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Search Results (784)

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17 pages, 1495 KiB  
Article
Assisting Standing Balance Recovery for Parkinson’s Patients with a Lower-Extremity Exoskeleton Robot
by Chi-Shiuan Lee, Lo-Ping Yu, Si-Huei Lee, Yi-Chia Chen and Chun-Ta Chen
Sensors 2024, 24(23), 7498; https://doi.org/10.3390/s24237498 (registering DOI) - 24 Nov 2024
Viewed by 378
Abstract
Parkinson’s disease (PD) is a neurodegenerative disorder and always results in balance loss. Although studies in lower-extremity exoskeleton robots are ample, applications with a lower-extremity exoskeleton robot for PD patients are still challenging. This paper aims to develop an effective assistive control for [...] Read more.
Parkinson’s disease (PD) is a neurodegenerative disorder and always results in balance loss. Although studies in lower-extremity exoskeleton robots are ample, applications with a lower-extremity exoskeleton robot for PD patients are still challenging. This paper aims to develop an effective assistive control for PD patients with a lower-extremity exoskeleton robot to maintain standing balance while being subjected to external disturbances. When an external force is applied to participants to force them to lose balance, the hip strategy for balance recovery based on the zero moment point (ZMP) metrics is used to generate a reference trajectory of the hip joint, and then, a model-free linear extended state observer (LESO)-based fuzzy sliding mode control (FSMC) is synthesized to regulate the human body to recover balance. Balance recovery trials for healthy individuals and PD patients with and without exoskeleton assistance were conducted to evaluate the performance of the proposed exoskeleton robot and balance recovery strategy. Our experiments demonstrated the potential effectiveness of the proposed exoskeleton robot and controller for standing balance recovery control in PD patients. Full article
(This article belongs to the Special Issue Challenges and Future Trends of Wearable Robotics2nd Edition)
22 pages, 4028 KiB  
Article
Longitudinal Motion System Identification of a Fixed-Wing Unmanned Aerial Vehicle Using Limited Unplanned Flight Data
by Nuno M. B. Matos and André C. Marta
Aerospace 2024, 11(12), 959; https://doi.org/10.3390/aerospace11120959 - 21 Nov 2024
Viewed by 366
Abstract
Acquiring knowledge of aircraft flight dynamics is crucial for simulation, control, mission performance and safety assurance analysis. In the fast-paced UAV market, long flight testing campaigns are hard to achieve, leaving limited controlled flight data and a significant amount of unplanned flight data. [...] Read more.
Acquiring knowledge of aircraft flight dynamics is crucial for simulation, control, mission performance and safety assurance analysis. In the fast-paced UAV market, long flight testing campaigns are hard to achieve, leaving limited controlled flight data and a significant amount of unplanned flight data. This work delves into the application of system identification techniques on unplanned flight data when faced with a shortage of dedicated flight test data. Based on a medium-sized, fixed-wing UAV, it focuses on the system identification of longitudinal dynamics using structural routine flight test data of pitch down and pitch up manoeuvres with no specific guidelines for the control inputs given. The proposed solution uses first- and second-order parameter-based models to build a non-linear dynamic model which, using a least square error optimisation algorithm in a time domain formulation, has its parameters tuned to converge the model behaviour with the real aircraft dynamics. The optimisation uses a combination of pitch, altitude, airspeed and pitch rate responses as a measure of model accuracy. Very significant improvements regarding the UAV model response are found when trimmed flight manoeuvres are used, resulting in proper estimation of important aerodynamic and control derivatives. Pitching moment and control derivatives are shown to be the crucial parameters. However, difficulties in estimation are shown for untrimmed flight manoeuvres. Better results were obtained when using multiple manoeuvres simultaneously in the optimisation error metric, as opposed to single manoeuvres that led to system bias. The proposed system identification procedure can be applied to any fixed-wing UAV without the need for specific flight testing campaigns. Full article
(This article belongs to the Section Aeronautics)
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<p>System identification methodology.</p>
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<p>Tekever AR5 model in <span class="html-italic">AVL</span>. Pink lines represent lifting surfaces and black circular lines represent the fuselage.</p>
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<p>Tekever AR5 point mass model.</p>
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<p>Force and moment calculations overview in <span class="html-italic">JSBSim</span>.</p>
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<p>Structural test manoeuvre example for a generic Tekever AR5 aircraft.</p>
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<p>Simulation environment algorithm overview.</p>
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<p>System identification optimisation algorithm.</p>
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<p>Results for the different error formulations and combinations of variables using the <span class="html-italic">JSBSim</span> validation scheme. (<b>a</b>) Improvement in each single error score. (<b>b</b>) Similarity between validation model variables and optimised model design variables.</p>
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<p>Methodology validation using two <span class="html-italic">JSBSim</span> models.</p>
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<p>Improvement in each error variable for all single variable optimisation cases. (<b>a</b>) Using the absolute error formulation. (<b>b</b>) Using the step error formulation.</p>
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<p>Optimisation of two distinct Tekever AR5 aircraft. (<b>a</b>) Aircraft #1. (<b>b</b>) Aircraft #2.</p>
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<p>System identification using a single manoeuvre for the Tekever AR5. (<b>a</b>) Aircraft response. (<b>b</b>) Optimisation error improvement score.</p>
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<p>Single-manoeuvre optimisation validation with two separate independent manoeuvres of the same Tekever AR5 aircraft. (<b>a</b>) First manoeuvre. (<b>b</b>) Second manoeuvre.</p>
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<p>Average error and standard deviation of the error results for nine manoeuvres for the initial and final solution of the single-manoeuvre optimisation. Manoeuvre #1 was the used manoeuvre for the optimisation. (<b>a</b>) Pitch <math display="inline"><semantics> <mi>θ</mi> </semantics></math> error. (<b>b</b>) Pitch rate <span class="html-italic">q</span> error. (<b>c</b>) Altitude <span class="html-italic">h</span> error. (<b>d</b>) Calibrated airspeed <math display="inline"><semantics> <msub> <mi>V</mi> <mrow> <mi>C</mi> <mi>A</mi> <mi>S</mi> </mrow> </msub> </semantics></math> error.</p>
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<p>Multi-manoeuvre optimisation results for two example manoeuvres used in the optimisation of the same Tekever AR5 aircraft. (<b>a</b>) Manoeuvre #4. (<b>b</b>) Manoeuvre #7.</p>
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<p>Mean and standard deviation of the error of the multi-manoeuvre optimisation. (<b>a</b>) Pitch <math display="inline"><semantics> <mi>θ</mi> </semantics></math>. (<b>b</b>) Pitch rate <span class="html-italic">q</span>. (<b>c</b>) Altitude <span class="html-italic">h</span>. (<b>d</b>) Calibrated airspeed <math display="inline"><semantics> <msub> <mi>V</mi> <mrow> <mi>C</mi> <mi>A</mi> <mi>S</mi> </mrow> </msub> </semantics></math>.</p>
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<p>Multi-manoeuvre optimisation results for the three validation manoeuvres of the same Tekever AR5 aircraft. (<b>a</b>) Manoeuvre #2. (<b>b</b>) Manoeuvre #5. (<b>c</b>) Manoeuvre #6.</p>
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21 pages, 9594 KiB  
Article
On the Lateral Stability System of Four-Wheel Driven Electric Vehicles Based on Phase Plane Method
by Yu-Jie Ma, Chih-Keng Chen and Xiao-Dong Zhang
Electronics 2024, 13(22), 4569; https://doi.org/10.3390/electronics13224569 - 20 Nov 2024
Viewed by 322
Abstract
To improve the handling and stability of four-wheel independent drive electric vehicles (FWID EVs), this paper introduces a hierarchical architecture lateral stability control system. The upper-level controller is responsible for generating the additional yaw moment required by the vehicle. This includes a control [...] Read more.
To improve the handling and stability of four-wheel independent drive electric vehicles (FWID EVs), this paper introduces a hierarchical architecture lateral stability control system. The upper-level controller is responsible for generating the additional yaw moment required by the vehicle. This includes a control strategy based on feedforward control and a Linear Quadratic Regulator (LQR) for handling assistance control, an LQR-based stability control, a PID controller-based speed-following control, and a stability assessment method. The lower-level controller uses Quadratic Programming (QP) to optimally distribute the additional yaw moment to the four wheels. A “normalized” method was proposed to determine vehicle stability. After comparing it with the existing double-line method, diamond method, and curved boundary method through the open-loop Sine with Dwell test and the closed-loop Double Lane Change (DLC)test simulation, the results demonstrate that this method is more sensitive and accurate in determining vehicle stability, significantly enhancing vehicle handling and stability. Full article
(This article belongs to the Special Issue Control Systems for Autonomous Vehicles)
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<p>Four-wheel vehicle dynamics model.</p>
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<p>Linear 2-DOF vehicle dynamics model.</p>
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<p><math display="inline"><semantics> <mrow> <mi>β</mi> <mo>−</mo> <mover accent="true"> <mi>β</mi> <mo>˙</mo> </mover> </mrow> </semantics></math> phase plane. Where the red circle represents the stability center, and the arrow indicates the location of the magnified section.</p>
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<p>Three typical phase plane stable region determination methods: (<b>a</b>) The double-line method; (<b>b</b>) The diamond method; (<b>c</b>) The curved boundary method.</p>
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<p>Phase plane stable region diagrams corresponding to different values of <math display="inline"><semantics> <mi>δ</mi> </semantics></math>.</p>
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<p>The relationship diagram of <math display="inline"><semantics> <mrow> <msub> <mi>β</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>β</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics></math> with <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>x</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mi>δ</mi> </semantics></math> when μ = 0.85.</p>
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<p>Evaluation index <math display="inline"><semantics> <mrow> <msub> <mi>I</mi> <mi>β</mi> </msub> </mrow> </semantics></math> for <span class="html-italic">β</span>.</p>
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<p>Relationship between input coefficient u and vehicle stability control weight coefficient <math display="inline"><semantics> <mi>W</mi> </semantics></math>.</p>
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<p>Block diagram of the overall control system.</p>
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<p>Block diagram of handling assistance controller.</p>
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<p>Block diagram of stability controller.</p>
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<p>Block diagram of speed-following controller.</p>
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<p>Linearization of the tire adhesion circle. Where, the red color represents the octagonal constraint, and the blue color represents the adhesion circle.</p>
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<p>Ramp input test: the relationship diagram between <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mi>y</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>δ</mi> <mrow> <mi>h</mi> <mi>a</mi> <mi>n</mi> <mi>d</mi> </mrow> </msub> <mo>,</mo> </mrow> </semantics></math> <math display="inline"><semantics> <mi>δ</mi> </semantics></math>. Where the red circle represents the steering angle coordinate corresponding to a lateral acceleration of 0.3 g, with a value of 22.92 degrees.</p>
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<p>Steering wheel input in the Sine with Dwell steering test.</p>
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<p>Results in Sine with Dwell steering test.</p>
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<p>Phase trajectory diagrams of <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>−</mo> <mover accent="true"> <mi>β</mi> <mo>˙</mo> </mover> </mrow> </semantics></math> in Sine with Dwell test. (<b>a</b>) Case A and Case D trajectory with Case A boundary; (<b>b</b>) Case B and Case D trajectory with Case B boundary; (<b>c</b>) Case C and Case D trajectory with Case C boundary.</p>
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<p>Responses of the four cases in Sine with Dwell test. (<b>a</b>) the stability control weight coefficient, (<b>b</b>) the yaw moment <math display="inline"><semantics> <mrow> <msub> <mi>M</mi> <mi>z</mi> </msub> </mrow> </semantics></math>, (<b>c</b>) distributed torque <math display="inline"><semantics> <mrow> <msub> <mi>T</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> </semantics></math>, (<b>d</b>) the wheel slip ratio <math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>Track layout for ISO 3888-1.</p>
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<p>Results of the four cases in DLC test with <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>x</mi> </msub> <mo>=</mo> <mn>80</mn> <mrow> <mo> </mo> <mi>km</mi> </mrow> <mo>/</mo> <mi mathvariant="normal">h</mi> </mrow> </semantics></math> (<b>a</b>) the trajectories; (<b>b</b>) lateral acceleration response; (<b>c</b>) yaw rate response; (<b>d</b>) side slip angle response. and <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>=</mo> <mn>0.3</mn> </mrow> </semantics></math>.</p>
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<p>Responses of the four cases in DLC test with <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>x</mi> </msub> <mo>=</mo> <mn>80</mn> <mrow> <mo> </mo> <mi>km</mi> </mrow> <mo>/</mo> <mi mathvariant="normal">h</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>=</mo> <mn>0.3</mn> </mrow> </semantics></math>. (<b>a</b>) the stability control weight coefficient, (<b>b</b>) the yaw moment <math display="inline"><semantics> <mrow> <msub> <mi>M</mi> <mi>z</mi> </msub> </mrow> </semantics></math>, (<b>c</b>) distributed torque <math display="inline"><semantics> <mrow> <msub> <mi>T</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> </semantics></math>, (<b>d</b>) the wheel slip ratio <math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>Phase trajectory diagrams of <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>−</mo> <mover accent="true"> <mi>β</mi> <mo>˙</mo> </mover> </mrow> </semantics></math> in DLC test with <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>x</mi> </msub> <mo>=</mo> <mn>80</mn> <mrow> <mo> </mo> <mi>km</mi> </mrow> <mo>/</mo> <mi mathvariant="normal">h</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>=</mo> <mn>0.3</mn> </mrow> </semantics></math>. (<b>a</b>) Case A and Case D trajectory with Case A boundary; (<b>b</b>) Case B and Case D trajectory with Case B boundary; (<b>c</b>) Case C and Case D trajectory with Case C boundary.</p>
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19 pages, 2710 KiB  
Article
Optimal Cost Design of RC T-Shaped Combined Footings
by Victor Manuel Moreno-Landeros, Arnulfo Luévanos-Rojas, Griselda Santiago-Hurtado, Luis Daimir López-León, Francisco Javier Olguin-Coca, Abraham Leonel López-León and Aldo Emelio Landa-Gómez
Buildings 2024, 14(11), 3688; https://doi.org/10.3390/buildings14113688 - 19 Nov 2024
Viewed by 310
Abstract
This paper shows the optimal cost design for T-shaped combined footings of reinforced concrete (RC), which are subjected to biaxial bending in each column to determine the steel areas and the thickness of the footings assuming a linear distribution of soil pressure. The [...] Read more.
This paper shows the optimal cost design for T-shaped combined footings of reinforced concrete (RC), which are subjected to biaxial bending in each column to determine the steel areas and the thickness of the footings assuming a linear distribution of soil pressure. The methodology used in this paper is as follows: First, the minimum contact surface between the footing and the ground is investigated. The design equations for the combined footing are then used to determine the objective function and its constraints to obtain the lowest cost, taking into account the ACI code requirements. Flowcharts are shown for the lowest cost and the use of Maple 15 software. The current model for design is developed as follows: A footing thickness is proposed, and then it is verified that the thickness complies with the effects produced by moments, bending shears, and punching shears. Furthermore, four numerical examples are presented under the same loads and moments applied to each column, with different conditions applied to obtain the optimal contact surface and then the minimum cost design. The results show that the optimal cost design (lowest cost) is more economical and more accurate than any other model, and there is no direct proportion between the minimum contact surface and lowest cost for the design of T-shaped combined footings. In this way, the minimum cost model shown in this work can be applied to the design of rectangular and T-shaped combined footings using optimization techniques. Full article
(This article belongs to the Section Building Structures)
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<p>T-shaped combined footing that assumes a linear distribution of soil pressure.</p>
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<p>Moments (critical sections).</p>
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<p>Bending shears (critical sections).</p>
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<p>Punching shears (critical sections).</p>
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<p>Maple software flowchart for optimal design of T-shaped combined footings.</p>
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<p>Flowchart of the optimal design model of T-shaped combined footings.</p>
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<p>Minimum costs to verify the proposed model.</p>
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28 pages, 914 KiB  
Systematic Review
Prognostic Factors in Patients Undergoing Physiotherapy for Chronic Low Back Pain: A Level I Systematic Review
by Alice Baroncini, Nicola Maffulli, Marco Pilone, Gennaro Pipino, Michael Kurt Memminger, Gaetano Pappalardo and Filippo Migliorini
J. Clin. Med. 2024, 13(22), 6864; https://doi.org/10.3390/jcm13226864 - 14 Nov 2024
Viewed by 356
Abstract
Background: Low back pain is common. For patients with mechanic or non-specific chronic LBP (cLBP), the current guidelines suggest conservative, nonpharmacologic treatment as a first-line treatment. Among the available strategies, physiotherapy represents a common option offered to patients presenting with cLBP. The [...] Read more.
Background: Low back pain is common. For patients with mechanic or non-specific chronic LBP (cLBP), the current guidelines suggest conservative, nonpharmacologic treatment as a first-line treatment. Among the available strategies, physiotherapy represents a common option offered to patients presenting with cLBP. The present systematic review investigates the prognostic factors of patients with mechanic or non-specific cLBP undergoing physiotherapy. Methods: In September 2024, the following databases were accessed: PubMed, Web of Science, Google Scholar, and Embase. All the randomised controlled trials (RCTs) which evaluated the efficacy of a physiotherapy programme in patients with LBP were accessed. All studies evaluating non-specific or mechanical LBP were included. Data concerning the following PROMs were collected: the pain scale, Roland Morris Disability Questionnaire (RMQ), and Oswestry Disability Index (ODI). A multiple linear model regression analysis was conducted using the Pearson Product–Moment Correlation Coefficient. Results: Data from 2773 patients were retrieved. The mean length of symptoms before the treatment was 61.2 months. Conclusions: Age and BMI might exert a limited influence on the outcomes of the physiotherapeutic management of cLBP. Pain and disability at baseline might represent important predictors of health-related quality of life at the six-month follow-up. Further studies on a larger population with a longer follow-up are required to validate these results. Full article
(This article belongs to the Special Issue Clinical Advances in Spine Disorders)
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<p>PRISMA flow chart of literature search.</p>
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<p>Cochrane risk of bias tool graph.</p>
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19 pages, 1202 KiB  
Article
Human Resource Management in Complex Environments: A Viable Model Based on Systems Thinking
by Mario Aguilar-Fernández, Graciela Salgado-Escobar and Andrés David Barragán-Hernández
Systems 2024, 12(11), 489; https://doi.org/10.3390/systems12110489 - 14 Nov 2024
Viewed by 396
Abstract
Developing the company’s capacity to deal with changing environments means ceasing to see processes as a traditional and linear model. Therefore, the objective of this research is to apply VSM to HRM to show its complexity. It is qualitative research, which is carried [...] Read more.
Developing the company’s capacity to deal with changing environments means ceasing to see processes as a traditional and linear model. Therefore, the objective of this research is to apply VSM to HRM to show its complexity. It is qualitative research, which is carried out in two moments. The first consists of a literature review in the WoS, and the second, is the design of the model “MV-HRM”, based on the approach of complex adaptive systems, viable system model, soft system methodology, and holistic theory. The MV-HRM consists of five systems: (S1) HRM processes, (S2) information system (S4) operational control, (S4) strategic planning and (S5) governance. The model emphasizes the relationships and interactions it has with its immediate and future environment. Finally, the contribution of the research is to show another look and understanding of the functioning of HRM, in addition to awakening the interest of strategists to develop best practices that allow them to respond in an agile way to the dynamic and complex environment. Full article
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<p>Recursive nature of the MV-HRM. Source: adapted from Beer [<a href="#B30-systems-12-00489" class="html-bibr">30</a>].</p>
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<p>Viable HRM model. Source: adapted from Beer [<a href="#B30-systems-12-00489" class="html-bibr">30</a>].</p>
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<p>MV-HRM feedback mechanisms. Source: own elaboration.</p>
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19 pages, 4517 KiB  
Article
Full-Range Moment–Curvature Relationships for Beams Made of Low-Hardening Aluminium Alloys
by Aleksander Szwed, Inez Kamińska and Cezary Ajdukiewicz
Materials 2024, 17(22), 5545; https://doi.org/10.3390/ma17225545 - 13 Nov 2024
Viewed by 408
Abstract
Aluminium alloys are characterised by a rounded stress–strain relationship, with no sharply defined yield point. For example, aluminium alloy grades 6061-T6, 6082-T6, and 7075-T6 exhibit low-hardening response, which is close to linear elastic-linear plastic hardening characteristics. Commonly, the behaviour of aluminium alloys is [...] Read more.
Aluminium alloys are characterised by a rounded stress–strain relationship, with no sharply defined yield point. For example, aluminium alloy grades 6061-T6, 6082-T6, and 7075-T6 exhibit low-hardening response, which is close to linear elastic-linear plastic hardening characteristics. Commonly, the behaviour of aluminium alloys is described by Ramberg–Osgood (RO) one-dimensional constitutive relationship in the format of strain in terms of stress. In the case of low-hardening response, an alternative Richard–Abbott (RA) relationship of stress as a function of strain can be used. Both relations are analytically irreversible, but the RA is more appropriate for use in slender beams theory. In the present study, we use the latter function to derive moment as an explicit function of curvature for the sectional relation of beams. Since the obtained relation is expressed via special functions, we also propose its close approximation, which is more useful for practical purposes. It is uncomplicated and reasonably accurate compared to available models. The predictive capabilities of the new moment–curvature models developed in this article are verified with experimental results available in the literature for beams tested under four-point and three-point bending. In the case of four-point beams, predictions show very good agreement with experiments, while for three-point bending of beams, higher discrepancies are observed. Full article
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<p>Stress–strain curves according to the one-dimensional model of elastic material for <span class="html-italic">n</span> = 1 and <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>→</mo> <mo>∞</mo> </mrow> </semantics></math> (piecewise linear). Graphical interpretation of material parameters: <span class="html-italic">E</span><sub>0</sub>, <span class="html-italic">E</span>, <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mn>0</mn> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mrow> <mi>L</mi> <mi>i</mi> <mi>m</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mn>0</mn> </msub> </mrow> </semantics></math>.</p>
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<p>Comparison of the stress–strain relations with experimental data for two aluminium alloys in the whole stable behaviour zone and in the initial strain zone: (<b>a</b>,<b>b</b>) for 6063-T66 (own experiments), (<b>c</b>,<b>d</b>) for 6061-T6 [<a href="#B29-materials-17-05545" class="html-bibr">29</a>].</p>
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<p>Comparison of the stress–strain relations with experimental data for two aluminium alloys in the whole stable behaviour zone and in the initial strain zone: (<b>a</b>,<b>b</b>) for 6063-T66 (own experiments), (<b>c</b>,<b>d</b>) for 6061-T6 [<a href="#B29-materials-17-05545" class="html-bibr">29</a>].</p>
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<p>Notation for considered beams and cross-sections: (<b>a</b>) four-point bending (B4), (<b>b</b>) three-point bending (B3), (<b>c</b>) rectangular hollow section of dimensions <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>×</mo> <mi>H</mi> <mo>×</mo> <mi>t</mi> </mrow> </semantics></math>.</p>
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<p>Moment–curvature curves according to Equation (13) (<math display="inline"><semantics> <mrow> <mi>M</mi> <mfenced> <mi>n</mi> </mfenced> </mrow> </semantics></math>) and Equation (28) (<math display="inline"><semantics> <mrow> <mi>M</mi> <mfenced> <mi>k</mi> </mfenced> </mrow> </semantics></math>) with line tangent at the origin and the asymptote for rectangular cross-section: (<b>a</b>) for the same data, (<b>b</b>) for fitted <span class="html-italic">k</span> exponent.</p>
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<p>Moment–curvature relations for the four-point bending of beam H50 × 95 × 10.5B4 tested in [<a href="#B29-materials-17-05545" class="html-bibr">29</a>]: (<b>a</b>) fitted Equation (13), (<b>b</b>) fitted Equation (28).</p>
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<p>Moment–curvature relations for the four-point bending of beam H95 × 50 × 10.5B4 tested in [<a href="#B29-materials-17-05545" class="html-bibr">29</a>]: (<b>a</b>) fitted Equation (13), (<b>b</b>) fitted Equation (28).</p>
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<p>Moment–curvature relations for the four-point bending of beam H70 × 120 × 10.5B4 tested in [<a href="#B29-materials-17-05545" class="html-bibr">29</a>]: (<b>a</b>) fitted Equation (13), (<b>b</b>) fitted Equation (28).</p>
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<p>Moment–curvature relations for the four-point bending of beam H120 × 70 × 10.5B4 tested in [<a href="#B29-materials-17-05545" class="html-bibr">29</a>]: (<b>a</b>) fitted Equation (13), (<b>b</b>) fitted Equation (28).</p>
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<p>Maximum moment-rotation curves and comparison with experimental data of [<a href="#B29-materials-17-05545" class="html-bibr">29</a>] for two exponents: (<b>a</b>) based on fit <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>1.89</mn> </mrow> </semantics></math>, (<b>b</b>) for reduced <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>1.1</mn> </mrow> </semantics></math>.</p>
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<p>Maximum moment-rotation curves and comparison with experimental data of [<a href="#B29-materials-17-05545" class="html-bibr">29</a>] for exponent: (<b>a</b>) based on fit <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>2.14</mn> </mrow> </semantics></math>, (<b>b</b>) for reduced <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>1.8</mn> </mrow> </semantics></math>.</p>
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<p>Maximum moment-rotation curves and comparison with experimental data of [<a href="#B29-materials-17-05545" class="html-bibr">29</a>] for two exponents: (<b>a</b>) based on fit <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>2.05</mn> </mrow> </semantics></math>, (<b>b</b>) for reduced <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>1.6</mn> </mrow> </semantics></math>.</p>
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<p>Maximum moment-rotation curves and comparison with experimental data of [<a href="#B29-materials-17-05545" class="html-bibr">29</a>] for two exponents: (<b>a</b>) based on fit <span class="html-italic">k</span> = 1.84, (<b>b</b>) for reduced <span class="html-italic">k</span> = 1.6.</p>
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<p>Prediction of maximum moment-rotation curves and comparison with experimental data of [<a href="#B29-materials-17-05545" class="html-bibr">29</a>] for beams: (<b>a</b>) H50 × 95 × 10.5B3, (<b>b</b>) H95 × 50 × 10.5B3.</p>
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<p>Prediction of maximum moment-rotation curves and comparison with experimental data of [<a href="#B29-materials-17-05545" class="html-bibr">29</a>] for beams: (<b>a</b>) H70 × 120 × 10.5B3, (<b>b</b>) H120 × 70 × 10.5B3.</p>
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21 pages, 8999 KiB  
Article
An MPC-DCM Control Method for a Forward-Bending Biped Robot Based on Force and Moment Control
by Zhongshan Wei, Wenyan Deng, Zhengyong Feng, Tao Wang and Xinxiang Huang
Electronics 2024, 13(22), 4374; https://doi.org/10.3390/electronics13224374 - 8 Nov 2024
Viewed by 518
Abstract
For a forward-bending biped robot with 10 degrees of freedom on its legs, a new control framework of MPC-DCM based on force and moment is proposed in this paper. Specifically, the Diverging Component of Motion (DCM) is a stability criterion for biped robots [...] Read more.
For a forward-bending biped robot with 10 degrees of freedom on its legs, a new control framework of MPC-DCM based on force and moment is proposed in this paper. Specifically, the Diverging Component of Motion (DCM) is a stability criterion for biped robots based on linear inverted pendulum, and Model Predictive Control (MPC) is an optimization solution strategy using rolling optimization. In this paper, DCM theory is applied to the state transition matrix of the system, combined with simplified rigid body dynamics, the mathematical description of the biped robot system is established, the classical MPC method is used to optimize the control input, and DCM constraints are added to the constraints of MPC, making the real-time DCM approximate to a straight line in the walking single gait. At the same time, the linear angle and friction cone constraints are considered to enhance the stability of the robot during walking. In this paper, MATLAB/Simulink is used to simulate the robot. Under the control of this algorithm, the robot can reach a walking speed of 0.75 m/s and has a certain anti-disturbance ability and ground adaptability. In this paper, the Model-H16 robot is used to deploy the physical algorithm, and the linear walking and obstacle walking of the physical robot are realized. Full article
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<p>Structure diagram of the Model-H16 robot.</p>
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<p>Model-H16 robot physical photo.</p>
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<p>Overall structure of the control system.</p>
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<p>Linear Inverted Pendulum Model image.</p>
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<p>The structure of the MPC controller.</p>
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<p>Foot ground force and its component force.</p>
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<p>QP optimization solution process.</p>
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<p>The article-link model of a biped robot.</p>
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<p>The structure of the PD controller.</p>
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<p>Photo of the leg swing.</p>
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<p>COM and DCM trajectories for low-speed walking.</p>
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<p>COM and DCM trajectories for low-speed walking.</p>
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<p>Accelerate the x-direction velocity of the walking center of mass.</p>
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<p>Leg trajectory during walking.</p>
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<p>Balance recovery effect under different disturbances in different directions.</p>
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<p>Walking gait in a straight line was photographed.</p>
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<p>Model-H16 linear walking center of mass and foot height. (<b>a</b>) The height of the center of mass. (<b>b</b>) The height of the end of the right leg for straight walking.</p>
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<p>Model-H16 walking and spanning gaits.</p>
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<p>The Model-H16 spans the walking center of mass and foot height.</p>
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11 pages, 2575 KiB  
Article
Load Modulation Affects Pediatric Lower Limb Joint Moments During a Step-Up Task
by Vatsala Goyal, Keith E. Gordon and Theresa Sukal-Moulton
Biomechanics 2024, 4(4), 653-663; https://doi.org/10.3390/biomechanics4040047 - 6 Nov 2024
Viewed by 415
Abstract
Introduction: Performance in a single step has been suggested to be a sensitive measure of movement quality in pediatric clinical populations. Although there is less information available in children with typical development, researchers have postulated the importance of analyzing the effect of body [...] Read more.
Introduction: Performance in a single step has been suggested to be a sensitive measure of movement quality in pediatric clinical populations. Although there is less information available in children with typical development, researchers have postulated the importance of analyzing the effect of body weight modulation on the initiation of stair ascent, especially during single-limb stance where upright stability is most critical. The purpose of this study was to investigate the effect of load modulation from −20% to +15% of body weight on typical pediatric lower limb joint moments during a step-up task. Methods: Fourteen participants between 5 and 21 years who did not have any neurological or musculoskeletal concerns were recruited to perform multiple step-up trials. Peak extensor support and hip abduction moments were identified during the push-off and pull-up stance phases. Linear regressions were used to determine the relationship between peak moments and load. Mixed-effects models were used to estimate the effect of load on hip, knee, and ankle percent contributions to peak support moments. Results: There was a positive linear relationship between peak support moments and load in both stance phases, where these moments scaled with load. There was no relationship between peak hip abduction moments and load. While the ankle and knee were the primary contributors to the support moments, the hip contributed more than expected in the pull-up phase. Discussion: Clinicians can use these results to contextualize movement differences in pediatric clinical populations, including in those with cerebral palsy, and highlight potential target areas for rehabilitation for populations such as adolescent athletes. Full article
(This article belongs to the Special Issue Personalized Biomechanics and Orthopedics of the Lower Extremity)
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<p>A participant in the experimental set-up with retro-reflective markers.</p>
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<p>Representative kinetic (<b>A</b>,<b>C</b>) and kinematic (<b>B</b>,<b>D</b>) profiles from one participant during a no-load step up for the trailing leg (<b>A</b>,<b>B</b>) and the leading leg (<b>C</b>,<b>D</b>). On each <span class="html-italic">x</span>-axis, 0% corresponds to the start of a step-up trial at leading leg lift-off while 100% corresponds to the end of the trial at trailing leg initial contact with the step. On each <span class="html-italic">y</span>-axis, a positive magnitude indicates joint flexion/abduction while a negative magnitude indicates joint extension/adduction. Average hip abduction moments are in red. Individual lower limb sagittal plane moments are in gray, including the hip (gray dash), knee (gray dash–dot), and ankle (gray dot). The sum of these individual joint moments equals the extensor support moments shown in blue. Shaded regions represent one standard deviation. The black boxes on plots (<b>A</b>,<b>C</b>) indicate the push-off and pull-up stance phases, respectively.</p>
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<p>Peak support moments vs. load for the (<b>A</b>) push-off and (<b>B</b>) pull-up stance phases. All values are divided by their respective values in the no-load condition. The linear regression for both stance phases showed a significant relationship between the two variables, with y = 0.817x + 0.973 for the push-off phase (R<sup>2</sup> = 0.278) and y = 0.933x + 1.02 for the pull-up phase (R<sup>2</sup> = 0.498).</p>
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<p>Individual hip (orange), knee (yellow), and ankle (green) percent contributions to peak extensor support moment at the time of peak support moment for all loading conditions in the push-off stance phase (<b>A</b>,<b>C</b>,<b>E</b>) and the pull-up stance phase (<b>B</b>,<b>D</b>,<b>F</b>). A negative percent contribution represents a joint moment in flexion, while a positive percent contribution represents a joint moment in extension. Significant pairwise comparisons are shown by black brackets (corrected <span class="html-italic">p</span> &lt; 0.001).</p>
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<p>Peak hip abduction moments (red) and peak support moments (blue) vs. age for the no-load condition during the push-off and pull-up stance phases. Each point represents an individual no-load trial. All moment values are divided by participant weight, and colored arrows on the far left show the direction of increasing moment magnitude. Pearson’s correlation was significant for all relationships, with r-values of (<b>A</b>) +0.830, (<b>B</b>) +0.833, (<b>C</b>) +0.304, and (<b>D</b>) +0.358. Results indicate that the magnitude of peak hip abduction increases with age, while the magnitude of peak support moment decreases with age.</p>
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25 pages, 421 KiB  
Article
Propagation Speeds of Relativistic Conformal Particles from a Generalized Relaxation Time Approximation
by Alejandra Kandus and Esteban Calzetta
Entropy 2024, 26(11), 927; https://doi.org/10.3390/e26110927 - 30 Oct 2024
Viewed by 432
Abstract
The propagation speeds of excitations are a crucial input in the modeling of interacting systems of particles. In this paper, we assume the microscopic physics is described by a kinetic theory for massless particles, which is approximated by a generalized relaxation time approximation [...] Read more.
The propagation speeds of excitations are a crucial input in the modeling of interacting systems of particles. In this paper, we assume the microscopic physics is described by a kinetic theory for massless particles, which is approximated by a generalized relaxation time approximation (RTA) where the relaxation time depends on the energy of the particles involved. We seek a solution of the kinetic equation by assuming a parameterized one-particle distribution function (1-pdf) which generalizes the Chapman–Enskog (Ch-En) solution to the RTA. If developed to all orders, this would yield an asymptotic solution to the kinetic equation; we restrict ourselves to an approximate solution by truncating the Ch-En series to the second order. Our generalized Ch-En solution contains undetermined space-time-dependent parameters, and we derive a set of dynamical equations for them by applying the moments method. We check that these dynamical equations lead to energy–momentum conservation and positive entropy production. Finally, we compute the propagation speeds for fluctuations away from equilibrium from the linearized form of the dynamical equations. Considering relaxation times of the form τ=τ0(βμpμ)a, with <a<2, where βμ=uμ/T is the temperature vector in the Landau frame, we show that the Anderson–Witting prescription a=1 yields the fastest speed in all scalar, vector and tensor sectors. This fact ought to be taken into consideration when choosing the best macroscopic description for a given physical system. Full article
(This article belongs to the Section Non-equilibrium Phenomena)
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<p>(Color online) Speeds of the two vector modes from Equation (<a href="#FD89-entropy-26-00927" class="html-disp-formula">89</a>). The fastest mode (top dot-dashed blue curve) attains the same maximum speed for <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and for <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>→</mo> <mo>−</mo> <mo>∞</mo> </mrow> </semantics></math> (top dotted light-blue horizontal line), indicating that the AW value is not exceeded at any value of <span class="html-italic">a</span>. Observe that the slowest mode speed (bottom, dashed light-blue curve) is zero for <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, so we recover the AW case [<a href="#B51-entropy-26-00927" class="html-bibr">51</a>] where only one non-null mode exists.</p>
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<p>(Color online) Speeds of the three scalar modes from Equation (<a href="#FD91-entropy-26-00927" class="html-disp-formula">91</a>). We see that the maximum speed of the fastest mode (top red short-dashed curve) corresponds to the AW solution <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> (top horizontal orange dotted line). The intermediate speed mode (long-dashed orange curve in the middle of the figure) also attains its minimum value at the AW value <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> (bottom horizontal yellow dotted line), and the speeds of this mode never exceed the ones of the fastest mode. These two modes are the generalization of the AW modes found elsewhere. The bottom, single-line purple curve corresponds to the speeds of a new, slowest mode, whose velocity for <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> is zero. Thus, we see that the AW case, for which there are only two propagating modes, is consistently included in our formalism.</p>
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<p>(Color online) Comparison of the maximum propagation speeds of each sector. The top dotted horizontal line corresponds to the AW (<math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>) scalar mode speed, short-dashed line immediately below corresponds to the velocities of the scalar fastest mode of our model. The middle dotted horizontal line and dot-dashed middle curve correspond to the vector mode speed for AW (<math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>) and to the speeds of our model, respectively. The bottom long-dashed horizontal line is the speed of the tensor mode, which agrees with the AW speed over the entire interval of <span class="html-italic">a</span> values considered. They verify <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>T</mi> </msub> <mo>&lt;</mo> <msub> <mi>v</mi> <mi>V</mi> </msub> <mo>&lt;</mo> <msub> <mi>v</mi> <mi>S</mi> </msub> </mrow> </semantics></math>.</p>
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12 pages, 929 KiB  
Article
Spontaneous Magnetization Induced by Antiferromagnetic Toroidal Ordering
by Satoru Hayami
Nanomaterials 2024, 14(21), 1729; https://doi.org/10.3390/nano14211729 - 29 Oct 2024
Viewed by 591
Abstract
The magnetic toroidal dipole moment, which is induced by a vortex-type spin texture, manifests itself in parity-breaking physical phenomena, such as a linear magnetoelectric effect and nonreciprocal transport. We elucidate that a staggered alignment of the magnetic toroidal dipole can give rise to [...] Read more.
The magnetic toroidal dipole moment, which is induced by a vortex-type spin texture, manifests itself in parity-breaking physical phenomena, such as a linear magnetoelectric effect and nonreciprocal transport. We elucidate that a staggered alignment of the magnetic toroidal dipole can give rise to spontaneous magnetization even under antiferromagnetic structures. We demonstrate the emergence of uniform magnetization by considering the collinear antiferromagnetic structure with the staggered magnetic toroidal dipole moment on a bilayer zigzag chain. Based on the model calculations, we show that the interplay between the collinear antiferromagnetic mean field and relativistic spin-orbit coupling plays an important role in inducing the magnetization. Full article
(This article belongs to the Special Issue Nanoscale Spintronics and Magnetism: From Fundamentals to Devices)
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<p>Schematic pictures of (<b>a</b>) the magnetic toroidal dipole (red arrow) consisting of magnetic dipoles (blue arrows) and (<b>b</b>) the magnetic dipole consisting of magnetic toroidal dipoles.</p>
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<p>(<b>a</b>) Schematic picture of the single zigzag-chain structure consisting of two sublattices, A and B. In each sublattice, the opposite potential gradient occurs in the <span class="html-italic">y</span> direction. <math display="inline"><semantics> <mrow> <mo>∇</mo> <mi>V</mi> </mrow> </semantics></math> represents the potential gradient arising from the lack of local inversion symmetry at the lattice site. (<b>b</b>) The staggered antiferromagnetic ordering, which induces the MTD moment along the <span class="html-italic">x</span> direction; the blue and red arrows stand for the spin and MTD, respectively. The picture is drawn by MultiPie [<a href="#B79-nanomaterials-14-01729" class="html-bibr">79</a>].</p>
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<p>Antiferromagnetic structure in the bilayer zigzag-chain structure consisting of four sublattices A, B, C, and D. In each zigzag chain, the magnetic toroidal dipole moment denoted by the red arrows along the <span class="html-italic">x</span> direction is induced in the staggered alignment of the magnetic dipole (spin) moment denoted by the blue arrows along the <span class="html-italic">z</span> direction. The staggered alignment of the magnetic toroidal dipole moment leads to the uniform magnetization denoted by the cyan arrows along the <span class="html-italic">y</span> direction. The picture is drawn by MultiPie [<a href="#B79-nanomaterials-14-01729" class="html-bibr">79</a>].</p>
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<p>Electronic band structures in (<b>a</b>) the paramagnetic state at <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0.3</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mn>2</mn> </msub> <mo>=</mo> <mrow> <mn>0.15</mn> </mrow> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msup> <mi>h</mi> <mi>FMT</mi> </msup> <mo>=</mo> <msup> <mi>h</mi> <mi>AFMT</mi> </msup> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, (<b>b</b>) the ferromagnetic toroidal dipole (uniform MTD) state at <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0.3</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msup> <mi>h</mi> <mi>FMT</mi> </msup> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msup> <mi>h</mi> <mi>AFMT</mi> </msup> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, and (<b>c</b>) antiferromagnetic toroidal dipole (staggered MTD) state at <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mn>2</mn> </msub> <mo>=</mo> <mrow> <mn>0.15</mn> </mrow> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msup> <mi>h</mi> <mi>FMT</mi> </msup> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msup> <mi>h</mi> <mi>AFMT</mi> </msup> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>. In (<b>c</b>), the color shows the momentum-resolved <span class="html-italic">y</span>-spin polarization.</p>
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<p>(<b>a</b>) Filling <math display="inline"><semantics> <msub> <mi>n</mi> <mi mathvariant="normal">e</mi> </msub> </semantics></math> and the mean field <math display="inline"><semantics> <msup> <mi>h</mi> <mi>AFMT</mi> </msup> </semantics></math> dependence of the uniform magnetization along the <span class="html-italic">y</span> direction <math display="inline"><semantics> <msub> <mi>M</mi> <mi>y</mi> </msub> </semantics></math>. The model parameters are the same as those used in <a href="#nanomaterials-14-01729-f004" class="html-fig">Figure 4</a>c. (<b>b</b>) <math display="inline"><semantics> <msub> <mi>n</mi> <mi mathvariant="normal">e</mi> </msub> </semantics></math> dependence of <math display="inline"><semantics> <msub> <mi>M</mi> <mi>y</mi> </msub> </semantics></math> at <math display="inline"><semantics> <mrow> <msup> <mi>h</mi> <mi>AFMT</mi> </msup> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>.</p>
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18 pages, 5900 KiB  
Article
Investigation into the Yaw Control of a Twin-Rotor 10 MW Wind Turbine
by Amira Elkodama, A. Abdellatif, S. Shaaban, Mostafa A. Rushdi, Shigeo Yoshida and Amr Ismaiel
Appl. Sci. 2024, 14(21), 9810; https://doi.org/10.3390/app14219810 - 27 Oct 2024
Viewed by 753
Abstract
Multi-rotor system (MRS) wind turbines can provide a competitive alternative to large-scale wind turbines due to their significant advantages in reducing capital, transportation, and operating costs. The main challenges of MRS wind turbines include the complexity of the supporting structure, mathematical modeling of [...] Read more.
Multi-rotor system (MRS) wind turbines can provide a competitive alternative to large-scale wind turbines due to their significant advantages in reducing capital, transportation, and operating costs. The main challenges of MRS wind turbines include the complexity of the supporting structure, mathematical modeling of the aerodynamic interaction between the rotors, and the yaw control mechanism. In this work, MATLAB 2018b/Simulink® software was used to model and simulate a twin-rotor wind turbine (TRWT), and an NREL 5 MW wind turbine was used to verify the model outputs. Different random signals of wind velocities and directions were used as inputs to each rotor to generate different thrust loads, inducing twisting moments on the main tower. A yaw controller system was adapted to ensure that the turbine constantly faced the wind to maximize the power output. A DC motor was used as the mechanism’s actuator. The goal was to achieve a compromise between aligning the rotors with the wind direction and reducing the torque induced on the main tower. A comparison between linear and nonlinear controllers was performed to test the yaw system actuator’s response at different wind speeds and directions. Sliding mode control (SMC) was chosen, as it was suitable for the nonlinearity of the system, and its performance showed a faster response compared with the PID controller, with a settling time of 0.17 sec and a very low overshoot. The controller used the transfer function of the motor to generate a sliding surface. The dynamic responses of the controlled angle are shown and discussed. The controller showed promising results, with a suitable response and low chattering signals. Full article
(This article belongs to the Section Energy Science and Technology)
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<p>Proposed TRWT configuration.</p>
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<p>Betz tube.</p>
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<p>WT mechanical system.</p>
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<p>Simplified DC motor closed-loop TF.</p>
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<p>DC motor with SMC and PID.</p>
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<p>C<sub>p</sub> vs. TSR curve.</p>
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<p>C<sub>p</sub> and λ Simulink results.</p>
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<p>V<sub>w</sub> vs. C<sub>p</sub> curve.</p>
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<p>Verification of V<sub>w</sub> vs. mechanical power per rotor.</p>
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<p>Verification of V<sub>w</sub> vs. thrust force per rotor.</p>
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<p>Twin-rotor mechanical outputs.</p>
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<p>Response of SMC vs. PID.</p>
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<p>SMC response.</p>
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<p>System’s chattering signal before applying SMC.</p>
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<p>Sliding mode surface control.</p>
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<p>Chattering signals before and after applying SMC control.</p>
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19 pages, 10643 KiB  
Article
Modelling and Transmission Characteristics Analysis of APU Pneumatic Servo System
by Fang Yang, Mengqi Wang, Yang Liu, Zipeng Guo and Lingyun Yue
Aerospace 2024, 11(11), 868; https://doi.org/10.3390/aerospace11110868 - 23 Oct 2024
Viewed by 577
Abstract
The auxiliary power unit (APU), which is a compact gas turbine engine, is employed to provide a stable compressed air supply to the aircraft. This compressed air is introduced into the various aircraft components via the pneumatic servo system, thereby ensuring the normal [...] Read more.
The auxiliary power unit (APU), which is a compact gas turbine engine, is employed to provide a stable compressed air supply to the aircraft. This compressed air is introduced into the various aircraft components via the pneumatic servo system, thereby ensuring the normal operation of the aircraft’s systems. The objective of this study is to examine the impact of parameter variation on the transmission characteristics of an APU pneumatic servo system, with a particular focus on the aerodynamic moment associated with the operating process of a butterfly valve. To this end, a mathematical model of the pneumatic servo system has been developed. The accuracy of the mathematical model was verified by means of numerical simulation and comparative analysis of experiments. The simulation model was established in the Matlab/Simulink environment. Furthermore, the effects of throttling area ratio, fixed throttling hole diameter, rodless chamber volume of actuator cylinder and gas supply temperature on the transmission characteristics of the system were discussed in greater detail. The findings of the research indicate that the throttle area ratio is insufficiently sized, which results in a deterioration of the system’s linearity. Conversely, an excessively large throttle area ratio leads to a reduction in the controllable range of the load axis and is therefore detrimental to the servo mechanism of the flow control. An increase in the diameter of the fixed throttling hole or a decrease in the volume of the rodless cavity of the actuator cylinder facilitates a rapid change in flow rate within the rodless cavity and an increase in the response speed of the load-rotating shaft of the servomechanism. An increase in the temperature of the gas supply from 30 °C to 230 °C results in a reduction in the response time of the system by a mere 0.2 s, which has a negligible impact on the transmission characteristics of the system. Full article
(This article belongs to the Section Aeronautics)
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<p>Pneumatic servo system structure schematic.</p>
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<p>Butterfly valve movement geometry structure schematic.</p>
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<p>System performance test schematic.</p>
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<p>Comparison curve between no load test and thermal dynamic test.</p>
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<p>Relation curve between aerodynamic moment and butterfly valve opening.</p>
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<p>Butterfly valve movement position structure schematic.</p>
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<p>Relation curve between load and butterfly valve opening.</p>
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<p>Comparison of torque motor test data and fitting curve.</p>
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<p>Comparison curve between test and simulation of static characteristics of single-nozzle baffle valve.</p>
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<p>Comparison curve between test and simulation of static characteristics of actuator cylinder butterfly valve.</p>
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<p>System simulation model.</p>
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<p>Static characteristic curve of baffle valve corresponding to different throttling area ratio.</p>
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<p>Pressure characteristic curve of control chamber under different fixed throttle hole diameters.</p>
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<p>Displacement characteristics curve of piston rod under different fixed throttle hole diameters.</p>
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<p>Speed characteristic curve of piston rod under different fixed throttle hole diameters.</p>
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<p>Butterfly valve opening characteristic curve under different fixed throttle hole diameters.</p>
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<p>Pressure characteristic curve of control chamber under different rodless cavity volume.</p>
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<p>Displacement characteristics curve of piston rod under different rodless cavity volume.</p>
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<p>Speed characteristic curve of piston rod under different rodless cavity volume.</p>
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<p>Butterfly valve opening characteristic curve under different rodless cavity volume.</p>
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<p>Pressure characteristic curve of control chamber under different gas supply temperature.</p>
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<p>Displacement characteristics curve of piston rod under different gas supply temperature.</p>
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<p>Speed characteristic curve of piston rod under different gas supply temperature.</p>
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<p>Butterfly valve opening characteristic curve under different gas supply temperature.</p>
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19 pages, 1861 KiB  
Article
Analysing Flexural Response in RC Beams: A Closed-Form Solution Designer Perspective from Detailed to Simplified Modelling
by Denis Imamović and Matjaž Skrinar
Mathematics 2024, 12(21), 3327; https://doi.org/10.3390/math12213327 - 23 Oct 2024
Viewed by 667
Abstract
This paper presents a detailed analytical approach for the bending analysis of reinforced concrete beams, integrating both structural mechanics principles and Eurocode 2 provisions. The general analytical expressions derived for the curvature were applied for the transverse displacement analysis of a simply supported [...] Read more.
This paper presents a detailed analytical approach for the bending analysis of reinforced concrete beams, integrating both structural mechanics principles and Eurocode 2 provisions. The general analytical expressions derived for the curvature were applied for the transverse displacement analysis of a simply supported reinforced concrete beam under four-point loading, focusing on key limit states: the initiation of cracking, the yielding of tensile reinforcement and the compressive failure of concrete. The displacement’s results were validated through experimental testing, showing a high degree of accuracy in the elastic and crack propagation phases. Deviations in the yielding phase were attributed to the conservative material assumptions within the Eurocode 2 framework, though the analytical model remained reliable overall. To streamline the computational process for more complex structures, a simplified model utilising a non-linear rotational spring was further developed. This model effectively captures the influence of cracking with significantly reduced computational effort, making it suitable for serviceability limit state analyses in complex loading scenarios, such as seismic impacts. The results demonstrate that combining detailed analytical methods with this simplified model provides an efficient and practical solution for the analysis of reinforced concrete beams, balancing precision with computational efficiency. Full article
(This article belongs to the Special Issue Computational Mechanics and Applied Mathematics)
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<p>Tri-linear moment–curvature diagram of cross-section.</p>
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<p>Stress and strain distribution over the cross-section height at the first crack initiation.</p>
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<p>Stress and strain distribution over the cross-section height at the initiation of the yielding of the tension (bottom) reinforcement.</p>
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<p>Stress and strain distribution over the cross-section height at the initiation of concrete failure at the top compressive fibre.</p>
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<p>Four-point-loaded, simply supported RC beam with differently rebar-reinforced rectangular cross-sections in the middle span and end span areas.</p>
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<p>Moment diagrams for three characteristic moment values on the left half of the beam.</p>
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<p>Testing setup.</p>
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<p>Comparing the experimental displacements with those predicted by the analytical model.</p>
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<p>Transversely deformed beam with equivalent rotational spring in the mid-point.</p>
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<p>Generalised tri-linear moment–rotation diagram for a rotational spring.</p>
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<p>Idealised FE model of an RC beam using three finite elements.</p>
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14 pages, 3247 KiB  
Article
Multiscale Damage Identification Method of Beam-Type Structures Based on Node Curvature
by Kai Ye, Shubi Zhang, Qiuzhao Zhang, Rumian Zhong and Wenda Wang
Buildings 2024, 14(11), 3336; https://doi.org/10.3390/buildings14113336 - 22 Oct 2024
Viewed by 456
Abstract
This paper proposes a multiscale damage identification method for beam-type structures based on node curvature. Firstly, based on the assumption that micro-damage has little effect on stress redistribution and the basic relationship between structural bending moment and curvature, combined with the denoising function [...] Read more.
This paper proposes a multiscale damage identification method for beam-type structures based on node curvature. Firstly, based on the assumption that micro-damage has little effect on stress redistribution and the basic relationship between structural bending moment and curvature, combined with the denoising function of wavelet analysis, the linear matrix equation before and after node curvature damage is solved using the singular value decomposition (SVD) method. Then, the theoretical feasibility of this method is verified with laboratory tests of a simply supported beam. Finally, the damage sensitivity and noise resistance of this method are verified using field measurements of a beam bridge. The results show that the nodal curvature serves as an indicator parameter for damage identification in beam-type structures, enabling the precise localization of damage within these structures. When utilizing a multiscale finite element model for analysis, the nodal curvature enhances the ability to identify both the location and severity of damage within small-scale elements. Furthermore, this method can provide a reference for the damage identification and health monitoring of other types of bridges. Full article
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<p>Schematic diagram of undamaged and damaged beams.</p>
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<p>Beam structure with a transverse crack.</p>
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<p>Numerical model test of simply supported steel beam.</p>
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<p>Damage identification results of simply supported beam.</p>
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<p>Damage identification results of simply supported beam.</p>
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<p>Xinyi River bridge.</p>
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<p>Finite element model of Xinyi River bridge.</p>
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<p>Damage identification results of Xinyi River bridge.</p>
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<p>Damage identification results of Xinyi River bridge.</p>
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<p>Damage identification results under noise interference.</p>
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<p>Damage identification results under noise interference.</p>
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