Search Results (21)

Identifying shear band locations is essential for precursor recognition and early warning of progressive failure in gravelly soil slopes. However, conventional displacement monitoring methods mainly capture macroscopic slope deformation and remain limited in detecting internal localized deformation and the spatial evolution of shear bands. To address this limitation, this study proposes an MEMS data-driven framework for predicting spatial rotation-angle responses and locating potential shear bands in gravelly soil slopes, with the aim of enhancing the perception of internal shear deformation and detecting potential instability zones. First, scaled laboratory model tests were conducted under different gravel contents, and MEMS sensors were embedded within the slope to measure cumulative rotation-angle responses during shear band formation. Second, based on a DEM model incorporating particle geometric morphology, the spatial differentiation of the rotation-angle field during shear band evolution was analyzed, and the experimental results were further validated. Finally, a shear band localization framework integrating PDL-GAN-based data augmentation with PCA + Gaussian regional rotation-angle field prediction was established. Potential shear band locations were then indirectly localized based on the positive–negative partitioning and abrupt amplitude changes in the predicted rotation angles. The results show that the DEM simulations agree well with the cumulative rotation-angle responses obtained from the laboratory tests, with mean absolute percentage errors of 9.79%, 6.03%, and 3.84% under the T1, T2, and T3 conditions, respectively. Within the shear band influence zone, the upper monitoring points mainly exhibit negative rotation-angle accumulation, whereas the lower monitoring points primarily show positive rotation-angle responses. A larger absolute rotation angle indicates a stronger controlling effect of the shear band on the corresponding monitoring point. The PCA + Gaussian model demonstrates strong overall performance in regional rotation-angle prediction, with MAE, RMSE, and CRPS values of 0.0803, 0.1024, and 0.0801, respectively. The model preserves the dominant deformation mode of the rotation-angle field and provides probabilistic prediction outputs. The proposed method enables the prediction of internal rotation-angle responses and facilitates the localization of potential shear band locations in gravelly soil slopes, providing data-driven technical support for precursor recognition and intelligent early warning of progressive slope failure. Full article

Short-term wastewater flow forecasting is essential for pump-station scheduling, influent-load regulation, and overflow-risk warning in wastewater treatment systems. However, wastewater flow series often exhibit strong nonlinearity, large-amplitude fluctuations, and sensitivity to model hyperparameters, which makes accurate real-time prediction challenging. To address these issues, this study proposes an attention-enhanced hybrid deep learning framework optimized by an Improved Harris Hawks Optimisation algorithm. The prediction target is the wastewater flow value at the next target time step, and the model uses only historical wastewater flow observations as input. The framework integrates a Temporal Convolutional Network to extract local fluctuation and multi-scale temporal features, a Bidirectional Long Short-Term Memory network to capture contextual dependencies within the historical input window, and a Simple Attention Module to recalibrate high-dimensional features and emphasize key information. The improved optimisation algorithm further enhances hyperparameter search through hybrid initialization, early-stage differential evolution mutation, stagnation detection with diversity injection, and late-stage Lévy flight perturbation. Experimental results show that the unoptimized Temporal Convolutional Network (TCN)–Bidirectional Long Short-Term Memory (BiLSTM)–Simple Attention Module (SimAM) model achieved an R² of 0.9697, an RMSE of 231.1821, and an MAE of 177.5324 on the validation set. After Improved Harris Hawks Optimization (IHHO) optimization, these values improved to 0.9728, 218.8228, and 161.8777, respectively. Compared with the unoptimized model, Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) were reduced by approximately 5.35% and 8.82%, respectively, while R² increased by 0.0031. These results indicate that the proposed framework improves prediction accuracy, stability, and robustness under the tested conditions. It provides a feasible technical solution for short-term wastewater flow forecasting and supports intelligent operation management of wastewater treatment systems. Full article

In this study, a detailed analytical-numerical study of the complex modified Korteweg–De Vries (mKdV) model with truncated M-fractional derivative is carried out to investigate the effects of the fractional order on nonlinear wave propagation. The fractional partial differential equation is solved by an appropriate fractional traveling wave transformation, which transforms it into a nonlinear ordinary differential equation. Two very powerful analytical methods are then used: the modified sub-equation method and the Kumar–Malik method, which give the exact closed-form solutions. The obtained semi-analytical numerical approximations are then obtained from the Differential Transformation Method (DTM). Bright and dark solitons, kink-type waves, periodic and rational solutions, exponential solutions, and Jacobi elliptic functions are found for a variety of parametric regimes. Explicit compatibility conditions and parametric constraints, which control the amplitude, width, and propagation, are derived. The DTM approximations are found to converge to the exact solutions with good accuracy, and the absolute errors are almost negligible, which validates the accuracy of the approximations and reliability of the solution. The three-dimensional visualizations of surface plots, two-dimensional profiles, and contour visualization further illustrate the dispersive dynamics and stability properties. Significance: This study shows that the truncated M-fractional derivative is a good operator to model memory-dependent nonlinear wave propagation. A new precise solution and reliable validation methods have been obtained for high-dimensional fractional nonlinear evolution equations in the hybrid analytical-numerical framework, which can be useful in plasma physics, nonlinear optics, and complex media. The present study contains restrictions for constant coefficients, a specific parametric regime, one fractional derivative definition, and experimental validation is not included. Future directions are limitations on constant coefficients, specific parametric regimes, one fractional derivative definition, and experimental validation is not included. The approach is to be extended in the future to variable coefficients, other fractional operators (Caputo, Riemann–Liouville), and to higher-order nonlinearities, and then to be experimentally tested in optical or plasma systems. Full article

Extreme cyclic temperature fluctuations (−200 °C to 200 °C) and inherent clearance nonlinearity in deployment hinges severely threaten the on-orbit deployment accuracy and dynamic stability of large variable-geometry spacecraft antennas for geosynchronous Earth orbit applications. However, current modeling approaches suffer from three critical limitations: single-configuration models requiring manual switching, there are inherent geometric nonlinear errors from conventional floating frame formulations, and incomplete thermo-mechanical coupling neglects the temperature effects on contact stiffness and friction. To address these gaps, we propose a unified high-fidelity dynamic model based on the Absolute Nodal Coordinate Formulation (ANCF). This model eliminates geometric errors and mesh mismatch, enables seamless multi-configuration deployment without switching, and fully incorporates temperature-dependent material properties and nonlinear contact forces. An improved Hilber–Hughes–Taylor-$\alpha$ implicit integration algorithm with second-order accuracy and unconditional stability is adopted to solve the strongly nonlinear differential-algebraic equations. Numerical results demonstrate that the proposed model achieves a calculation error below 3% against experimental data, significantly outperforming the traditional floating frame of reference formulation with an error of 15–22%. Non-uniform temperature fields increase thermally induced vibration amplitudes by 32–45%, and every 0.1 increase in the friction coefficient raises the impact force at the clearance hinge by 15–20%. The proposed unified modeling framework provides a solid theoretical basis for deployment stability prediction and the on-orbit control optimization of large variable-geometry spacecraft antennas. Full article

The Lutan-1 (LT-1) mission is the first civilian L-band differential interferometric synthetic aperture radar (SAR) system in China, with interferometry as its primary application. The system comprises two multi-polarimetric satellites, LT-1A and LT-1B. For the purpose of quantitative application from SAR images of Lutan-1 satellites, the relationship between the SAR image intensity and the backscattering coefficient of ground objects should be established by radiometric calibration. Field radiometric calibration provides absolute calibration constants, but it suffers from beam coverage. Internal on-board calibration, by contrast, tracks relative changes in radiometric performance but cannot yield absolute calibration constants. Therefore, we develop a method that combines on-board internal calibration with field radiometric calibration to monitor the radiometric performance of LT-1 satellites and to analyze the variation patterns revealed by both internal and field calibrations. We monitor the amplitude and phase trend of internal calibration, calculate absolute calibration constants from field calibration, and refine and evaluate the absolute calibration constants. We analyzed the internal calibration data and SAR calibration data of the LT-1 satellite from 2023 to 2025. The results show that the TRMs of the LT-1 satellite exhibit a slight decline over time, and the magnitude of the decrease in LT-1B is greater than that of LT-1A. The slight decrease in internal calibration has not yet led to visible changes in the absolute calibration constant for LT-1A, while the absolute calibration constants decrease slightly for LT-1B. After removing the calibration constant outliers and correcting the gain difference among the beams for the LT-1A satellite, absolute radiometric accuracy is improved from 0.40 dB (1σ) to 0.25 dB (1σ). The absolute radiometric accuracy of the LT-1B satellite is 0.38 dB (1σ). It gives a reference for radiometric performance monitoring of the SAR satellite over a long period. Full article

River levees in Taiwan are exposed to typhoons, earthquakes, and long-term erosion and scour, which often cause subsurface voids of varying severity within the levee body. This study conducted a quantitative physical analysis of 0.15 m-thick concrete specimens containing voids of different dimensions (widths of 0.10–0.40 m and sizes of 0.06–0.15 m). The specimens were scanned using ground-penetrating radar (GPR) antennas with center frequencies ranging from 750 MHz to 2.3 GHz. Variations in electromagnetic-wave reflection amplitude within the material were used to determine void size along the X-axis, whereas the depths corresponding to the reflection points were quantified along the Y-axis. The void area was then estimated based on the X-Y coverage. The results showed that absolute amplitude differentiation provided distinct quantitative features that reflected the presence of voids of various sizes. The proposed method was further validated using an actual river-levee scour case. The findings of this study offer a practical reference for the inspection, maintenance, and repair of river levees. Full article

Fractional differential equations have emerged as a prominent focus of modern scientific research due to their advantages in describing the complexity and nonlinear behavior of many physical phenomena. In particular, when considering problems with initial-boundary value conditions, the solution of nonlinear fractional differential equations becomes particularly important. This paper aims to explore the fractional soliton solutions for the three-component fractional nonlinear Schrödinger (TFNLS) equation under the zero background. According to the Lax pair and fractional recursion operator, we obtain fractional nonlinear equations with Riesz fractional derivatives, which ensure the integrability of these equations. In particular, by the completeness relation of squared eigenfunctions, we derive the explicit form of the TFNLS equation. Subsequently, in the reflectionless case, we construct the fractional N-soliton solutions via the Riemann–Hilbert (RH) method. The analysis results indicate that as the order of the Riesz fractional derivative increases, the widths of both one-soliton and two-soliton solutions gradually decrease. However, the absolute values of wave velocity, phase velocity, and group velocity of one component of the vector soliton exhibit an increasing trend, and show power-law relationships with the amplitude. Full article

The development of simple and yet accurate formulations of frequency–amplitude relationships for non-conservative nonlinear oscillators is an important issue. The present paper is concerned with integral-type frequency–amplitude formulas in the dimensionless time domain and time domain to accurately determine vibrational frequencies of nonlinear oscillators. The novel formulation is a balance of kinetic energy and the work during motion of the nonlinear oscillator within one period; its generalized formulation permits a weight function to appear in the integral formula. The exact values of frequencies can be obtained when exact solutions are inserted into the formulas. In general, the exact solution is not available; hence, low-order periodic functions as trial solutions are inserted into the formulas to obtain approximate values of true frequencies. For conservative nonlinear oscillators, a powerful technique is developed in terms of a weighted integral formula in the spatial domain, which is directly derived from the governing ordinary differential equation (ODE) multiplied by a weight function, and integrating the resulting equation after inserting a general trial ODE to acquire accurate frequency. The free parameter is involved in the frequency–amplitude formula, whose optimal value is achieved by minimizing the absolute error to fulfill the periodicity conditions. Several examples involving two typical non-conservative nonlinear oscillators are explored to display the effectiveness and accuracy of the proposed integral-type formulations. Full article

The shear characteristics of the frozen soil–concrete interface are core parameters in frost heave resistance design in cold-region engineering, and the influence mechanism of interface roughness on these characteristics is not clear. In this study, the regulatory effect of different roughness levels (R-0 to R-4) on the interfacial freezing strength was quantitatively analyzed for the first time through direct shear tests, and the evolution characteristics of the contribution ratio of the ice cementation strength were revealed. The results show that the peak shear strength of the interface increases significantly with the roughness (when the normal stress is 400 kPa and the water content is 14%, the increase in R-4 is 47.7% compared with R-0); the ice cementation strength increases synchronously and its contribution ratio increases with the increase in roughness. Although the absolute value of the residual strength increase is small, the relative amplitude is larger (178.5% increase under the same working conditions). The peak cohesion increased significantly with the roughness (R-0 to R-4 increased by 268.6%), while the residual cohesion decreased. The peak and residual internal friction angle increased slightly with the roughness. The study clarifies the differential influence mechanism of roughness on the interface’s shear parameters and provides a key quantitative basis for the anti-frost heave design of engineering interfaces in cold regions. Full article

A new frequency–amplitude formula by improving an ancient Chinese mathematics method results in a modification of He’s formula. The Chinese mathematics method that expresses via a fixed-point Newton form is proven to be equivalent to the original nonlinear frequency equation. We modify the fixed-point Newton method by adding a term in the denominator, and then a new frequency–amplitude formula including a parameter is derived. Upon using the new frequency formula with the parameter by minimizing the absolute error of the periodicity condition, one can significantly raise the accuracy of the frequency several orders. The innovative idea of a linearly perturbed frequency equation is a simple extension of the original frequency equation, which is supplemented by a linear term to acquire a highly precise frequency for the nonlinear oscillators. In terms of a differentiable weight function, an integral-type formula is coined to expeditiously estimate the frequency; it is a generalized conservation law for the damped nonlinear oscillator. To seek second-order periodic solutions of nonlinear oscillators, a linearized residual Galerkin method (LRGM) is developed whose process to find the second-order periodic solution and the vibrational frequency is quite simple. A hybrid method is achieved through a combination of the linearly perturbed frequency equation and the LRGM; very accurate frequency and second-order periodic solutions can be obtained. Examples reveal high efficacy and accuracy of the proposed methods; the mathematical reliability of these methods is clarified. Full article

This work presents a physics-guided parameter estimation framework for cold spray additive manufacturing (CSAM), focusing on simulating and validating deposit profiles across diverse process conditions. The proposed model employs a two-zone flow representation: quasi-constant velocity near the nozzle exit followed by an exponentially decaying free jet to capture particle acceleration and impact dynamics. The framework employs a comprehensive approach by numerically integrating drag-dominated particle trajectories to predict deposit formation with high accuracy. This physics-based framework incorporates both operational and geometric parameters to ensure robust prediction capabilities. Operational parameters include spray angle, standoff distance, traverse speed, and powder feed rate, while geometric factors encompass nozzle design characteristics such as exit diameter and divergence angle. Validation is performed using 36 experimentally measured profiles of commercially pure titanium powder. The simulator shows excellent agreement with the experimental data, achieving a global root mean square error (RMSE) of 0.048 mm and a coefficient of determination $R^2=0.991$, improving the mean absolute error by more than 40% relative to a neural network-based approach. Sensitivity analyses reveal that nozzle geometry, feed rate, and critical velocity strongly modulate the amplitude and shape of the deposit. Notably, decreasing the nozzle exit diameter or divergence angle significantly increases local deposition rates, while increasing the standoff distance dampens particle velocities, thereby reducing deposit height. Although the partial differential equation (PDE)-based framework entails a moderate increase in computational time—about 50 s per run, roughly 2.5 times longer than simpler empirical models—this remains practical for most process design and optimization tasks. Beyond its accuracy, the PDE-based simulation framework’s principal advantage lies in its minimal reliance on sampling data. It can readily be adapted to new materials or untested process parameters, making it a powerful predictive tool in cold spray process design. This study underscores the simulator’s potential for guiding parameter selection, improving process reliability and offering deeper physical insights into cold spray deposit formation. Full article

The nonlinear dynamics of the cable–buoy structure in marine engineering present significant analytical challenges due to the complex motion of the buoy, which impacts the system’s dynamic response. The drag force acting on the structure can be categorized into the absolute velocity and relative velocity models, distinguished by their reference frames. The absolute velocity model incorporates flow velocity coupling terms, offering higher accuracy but at the expense of increased computational complexity. In contrast, the relative velocity model is computationally simpler and therefore more widely adopted. Nevertheless, the accuracy and applicability of these simplified models remain open to further in-depth investigation. To address these challenges, this study derives coupled differential equations for the cable–buoy structure based on the two drag force models. Galerkin discretization is then employed to construct coupled systems that account for nonlinear buoy motion, as well as decoupled systems assuming linear buoy motion. The modulation equations for the system’s primary resonance response are derived using the method of multiple scales. Numerical results indicate that changes in cable parameters lead to complex modal coupling behaviors in the system. The flow velocity coupling terms in the absolute velocity drag force model enhance the system’s damping effect, and the relative velocity drag force model, which omits these coupling terms, results in increased system response amplitudes. Although neglecting nonlinear buoy motion has little impact on the cable’s dynamic response, it significantly reduces the amplitude of the buoy’s dynamic motion. The relative velocity drag force model and the decoupled system can serve as effective simplifications for analyzing the dynamic responses of cable–buoy systems, providing a balance between computational efficiency and result accuracy. Variations in system parameters cause both qualitative and quantitative changes in the system’s nonlinear stiffness characteristics. Full article

To solve the nonlinear vibration problems of second- and third-order nonlinear oscillators, a modified harmonic balance method (HBM) is developed in this paper. In the linearized technique, we decompose the nonlinear terms of the governing equation on two sides via a constant weight factor; then, they are linearized with respect to a fundamental periodic function satisfying the specified initial conditions. The periodicity of nonlinear oscillation is reflected in the Mathieu-type ordinary differential equation (ODE) with periodic forcing terms appeared on the right-hand side. In each iteration of the linearized harmonic balance method (LHBM), we simply solve a small-size linear system to determine the Fourier coefficients and the vibration frequency. Because the algebraic manipulations required for the LHBM are quite saving, it converges fast with a few iterations. For the Duffing oscillator, a frequency–amplitude formula is derived in closed form, which improves the accuracy of frequency by about three orders compared to that obtained by the Hamiltonian-based frequency–amplitude formula. To reduce the computational cost of analytically solving the third-order nonlinear jerk equations, the LHBM invoking a linearization technique results in the Mathieu-type ODE again, of which the harmonic balance equations are easily deduced and solved. The LHBM can achieve quite accurate periodic solutions, whose accuracy is assessed by using the fourth-order Runge–Kutta numerical integration method. The optimal value of weight factor is chosen such that the absolute error of the periodic solution is minimized. Full article

Due to its capacity to unveil the dynamic characteristics of time series data, entropy has attracted growing interest. However, traditional entropy feature extraction methods, such as permutation entropy, fall short in concurrently considering both the absolute amplitude information of signals and the temporal correlation between sample points. Consequently, this limitation leads to inadequate differentiation among different time series and susceptibility to noise interference. In order to augment the discriminative power and noise robustness of entropy features in time series analysis, this paper introduces a novel method called Tsallis entropy-based complexity-improved permutation entropy casualty plane (TC-IPE-CP). TC-IPE-CP adopts a novel symbolization approach that preserves both absolute amplitude information and inter-point correlations within sequences, thereby enhancing feature separability and noise resilience. Additionally, by incorporating Tsallis entropy and weighting the probability distribution with parameter q, it integrates with statistical complexity to establish a feature plane of complexity and entropy, further enriching signal features. Through the integration of multiscale algorithms, a multiscale Tsallis-improved permutation entropy algorithm is also developed. The simulation results indicate that TC-IPE-CP requires a small amount of data, exhibits strong noise resistance, and possesses high separability for signals. When applied to the analysis of heart rate signals, fault diagnosis, and underwater acoustic signal recognition, experimental findings demonstrate that TC-IPE-CP can accurately differentiate between electrocardiographic signals of elderly and young subjects, achieve precise bearing fault diagnosis, and identify four types of underwater targets. Particularly in underwater acoustic signal recognition experiments, TC-IPE-CP achieves a recognition rate of 96.67%, surpassing the well-known multi-scale dispersion entropy and multi-scale permutation entropy by 7.34% and 19.17%, respectively. This suggests that TC-IPE-CP is highly suitable for the analysis of complex time series. Full article

We experimentally incubate a ground-breaking design, for the first time, of concurrent electro-optical semiconductor optical amplifier Mach–Zehnder interferometer mixing (SOA-MZI) based on a differential transformation methodology. Projecting the simultaneous electro-optical mixing system and improving its efficiency and quality achievement in optical and electrical features is a crucial task due to the characteristics of an optical pulse source (OPS) operating with a repetition rate of $f=$ 58.5 GHz and a pulse width duration of 1 picosecond (ps). The resultant of the contemporaneous electro-optical mixing exhibits exceptional passive power stability, reaching 0.8% RMS over a two-hour period. Furthermore, when the optical bandpass filter is controlled at the data wavelength of 1540 nm, we achieve up to 30 dBm of the overall mean output power with an optical conversion gain of 46 dB and an exceptionally high optical signal-to-noise ratio reaching 80 dB. Using orthogonal frequency division multiplexing (OFDM) signals, each data subcarrier is modulated using 128 quadratic amplitude modulation (128-QAM) at carrier frequencies $f_k$ and simultaneously up-mixed to high aim frequencies $nf\pm f_k$ at the SOA-MZI output. Additionally, the resulting OFDM_128-QAM up-mixed signal is examined using the specifications for the error vector magnitudes (EVMs) and the electrical conversion gains (ECGs). The SOA-MZI mixing experiment can handle high frequencies up to 120 GHz. Positive ECGs are followed by a sharp reduction over the entire band of the aim frequencies. The highest frequency range achieved during the realistic investigation is shown at $2f+f_4=$ 120 GHz, where the EVM reaches 8% with a symbol rate of 15 GSymb/s. Furthermore, the concurrent OFDM_128-QAM up-mixed signal achieves an absolute maximum bit rate of 80.4 Gbit/s. The investigation into the simultaneous electro-optical mixing regime is finally supported by unmatched characterization improvements. Full article