a spatial-temporal fusion feature map. Finally, a decoder section utilizes TimeStacked Convolutional Neural Networks to predict future trajectories. The final validation on the ETH and UCY datasets yielded experimental results with an Average Displacement Error(ADE) of 0.34 and an Final Displacement Error(FDE) of 0.55. The visualization results further demonstrated the rationality of the model.

Electronic brake system-based hierarchical motion control of commercial vehicle for autonomous obstacle avoidance

As a high-level autonomous driving technology, efficient and safe automatic obstacle avoidance on highway is one of the critical and ongoing topics that requires in-depth research for commercial vehicles. Electronic control air pressure brake system, owing to its fast response and active braking ability, is an effective active-chassis technology to function path tracking and stability control in such condition. Yaw motion stability control problem of autonomous driving commercial vehicle based on active braking control with electronic air brake system for automatic obstacle avoidance is investigated. First, a hierarchical yaw motion dynamics control architecture is introduced after vehicle and brake system modeling. The quintic polynomial curve-based trajectory planning method and a Model Predictive Control based trajectory tracking control strategy are formulated. Second, to evade the possible stability losing issue in this circumstance, Cubature Kalman Filter (CKF) is utilized to estimate the vehicle motion states, and a fuzzy PID control-based differential brake stability control strategy is designed for the electronic brake system composed of front-and-rear two sets of dual-channel pressure regulator and ABS solenoid valve. Finally, the proposed hierarchical yaw stability control strategy for a commercial vehicle in typical obstacle avoidance conditions is comparatively verified based on the joint simulation tools. After the yaw stability control, the peak value of the lateral displacement error of trajectory tracking can be reduced by 44.7%. The yaw stability control strategy based on fuzzy PID control can reduce the yaw rate by 46%–57% and the sideslip angle by 60%–73% under different conditions. The results show that the proposed control strategy can effectively improve the yaw stability of the vehicle while avoiding obstacles at high speed.

PB-Trajectron: Physics bounded neural network for generalized trajectory prediction

Vehicle trajectory prediction is a critical technology in autonomous driving systems, as the quality of prediction directly affects downstream path planning and vehicle control. Although recent studies have shown that models combining kinematic rules with data-driven methods exhibit better interpretability in trajectory prediction, these models often adopt fixed constraint strengths, limiting their generalization ability in diverse traffic scenarios. This fixed constraint strength design restricts the model’s adaptability to different traffic environments.To address this issue, we propose PB-Trajectron, a dynamic integration mechanism that enhances the model’s prediction performance and generalization capability. PB-Trajectron is a dynamic integration mechanism that combines vehicle kinematic rules with deep learning prediction models for generalized vehicle trajectory prediction. The model integrates physics-based motion models and Deep Neural Networks (DNNs) to provide reasonable physical explanations for predicting vehicle trajectories at different speeds. First, we establish two vehicle kinematic constraints applicable to different prediction scenarios, enabling the agent to switch between these constraints based on the causal relationships between vehicle motion states to avoid generating non-physical trajectory results. Second, we propose a kinematic constraint decision framework based on velocity thresholds, which demonstrates adaptive adjustment, allowing the agent to switch tasks according to real-time state conditions and adaptively adjust the contribution of different physical constraints based on actual vehicle speeds. Finally, we investigate the advantages of PB-Trajectron in Out-of-Domain(OOD) generalization.Cross-scenario experiments on the nuScenes dataset show that, compared to previous methods, PB-Trajectron reduces the final displacement error by 7.69% when the prediction step length is 4. Furthermore, out-of-domain generalization tests on the INTERACTION dataset demonstrate that PB-Trajectron achieves a 12.23% reduction in average prediction error on datasets from different countries and scenarios compared to previous methods. The proposed mechanism can better adapt to complex and diverse traffic scenarios, laying the foundation for explainable and robust autonomous driving systems.

An Orbital-attitude Coupled Control Framework for a Full-scale Flexible Electric Solar Wind Sail Spacecraft in Orbital Transformation Missions

In this work, a novel orbital-attitude coupled control framework is developed for the electric solar wind sail (E-sail) spacecraft, aiming to handle the orbital transformation and attitude maneuver simultaneously. In the framework, the desired attitude parameters and the slow-varying voltage component are provided by the orbital control strategy, while the current attitude parameters and the fast-varying voltage component are manipulated by the attitude control strategy to approach their desired values. The orbital-attitude coupled characteristics of the E-sail spacecraft, including the flexibility-induced coupling effect, are fully described by the referenced nodal coordinate formulation. Considering the input saturation conditions, the governing equation for the orbital control strategy is then derived, in which the in-plane and out-of-plane displacement and velocity errors are prescribed as the state variables to be eliminated. An integral sliding mode control (ISMC) scheme is proposed to improve the robustness against the unmeasurable disturbance term. A model predictive control (MPC) scheme is introduced to enhance the convergence efficiency, where a quadratic optimization is performed to plan the desired attitude parameters and voltage components within the prediction horizon. To evaluate the control performance in the orbital transformation and attitude maneuver missions on the displaced non-Keplerian orbit, a series of scenarios with complex initial conditions are simulated under different control schemes, including the ISMC-MPC compound scheme. The results show that the control strategy designed under the rigid-body assumptions may not be feasible for the flexible E-sail spacecraft, while the investigated control strategy realizes the accurate and efficient convergence of the orbital and attitude variables on both the rigid and flexible E-sail spacecraft with the tether deformation stabilized.

Flow characteristics and factors affecting flow pulsation of external meshing herringbone gear pump

To enhance the outlet flow stability of the external herringbone gear pump, an analysis was conducted on the main influencing factors, key geometric parameters were identified, and a numerical model was developed for fluid analysis. A numerical model was then established for fluid analysis. The accuracy of the numerical model was verified by comparing it with experimental results, with simulation errors of displacement and volumetric efficiency being &lt; 5%, ensuring the simulation's accuracy. The simulation results indicated that the pump's head (49.7808 m) and outlet pressure (4.9285 bar) remained stable. At 700 rev/min, the simulated volumetric efficiency was 82.94%. Subsequently, the impact of helix angle, changes in center distance, and tip clearance on outlet flow stability were analyzed. The analysis revealed that increasing the helix angle from 27° to 30° could reduce flow pulsation. A slight reduction in center distance from 180.3 (δ = +0.3 mm) to 179.9 mm (δ = −0.1 mm) effectively decreased mass flow difference and outlet pressure pulsation, enhancing outlet output stability. Reducing tip clearance from 0.25 to 0.12 mm, while meeting design requirements, resulted in more stable pressure and lift output. These results ensured smooth pump operation, improved outlet output stability, and met low-flow pulsation requirements. This study offered valuable insights into the design and production of the external meshing herringbone gear pump.

Model predictive control with real-time variable weight for civil aircraft towing taxi-out control systems

Unlike the traditional method of taxying, where civil aircraft reach the runway by relying on their engines, the new mode of towing taxi-out may become preferred because of its lower energy consumption, lower emissions, and higher efficiency. To improve the tracking accuracy and lateral stability of the towing system, this study used a two-level time-varying weight control method (RMPC) based on model predictive control (MPC) and fuzzy control. The tractor speed and front wheel angle were set as the control variables in the MPC controller, and the real-time lateral displacement error and yaw angle error of the tractor were set as the fuzzy control inputs. The influence of the weight matrix on the accuracy and stability of path tracking was coordinated by online optimization of the MPC objective function weight. The simulations of multiple working conditions were performed using TruckSim software in Simulink, which showed that the proposed control method can limit the lateral displacement error of the tractor and aircraft within 0.4 m, which can be reduced by 70.83% and 77.4% compared with the single MPC, respectively. Additionally, the maximum yaw angle errors of the tractor and aircraft are reduced by 76.11% and 51.31% compared with the single MPC, respectively. Furthermore, the yaw angle error of tractors can be limited to 4° and that of aircraft can be limited to 6.5°, which is an improvement of the lateral stability and driving safety for the civil aircraft towing system. The new controller may provide technical insights and support for the practical development and safe application of the towing taxi-out mode.

Direct torque control of bearingless induction motor based on super-twisting sliding mode control

A bearingless induction motor (BIM) is an innovative magnetic levitation motor that incorporates torque system and suspension systems. Aiming to improve the anti-interference and levitation performance of the BIM, a second-order super-twisting sliding mode direct torque control strategy (STSM-DTC) is proposed. Initially, the basic principles and convergence conditions of the super-twisting algorithm are analysed. Subsequently, corresponding sliding mode surfaces are constructed according to speed, torque, and stator flux error, and the corresponding super-twisting sliding mode controllers (STSMC) are designed in the torque system. The STSMCs are designed based on the rotor radial displacement error and further enhanced by incorporating a differential loop in the suspension system. The hyperbolic tangent function tanh(x) is used as the switching function. Simulation and experimental of the BIM STSM-DTC system show that the STSM-DTC strategy effectively improves the anti-interference ability and suspension performance of the BIM, and show better dynamic response.

Dynamic analysis and shape sensing of pipes subjected to water hammer by the inverse finite element method

Pipe structures are commonly employed in modern industries. However, the transient pressure induced by water hammer leads to a high risk of structural damage, highlighting the importance of Structural Health Monitoring (SHM). The inverse Finite Element Method (iFEM) offers a way to reverse structural deformations based on a set of discrete strain data. In this paper, the water hammer phenomenon in a Reservoir-Pipe-Valve (RPV) system is investigated. The element iQS4 is adopted to reconstruct dynamic deformations for the pipe using iFEM. The water hammer resulting from an instantaneous closure of the valve can generate significant fluid pressure, leading to severe pipe vibrations. The vibration deformations can be monitored by iFEM. The maximum error of the pipe nodal displacement is below 3 % and the average error is below 2 % in the proposed several sensor location cases, even the mesh of iFEM is coarser than the FE model. Among the sparse sensor location cases, the X path which is suitable for Fiber Bragg Grating (FBG) sensors has the highest accuracy of the displacement reconstruction. The results reveal a promising prospect in the real-time monitoring based on iFEM for pipes.

GSTGM: Graph, spatial–temporal attention and generative based model for pedestrian multi-path prediction

Pedestrian trajectory prediction in urban environments has emerged as a critical research area with extensive applications across various domains. Accurate prediction of pedestrian trajectories is essential for the safe navigation of autonomous vehicles and robots in pedestrian-populated environments. Effective prediction models must capture both the spatial interactions among pedestrians and the temporal dependencies governing their movements. Existing research primarily focuses on forecasting a single trajectory per pedestrian, limiting its applicability in real-world scenarios characterised by diverse and unpredictable pedestrian behaviours. To address these challenges, this paper introduces the Graph Convolutional Network, Spatial–Temporal Attention, and Generative Model (GSTGM) for pedestrian trajectory prediction. GSTGM employs a spatiotemporal graph convolutional network to effectively capture complex interactions between pedestrians and their environment. Additionally, it integrates a spatial–temporal attention mechanism to prioritise relevant information during the prediction process. By incorporating a time-dependent prior within the latent space and utilising a computationally efficient generative model, GSTGM facilitates the generation of diverse and realistic future trajectories. The effectiveness of GSTGM is validated through experiments on real-world scenario datasets. Compared to the state-of-the-art models on benchmark datasets such as ETH/UCY, GSTGM demonstrates superior performance in accurately predicting multiple potential trajectories for individual pedestrians. This superiority is measured using metrics such as Final Displacement Error (FDE) and Average Displacement Error (ADE). Moreover, GSTGM achieves these results with significantly faster processing speeds.

Three-dimensional continuum point cloud method for large deformation and its verification

This study presents a strong form based meshfree collocation method, which is named Continuum Point Cloud Method, to solve nonlinear field equations derived from classical mechanics for deformed bodies in three-dimensional Euclidean space. The method and its implementation are benchmarked against a nonlinear vector field using manufactured solutions. The analysis of mechanical fields firstly focuses on the study of St. Venant Kirchhoff and compressible neo-Hookean materials. Results for various initial boundary value problems are presented, including benchmark cases involving unidirectional tension and simple shear. Subsequently, the study concludes with an analysis of a displacement-controlled simulation of a compressible neo-Hookean material, specifically a bar that is pulled to 50% of its original length and rotated 90°. The pure tension case yields a 1.5% error in displacement between computed and expected values and a combined tension and torsion loading case provides further insight into material behavior under complex loading conditions. The resulting normal axial and transverse stress-strain curves are also presented. Finally, the consistency and robustness of the proposed nonlinear numerical schemes are successfully demonstrated through various numerical experiments.

Development and testing of a discrete coil magnetostrictive actuator

Active combustion control (ACC) technology is an effective measure for suppressing the combustion oscillation of aero-engines. The magnetostrictive actuator is the most suitable choice for the ACC actuator due to its excellent high-frequency characteristics and high-temperature resistance. In order for the magnetostrictive actuator to produce high-frequency displacement, the constant current driver must have sufficient power, which results in a larger mass of the driver. A solution is to use multi-channel and low-power constant current driver. Therefore, the coil of the magnetostrictive actuator is axially dispersed and driven by two four-channel servo amplifiers. The driver’s mass is significantly reduced while maintaining the same electromagnetic conversion effect. In addition, an analytical model of a discrete coil magnetostrictive actuator is established, and a series of experiments are conducted. The maximum hysteresis error of output displacement at 200 Hz is reduced by 15.2%. Furthermore, under PID closed-loop control, the root mean square (RMS) error is less than 2% when tracking a 10 Hz sinusoidal displacement with coil switching drive.

Fuzzy-pid control design of biped robot based on motion capture technology

Abstract To improve the precision of the biped robot’s walking control system, a fuzzy PID controller with a variable theory domain was added to the design of the biped robot’s lower limb control system to optimize the tracking process of joint angular displacement and improve the motion effect. Firstly, the motion capture experiment is carried out to obtain the angular displacement data of the joint. The theoretical angle was calculated according to the biped robot’s lower limb diagram model and kinematics equation, and the expected trajectory was obtained by simple gait planning and using MATLAB to verify the validity of the angle parameters. Then the fuzzy PID controller of the lower limb joint was established, and the variable theory domain fuzzy controller was established by introducing the expansion factor. Finally, the Simulink test bench is built to simulate the two controllers, and the expected data and simulation data are compared. The results show that the error range of the variable theory domain fuzzy controller is only ±2°, and the variable theory domain adaptive fuzzy controller can accurately track the desired trajectory, reduce the joint angular displacement error of the biped robot, ensure the precision and stability of the biped robot motion, and basically meet the requirements of practical production.

Theoretical and experimental investigations on a data-driven trajectory planning scheme for dynamic shape control of piezo-actuated compliant morphing structures

Piezo-actuated compliant morphing structures can transmit motion and force via elastic deformation with lower weight, simplified design, and higher accuracy, a typical example is the variable camber wing. However, the rapid shape change of compliant structures is a challenging control problem because it often results in a high level of vibration due to the structural flexibility necessary to achieve the morphing requirement. This study presents a model-free data-driven trajectory planning approach based on spline curves and surrogate-based optimization (SBO) to obtain smooth “rest-to-rest” morphing trajectories. The macro-fiber composite (MFC) patches are used for piezoelectric actuators to generate elastic deformation. The flexible beam and variable camber wing are used for both linear numerical simulation and experimental tests with various nonlinearities and uncertainties. An optimization criterion is proposed to minimize both transient and residual vibrations during the “rest-to-rest” motion. An extraordinarily terminal displacement error function is added to eliminate the effects of the hysteresis and creep of the actuator. The control inputs, i.e., voltage profiles for the MFCs, are defined using cubic spline curves via only a few control points. Then, the optimization problem is solved by employing a Kriging surrogate model-based algorithm integrated with the expected improvement (EI) infilling-sampling criterion, which constructs an efficient algorithm similar to reinforcement learning. The optimal morphing trajectories can be highly efficiently obtained by using only 4 control points and less than 150 samplings. The experimental results of both the plate model and the variable camber wing model show that the proposed method can not only achieve a smooth dynamic morphing trajectory with minimized vibration but also automatically compensate for hysteresis and creep. The proposed method provides an effective means for the rapid realization of an optimized morphing trajectory for compliant morphing structures.

Investigation on the biaxial tensile testing method for metal foil using cruciform specimen

The assessment of mechanical properties of metal foil under complicated stress states poses a considerable challenge, requiring the development of new testing methods and the optimization of new specimen geometry. In this research, the biaxial tensile method and specimen shape were designed and optimized by using simulation and experiment. It is determined that the strain measurement area can be suggested as the central area of 0.6 to 0.8 times the arm width. The influence of different parameters on the tensile results of cruciform specimens was comprehensively evaluated by finite element method and multi-factor analysis. The results indicate that the number of slits markedly impacts the stress–strain uniformity and shear stress in the central region, followed by the slit length. The effect of the arm width and the slit width is comparable, more influential than the corner radius. According to the analyzed results and application requirements, a four-axis independently driven biaxial tensile test machine for small scale samples was fabricated. During the biaxial tension, the center point offset of the specimen remains within ±0.01 mm. The displacement and load synchronization errors do not exceed 0.01 mm and 50 N, respectively, facilitating the precise control of four-axis synchronization. Conclusively, cruciform specimens featuring diverse geometric characteristics were designed for industrial pure titanium, 304 stainless steel, and Inconel 718 superalloy with thickness of less than 0.3 mm. The biaxial tensile tests were performed to delineate the yield loci, revealing notable anisotropy and size effect. The validation confirms the suitability of the testing method and optimized cruciform specimens for conducting biaxial tensile mechanical properties testing on metal foils characterized by diverse types and thicknesses.

Simultaneous Coherent and Displacement Compounding for 2-D Noninvasive Carotid Strain Imaging: A Proof of Principle Study.

Arteriosclerosis results from lipid buildup in artery walls, leading to plaque formation, and is a leading cause of death. Plaque rupture can cause blood clots that might lead to a stroke. Distinguishing plaque types is a challenge, but ultrasound (US) elastography can help by assessing plaque composition based on strain values. Since the artery has a circular structure, an accurate axial and lateral displacement strategy is needed to derive the radial and circumferential strains. A high-precision lateral displacement is challenging due to the lack of phase information in the lateral direction of the beamformed RF data. Previously, our group has developed a compounding technique in which the lateral displacement is estimated using triangulation of the axial displacement estimated from transmitting and beamforming US beams at ±20°. However, transmitting with a single plane wave will reduce signal-to-noise and contrast-to-noise ratio as well as lateral resolution. In this article, we combine our displacement compounding with coherent compounding. Instead of transmitting a single plane wave, multiple plane waves are transmitted at certain angles centered on the angle of the beamforming grids, and then, the backscattered wavefronts are beamformed and coherently compounded on the center of the transmit beams (-20°, +20°, and 0°). The numerical investigation using the GE9LD probe ( f0 = 5.32 MHz, pitch = 230 μ m, and width = 43.9 mm) led us to 19 plane waves spanning angles within -10° to 10° (with respect to center of the transmit beams), resulting in a total of 57 plane wave transmit (for three beamforming grids at 0° and ±20°). FIELD II simulations of a cylindrically shaped phantom (mimicking the carotid artery) at a signal-to-noise ratio (SNR) ≥ 20 dB show that the proposed method decreases the root-mean-square error (RMSE) of the lateral displacement and strain estimations by 40% and 45% compared to the previous method, respectively. The results of our experiments with a carotid artery phantom [made out of 10% polyvinyl alcohol (PVA)] show that the proposed method provides strain images with higher quality and more in agreement with the theory, with 26% lower standard deviation, especially at the peak systolic phase. The proposed method paves the path toward improved quality in vivo 2-D strain imaging using our displacement compounding technique and translating it to 3-D with a row-column array.