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Search Results (22,064)

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28 pages, 4625 KiB  
Article
Bayesian Identification of High-Performance Aircraft Aerodynamic Behaviour
by Muhammad Fawad Mazhar, Syed Manzar Abbas, Muhammad Wasim and Zeashan Hameed Khan
Aerospace 2024, 11(12), 960; https://doi.org/10.3390/aerospace11120960 - 21 Nov 2024
Abstract
In this paper, nonlinear system identification using Bayesian network has been implemented to discover open-loop lateral-directional aerodynamic model parameters of an agile aircraft using a grey box modelling structure. Our novel technique has been demonstrated on simulated flight data from an F-16 nonlinear [...] Read more.
In this paper, nonlinear system identification using Bayesian network has been implemented to discover open-loop lateral-directional aerodynamic model parameters of an agile aircraft using a grey box modelling structure. Our novel technique has been demonstrated on simulated flight data from an F-16 nonlinear simulation of its Flight Dynamic Model (FDM). A mathematical model has been obtained using time series analysis of a Box–Jenkins (BJ) model structure, and parameter refinement has been performed using Bayesian mechanics. The aircraft nonlinear Flight Dynamic Model is adequately excited with doublet inputs, as per the dictates of its natural frequency, in accordance with non-parametric modelling (Finite Impulse Response) estimates. Time histories of optimized doublet inputs in the form of aileron and rudder deflections, and outputs in the form of roll and yaw rates are recorded. Dataset is pre-processed by implementing de-trending, smoothing, and filtering techniques. Blend of System Identification time-domain grey box modelling structures to include Output Error (OE) and Box–Jenkins (BJ) Models are stage-wise implemented in multiple flight conditions under varied stochastic models. Furthermore, a reduced order parsimonious model is obtained using Akaike information Criteria (AIC). Parameter error minimization activity is conducted using the Levenberg–Marquardt (L-M) Algorithm, and parameter refinement is performed using the Bayesian Algorithm due to its natural connection with grey box modelling. Comparative analysis of different nonlinear estimators is performed to obtain best estimates for the lateral–directional aerodynamic model of supersonic aircraft. Model Quality Assessment is conducted through statistical techniques namely: Residual Analysis, Best Fit Percentage, Fit Percentage Error, Mean Squared Error, and Model order. Results have shown promising one-step model predictions with an accuracy of 96.25%. Being a sequel to our previous research work for postulating longitudinal aerodynamic model of supersonic aircraft, this work completes the overall aerodynamic model, further leading towards insight to its flight control laws and subsequent simulator design. Full article
(This article belongs to the Section Aeronautics)
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Figure 1
<p>Research Framework.</p>
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<p>Top Level Simulink Model of Aircraft Flight Dynamic Model (MATLAB-2021b).</p>
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<p>F-16 6-DOF Dynamics [<a href="#B39-aerospace-11-00960" class="html-bibr">39</a>].</p>
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<p>Optimal Input Design Flowchart.</p>
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<p>Bayesian Implementation Flowchart.</p>
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<p>F-16 Kinematics Variables [<a href="#B39-aerospace-11-00960" class="html-bibr">39</a>].</p>
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<p>Non-Parametric (FIR) Model of Aircraft.</p>
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<p>Bode Plot Aircraft Lateral Dynamics.</p>
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<p>Simulated Time-Skewed 2-1-1 Doublet Inputs—Aileron (δa) and Rudder (δr).</p>
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<p>Roll and Yaw Rate Time histories in repose to 2-1-1 Doublet Inputs.</p>
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<p>Roll and Pitch Angle time histories to 2-1-1 Doublet Inputs.</p>
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<p>Aircraft Parameter Refinement Flow chart.</p>
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<p>(<b>a</b>) Initial OE Model; (<b>b</b>) Reduced Order OE Model; (<b>c</b>) Initial BJ Model; (<b>d</b>) Optimized BJ Model; (<b>e</b>) Residual Correlation; (<b>f</b>) pdf of Model Parameters; (<b>g</b>) Posterior Sensitivity Analysis (K-L Divergence)—Straight and Level Flight.</p>
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<p>(<b>a</b>) Initial OE Model; (<b>b</b>) Reduced Order OE Model; (<b>c</b>) Initial BJ Model; (<b>d</b>) Optimized BJ Model; (<b>e</b>) Residual Correlation; (<b>f</b>) pdf of Model Parameters; (<b>g</b>) Posterior Sensitivity Analysis (K-L Divergence)—Straight and Level Flight.</p>
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<p>(<b>a</b>) Initial OE Model; (<b>b</b>) Reduced Order OE Model; (<b>c</b>) Initial BJ Model; (<b>d</b>) Optimized BJ Model; (<b>e</b>) Residual Correlation; (<b>f</b>) pdf of Model Parameters; (<b>g</b>) Posterior Sensitivity Analysis (K-L Divergence)—Coordinated Turn Flight.</p>
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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
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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23 pages, 547 KiB  
Article
Reliability Model of Battery Energy Storage Cooperating with Prosumer PV Installations
by Magdalena Bartecka, Piotr Marchel, Krzysztof Zagrajek, Mirosław Lewandowski and Mariusz Kłos
Energies 2024, 17(23), 5839; https://doi.org/10.3390/en17235839 - 21 Nov 2024
Abstract
The energy transition toward low-carbon electricity systems has resulted in a steady increase in RESs. The expansion of RESs has been accompanied by a growing number of energy storage systems (ESSs) that smooth the demand curve or improve power quality. However, in order [...] Read more.
The energy transition toward low-carbon electricity systems has resulted in a steady increase in RESs. The expansion of RESs has been accompanied by a growing number of energy storage systems (ESSs) that smooth the demand curve or improve power quality. However, in order to investigate ESS benefits, it is necessary to determine their reliability. This article proposes a four-state reliability model of a battery ESS operating with a PV system for low-voltage grid end users: households and offices. The model assumes an integration scenario of an ESS and a PV system to maximize autoconsumption and determine generation reliability related to energy availability. The paper uses a simulation approach and proposes many variants of power source and storage capacity. Formulas to calculate the reliability parameters—the intensity of transition λ, resident time Ti, or stationary probabilities—are provided. The results show that increasing the BESS capacity above 80% of daily energy consumption does not improve the availability probability, but it may lead to an unnecessary cost increase; doubling the PV system capacity results in a decrease in the unavailability probability by almost half. The analysis of the results by season shows that it is impossible to achieve a high level of BESS reliability in winter in temperate climates. Full article
15 pages, 7374 KiB  
Article
Hysteresis Compensation and Butterworth Pattern-Based Positive Acceleration Velocity Position Feedback Damping Control of a Tip-Tilt-Piston Piezoelectric Stage
by Helei Zhu, Jinfu Sima, Peixing Li, Leijie Lai and Zhenfeng Zhou
Actuators 2024, 13(12), 468; https://doi.org/10.3390/act13120468 - 21 Nov 2024
Abstract
In order to solve the hysteresis nonlinearity and resonance problems of piezoelectric stages, this paper takes a three-degree-of-freedom tip-tilt-piston piezoelectric stage as the object, compensates for the hysteresis nonlinearity through inverse hysteresis model feedforward control, and then combines the composite control method of [...] Read more.
In order to solve the hysteresis nonlinearity and resonance problems of piezoelectric stages, this paper takes a three-degree-of-freedom tip-tilt-piston piezoelectric stage as the object, compensates for the hysteresis nonlinearity through inverse hysteresis model feedforward control, and then combines the composite control method of positive acceleration velocity position feedback damping control and high-gain integral feedback controller to suppress the resonance of the system and improve the tracking speed and positioning accuracy. Firstly, the three-degree-of-freedom motion of the end-pose is converted into the output of three sets of piezoelectric actuators and single-axis control is performed. Then, the rate-dependent Prandtl–Ishlinskii model is established and the parameters of the inverse model are identified. The accuracy and effectiveness of parameter identification are verified through open-loop and closed-loop compensation experiments. After that, for the third-order system, the parameters of positive acceleration velocity position feedback damping control and high-gain integral feedback controller are designed as a whole based on the pattern of the Butterworth filter. The effectiveness of the design method is proved by step signal and triangle wave signal trajectory tracking experiments, which suppresses the resonance of the system and improves the bandwidth of the system and the tracking speed of the stage. Full article
(This article belongs to the Section Control Systems)
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<p>Three-degree-of-freedom tip-tilt-piston piezoelectric stage experimental system.</p>
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<p>Relationship between the output displacements of three sets of PEAs and 3-DOF motion.</p>
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<p>Rate-dependent hysteresis and resonance characteristics of PEA1. (<b>a</b>) Rate-dependent hysteresis characteristics. (<b>b</b>) Resonance characteristics.</p>
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<p>Identification results and errors of inverse PI models. (<b>a</b>) PEA1. (<b>b</b>) PEA2. (<b>c</b>) PEA3. (<b>d</b>) Identification errors.</p>
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<p>System control block diagram.</p>
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<p>Open-loop and closed-loop trajectory tracking results. (<b>a</b>) PEA1 open-loop. (<b>b</b>) PEA2 open-loop. (<b>c</b>) PEA3 open-loop. (<b>d</b>) PEA1 closed-loop. (<b>e</b>) PEA2 closed-loop. (<b>f</b>) PEA3 closed-loop.</p>
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<p>Frequency response comparison between experimental results and identification results. (<b>a</b>) PEA1. (<b>b</b>) PEA2. (<b>c</b>) PEA3.</p>
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<p>PAVPF control block diagram.</p>
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<p>Ideal pole distribution in Butterworth filter pattern.</p>
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<p>Comparison of stage frequency response characteristics. (<b>a</b>) PEA1. (<b>b</b>) PEA2. (<b>c</b>) PEA3.</p>
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<p>Step signal tracking experiment. (<b>a</b>) PEA1. (<b>b</b>) PEA2. (<b>c</b>) PEA3.</p>
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<p>Composite control block diagram.</p>
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<p>Tracking results and tracking errors of triangle wave signals. Tracking results: (<b>a</b>) PEA1. (<b>b</b>) PEA2. (<b>c</b>) PEA3. Tracking errors: (<b>d</b>) PEA1. (<b>e</b>) PEA2. (<b>f</b>) PEA3.</p>
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14 pages, 295 KiB  
Article
Properties of the SURE Estimates When Using Continuous Thresholding Functions for Wavelet Shrinkage
by Alexey Kudryavtsev and Oleg Shestakov
Mathematics 2024, 12(23), 3646; https://doi.org/10.3390/math12233646 - 21 Nov 2024
Abstract
Wavelet analysis algorithms in combination with thresholding procedures are widely used in nonparametric regression problems when estimating a signal function from noisy data. The advantages of these methods lie in their computational efficiency and the ability to adapt to the local features of [...] Read more.
Wavelet analysis algorithms in combination with thresholding procedures are widely used in nonparametric regression problems when estimating a signal function from noisy data. The advantages of these methods lie in their computational efficiency and the ability to adapt to the local features of the estimated function. It is usually assumed that the signal function belongs to some special class. For example, it can be piecewise continuous or piecewise differentiable and have a compact support. These assumptions, as a rule, allow the signal function to be economically represented on some specially selected basis in such a way that the useful signal is concentrated in a relatively small number of large absolute value expansion coefficients. Then, thresholding is performed to remove the noise coefficients. Typically, the noise distribution is assumed to be additive and Gaussian. This model is well studied in the literature, and various types of thresholding and parameter selection strategies adapted for specific applications have been proposed. The risk analysis of thresholding methods is an important practical task, since it makes it possible to assess the quality of both the methods themselves and the equipment used for processing. Most of the studies in this area investigate the asymptotic order of the theoretical risk. In practical situations, the theoretical risk cannot be calculated because it depends explicitly on the unobserved, noise-free signal. However, a statistical risk estimate constructed on the basis of the observed data can also be used to assess the quality of noise reduction methods. In this paper, a model of a signal contaminated with additive Gaussian noise is considered, and the general formulation of the thresholding problem with threshold functions belonging to a special class is discussed. Lower bounds are obtained for the threshold values that minimize the unbiased risk estimate. Conditions are also given under which this risk estimate is asymptotically normal and strongly consistent. The results of these studies can provide the basis for further research in the field of constructing confidence intervals and obtaining estimates of the convergence rate, which, in turn, will make it possible to obtain specific values of errors in signal processing for a wide range of thresholding methods. Full article
14 pages, 14695 KiB  
Article
Identification and Regulation of Cold Rolling Interface State Based on a Novel Modified Forward Slip Model
by Yanli Xin, Zhiying Gao, Yong Zang and Xiaoyong Wang
Lubricants 2024, 12(12), 404; https://doi.org/10.3390/lubricants12120404 - 21 Nov 2024
Abstract
With the development of rolled steel strips towards higher strength and thinner thickness, negative forward slip has been frequently observed during the process of cold rolling, and this phenomenon closely related to interface is believed to seriously influence rolling stability. However, the existing [...] Read more.
With the development of rolled steel strips towards higher strength and thinner thickness, negative forward slip has been frequently observed during the process of cold rolling, and this phenomenon closely related to interface is believed to seriously influence rolling stability. However, the existing classic forward slip models are limited to calculating positive forward slip values and cannot reflect negative forward slip effects. Therefore, in this paper, based on BLAND-FORD forward slip theory, a novel modified forward slip model capable of predicting negative forward slip is established and verified, in which the corresponding flattened curve is characterized and a compensation coefficient related to actual tension and coil number is supplemented. Then, a dimensionless sensitivity factor is defined to compare and analyze the influences of various parameters on forward slip through the modified model, in order to pick a more effective and reasonable regulation approach. Finally, an idea of keeping stable forward slip through dynamic tension regulation is suggested and applied in the actual rolling process, and it is drawn that this strategy can be used to avoid fluctuations of process parameters and suppress mill chatter. As a result, the presented modified forward slip model can identify both positive and negative forward slips and is helpful in regulating the interface state and improving the stability of the rolling process. Full article
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<p>Schematic diagram of the metal flow velocity in the deformation zone.</p>
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<p>Schematic diagram of negative forward slip.</p>
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<p>Rolling process parameters of the first production line: (<b>a</b>) rolling speed; (<b>b</b>) tension stress; (<b>c</b>) rolling force; (<b>d</b>) forward slip.</p>
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<p>Rolling process parameters of the second production line: (<b>a</b>) rolling speed; (<b>b</b>) tension stress; (<b>c</b>) rolling force; (<b>d</b>) forward slip.</p>
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<p>Comparison results of forward slip on the first production line. (<b>a</b>) Results of the BLAND-FORD forward slip model. (<b>b</b>) Results of the modified forward slip.</p>
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<p>Comparison results of forward slip on the second production line. (<b>a</b>) Results of the BLAND-FORD forward slip model. (<b>b</b>) Results of the modified forward slip.</p>
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<p>Relationship between compensation factor and coil number.</p>
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<p>Application of the modified forward slip model. (<b>a</b>) Comparison of the forward slip values for the 24th coil. (<b>b</b>) Comparison of the forward slip values for the 54th coil.</p>
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<p>Influence of the parameters on forward slip. (<b>a</b>) Exit thickness of the strip. (<b>b</b>) Reduction ration. (<b>c</b>) Roll radius. (<b>d</b>) Friction coefficient. (<b>e</b>) Inlet tension stress. (<b>f</b>) Exit tension stress.</p>
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<p>Dimensionless sensitivity factors.</p>
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<p>Phenomenon of negative forward slip in actual production. (<b>a</b>) The first steel coil. (<b>b</b>) The second steel coil.</p>
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<p>Response of the vibration and rolling process parameters. (<b>a</b>) Rolling speed. (<b>b</b>) Inlet tension force. (<b>c</b>) Vibration acceleration. (<b>d</b>) Exit tension force. (<b>e</b>) Forward slip. (<b>f</b>) Tension force difference.</p>
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<p>Influence of the friction coefficient and inlet tension force on forward slip and the forward slip contour map. (<b>a</b>) Influence of friction coefficient and inlet tension force on forward slip. (<b>b</b>) Forward slip contour map.</p>
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<p>Comparison of forward slip before the speed reduction.</p>
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<p>Comparison before and after tension control.</p>
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10 pages, 2220 KiB  
Article
Prediction of Blast Vibration Velocity of Buried Steel Pipe Based on PSO-LSSVM Model
by Hongyu Zhang, Shengwu Tu, Senlin Nie and Weihua Ming
Sensors 2024, 24(23), 7437; https://doi.org/10.3390/s24237437 - 21 Nov 2024
Abstract
In order to ensure the safe operation of adjacent buried pipelines under blast vibration, it is of great practical engineering significance to accurately predict the peak vibration velocity ofburied pipelines under blasting loads. Relying on the test results of the buried steel pipe [...] Read more.
In order to ensure the safe operation of adjacent buried pipelines under blast vibration, it is of great practical engineering significance to accurately predict the peak vibration velocity ofburied pipelines under blasting loads. Relying on the test results of the buried steel pipe blast model test, a sensitivity analysis of relevant influencing factors was carried out by using the gray correlation analysis method. A least squares support vector machine (LS-SVM) model was established to predict the peak vibration velocity of the pipeline and determine the best parameter combination in the LS-SVM model through a local particle swarm optimization (PSO), and the results of the PSO-LSSVM model were predicted. These were compared with BP neural network model and Sa’s empirical formula. The results show that the fitting correlation coefficient (R2), root mean square error (RMSE), average relative error (MRE), and Nash coefficient (NSE) of the PSO-LSSVM model for the prediction of pipeline peak vibration velocity are 91.51%, 2.95%, 8.69%, and 99.03%, showing that the PSO-LSSVM model has a higher prediction accuracy and better generalization ability, which provides a new idea for the vibration velocity prediction of buried pipelines under complex blasting conditions. Full article
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<p>Processing flow of PSO-LSSVM model.</p>
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<p>Model test layout diagram.</p>
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<p>Installation diagram of blast vibration meter.</p>
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<p>Fitness curve of PSO-LSSVM model.</p>
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<p>A comparison between the true value and the predicted value of the training sample of the PSO-LSSVM model.</p>
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<p>Comparison of prediction results of different models.</p>
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9 pages, 5150 KiB  
Article
Reliability Study of Fiber Coupling Efficiency of 980 nm Semiconductor Laser
by Gang Liu, Shuhao Pang, Xin Zhang, Mingzhi Tang, Lei Liang, Rui Li and Rui Huang
Photonics 2024, 11(12), 1101; https://doi.org/10.3390/photonics11121101 - 21 Nov 2024
Abstract
In order to improve the stability of semiconductor laser fiber coupling efficiency, based on the coupling principle, the optimal parameters for semiconductor laser fiber coupling were simulated to be θ = 45°, r = 3.25 μm, and z = 5.65 μm. By optimizing [...] Read more.
In order to improve the stability of semiconductor laser fiber coupling efficiency, based on the coupling principle, the optimal parameters for semiconductor laser fiber coupling were simulated to be θ = 45°, r = 3.25 μm, and z = 5.65 μm. By optimizing the structure and position of the lens fiber, it has been experimentally proven that the maximum fiber coupling efficiency of the 980 nm semiconductor laser can reach 87.1%, and the average coupling efficiency can also reach 84%. After temperature cycling and aging experiments, the average coupling efficiency of the device was 81.7%, indicating a decrease in coupling efficiency. At the same time, the effect of fiber stress on the reliability of coupling efficiency was analyzed, and the stability and consistency of the device before and after temperature cycling were explored. In future work, it will be necessary to further optimize the thermal stress caused by UV glue curing and tail pipe soldering, find suitable process parameters, and obtain stable and reliable coupling modules. Full article
(This article belongs to the Section Lasers, Light Sources and Sensors)
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Figure 1
<p>Schematic diagram of device structure and wedge-shaped lens fiber: (<b>a</b>) schematic diagram of device structure; (<b>b</b>) top view of wedge-shaped lens optical fiber; (<b>c</b>) side view of wedge-shaped lens optical fiber.</p>
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<p>Simulation results of the relationship between half wedge angle (<b>a</b>), arc radius (<b>b</b>), axial distance (<b>c</b>), and coupling efficiency.</p>
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<p>Schematic diagram of LD chip output optical power.</p>
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<p>Schematic diagram of experimental coupling device (<b>a</b>) and coupling results (<b>b</b>).</p>
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<p>(<b>a</b>,<b>b</b>) show the laser far-field profile distributions of the slow and fast axes at 80 mA; (<b>c</b>,<b>d</b>) show the laser far-field profile distributions of the slow and fast axes at 780 mA.</p>
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<p>Picture of LD and wedge-shaped lens fiber structure.</p>
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<p>Schematic diagram of fiber optic output power and coupling efficiency results.</p>
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<p>Schematic diagram of changes in coupling efficiency of different samples before and after temperature cycling.</p>
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24 pages, 11045 KiB  
Article
Comparative Study on Online Prediction of TP2 Rolled Copper Tube Wall Thickness Based on Different Proxy Models
by Fengli Yue, Zhuo Sha, Hongyun Sun, Huan Liu, Dayong Chen, Jinsong Liu and Chuanlai Chen
Materials 2024, 17(23), 5685; https://doi.org/10.3390/ma17235685 - 21 Nov 2024
Abstract
The wall thickness of the TP2 copper tube casting billet is not uniform after a three-roll planetary rotational rolling, which affects the wall thickness uniformity of the copper tube in the subsequent process. In order to study the influence of wall thickness at [...] Read more.
The wall thickness of the TP2 copper tube casting billet is not uniform after a three-roll planetary rotational rolling, which affects the wall thickness uniformity of the copper tube in the subsequent process. In order to study the influence of wall thickness at different positions of copper pipe after rolling on the wall thickness of copper pipe after joint drawing, an online ultrasonic test platform was used to measure the wall thickness of copper pipe after tying, and based on the test data, a finite element model of copper pipe billet was established, and the numerical simulation of joint drawing wall thickness was conducted. Based on the results of the ultrasonic testing experiment and finite element simulation, different neural network models were used to predict the joint tensile wall thickness with the data of the ultrasonic testing experiment as input and the results of finite element simulation as output. The prediction effect of different neural network models was compared, and the results showed that the prediction and fitting effect of the SVM model was better, but overfitting occurred during the fitting process. Furthermore, particle swarm optimization is used to optimize the penalty parameter C and the kernel parameter g in the SVM model. Compared with the traditional SVM model, the PSO–SVM model is more suitable for the prediction of joint tensile wall thickness, which can better guide the production to solve this problem. Full article
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<p>Three-roll rotary rolling.</p>
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<p>Ultrasonic experiment process after rolling.</p>
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<p>Wall thickness detection device.</p>
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<p>Probe position distribution: (<b>a</b>) Thickness probe set below; (<b>b</b>) Thickness measuring probe group ((<b>a</b>) is located in the Lower detection sink in <a href="#materials-17-05685-f003" class="html-fig">Figure 3</a>; (<b>b</b>) is located in the Upper detection framework in <a href="#materials-17-05685-f003" class="html-fig">Figure 3</a>).</p>
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<p>Thickness probe.</p>
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<p>Data analyzing and processing system.</p>
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<p>Ultrasonic thickness measurement by liquid immersion method.</p>
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<p>Comparison of wall thickness data: (<b>a</b>) Ultrasonic testing data; (<b>b</b>) Hand measurement data.</p>
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<p>Establishment of initial tube blank.</p>
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<p>Initial finite element model of pipe.</p>
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<p>Tensile test: (<b>a</b>) Tensile specimen of TP2 copper; (<b>b</b>) Electronic universal testing machine; (<b>c</b>) Real stress–strain curve measured for 3 specimens.</p>
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<p>Wall thickness measurement: (<b>a</b>) Finite element model wall thickness data; (<b>b</b>) Spiral micrometer measurement data.</p>
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<p>Predictive implementation framework.</p>
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<p>RF neural network topology.</p>
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<p>RBF neural network topology.</p>
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<p>Different neural network verification results: (<b>a</b>) BP neural network training set; (<b>b</b>) BP neural network test set; (<b>c</b>) SVM neural network training set; (<b>d</b>) SVM neural network test set; (<b>e</b>) RF neural network training set; (<b>f</b>) RF neural network test set; (<b>g</b>) RBF neural network training set; (<b>h</b>) RBF neural network test set.</p>
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<p>Finite element simulation of wall thickness: (<b>a</b>) the first pull wall thickness; (<b>b</b>) the second pull wall thickness.</p>
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<p>PSO–SVM prediction flow chart.</p>
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<p>Variation curve of fitness.</p>
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<p>The prediction results of the two models: (<b>a</b>) SVM training set; (<b>b</b>) SVM test set; (<b>c</b>) PSO–SVM training set; (d) PSO–SVM test set.</p>
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<p>Production measurement.</p>
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16 pages, 4570 KiB  
Article
Study of the Possibility to Combine Deep Learning Neural Networks for Recognition of Unmanned Aerial Vehicles in Optoelectronic Surveillance Channels
by Vladislav Semenyuk, Ildar Kurmashev, Dmitriy Alyoshin, Liliya Kurmasheva, Vasiliy Serbin and Alessandro Cantelli-Forti
Modelling 2024, 5(4), 1773-1788; https://doi.org/10.3390/modelling5040092 - 21 Nov 2024
Abstract
This article explores the challenges of integrating two deep learning neural networks, YOLOv5 and RT-DETR, to enhance the recognition of unmanned aerial vehicles (UAVs) within the optical-electronic channels of Sensor Fusion systems. The authors conducted an experimental study to test YOLOv5 and Faster [...] Read more.
This article explores the challenges of integrating two deep learning neural networks, YOLOv5 and RT-DETR, to enhance the recognition of unmanned aerial vehicles (UAVs) within the optical-electronic channels of Sensor Fusion systems. The authors conducted an experimental study to test YOLOv5 and Faster RT-DETR in order to identify the average accuracy of UAV recognition. A dataset in the form of images of two classes of objects, UAVs, and birds, was prepared in advance. The total number of images, including augmentation, amounted to 6337. The authors implemented training, verification, and testing of the neural networks exploiting PyCharm 2024 IDE. Inference testing was conducted using six videos with UAV flights. On all test videos, RT-DETR-R50 was more accurate by an average of 18.7% in terms of average classification accuracy (Pc). In terms of operating speed, YOLOv5 was 3.4 ms more efficient. It has been established that the use of RT-DETR as the only module for UAV classification in optical-electronic detection channels is not effective due to the large volumes of calculations, which is due to the relatively large number of parameters. Based on the obtained results, an algorithm for combining two neural networks is proposed, which allows for increasing the accuracy of UAV and bird classification without significant losses in speed. Full article
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<p>Data set preparation in Roboflow.com service: (<b>a</b>) Annotation of UAVs and birds; (<b>b</b>) Data set partitioning interface for training, validation, and testing of neural networks.</p>
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<p>Metrics of the results of training the YOLOv5 neural network for 100 epochs (O<span class="html-italic">x</span>-axis): (<b>a</b>) Precision; (<b>b</b>) Recall; (<b>c</b>) mAP50; (<b>d</b>) mAP50-95.</p>
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<p>Metrics of the results of training the YOLOv5 neural network for 100 epochs (O<span class="html-italic">x</span>-axis): (<b>a</b>) Precision; (<b>b</b>) Recall; (<b>c</b>) mAP50; (<b>d</b>) mAP50-95.</p>
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<p>Metrics of the results of training the RT-DETR neural network for 100 epochs (axis Ox): (<b>a</b>) Precision; (<b>b</b>) Recall; (<b>c</b>) mAP50; (<b>d</b>) mAP50-95.</p>
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<p>Metrics of the results of training the RT-DETR neural network for 100 epochs (axis Ox): (<b>a</b>) Precision; (<b>b</b>) Recall; (<b>c</b>) mAP50; (<b>d</b>) mAP50-95.</p>
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<p>Example of data obtained as a result of validation of the YOLOv5 experimental model.</p>
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<p>Example of data obtained from the validation of the RT-DETR experimental model.</p>
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<p>Frames from inference tests of trained neural network models: (<b>a</b>,<b>c</b>) RT-DETR-R50; (<b>b</b>,<b>d</b>) YOLOv5s.</p>
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<p>Frames from inference tests of trained neural network models: (<b>a</b>,<b>c</b>) RT-DETR-R50; (<b>b</b>,<b>d</b>) YOLOv5s.</p>
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<p>Comparative diagram of the values of the average class probability in UAV recognition by trained neural network models.</p>
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<p>Algorithm for combining trained neural network models YOLOv5s and RT-DETR-R50.</p>
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27 pages, 7577 KiB  
Article
Design and Experiment of Obstacle Avoidance Mower in Orchard
by Yi Yang, Yichuan He, Zhihui Tang and Hong Zhang
Agriculture 2024, 14(12), 2099; https://doi.org/10.3390/agriculture14122099 - 21 Nov 2024
Viewed by 40
Abstract
In order to solve the problem of mowing between plants in Xinjiang trunk orchards, an obstacle avoidance mower suitable for trunk orchard planting mode was designed. The whole structure, working principle and main parameter design of the obstacle avoidance mower are introduced. The [...] Read more.
In order to solve the problem of mowing between plants in Xinjiang trunk orchards, an obstacle avoidance mower suitable for trunk orchard planting mode was designed. The whole structure, working principle and main parameter design of the obstacle avoidance mower are introduced. The finite element analysis and kinematic analysis of the cutter are carried out on the premise of using a Y-shaped cutter and its arrangement, and the condition that the inter-row mower does not leak is determined. Through the modal analysis of the frame, the range of the first six natural frequencies of the frame is determined and compared with the frequency of the main excitation source of the machine to determine the rationality of the frame design. On the premise of simplifying the inter-plant obstacle avoidance mechanism into a two-dimensional model for kinematics analysis, the motion parameters of the key components of the machine were determined. At the same time, the virtual kinematics simulation single-factor test of the designed inter-plant obstacle avoidance device was carried out with the help of ADAMS 2020 software. Through the reduction in and calculation of the motion trajectory of the simulation test, it was finally determined that the forward speed of the machine, the elastic coefficient of the reset spring and the compression speed of the hydraulic cylinder were the main influencing factors of the inter-plant obstacle avoidance mower. The orthogonal test was designed and the optimal solution of the three test factors was determined. The optimal solution is taken for further field test verification. The results show that when the tractor forward speed is 1.5 km∙h−1, the hydraulic cylinder compression speed is 225 mm∙s−1, and the elastic coefficient of the reset spring is 29 N∙mm−1, the average leakage rate between the orchard plants is 7.64%, and the obstacle avoidance pass rate is 100%. The working stability is strong and meets the design requirements. Full article
(This article belongs to the Section Agricultural Technology)
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<p>The overall structure diagram of the orchard inter-plant obstacle avoidance mower. 1: Suspension device; 2: hydraulic oil tank; 3: transmission belt shell; 4: belt pulley drive shaft; 5: cylindrical guide rail; 6: cooling fan; 7: frame; 8: lawn mower roller; 9: lawn mower; 10: telescopic rod; 11: hydraulic directional valve; 12: obstacle avoidance disc; 13: obstacle avoidance rod; 14: spring; 15: obstacle avoidance disc bracket; 16: inter-row mower; 17: protective disc; 18: pressing roller; 19: stent; 20: gear box.</p>
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<p>Transmission system diagram of mower. 1. Mowing roller. 2. Hydraulic pump. 3. Transfer box. 4. Transmission shaft. 5. Drive pulley. 6. Drive pulley. 7. Belt. 8. Input shaft.</p>
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<p>The arrangement of pins on the roller shaft. (<b>a</b>) Helix arrangement. (<b>b</b>) Symmetrical arrangement. (<b>c</b>) Interlaced arrangement. (<b>d</b>) Symmetrical staggered arrangement.</p>
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<p>Cutter meshing diagram.</p>
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<p>Cutter statics simulation results. (<b>a</b>) Equivalent elastic deformation cloud diagram of cutter. (<b>b</b>) Cutter displacement deformation cloud map. (<b>c</b>) Cutter stress deformation cloud diagram.</p>
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<p>Cutter trajectory diagram.</p>
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<p>Three-dimensional model of frame.</p>
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<p>Frame finite element model.</p>
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<p>Frame of the first six-order modal analysis diagram.</p>
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<p>Automatic obstacle avoidance device between plants. 1. Hydraulic motor. 2. Cutterhead. 3. Connecting shaft. 4. Breakthrough rod. 5. Control valve. 6. Connecting plate. 7. Cylinder.</p>
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<p>Motion diagram of automatic obstacle avoidance device between plants. 1. Cutterhead. 2. Cutterhead connecting plate. 3. Connecting plate. 4. Hydraulic cylinder. Note: N is the position of the cutter head under the compression state of the hydraulic cylinder; n′ is the position of the cutter head in the elongation state of the hydraulic cylinder; R is the radius of the cutter head and the length of the hydraulic cylinder in the compressed state; l<sub>1</sub> is the length of the hydraulic cylinder in compression state. <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi mathvariant="normal">l</mi> </mrow> <mrow> <mn>1</mn> </mrow> <mrow> <mo>´</mo> </mrow> </msubsup> </mrow> </semantics></math> the length of the hydraulic cylinder in the telescopic state; L is the distance between the position of the hydraulic cylinder and the connecting plate; l<sub>3</sub> is the position of both ends of the connecting plate; l<sub>4</sub> is the distance between the midpoint of the cutter connection plate of the cutter head; l<sub>5</sub> is the distance between the center of the cutter head in the two middle states; l<sub>6</sub> is the distance between the two connection points in two states; l<sub>7</sub> is the distance between point O and E′; l<sub>8</sub> is the distance between two points of DE; l<sub>9</sub> is the distance between EE′; <math display="inline"><semantics> <mrow> <mi>α</mi> </mrow> </semantics></math> is the angle between OA and AB; <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math> is the angle between BA and B′A; θ<sub>1</sub> is the angle between OA and OB. θ<sub>2</sub> is the angle between OA and OB′; <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math> is the angle between OD and OB; <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> </mrow> </semantics></math> is the angle between OD′ and OB′; <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mn>4</mn> </mrow> </msub> </mrow> </semantics></math> is the angle between OB and OB′; <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mn>5</mn> </mrow> </msub> </mrow> </semantics></math> is the angle between OD and OB′; <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mn>6</mn> </mrow> </msub> </mrow> </semantics></math> is the angle between OD and OD′; <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mn>7</mn> </mrow> </msub> </mrow> </semantics></math> is the angle between OE and OD; <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mn>8</mn> </mrow> </msub> </mrow> </semantics></math> is the angle between D′ D and OD; and h is the vertical distance between the center of the cutter head in the two states.</p>
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<p>Simulation model of obstacle avoidance mowing device between plants. 1. Grassland 2. Pear tree. 3. Pear tree spacing. 4. Rack. 5. Barrier plate. 6. Barrier rod.</p>
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<p>Constraint relationship diagram of obstacle avoidance mower between orchard plants. 1. Obstacle avoidance disc drive. 2. Fixed pair. 3. Rotating pair. 4. Axis rotation drive.</p>
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<p>Model validation information.</p>
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<p>Simulation operation process of obstacle avoidance lawn mower in orchard. Note: (<b>a</b>): inter-row mowing operation stage; (<b>b</b>): obstacle avoidance rod touch tree stage; (<b>c</b>): inter-row obstacle avoidance stage; (<b>d</b>): obstacle avoidance end stage.</p>
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<p>Area of cutter cutting area.</p>
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<p>The influence curve of various factors on the working efficiency of the inter-plant obstacle avoidance mower. (<b>a</b>) The relationship between the forward speed of the machine and the leakage cutting rate. (<b>b</b>) The relationship between the compression speed of hydraulic cylinder and the leakage cutting rate. (<b>c</b>) Relationship between elastic coefficient of reset spring and leakage cutting rate. (<b>d</b>) The relationship between cutter diameter and leakage cutting rate.</p>
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<p>Effects of interaction of various factors on the rate of missing cutting between plants. (<b>a</b>) The interaction of AC on missing cutting G1 between plants. (<b>b</b>) The interaction of BC on missing cutting G1 between plants. (<b>c</b>) The interaction of AB on missing cutting G1 between plants.</p>
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<p>Optimal parameter combination configuration diagram.</p>
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<p>(<b>a</b>) Test site. (<b>b</b>) Obstacle avoidance mower prototype.</p>
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<p>Field test verification. (<b>a</b>) Before mowing operation. (<b>b</b>) After mowing operation (between rows). (<b>c</b>) After mowing operation (between plants).</p>
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18 pages, 3226 KiB  
Article
Power Truncated Positive Normal Distribution: A Quantile Regression Approach Applied to Health Databases
by Karol I. Santoro, Héctor J. Gómez, Isaac E. Cortés, Tiago M. Magalhães and Diego I. Gallardo
Axioms 2024, 13(12), 811; https://doi.org/10.3390/axioms13120811 - 21 Nov 2024
Viewed by 91
Abstract
In this paper we present a new extension of the truncated positive normal (TPN) model, called power truncated positive normal. This extension incorporates a shape parameter that provides more flexibility to the model. In addition, this new extension was reparameterized based on the [...] Read more.
In this paper we present a new extension of the truncated positive normal (TPN) model, called power truncated positive normal. This extension incorporates a shape parameter that provides more flexibility to the model. In addition, this new extension was reparameterized based on the p-th quantile of the distribution in order to perform quantile regression. The initial values were calculated from a modification of the moment estimators, which allowed the maximum likelihood estimators to be obtained. A simulation study was carried out which suggests good behavior of the maximum likelihood estimators in finite samples. Finally, two applications using health databases are presented. Full article
(This article belongs to the Special Issue Advances in the Theory and Applications of Statistical Distributions)
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<p>Pdf, cdf and hazard function for the <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>T</mi> <mi>P</mi> <mi>N</mi> <mo>(</mo> <mi>σ</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mi>λ</mi> <mo>,</mo> <mi>γ</mi> <mo>)</mo> </mrow> </semantics></math> model with different combinations for <math display="inline"><semantics> <mi>λ</mi> </semantics></math> and <math display="inline"><semantics> <mi>α</mi> </semantics></math>.</p>
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<p>Particular cases of the PTPN distribution.</p>
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<p>Shape of <math display="inline"><semantics> <mrow> <mi>u</mi> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and some selected values of <math display="inline"><semantics> <mi>α</mi> </semantics></math> and <math display="inline"><semantics> <mi>λ</mi> </semantics></math>.</p>
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<p>(<b>a</b>) Plots of the kurtosis for PTPN (<math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mi>λ</mi> <mo>,</mo> <mi>γ</mi> </mrow> </semantics></math>). (<b>b</b>) Plots of the skewness for PTPN (<math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mi>λ</mi> <mo>,</mo> <mi>γ</mi> </mrow> </semantics></math>).</p>
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<p>Entropy for the <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>T</mi> <mi>P</mi> <mi>N</mi> <mo>(</mo> <mi>σ</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mi>λ</mi> <mo>,</mo> <mi>γ</mi> <mo>)</mo> </mrow> </semantics></math> model.</p>
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<p>Histogram of the variable <tt>Iron</tt> and the estimated pdf: PTPN (black line), TPN (red line) and PHN (green line).</p>
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<p>QQ-plots of (<b>a</b>) PTPN, (<b>b</b>) TPN and (<b>c</b>) PHN models, in <tt>Iron</tt> data.</p>
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<p>Quantile residuals (<b>a</b>), likelihood displacement (<b>b</b>) and generalized Cook’s distance (<b>c</b>) resulting from fitting the RPTPN model at <math display="inline"><semantics> <mrow> <mi>p</mi> <mo>=</mo> <mn>0.3</mn> </mrow> </semantics></math>.</p>
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10 pages, 254 KiB  
Article
Extremal k-Connected Graphs with Maximum Closeness
by Fazal Hayat and Daniele Ettore Otera
Axioms 2024, 13(12), 810; https://doi.org/10.3390/axioms13120810 - 21 Nov 2024
Viewed by 108
Abstract
Closeness is a measure that quantifies how quickly information can spread from a given node to all other nodes in the network, reflecting the efficiency of communication within the network by indicating how close a node is to all other nodes. For a [...] Read more.
Closeness is a measure that quantifies how quickly information can spread from a given node to all other nodes in the network, reflecting the efficiency of communication within the network by indicating how close a node is to all other nodes. For a graph G, the subset S of vertices of V(G) is called vertex cut of G if the graph GS becomes disconnected. The minimum cardinality of S for which GS is either disconnected or contains precisely one vertex is called connectivity of G. A graph is called k-connected if it stays connected even when any set of fewer than k vertices is removed. In communication networks, a k-connected graph improves network reliability; even if up to k1 nodes fail, the network remains operational, maintaining connectivity between devices. This paper aims to study the concept of closeness within n-vertex graphs with fixed connectivity. First, we identify the graphs that maximize the closeness among all graphs of order n with fixed connectivity k. Then, we determine the graphs that achieve the maximum closeness within all k-connected graphs of order n, given specific fixed parameters such as diameter, independence number, and minimum degree. Full article
(This article belongs to the Special Issue Recent Developments in Graph Theory)
24 pages, 1713 KiB  
Article
Stability Optimization of Explicit Runge–Kutta Methods with Higher-Order Derivatives
by Gerasim V. Krivovichev
Algorithms 2024, 17(12), 535; https://doi.org/10.3390/a17120535 - 21 Nov 2024
Viewed by 95
Abstract
The paper is devoted to the parametric stability optimization of explicit Runge–Kutta methods with higher-order derivatives. The key feature of these methods is the dependence of the coefficients of their stability polynomials on free parameters. Thus, the integral characteristics of stability domains can [...] Read more.
The paper is devoted to the parametric stability optimization of explicit Runge–Kutta methods with higher-order derivatives. The key feature of these methods is the dependence of the coefficients of their stability polynomials on free parameters. Thus, the integral characteristics of stability domains can be considered as functions of free parameters. The optimization is based on the numerical maximization of the area of the stability domain and the length of the stability interval. Runge–Kutta methods with higher-order derivatives, presented in previous works, are optimized. The optimal values of parameters are computed for methods of fourth, fifth, and sixth orders. In numerical experiments, optimal parameter values are used for the construction of high-order schemes for the method of lines for problems with partial differential equations. Problems for linear and nonlinear hyperbolic and parabolic equations are considered. Additionally, an optimized scheme is used in lattice Boltzmann simulations of gas flow. As the main result of computations and comparison with existing methods, it is demonstrated that optimized schemes have better stability properties and can be used in practice. Full article
(This article belongs to the Section Algorithms for Multidisciplinary Applications)
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<p>Boundaries of stability domains for GJRKMs for the non-autonomous equation for <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math> and cRKM for <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>.</p>
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<p>Boundaries of stability domains for TDRKMs with <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>.</p>
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<p>Boundaries of stability domains for TDRKMs with <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math> and cRKM with <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>6</mn> </mrow> </semantics></math>.</p>
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<p>Boundaries of stability domains for ThDRKMs at <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> and classical RKM at <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>.</p>
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<p>Boundaries of stability domains for ThDRKMs at <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math> and classical RKM at <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>7</mn> </mrow> </semantics></math>.</p>
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<p>Stability domains of fourth-order methods.</p>
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<p>Spectrum of matrix <math display="inline"><semantics> <mi mathvariant="bold">B</mi> </semantics></math>, corresponding to sixth-order approximations of the second derivative.</p>
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<p>Spectrum of Jacobian matrix, corresponding to high-order approximations of the second derivative: (<b>a</b>) fourth-order approximation; (<b>b</b>) fifth-order approximation; (<b>c</b>) sixth-order approximation.</p>
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<p>Plots of the logarithms of the absolute values of local error differences: (<b>a</b>) GJRKMs; (<b>b</b>) TDRKMs, <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>; (<b>c</b>) TDRKMs, <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>, <span class="html-italic">R</span> corresponds to method from [<a href="#B33-algorithms-17-00535" class="html-bibr">33</a>]; (<b>d</b>) ThDRKMs, <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, <span class="html-italic">R</span> corresponds to method from [<a href="#B28-algorithms-17-00535" class="html-bibr">28</a>]; (<b>e</b>) ThDRKMs, <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>, <span class="html-italic">R</span> corresponds to method from [<a href="#B28-algorithms-17-00535" class="html-bibr">28</a>].</p>
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<p>Work-precision plots for fourth-order GJRKM, applied to the problem for the Lorenz system.</p>
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<p>The spectrum of the Jacobian matrix for the case of the system of discrete kinetic equations.</p>
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<p>Plots of the logarithm of the practical estimations of local errors for GJRKMs.</p>
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<p>Work-precision plots for fourth-order GJRKM, applied to the problem for the system of kinetic equations.</p>
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14 pages, 3794 KiB  
Article
Development of a Battery Diagnostic Method Based on CAN Data: Examining the Accuracy of Data Received via a Communication Network
by Balázs Baráth, Gergő Sütheö and Letícia Pekk
Energies 2024, 17(22), 5808; https://doi.org/10.3390/en17225808 - 20 Nov 2024
Viewed by 203
Abstract
In order to reduce the emissions caused by internal combustion engine vehicles, the industry is introducing more and more electric or hybrid vehicles to the market nowadays. The battery cells and modules of these vehicles require a lot of care, as improper or [...] Read more.
In order to reduce the emissions caused by internal combustion engine vehicles, the industry is introducing more and more electric or hybrid vehicles to the market nowadays. The battery cells and modules of these vehicles require a lot of care, as improper or improperly maintained battery units can cause serious problems inside vehicles and can be extremely dangerous. The safest solution is to keep this unit of a vehicle under constant supervision so that it can be repaired immediately in case of an issue. Since all necessary data can be extracted from a vehicle’s communication network(s) through standard communication protocols, it is advisable to use them for continuous monitoring and diagnostics of units, while also considering cost-effectiveness and simplicity. The data received from here can also be used for measurement of electric powertrains and other parameters. However, since these data go through many conversions and computers (ECUs) before reaching us, their accuracy is questionable. In this study, we present our own custom battery diagnostic tool based on data extracted from a communication network. With the help of commercially available diagnostic tools, we also compare several measurements of the extent of the error limits of the data arriving at the communication network, how far they differ from the real values, and with the help of these, we analyze the accuracy of the device we have made. We present the commonly used Controller Area Network (CAN) communication protocol for passenger vehicles and briefly describe the construction of the high-voltage battery unit of the test vehicle. Full article
(This article belongs to the Section D2: Electrochem: Batteries, Fuel Cells, Capacitors)
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Figure 1
<p>Physical structure of the CAN bus.</p>
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<p>Bit rate and bus length ratio [<a href="#B14-energies-17-05808" class="html-bibr">14</a>].</p>
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<p>Structure of a CAN message frame.</p>
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<p>The process of deciding the right to use a bus.</p>
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<p>Diagnostic tools used for measurement.</p>
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<p>The process of operation of the diagnostic tool we developed.</p>
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<p>Construction and connection of our device.</p>
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<p>Battery monitoring system interface created by us.</p>
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<p>Battery unit measurement points.</p>
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<p>Diagnostics 1 discrepancy.</p>
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<p>Diagnostics 2 discrepancy.</p>
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<p>Own device discrepancy.</p>
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