Search Results (43)

Direct adoption of nationwide generalized biomass models often causes systematic prediction errors when applied to forest biomass estimation in Hunan Province. This study developed localized multi–component compatible biomass model systems for Chinese fir, poplar and oak based on 461 felled–tree specimens sampled from 14 administrative cities of Hunan Province during 2022–2023. Individual allometric equations were first fitted via weighted least squares, and hierarchical compatible model structures were further established by algebraic component summation and proportional scaling under simultaneous equation constraints. The final total–biomass compatible equations were: Chinese fir: $B_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}=0.065662D^{1.750420}{H}^{0.780381}+0.024760{(D}^2{H)}^{0.774387}$; Poplar: $B_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}=0.046471D^{2.171796}{H}^{0.462424}+0.013116·{(D}^2{H)}^{0.822310}$; Oak: $B_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}=0.0927573{\left(D^{2}H\right)}^{0.89013}+0.018969{\left(D^{2}H\right)}^{0.89162}$. R² values for total and aboveground biomass exceeded 0.92 and prediction accuracy exceeded 96%, with TRE within ±3% for all species. Root biomass models reached prediction accuracy higher than 78% with R² > 0.78. Stem, wood and bark sub–models achieved distinctly better fitting performance than branch and foliage sub–models, and strict hierarchical compatibility was guaranteed among total and component biomass predictions. Calibrated exclusively with local field data, these models effectively eliminate regional systematic estimation bias and only require readily measurable DBH and tree height as input variables, serving as reliable tools for regional forest biomass assessment and routine forest resource monitoring across Hunan Province. Full article

A global, uniform two-variable analytic approximation for the modified Bessel function $I_{\nu }\left(x\right)$ is presented, valid for all real x and for orders $-1/2\le \nu \le 1/4$. The approximation is constructed using a two-variable multipoint quasi-rational approximation (MPQA) approach, in which the argument x and the order $\nu$ are treated simultaneously as independent variables. The method consistently incorporates the power-series expansion at small arguments and the asymptotic behavior at large arguments, leading to an explicit analytic representation that preserves the correct limiting behaviors. The resulting approximation remains suitable for analytical differentiation and integration, while all parameters are obtained from linear equations, avoiding numerical fitting procedures. A numerical analysis over the entire domain considered shows excellent agreement with the exact function. The largest relative error observed is ${\epsilon }_r=0.0213$, occurring at $\nu =-0.34$ and $x=2.56$. These results indicate that the proposed approximation provides an accurate and efficient analytic representation of $I_{\nu }\left(x\right)$ throughout the investigated domain. Full article

Time–space fractional diffusion equations are widely used to model anomalous transport in heterogeneous biological tissues, where memory effects, spatial nonlocality, and coefficient variability are intrinsically coupled. However, existing numerical approaches typically treat these aspects in isolation, and a fully discrete framework that simultaneously accounts for heterogeneity, long-memory effects, and computational efficiency remains lacking. In this work, a fully discrete numerical method is developed and analyzed. The method integrates heterogeneous diffusion coefficients and memory-efficient temporal discretization within a unified variational framework. It combines a finite element approximation of a spectral fractional elliptic operator with an implicit $L^1$ discretization of the Caputo derivative enhanced by a sum-of-exponentials approximation of the memory kernel. Unconditional stability, preservation of a discrete energy structure, and a fully discrete error estimate are established, explicitly separating temporal, spatial, and kernel approximation errors. The proposed approach reduces memory complexity from $\mathcal{O}\left(N\right)$ to $\mathcal{O}(logN)$ without compromising accuracy. Numerical experiments confirm the theoretical convergence rates, demonstrate stable behavior across all tested configurations, and illustrate the impact of heterogeneous coefficients on anomalous transport dynamics. Full article

This study presents a comprehensive thermal analysis, design, and optimization framework for electrothermal heating systems integrated into composite wing structures. Thermal behavior is first investigated using finite volume simulations conducted with a commercial solver. An in-house thermal solver is then developed based on the governing heat transfer equations and a second-order finite difference discretization scheme. The in-house solver is validated against the commercial solver, showing a maximum deviation of less than 1%. The validated solver is subsequently coupled with a genetic algorithm to perform multi-objective optimization of the electrothermal heating system. A novel correlation for the convection heat transfer coefficient over airfoil surfaces is developed based on extensive turbulent flow simulations and a genetic algorithm. The developed correlation equation has significantly lower percent relative error (from 34% to 6%) compared to flat plate correlations. The developed convection coefficient is incorporated into the optimization process. Key design variables, including heat generation intensity, heater strip dimensions, and the thermal conductivity of composite and surface protection materials, are included in the optimization process. An original objective function is formulated to simultaneously minimize electrical power consumption, prevent ice formation on the external surface, and limit internal temperatures to safe operating ranges for composite materials. The optimized design is evaluated under both spatially varying and constant convection heat transfer coefficients to assess the impact of convection modeling assumptions. The proposed methodology provides a unified and extensible framework for the optimal design of electrothermal ice protection systems and can be readily extended to three-dimensional composite wing configurations. Full article

The predictive current control for the permanent magnet synchronous machine (PMSM) shows great potential in applications like flywheel energy storage, owing to its fast dynamic response and simple structure. However, under low carrier ratio conditions, conventional deadbeat predictive current control (DPCC) exhibits drawbacks such as significant current prediction error, inaccurate instruction voltage calculation, and severe torque and flux linkage coupling. This paper proposes an improved DPCC method suitable for both high and low carrier ratio operation of the PMSM. First, a modified stator voltage equation is established considering rotor flux orientation error. By treating the dq-coordinates as stationary and accounting for rotor rotation within the control period, a dynamic PMSM model is developed, effectively suppressing cross-axis coupling under low carrier ratios. Simultaneously, a multi-coordinate variable synchronization method is also introduced to eliminate prediction and voltage errors caused by cross-coordinate computation, enabling precise deadbeat control across all carrier ratios. The experimental results demonstrate that the proposed method enhances torque-flux decoupling, improves current prediction and tracking accuracy at low carrier ratios, and offers a reliable solution for dynamic control in flywheel energy storage systems. Full article

Controlling autonomous vehicles to follow a desired lateral trajectory presents a significant challenge. Developers of lateral control systems often find it difficult to simultaneously bring both lateral error and heading angle error close to zero while smoothly following the curvature of the road. This paper introduces the design and development of a control strategy for lateral trajectory following using the backstepping control method, which successfully achieves the goal of stabilization and tracking. The controller comprises a backstepping feedback control law to regulate the errors and stabilize the vehicle by controlling the yaw rate, along with a dynamic feedforward component to compensate for road curvature and further eliminate steady-state errors on curved roads. The controller is built upon the dynamic bicycle model, enhanced by integrating the error dynamics into the state space equation, which allows for the inclusion of errors as state variables. The global uniform stability of the feedback control law is proven using Lyapunov stability theory and the LaSalle–Yoshizawa theorem. The stability and tracking performance of the controller are validated through simulation and experimental results obtained from a test vehicle on a public highway. Full article

In surface energy tests of asphalt materials, the inaccuracy of the calculation method (e.g., least squares (LS)) and the arbitrary selection of chemical reagent combinations lead to unstable results, threatening the quantitative evaluation of asphalt–aggregate adhesion durability. This study addresses these two scientific deficiencies with the following findings: (1) when simultaneous equations are used to calculate the asphalt surface energy parameters, the total least squares method should be used instead of the classical least squares method to reduce the fitting error; (2) the selection of the reagent combination should be based on which one is the most rational in terms of the physical characterization, leap degree, abnormal values, and other requirements, and the reagent combination with the fewest abnormal values should be chosen as the best scheme. The results show that (1) compared with the classical least squares method, the total least squares method reduces the fitting error between the calculated and real values of asphalt surface energy parameters and improves the accuracy and stability of the calculation results; (2) the best reagent combination scheme is WFSD (distilled water + formamide + dimethyl sulfoxide + diiodomethane). The calculated values of asphalt surface energy parameters were more accurate and reasonable, and the calculation results had no abnormal values. Compared with WFEG (distilled water + formamide + ethylene glycol + glycerol), the error rate of the reagent combination scheme WFSD in calculating the total surface energy of two kinds of asphalt was reduced by 17.71% and 64.80%, respectively. These findings establish a reliable framework for the accurate quantification of surface energy, addressing the critical issue of reagent-dependent variability in the results and strengthening the scientific basis for evaluating the durability of asphalt pavement. Full article

The measurement of apparent dielectric permittivity (ε_s) by low-frequency capacitance sensors and its conversion to the volumetric water content of soil (θ) through a factory calibration is a valuable tool in precision irrigation. Under certain soil conditions, however, ε_s readings are substantially affected by the bulk soil electrical conductivity (EC_b) variability, which is omitted in default calibration, leading to inaccurate θ estimations. This poses a challenge to the reliability of the capacitance sensors that require soil-specific calibrations, considering the EC_b impact to ensure the accuracy in θ measurements. In this work, a multivariate calibration equation (multivariate) incorporating both ε_s and EC_b for the determination of θ by the capacitance WET sensor (Delta-T Devices Ltd., Cambridge, UK) is examined. The experiments were conducted in the laboratory using the WET sensor, which measured θ, ε_s, and EC_b simultaneously over a range of soil types with a predetermined actual volumetric water content value (θ_m) ranging from θ = 0 to saturation, which were obtained by wetting the soils with four water solutions of different electrical conductivities (EC_i). The multivariate model’s performance was evaluated against the univariate CAL and the manufacturer’s (Manuf) calibration methods with the Root Mean Square Error (RMSE). According to the results, the multivariate model provided the most accurate θ estimations, (RMSE ≤ 0.022 m³m⁻³) compared to CAL (RMSE ≤ 0.027 m³m⁻³) and Manuf (RMSE ≤ 0.042 m³m⁻³), across all the examined soils. This study validates the effects of EC_b on θ for the WET and recommends the multivariate approach for improving the capacitance sensors’ accuracy in soil moisture measurements. Full article

In scientific and engineering disciplines, vectorial problems involving systems of equations or functions with multiple variables frequently arise, often defying analytical solutions and necessitating numerical techniques. This research introduces an efficient numerical scheme capable of simultaneously approximating all roots of nonlinear equations with a convergence order of ten, specifically designed for vectorial problems. Random initial vectors are employed to assess the global convergence behavior of the proposed scheme. The newly developed method surpasses methods in the existing literature in terms of accuracy, consistency, computational CPU time, residual error, and stability. This superiority is demonstrated through numerical experiments tackling engineering problems and solving heat equations under various diffusibility parameters and boundary conditions. The findings underscore the efficacy of the proposed approach in addressing complex nonlinear systems encountered in diverse applied scenarios. Full article

Forest biomass and carbon storage models are crucial for inventorying, monitoring, and assessing forest resources. This study develops models specific to China’s diverse forests, offering a methodological foundation for national carbon storage estimation and a quantitative basis for national, regional, and global carbon sequestration projections. Utilizing data from 52,700 permanent plots obtained during China’s 9th national forest inventory, we calculated biomass and carbon storage per hectare for 35 tree species groups using respective individual tree biomass models and carbon factors. We then constructed a three-level volume-based model system for forest biomass and carbon storage, applying weighted regression, dummy variable modeling, and simultaneous equations with error-in-variables. This system encompasses one population of forests, three forest categories (level I), 20 forest types (level II), and 74 forest sub-types (level III). Finally, the assessment of these models was carried out with six evaluation indices, and comparative analyses with previously established biomass models of three major forest types were conducted. Determination coefficients (R²) for the population average model, and three dummy models on levels I, II, and III, exceed 0.78, 0.85, 0.92, and 0.95, respectively, with corresponding mean prediction errors (MPEs) of 0.42%, 0.34%, 0.24%, and 0.19%, and mean percent standard errors (MPSEs) of approximately 22%, 21%, 15%, and 12%. Models for 20 forest types and 74 sub-types yield R² values above 0.87 and 0.85, with MPE values below 3% and 5%, respectively. Notably, the estimates of previous biomass models of three major forest types demonstrated considerable uncertainty, with TRE ranging from −20% to 74%. However, accuracy has improved with larger sample sizes. In total biomass and carbon storage estimations, the R² values of dummy models for levels I, II, and III progressively increase and MPSE and MPE values decrease, whereas TRE approximates zero. The tiered model system of simultaneous equations developed herein offers a quantitative framework for precise evaluations of biomass and carbon storage on different scales. For enhanced accuracy in such estimations, applying level III models is recommended whenever feasible, especially for national estimation. Full article

Joint localization and synchronization (JLAS) is a technology that simultaneously determines the spatial locations of user nodes and synchronizes the clocks between user nodes (UNs) and anchor nodes (ANs). This technology is crucial for various applications in wireless sensor networks. Existing solutions for JLAS are either computationally demanding or not resilient to noise. This paper addresses the challenge of localizing and synchronizing a mobile user node in broadcast-based JLAS systems using sequential one-way time-of-arrival (TOA) measurements. The AN position uncertainty is considered along with clock offset and skew. Two redundant variables that couple the unknowns are introduced to pseudo-linearize the measurement equation. In projecting the equation to the nullspace spanned by the coefficients of the redundant variables, the affection of them can be eliminated. While the closed-form projection solution provides an initial point for iteration, it is suboptimal and may not achieve the Cramér-Rao lower bound (CRLB) when noise or AN position error is relatively large. To improve performance, we propose a novel robust iterative solution (RIS) formulated through factor graphs and developed via message passing. The RIS outperforms the common Gauss–Newton iteration, especially in high-noise scenarios. It exhibits a lower root mean-square error (RMSE) and a higher probability of converging to the optimal solution, while maintaining manageable computational complexity. Both analytical results and numerical simulations validate the superiority of the proposed solution in terms of performance, resilience, and computational load. Full article

An online measurement method is proposed in this paper, and a system is established for detecting the excitation impedance of current transformers (CTs) based on Norton’s theorem. The theorem is carried out by connecting a resistance and an inductance at the secondary side port of the CT to get the equations for calculating the impedance. The iterative method is used to solve the equations, and the solution is revised to consider the nonlinearity of the core. The main variable in the equations is the variation of the secondary current with the resistance or inductance. To obtain the secondary current variation accurately, which is less than 1‰ of the current, a differential method is proposed, which is based on charging two capacitors and measuring the difference of their voltages instead of measuring each current separately first and then obtaining the current variation by subtraction. This is equivalent to saving two currents first and then measuring the current difference. The differential method avoids the problem of error amplification in the process of measuring two currents separately first and then subtracting them to obtain the current variation and solves the problem that two currents do not appear simultaneously. The results verify the correctness and accuracy of the proposed method and system. The acquisition of the excitation impedance is the basis for obtaining the working characteristics of CT cores, including magnetic and loss characteristics, as well as the error of CTs. Full article

This study aimed to develop simultaneous models with universal applicability for the estimation of the main factors of forest stands based on airborne LiDAR data and to provide a reference for standardizing the approach and evaluation indices of main forest factor modeling. Using airborne LiDAR and field survey data from 190 sample plots in spruce (Picea spp.), fir (Abies spp.), and spruce–fir mixed forests in Northeast China, the simultaneous models for estimating the main factors of forest stands were developed. To develop the models, the relationships between mean tree height, stand basal area, stand volume, and the main metrics of the LiDAR data and the correlations between eight quantitative factors of forest stands were considered, and the error-in-variable simultaneous equations approach was employed to fit the models. The results showed that the mean prediction errors (MPEs) of eight forest stand factors estimated by the simultaneous models were mostly within 5%, and only the MPE of the number of trees per hectare exceeded 5%. The mean percentage standard errors (MPSEs) of the estimates, including the mean diameter at the breast height (DBH), mean tree height, and mean dominant tree height, were within 15%; the MPSEs of the estimates of the stand basal area, volume, biomass, and carbon stock per hectare were within 25%; and only the MPSE of the estimated number of trees per hectare exceeded 30%. The coefficients of determination (R²) of the core prediction models for the volume, biomass, and carbon storage were all greater than 0.7. It can be concluded that estimating the main factors of forest stands based on the combination of LiDAR and field survey data is technically feasible, and the simultaneous models developed in this study for the estimation of the eight main stand factors of spruce–fir forests can meet the precision requirements of forest resource inventory, except for the number of trees, indicating that the models can be applied in practice. Full article

The unstructured mechanistic model (UMM) allows for modeling the macro-scale of a phenomenon without known mechanisms. This is extremely useful in biomanufacturing because using the UMM for the joint estimation of states and parameters with an extended Kalman filter (JEKF) can enable the real-time monitoring of bioprocesses with unknown mechanisms. However, the UMM commonly used in biomanufacturing contains ordinary differential equations (ODEs) with unshared parameters, weak variables, and weak terms. When such a UMM is coupled with an initial state error covariance matrix $\mathbf{P}(t=0)$ and a process error covariance matrix $\mathbf{Q}$ with uncorrelated elements, along with just one measured state variable, the joint extended Kalman filter (JEKF) fails to estimate the unshared parameters and state simultaneously. This is because the Kalman gain corresponding to the unshared parameter remains constant and equal to zero. In this work, we formally describe this failure case, present the proof of JEKF failure, and propose an approach called SANTO to side-step this failure case. The SANTO approach consists of adding a quantity to the state error covariance between the measured state variable and unshared parameter in the initial P(t = 0) of the matrix Ricatti differential equation to compute the predicted error covariance matrix of the state and prevent the Kalman gain from being zero. Our empirical evaluations using synthetic and real datasets reveal significant improvements: SANTO achieved a reduction in root-mean-square percentage error (RMSPE) of up to approximately 17% compared to the classical JEKF, indicating a substantial enhancement in estimation accuracy. Full article

Simulating solute transport in heterogeneous porous media poses computational challenges due to the high-resolution meshing required for traditional solvers. To overcome these challenges, this study explores a mesh-free method based on deep learning to accelerate solute transport simulation. We employ Physics-informed Neural Networks (PiNN) with a periodic activation function to solve solute transport problems in both homogeneous and heterogeneous porous media governed by the advection-dispersion equation. Unlike traditional neural networks that rely on large training datasets, PiNNs use strong-form mathematical models to constrain the network in the training phase and simultaneously solve for multiple dependent or independent field variables, such as pressure and solute concentration fields. To demonstrate the effectiveness of using PiNNs with a periodic activation function to resolve solute transport in porous media, we construct PiNNs using two activation functions, sin and tanh, for seven case studies, including 1D and 2D scenarios. The accuracy of the PiNNs’ predictions is then evaluated using absolute point error and mean square error metrics and compared to the ground truth solutions obtained analytically or numerically. Our results demonstrate that the PiNN with sin activation function, compared to tanh activation function, is up to two orders of magnitude more accurate and up to two times faster to train, especially in heterogeneous porous media. Moreover, PiNN’s simultaneous predictions of pressure and concentration fields can reduce computational expenses in terms of inference time by three orders of magnitude compared to FEM simulations for two-dimensional cases. Full article