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Measurement of the cervical range of motion (CROM) is significant for early diagnosis of cervical spondylosis and determination of the severity of the disease. Aiming at the problem of convenient and continuous measurement of CROM and the reduction of the impact of data fluctuations, this paper proposes a low‐cost method for testing and analyzing CROM. This paper analyzes the correspondence between smartphone orientation sensor angle and CROM, obtains smartphone orientation sensing data, and uses the extreme‐point symmetric mode decomposition method by calculating the energy of the difference value to extract the adaptive global mean curve of the CROM data, and calculates the cervical ROM. The statistical analysis of the CROM test results is carried out. Results show that the method proposed can obtain the CROM including flexion and extension, lateral flexion, and rotation in a single measurement, which has the advantages of continuous measurement and low cost. [ABSTRACT FROM AUTHOR]

This paper presents a novel bolt looseness detection method for power transmission towers based on vibration signal analysis. The proposed method utilizes pulse excitation to extract the vibration signal of the tower, which is then adaptively decomposed using the Variational Mode Decomposition of Spider Wasp optimizer (SWVMD). This overcomes limitations of traditional Variational Mode Decomposition methods by leveraging bio‐inspired optimization to improve signal decomposition. Simulated signals processed with different optimization methods verify the superiority of the SWO approach. Field tests on a 110‐kV transmission tower further demonstrate the effectiveness of the proposed SWVMD technique for analyzing on‐site vibration data. A new improved intrinsic multiscale sample entropy feature is also introduced for bolt state characterization. A Spider Wasp Support Vector Machine classifier is developed to realize accurate bolt loosening monitoring using the extracted features. Dynamic response tests under varying bolt conditions show that the method can identify early loosening and reduce tower damage risks compared to conventional techniques. This novel vibration‐based detection framework presents an innovative application of nature‐inspired computing for power infrastructure health monitoring. [ABSTRACT FROM AUTHOR]

The optimization of Multidimensional Knapsacks with Family‐Split Penalties has been introduced in the literature as a variant of the more classical Multidimensional Knapsack and Multi‐Knapsack problems. This problem deals with a set of items partitioned in families, and when a single item is picked to maximize the utility, then all items in its family must be picked. Items from the same family can be assigned to different knapsacks, and in this situation split penalties are paid. This problem arises in real applications in various fields. This paper proposes a new exact and fast algorithm based on a specific Combinatorial Benders Cuts scheme. An extensive experimental campaign computationally shows the validity of the proposed method and its superior performance compared to both commercial solvers and state‐of‐the‐art approaches. The paper also addresses algorithmic flexibility and scalability issues, investigates challenging cases, and analyzes the impact of problem parameters on the algorithm behavior. Moreover, it shows the applicability of the proposed approach to a wider class of realistic problems, including fixed costs related to each knapsack utilization. Finally, further possible research directions are considered. [ABSTRACT FROM AUTHOR]

This paper proposes a deep learning method to predict the electromagnetic emission spectrum in the electromagnetic compatibility (EMC) test of aerospace products. A threshold‐based data decomposition method is used to propose the spike signal, reconstruct the original test data, and solve the contradiction between the overfitting and prediction accuracy of the deep learning method to deal with the EMC test spectrum. Using a long short‐term memory neural network architecture for predicting electromagnetic emission spectrum, the Bayesian optimization method is used to optimize the network hyperparameter, and the acquisition function is introduced into the loss function to improve the comprehensive training optimization of deep learning network. Apply the method to three numerical examples: signal line current conduction emission, power line voltage conduction emission, and electric field radiation emission. The analysis results indicate that at a 95% confidence level, the predicted electromagnetic emission spectrum is basically consistent with the test results. The prediction results can be used as the basis for EMC evaluation of aerospace electronic equipment. [ABSTRACT FROM AUTHOR]

The paper presents a new method for the decomposition of the horizontal wind divergence among linear waves on the sphere: inertia‐gravity (IG), mixed Rossby‐gravity (MRG), Kelvin and Rossby waves. The work is motivated by the need to quantify the vertical velocity and momentum fluxes in the tropics where the distinction between the Rossby and gravity regime, present in the extratropics, becomes obliterated. The method leads to divergence power spectra as a function of latitude and pressure. The spectra follow the same power laws as the vertical kinetic energy spectra for different wave types. The key novel aspect of the work is the coexistence of wave types at the same zonal wavenumbers. Applied to ERA5 data in August 2018, the new method reveals that the zonally‐integrated Kelvin wave divergence makes up about 19% of the upper‐troposphere divergence within 10°S–10°N. The MRG wave divergence has four times smaller magnitude. The relative roles of the two waves vary with scale. Overall small roles of the Kelvin and MRG waves in the tropical divergence is explained by decomposing their kinetic energies into rotational and divergent parts. The beta effects produces less then 5% of the tropospheric divergence associated with Rossby waves. The majority of divergence belongs to IG modes and is nearly equipartitioned between the eastward‐ and westward‐propagating IG modes in the upper troposphere, whereas stratospheric partitioning depends on the background flow. Plain Language Summary: The horizontal circulation is commonly discussed using divergence and vorticity instead of the two wind components. The advantage is that vorticity and divergence characterize the Rossby wave and inertia‐gravity (IG) wave dynamics, respectively, thereby offering an easier understanding of wave processes. The two wave regimes are well separated in extratropics also in the wavenumber and frequency space. However, there is no regime separation in the tropics where IG waves shape variability at all scales including low‐frequency variability. Furthermore, two additional waves are present, Kelvin waves and mixed Rossby‐gravity (MRG) waves that span the wavenumber and frequency space between Rossby and IG waves. This study aims at a better understanding of partitioning between divergent and rotational components of equatorial waves. In particular, Kelvin and MRG waves have significant variances at the same scales as Rossby and IG waves calling for an approach that quantifies their divergence at the same wavenumbers. This paper develops such an approach for the spherical atmosphere and demonstrates it on the ERA5 data in August 2018. One important result is that the Kelvin and MRG wave constitute up to approximately 25% of divergence in the tropical upper troposphere, mainly in Kelvin waves. Key Points: A new method couples divergence with wave circulation as a function of latitude and pressure levelDivergence quantification accounts for wave types sharing the same zonal scale, which is crucial for disentangling tropical flowsApplied to ERA5, the new method highlights vortical nature of mixed Rossby‐gravity waves and large‐scale Kelvin waves [ABSTRACT FROM AUTHOR]

The stabilization problem for uncertain discrete‐time singular Markovian jump systems (DSMJSs) with time‐varying delays is comprehensively covered in this paper. An updated Lyapunov–Krasovskii functional is presented via a discrete state decomposition method. With the help of this constructed Lyapunov–Krasovskii functional, some delay‐ and mode‐dependent sufficient conditions for the open‐loop DSMJSs are derived. Based on these circumstances, a memory mode‐dependent state feedback control is used to create a closed‐loop DSMJS with parameter uncertainties that is regular and causal. And then, the stochastically admissible conditions are attained. Through the exact calculation of each decomposition component for the designed memory state feedback controller, the intended memory state feedback controller settings are determined. It should be mentioned that the algorithm suggested in this article expands the controller design's feasibility and flexibility. The numerical results show how the approach is superior to previous ones, and the given results are less conservative. [ABSTRACT FROM AUTHOR]

In this article, we investigate the existence and uniqueness of solutions to a generalized nonlinear functional integral equation (G‐NLFIE) associated with certain epidemic models of infectious diseases, defined within the Banach space C[0,1]$$ C\left[0,1\right] $$. Our existence results include several specific cases of nonlinear functional integral equations that commonly occur in nonlinear sciences. We then introduce an iterative algorithm that combines Adomian's decomposition method (ADM) with the modified homotopy perturbation method (mHPM) to approximate solutions to the G‐NLFIE. The paper addresses the convergence properties and error analysis of this method. Finally, we present numerical examples to demonstrate the effectiveness and efficiency of our proposed approach. [ABSTRACT FROM AUTHOR]

ABSTRACT Trilinearity is a property of some chemical data that leads to unique decompositions when curve resolution or multiway decomposition methods are used. Curve resolution algorithms, such as Multivariate Curve Resolution–Alternating Least Squares (MCR‐ALS), can provide trilinear models by implementing the trilinearity condition as a constraint. However, some trilinear analytical measurements, such as excitation–emission matrix (EEM) measurements, usually exhibit systematic patterns of missing data due to the nature of the technique, which imply a challenge to the classical implementation of the trilinearity constraint. In this instance, extrapolation or imputation methodologies may not provide optimal results. Recently, a novel algorithmic strategy to constrain trilinearity in MCR‐ALS in the presence of missing data was developed. This strategy relies on the sequential imposition of a classical trilinearity restriction on different submatrices of the original investigated dataset, but, although effective, was found to be particularly slow and requires a proper submatrix selection criterion. In this paper, a much simpler implementation of the trilinearity constraint in MCR‐ALS capable of handling systematic patterns of missing data and based on the principles of the Nonlinear Iterative Partial Least Squares (NIPALS) algorithm is proposed. This novel approach preserves the trilinearity of the retrieved component profiles without requiring data imputation or subset selection steps and, as with all other constraints designed for MCR‐ALS, offers the flexibility to be applied component‐wise or data block‐wise, providing hybrid bilinear/trilinear models. Furthermore, it can be easily extended to cope with any trilinear or higher‐order dataset with whatever pattern of missing values. [ABSTRACT FROM AUTHOR]

The inverted velocity model obtained from the reflection tomography based on the angle domain common‐image gathers has a certain fuzziness. The inverted velocity model's stratigraphic interface is always not clear enough in areas with complex stratigraphic structure. In order to improve the accuracy and resolution of the inverted velocity model, a double‐difference constraint condition is added on the basis of minimizing the absolute travel‐time residual at the subsurface imaging points. This constraint makes the inverted velocity model local structure information more refined by minimizing the differential travel‐time residual at adjacent imaging points (i.e. closely spaced points within the same layer) and makes the variation of velocity model information within a certain range more accurate. The method in this paper is based on angle domain common‐image gathers, the tomography inversion equation is established by using the ray tracing method, and the conversion relationship between the traveltime residual and the residual curvature of the angle domain common‐image gathers. Then, by adding differential constraint and double‐differential constraint conditions and using the least squares QR decomposition method to solve the set of equations, the inverted velocity model can be obtained through multiple iterations, which provides a high‐precision velocity field for the migration and improves the accuracy of seismic imaging. Numerical experiments on both one typical model and a field data example demonstrate the effectiveness of the proposed double‐difference constrained elastic reflection tomography in generating high‐precision velocity models. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to explore economic inequality in 'the Belt and Road' region where the investigation of the economic status is important but remains underdeveloped. The application of night‐time satellite imagery in 2015 can effectively make up for the shortcomings of insufficient data at various scales, especially for developing countries. We explored inequality at a multi‐scale level using the Theil decomposition method. As a result, (1) night‐time light data can present economic development and assess inequality in 'the Belt and Road' region. (2) The between‐sub‐region inequality contributed most to disparity, while the between‐country inequality was the least. Night‐time light data in West Asia and Central and Eastern Europe was higher than that in other sub‐regions. Countries within Central, Southeast and West Asia exhibited high inequalities, indicating an obvious sub‐regional pattern. (3) Both positive and negative impacts of economic growth on inequality are observed, indicating that 'the Belt and Road' countries are in different stages of economic development. Nightlight satellite imagery can effectively monitor social‐economic development and will play an important role in the implementation of 'the Belt and Road' initiative and achieving the sustainable development goals. [ABSTRACT FROM AUTHOR]

Based on a Fairlie decomposition method, this paper analyzes the drivers of gender gaps in financial inclusion in Cameroon. We use Finscope 2017 data for Cameroon and assess six distinct financial inclusion variables grouped into two dimensions mainly, access to and use of financial products and services. Our results show that there is a gap in all indicators of access to and use of financial products and services in favor of men. The results also show that the largest contributor to the gender gap in access to financial products and services is income, with more than 50% of the contribution, whereas the largest contributor to the gender gap in the use of financial products and services is education with an average contribution of more than 35%. Based on the above findings, decision‐makers in Cameroon must conduct economic policies toward facilitating equitable access to education, by providing incentives to attract women to gain higher education. [ABSTRACT FROM AUTHOR]

In this paper, the Lagrange stability (LS) for quaternion memristive neural networks with time delay is taken into consideration. On the strength of Lyapunov function, conclusions are derived such that the resultant system is stable in Lagrange sense. The analysis procedure adopts properties of quaternions instead of conventional decomposition method. The nonlinear scalarization approach is further exploited to compare the size of the quaternion, which makes the convex closures formed by quaternions more noteworthy. [ABSTRACT FROM AUTHOR]

As a kind of commutative and associative four-dimensional algebra, commutative quaternion has better applications in color image and signal processing than quaternion. Matrix decomposition is of great concern in the theoretical study and numerical calculation of commutative quaternion. Two kinds of disadvantages of commutative quaternion make the decomposition of commutative quaternion matrix extremely difficult. On one hand, commutative quaternion is not a kind of complete four dimensional division algebra because of the zero divisors. On the other hand, computing the inverse of commutative quaternion is very complicated. In this paper, the semi-tensor product (STP) of matrices will be used to overcome the above two kinds of shortcomings. And we will propose a real structure-preserving algorithm based on STP of matrices for commutative quaternion LU decomposition, which makes full use of high-level operations, relation of operations between commutative quaternion matrices and their L-representation matrices. Numerical experiments will be provided to demonstrate the efficiency of the real structure-preserving algorithm based on STP of matrices. Meanwhile, we will apply the structure-preserving algorithm for strict image authentication. [ABSTRACT FROM AUTHOR]

Summary: The reduced‐order observer‐based finite‐time control problem for one‐sided Lipschitz nonlinear switched singular systems is addressed in this paper. First, the design method of the reduced‐order observer is given via state transformation. Then, based on the average dwell time (ADT) approach, some new sufficient conditions for regularity, impulse‐freeness, have a unique solution and finite‐time boundedness (FTB) of the dynamic augmented systems are obtained by exploring the reduced‐order observer‐based controller. Further, the lower finite‐time bound can be obtained by using singular value decomposition method. And the state feedback gain and the observer gain are computed by solving linear matrix inequalities (LMIs). Finally, the validity of the obtained method is illustrated by means of a numerical example and a DC motor system. [ABSTRACT FROM AUTHOR]

Tensor ring (TR) decomposition has been widely applied as an effective approach in a variety of applications to discover the hidden low‐rank patterns in multidimensional and higher‐order data. A well‐known method for TR decomposition is the alternating least squares (ALS). However, solving the ALS subproblems often suffers from high cost issue, especially for large‐scale tensors. In this paper, we provide two strategies to tackle this issue and design three ALS‐based algorithms. Specifically, the first strategy is used to simplify the calculation of the coefficient matrices of the normal equations for the ALS subproblems, which takes full advantage of the structure of the coefficient matrices of the subproblems and hence makes the corresponding algorithm perform much better than the regular ALS method in terms of computing time. The second strategy is to stabilize the ALS subproblems by QR factorizations on TR‐cores, and hence the corresponding algorithms are more numerically stable compared with our first algorithm. Extensive numerical experiments on synthetic and real data are given to illustrate and confirm the above results. In addition, we also present the complexity analyses of the proposed algorithms. [ABSTRACT FROM AUTHOR]

The tracking control problem of non‐holonomic mobile robot systems has been extensively investigated in the past decades, however, most of the existing control strategies were developed specifically for the fixed‐point tracking. This technical note focuses on the region tracking control for a non‐holonomic mobile robot system with parameter uncertainties in the robot dynamics. With the system decomposition and adaptive control method, some restrictions imposed on the angular and linear velocities of the non‐holonomic mobile robot in recent literature are removed, enabling to track dynamic trajectories with any values of the angular and line velocities. The proposed adaptive control scheme can simultaneously solve both the regulation and region tracking problems of a non‐holonomic mobile robot with one passive wheel and two actuated wheels. By utilizing the designed control laws, the mobile robot system is able to globally reach inside a moving region specified by potential functions whose path can be a circular curve, a straight line, or sinusoidal curve, by using a single adaptive controller. Since the dynamic region can be specified arbitrarily small, the fixed‐point tracking can be regarded as a special case of region tracking studied in this paper. Compared with the traditional fixed‐point tracking, region tracking has more flexibility and better robustness. Numerical results are presented to show the effectiveness of the designed strategy. [ABSTRACT FROM AUTHOR]

Catalogs of refactoring have key importance in software maintenance and evolution, since developers rely on such documents to understand and perform refactoring operations. Furthermore, these catalogs constitute a reference guide for communication between practitioners since they standardize a common refactoring vocabulary. Fowler's book describes the most popular catalog of refactorings, which documents single and well‐known refactoring operations. However, sometimes, refactorings are composite transformations, that is, a sequence of refactorings is performed over a given program element. For example, a sequence of Extract Method operations (a single refactoring) can be performed over the same method, in one or in multiple commits, to simplify its implementation, therefore, leading to a Method Decomposition operation (a composite refactoring). In this paper, we propose and document a catalog with eight composite refactorings. We also implement a set of scripts to mine composite refactorings by preprocessing the results of refactoring detection tools. Using such scripts, we search for composites in a representative refactoring oracle with hundreds of confirmed single refactoring operations. Next, to complement this first study, we also search for composites in the full history of 10 well‐known open‐source projects. We characterize the detected composite refactorings, under dimensions such as size and location. We conclude by addressing the applications and implications of the proposed catalog. [ABSTRACT FROM AUTHOR]

The Levin‐Nohel integro‐differential equation is one of the famous equations in various fields of science and engineering. It was first studied by Volterra in connection with biological applications. This paper deals with the nonlinear neutral Levin‐Nohel integro‐differential equation with Caputo fractional derivative and variable delays. The Ulam‐Hyers‐Rassias stability, Ulam‐Hyers stability, semi‐Ulam‐Hyers‐Rassias stability are studied. The existence and uniqueness of solutions are established by using Krasnoselskii's fixed point theorem and contraction mapping principle. An illustrative example is also given and that is studied by the help of the Adomian decomposition method. [ABSTRACT FROM AUTHOR]

Summary: Exploring the associations between microRNAs (miRNAs) and diseases can identify potential disease features. Prediction of miRNA‐skin cancer associations has become an effective method for detecting skin cancer, as direct detection of skin cancer is challenging. However, traditional binary associations prediction methods overlook high‐order feature differences of miRNAs in different types of skin cancer. Although current tensor decomposition methods have addressed this, they assume a consistent composition standard of global tensor elements, ignoring differences in the composition standards of local sub‐tensors. This leads to poor prediction accuracy and comprehensiveness and fails to consider the credibility and diversity requirements of patients and doctors in practical applications. In this paper, we represent miRNA‐skin cancer associations as a tensor and employ tensor decomposition for tensor completion to achieve prediction purposes. First, we propose a credibility evaluation indicator and introduce four objective functions: accuracy, comprehensiveness, credibility, and diversity, to construct a many‐objective local tensor factorization model (MOLTF). Then, to avoid wrong individuals when solving this model with genetic algorithms, we propose a corrected single‐point crossover operator and a corrected multi‐point mutation operator. On the miRNA‐disease dataset HMDD v3.2, our algorithm improves accuracy by 14.5% compared to the recent baseline, demonstrating its effectiveness. [ABSTRACT FROM AUTHOR]

The possibilities offered by the use of variational mode decomposition–based Hilbert marginal spectrum and the differential cepstrum for gas‐bearing detection are studied in this paper. We propose a novel variational mode decomposition–based Hilbert marginal differential cepstrum for hydrocarbon detection. Variational mode decomposition–based Hilbert marginal spectrum is first computed. Then discrete cosine transform is carried out to the differential logarithmic variational mode decomposition–based Hilbert marginal spectrum to obtain the variational mode decomposition–based Hilbert marginal differential cepstrum. For hydrocarbon detection, the seismic amplitude anomaly section is generated by extracting the first and second common quefrency sections. Compared with the traditional Fourier‐based cepstrum, the wavelet‐based cepstrum and the Berthil cepstrum, it has the ability to effectively reveal more detailed frequency‐dependent amplitude anomalies with high accuracy and resolution. Model tests and field data applications from a carbonate reservoir in China show that the variational mode decomposition‐based Hilbert marginal differential cepstrum can provide a better gas‐prone interpretation. The proposed method can be a complementary approach to current cepstrum‐based hydrocarbon detection methods and the spectrum decomposition methods. [ABSTRACT FROM AUTHOR]

A linear forest is a disjoint union of path graphs. The linear arboricity of a graphG $G$, denoted by la(G) $\text{la}(G)$, is the least number of linear forests into which the graph can be partitioned. Clearly, la(G)≥⌈Δ(G)∕2⌉ $\text{la}(G)\ge \lceil {\rm{\Delta }}(G)\unicode{x02215}2\rceil $ for any graph of maximum degree Δ(G) ${\rm{\Delta }}(G)$. For the upper bound, the long‐standing Linear Arboricity Conjecture (LAC) due to Akiyama, Exoo, and Harary from 1981 asserts that la(G)≤⌈(Δ(G)+1)∕2⌉ $\text{la}(G)\le \lceil ({\rm{\Delta }}(G)+1)\unicode{x02215}2\rceil $. A graph is a pseudoforest if each of its components contains at most one cycle. In this paper, we prove that the union of any two pseudoforests of maximum degree up to 3 can be decomposed into three linear forests. Combining it with a recent result of Wdowinski on the minimum number of pseudoforests into which a graph can be decomposed, we prove that the LAC holds for the following simple graph classes: k $k$‐degenerate graphs with maximum degree Δ≥3k−1 ${\rm{\Delta }}\ge 3k-1$, all graphs on nonnegative Euler characteristic surfaces provided the maximum degree Δ≠7 ${\rm{\Delta }}\ne 7$, and graphs on negative Euler characteristic ϵ $\epsilon $ surfaces provided the maximum degree Δ≥35+49−24ϵ4−1 ${\rm{\Delta }}\ge 3\unicode{x02308}\frac{5+\sqrt{49-24\epsilon }}{4}\unicode{x02309}-1$, as well as graphs with no Kt ${K}_{t}$‐minor satisfying some conditions on maximum degrees. [ABSTRACT FROM AUTHOR]

This paper investigates distributed cooperative learning event‐triggered control for discrete‐time strict‐feedback nonlinear multi‐agent systems with an identical system structure and different recurrent reference orbits. A clever system decomposition method is firstly proposed to divide every n$$ n $$‐order agent system into n$$ n $$ first‐order subsystems, which makes it possible to solve the tough problem that every estimated neural weight cannot converge to an unique ideal value based on the existing control scheme. By constructing two interaction typologies, a novel distributed cooperative weight updating law is designed by the introduction of the internal interaction terms between n$$ n $$ subsystems of every agent, the external interaction terms between agents, and the triggering mechanism between agents. With the combination of the graph multiplication operation, the consensus theory and the matrix null space property, the proposed cooperative event‐triggered control scheme guarantees that every agent can track their corresponding recurrent reference trajectories. And further the exponential convergence of all agents' neural estimated weights to a close vicinity around their mutual and unique ideal weights is verified under the condition that the directed interaction topology between agents is strongly connected and balanced. Such a weight convergence makes the proposed scheme has some significant advantages including the small data storage space, the convenient knowledge reuse, the good generalization ability, and the low communication burden. By reinvoking the saved constant weights, a static learning controller is presented for the high‐performance control of similar diversified tracking tasks. Simulation studies and some comparisons are given to show the advantages and effectiveness of the presented scheme. [ABSTRACT FROM AUTHOR]

This paper presents a new formulation for solving the expansion planning of transmission lines and energy storage systems while considering the integration of electricity and gas networks. The proposed model is a bi‐level stochastic planning model. It involves transmission and battery expansion planning at one level, and gas network modeling at the other. The study addresses the impact of high penetration of renewable resources and security constraints on both the electricity and gas networks within the context of network expansion planning. The proposed model is a stochastic mixed‐integer linear programming model at both levels, and its challenging solution is achieved through reformulation and decomposition methods. Two experimental networks are analyzed: a 6‐node network and the IEEE RTS 24‐bus network for the electricity network, coupled with 5‐node and 10‐node gas network systems. The results demonstrate the efficiency of the proposed model. Simulation results indicate that the proposed model is highly effective in scenarios where power and gas network lines are disconnected, preventing load shedding even when the integrated network lines are disconnected. [ABSTRACT FROM AUTHOR]

In this paper, new fast computing methods for partial differential equations with variable coefficients are studied and analyzed. They are two kinds of two‐sided Krylov enhanced proper orthogonal decomposition (KPOD) methods. First, the spatial discrete scheme of an advection‐diffusion equation is obtained by Galerkin approximation. Then, an algorithm based on a two‐sided KPOD approach involving the block Arnoldi and block Lanczos processes for the obtained time‐varying equations is put forward. Moreover, another type of two‐sided KPOD algorithm based on Laguerre orthogonal polynomials in frequency domain is provided. For the two kinds of two‐sided KPOD methods, we present a theoretical analysis for the moment matching of the discrete time‐invariant transfer function in time domain and give the error bound caused by the reduced‐order projection between the Galerkin finite element solution and the approximate solution of the two‐sided KPOD method. Finally, the feasibility of four two‐sided KPOD algorithms is verified by several numerical results with different inputs and setting parameters. [ABSTRACT FROM AUTHOR]

This paper investigates the optimal tracking performance based on the codec, colored noise, and bandwidth constraints in the network time‐delay systems. Choosing the optimal two‐degree‐of‐freedom compensator and the dominant expression of the system optimal tracking performance is obtained after Youla parameterization by using the coprime factorizations method and spectral decomposition technology. The result shows that the tracking performance of the system is determined by the nonminimum phase zero and unstable pole of the controlled plant. Moreover, codec, colored noise, and bandwidth constraints can also significantly impact the performance. Finally, two simulation examples prove the accuracy of the theory. [ABSTRACT FROM AUTHOR]

A method for photovoltaic (PV) power interval prediction based on double sample entropy framework and integrated bidomain decomposition deep learning is proposed to address the volatility, randomness, intermittency and timeliness of PV power prediction. By using the integrated bidomain decomposition method under the framework of double sample entropy, the PV power time series is decomposed into several components with similar complexity and the deep learning network is used to learn and predict the results of each component reconstruction to obtain point predictions. The quantile regression method is then used based on the point prediction to obtain interval predictions. The actual calculation examples show that the RMSE and CPRS of the proposed method are reduced by an average of 45.56% and 31.42%, respectively, compared with other integrated bidomain decomposition deep learning methods that are not in the double sample entropy framework and single decomposition deep learning methods. [ABSTRACT FROM AUTHOR]

This study compares the ozone valleys over the Tibetan Plateau (TP) and the Rocky Mountains (RM) using the ERA5 reanalysis data set. The dynamical transport of the ozone over these two regions is analyzed using the Lorenz circulation decomposition method. The ozone content valley over TP is observed around 200–50 hPa (upper troposphere and lower stratosphere, or UTLS), and that over RM is around 300–100 hPa. It is shown that the TP ozone content is smaller than that over RM. By analyzing the spatiotemporal distribution of the ozone content and the general circulation, the anticyclone over Southern Asian (SAH) plays a significant role in existence of the TP ozone valley, and the ozone content flux reaches its maximum in July. Large‐scale terrain and related general circulation determine the ozone valley appearance. Further analysis suggests that stationary transport has a larger impact on the ozone valley formation than the transient transport. The transport by the zonal circulation nearly cancels out most of that by the meridional circulation, due to the fact that the zonal transport magnitude is nearly equal to the meridional transport. The transport center over the RM is much weaker than that over the TP. Furthermore, the contrasts between transient and stationary transports are less evident over RM than over TP. The eddy‐driven stationary ozone transport flux significantly impacts the development of the two low ozone centers across these large terrains. Plain Language Summary: Extremely low ozone content has been observed over the Arctic, Antarctic, and high‐terrain regions. Ozone absorbs most wavelengths of UV radiation, therefore understanding the formation of ozone valley plays an important role for climate research. We compared the climatic features of ozone valleys over two high‐terrain regions (i.e., Tibetan Plateau (TP) and Rocky Mountains (RM)). Dynamical transport is investigated using Lorenz circulation decomposition, and it shows the eddy stationary transport has a significant impact. The total dynamical transport of ozone over the RM is much weaker than that over the TP. This study advances our knowledge of ozone valley formation over these two regions. Key Points: The ozone valleys exist over both the Tibetan Plateau (TP) and the Rocky Mountains (RM)The TP ozone valley is stronger and locates higher than that over the RM, consistent with the terrain contrastThe stationary transport by the climatological eddies dominates the ozone budget for both high‐terrain regions [ABSTRACT FROM AUTHOR]

The rotor blades of an axial‐flow turbine are cantilever structures, and there is inevitably a gap between them and the casing. Due to factors such as rotor wear and unit vibration, the eccentricity of the impeller will change during the operation of the turbine, resulting in the impeller being affected by additional radial forces, which can even lead to rubbing or biting between the impeller and the casing. To monitor the eccentricity of the impeller and the additional radial forces in real time during the operation of the turbine, this study conducted numerical simulations of the internal flow of the turbine under different eccentricities of the impeller, and analyzed the characteristics of pressure pulsation and impeller radial force in the turbine using the variational mode decomposition method. The results showed that there was a good linear relationship between the eccentricity of the impeller and the amplitude of the frequency corresponding to the rotor in pressure pulsation at the monitoring point and the Alford force acting on the impeller. Based on this finding, we established mathematical formulas for the relationship between the pressure pulsation at the monitoring point and the eccentricity of the impeller, as well as the eccentricity of the impeller and the Alford force acting on it. According to these formulas, we only need to monitor the pressure pulsation during the operation of the turbine to realize the real‐time monitoring of the eccentricity of the impeller and the Alford force, which is of great significance for ensuring the safe and stable operation of the turbine. [ABSTRACT FROM AUTHOR]

Two‐dimensional (2‐D) hybrid model is developed to investigate the second harmonic (SH) generation of electromagnetic ion cyclotron (EMIC) waves. Applying the singular value decomposition method to simulated fields, we show that the SH exhibits wave properties analogous to typical EMIC waves generated by ion cyclotron instabilities, that is, left‐hand polarization and small wave normal angle. However, the bicoherence index inferred from simulated fields reflects a strong phase coupling between the fundamental wave (FW) and the SH, illustrating the nonlinear generation of the SH by the FW. The necessary conditions, especially for the wave vector relation, are further verified from a 2‐D perspective. The simulated amplitude ratios well meet the theoretical results only in the SH saturation stage, while the necessary conditions remain satisfied almost throughout the simulation. This study provides a comprehensive analysis of the SH excitation in a 2‐D simulation domain, contributing to a deeper understanding of EMIC wave nonlinear generation. Plain Language Summary: Recent studies have unveiled the generation of nonlinear second harmonics (SH) of electromagnetic ion cyclotron (EMIC) waves. The SH is nonlinearly driven by the fundamental wave (FW) and satisfies the necessary conditions: ω2 = 2ω1 and k2 = 2k1, where ω1 (ω2) and k1 (k2) are the frequency and the wave vector of the FW (SH), respectively. Previous studies have relied on one‐dimensional (1‐D) hybrid simulations to investigate the SH. However, 1‐D simulations allow waves to propagate along a single dimension and lack spatial variation of the field orthogonal to this dimension, which impedes the complete verification of the relation k2//k1. Thus, in this study, the SH generation is modeled by two‐dimensional (2‐D) hybrid codes. The simulated SH exhibits characteristics similar to typical EMIC waves with left‐hand polarization and small wave normal angle. The bicoherence index is utilized to reveal the phase coupling between the SH and FW. The necessary conditions, especially for the wave vector relation, are verified from a 2‐D perspective for the first time. Additionally, the amplitude ratios of the SH to the FW and their phase velocities are compared with theoretical results. The comprehensive analyses of this study provide substantial evidence for the SH generation mechanism. Key Points: Two‐dimensional (2‐D) hybrid codes are developed to model the nonlinear second‐harmonic (SH) generation of electromagnetic ion cyclotron wavesThe necessary conditions required by the SH generation mechanism are verified from a 2‐D perspectiveThe theoretical amplitude ratios between harmonics are only satisfied in the SH saturation stage [ABSTRACT FROM AUTHOR]

With the increasing penetration of grid‐scale wind energy systems, accurate wind power forecasting is critical to optimizing their integration into the power system, ensuring operational reliability, and enabling efficient system asset utilization. Addressing this challenge, this study proposes a novel forecasting model that combines the long‐short‐term memory (LSTM) neural network with two signal decomposition techniques. The EMD technique effectively extracts stable, stationary, and regular patterns from the original wind power signal, while the VMD technique tackles the most challenging high‐frequency component. A deep learning‐based forecasting model, i.e. the LSTM neural network, is used to take advantage of its ability to learn from longer sequences of data and its robustness to noise and outliers. The developed model is evaluated against LSTM models employing various decomposition methods using real wind power data from three distinct offshore wind farms. It is shown that the two‐stage decomposition significantly enhances forecasting accuracy, with the proposed model achieving R2$R^2$ values up to 9.5% higher than those obtained using standard LSTM models. [ABSTRACT FROM AUTHOR]