Nonlinear Processes Research Articles

Water-exit dynamics of a ventilated underwater vehicle in wave environments with a combination of computational fluid dynamics and machine learning

A ventilated vehicle exiting water in a wave environment is a complex nonlinear process, and the mechanism by which the wave conditions influence this process remains poorly understood. This paper describes realistic simulations of a ventilated vehicle exiting a water body under various wave conditions. Comprehensive analysis is conducted for a range of distinct wave scenarios, and a machine learning-based method is developed for the rapid forecasting of vehicle-related parameters. A three-layer backpropagation neural network is constructed, and its prediction performance is verified. Subsequently, predictive and optimization procedures are employed to determine the optimal wave phase for the water exit of the vehicle. Different wave conditions are shown to significantly affect the evolution of the ventilated cavity as well as the kinematic and loading characteristics of the vehicle. The pitch angular velocity and angle at the moment when the head of the vehicle reaches the free surface exhibit a positive cosine trend under different wave conditions. No regularity of the pitch angular velocity at the moment when the tail reaches the free surface is evident. The neural network exhibits exceptional proficiency in predicting the motion parameters and load characteristics of the vehicle. The optimal point for the vehicle to exit the water is determined to be at a wave phase of 0.125π, while the most hazardous point occurs when the wave phase is 1.1875π.

Application of DMD method to eccentric self-excited vibration of tubular turbine runner

Tubular turbines are widely used in the development and utilization of low-head marine energy. The cantilever type runner inevitably leads to gap between the chamber and blade tip, and non-standard installation can easily lead to eccentric runner, affecting the safe and stable operation of turbine. The overall process of self-excited vibration is an obvious nonlinear process, so the applicability of traditional methods needs to be discussed. In recent years, reduced-order modelling methods based on linear dynamic systems have gradually been introduced into the analysis of hydraulic machinery, and have achieved certain results. Therefore, this study combines computational fluid dynamics (CFD) and dynamic mode decomposition (DMD) methods to conduct low-dimensional mode decomposition and comparative analysis of self-excited vibration caused by different runner eccentricities of tubular turbine. The research shows that as the runner eccentricity continues to increase, the modal frequency distribution of self-excited vibration becomes complex. The DMD method disassembles the low-level representations of self-excited vibration signals, greatly enriching the understanding of eccentric self-excited vibration of the runner, and providing assurance for the safe and stable operation of tubular turbines.

To the anniversary of the Department of Nonlinear Physics of Saratov State University

2023 marks the 25th anniversary of the formation of the Department of Nonlinear Physics of Saratov State University. The department has developed and implements training programs on the general course of physics, physics of nonlinear processes, physics of wave processes in magnetic fields and structures.

Relevance variable selection variational auto-encoder network for quality-related nonlinear process monitoring

Quality-related process monitoring is essential for revealing changes in product quality and ensuring industrial safety. Therefore, it is crucial to distinguish enough quality-related features within the data. To learn the nonlinear characteristics and obtain quality-related features in process data, a novel process monitoring method named relevance variable selection variational auto-encoder (RVS-VAE) is proposed. Firstly, to enhance the strong quality-related variables and learn the time correlation, the normalized original data is weighted by mutual information and augmented into data matrices. Secondly, the RVS strategy is proposed to select the most quality-related variables from the latent features. These quality-related features are further utilized to monitor the process. What is more, when a fault is detected, relevance variable relative contribution (RVRC) method is presented to locate the fault variables. Finally, performance of the proposed RVS-VAE method is evaluated through comparative experiments on tennessee eastman (TE) process.

Investigation of Hydrodynamics Characteristics of Fluidized Bed with back propagation Artificial Neural Network (BPANN)

Correlations have also been developed with system parameters by using dimensional analysis and an artificial neural network approach. The paper describes an investigation for the thermal design of a fluidized bed cooler and prediction of heat transfer rate among the media categories. It is devoted to the thermal design of such equipment and their application in the industrial fields. In the present work, an extensive ANN by using back propagation (BP) has been carried out to correlate the expansion ratio, fluctuation ratio in gas-solid fluidized bed. Back propagation network is the most well-known and widely used among the current types of neural network system, several applications of ANN for modeling of nonlinear process systems and subsequent control were reported. In back-propagation, different ANN structures (I×H×O) with varying number of neurons in the hidden layer were used as a tool for training input and output data for prediction value of hydrodynamic characteristics of the bed system. It was noted that ring models are the best ones in reducing bed expansion ratio and fluctuation ratio around (25%) and (23.22%).

The methodology for adaptive modeling and forecasting nonlinear and nonstationary processes

The study is directed towards development of systemic methodology for modeling and forecasting nonlinear and nonstationary processes in economy, finances and other areas of human activities. There exist multiple problems that are to be solved with the data of such type practically in all areas of human activities: such as constructing adequate models including estimation and forecasting state of a system under investigation; technical, economic and medical diagnostics; automatic control in technologies; moving objects control; financial and other risk estimation and management; risk factor interaction; control and monitoring of microclimate in greenhouses and industrial enterprises; decision making support in business; dynamic strategic planning in production; providing stability for critical economic infrastructure etc. The structure and parameter adaptation procedures for the regression and probabilistic models are proposed as well as respective information system architecture and functional layout are developed. The system development is based on the system analysis principles such as hie­rarchical architecture of the system, adaptive approach to model structure estimation, optimization of model parameter estimation procedures, functional completeness of the system providing for autonomous operation of the system, identification and taking into consideration of possible uncertainties available in the process of data processing and mathematical model development, application of appropriate sets of quality criteria that are guarantying high quality of intermediate and final results of data analysis. The possible uncertainties are inherent to data collecting, model constructing and forecasting procedures, and play the role of negative influence factors to the computational procedures of proposed information system. Reduction of their influence is favorable for enhancing the quality of intermediate and final results of computations. The illustrative examples of practical application of the methodology developed proving the system functionality are provided.

Process monitoring via dependence description based on variable selection and vine copula

Process monitoring is crucial to ensure the safety of industrial processes. Generally, the monitoring process involves all measured variables; however, large industrial processes contain many redundant variables. For a method based on describing the intrinsic correlation relationships among variables, the vine copula-based dependence description (VCDD) method shows significant advantages for describing nonlinear and non-Gaussian processes. However, redundant and irrelevant variables adversely affect the correlation between variables containing the most important information, reducing model performance. The lack of research in this area may substantially weaken the advantages of VCDD for fault monitoring. Therefore, this article introduces a variable selection vine copula dependence description monitoring model. It utilizes known faults as validation data to select the relevant variables for constructing the VCDD model, specifically designed for monitoring known faults. Furthermore, to prevent information loss, the remaining unselected variables are also employed to create a separate VCDD model, dedicated to monitoring unknown faults. The performance of the proposed method is verified by a numerical example, the Tennessee-Eastman process and the Penicillin fermentation process.

Polarization-insensitive and polarization-controlled dual-band third-harmonic generation in silicon metasurfaces driven by quasi-bound states in the continuum

High-refractive-index nanostructures offer versatile opportunities for nonlinear optical effects, due to their ability to strongly confine field into a subwavelength scale. Herein, we propose a rhomboidal amorphous silicon metasurface to realize high-efficiency dual-band third-harmonic generation (THG), based on the supported dual quasi-bound states in the continuum (Q-BICs). Owing to the very large field confinement inside the metasurface empowered by Q-BICs, the THG efficiency up to 3.74 × 10−3 with the peak pump intensity of 30 MW/cm2 is observed. Meanwhile, thanks to the very high quality factor of Q-BICs, the ultra-narrow nonlinear process with the full width at half maximum less than 1 nm is also witnessed, suggesting the good monochromaticity. Interestingly, the dual-band THG is verified to be polarization-dependent and polarization-insensitive, respectively. The finite element method simulations exhibit that the polarization-dependent THG is attributed to the Q-BIC driven by the electric quadrupole characterized by a pair of anti-parallel electric dipoles along the x axis, which are only excited by the x-linearly polarized light. On the contrary, the polarization-insensitive THG is enabled by another Q-BIC governed by the magnetic dipole resonance with circular electric field vectors, which can be excited by any linearly polarized light. The polarization-controlled and polarization-independent dual-band THG enabled by the physics of Q-BICs would open possibilities for designing switchable nonlinear light sources. The proposed dual Q-BICs scheme undoubtedly can serve as a universal recipe for other nonlinear effects, including sum-frequency generation, difference-frequency generation, and high-order harmonics.

Singularly perturbative behaviour of nonlinear advection–diffusion-reaction processes

The purpose of this paper is to use a wavelet technique to generate accurate responses for models characterized by the singularly perturbed generalized Burgers-Huxley equation (SPGBHE) while taking multi-resolution features into account. The SPGBHE’s behaviours have been captured correctly depending on the dominance of advection and diffusion processes. It should be noted that the required response was attained through integration and by marching on time. The wavelet method is seen to be very capable of solving a singularly perturbed nonlinear process without linearization by utilizing multi-resolution features. Haar wavelet method results are compared with corresponding results in the literature and are found in agreement in determining the numerical behaviour of singularly perturbed advection–diffusion processes. The most outstanding aspects of this research are to utilize the multi-resolution properties of wavelets by applying them to a singularly perturbed nonlinear partial differential equation and that no linearization is needed for this purpose.

Quantification of Shortwave Surface Albedo Feedback Using a Neural Network Approach

Radiative transfer is a nonlinear process. Despite this, most current methods to evaluate radiative feedback, such as the kernel method, rely on linear assumptions. Neural network (NN) models can emulate nonlinear radiative transfer due to their structure and activation functions. This study aims to test whether NNs can be used to evaluate shortwave radiative feedbacks and to assess their performance. This study focuses on the shortwave radiative feedback driven by surface albedo. An NN model is first trained using idealized cases, simulating truth values from a radiative transfer model via the partial radiative perturbation method. Two heuristic cases are analyzed: univariate feedback, perturbing the albedo; and bivariate feedback, perturbing the albedo and cloud cover concurrently. These test the NN’s ability to capture nonlinearity in the albedo–flux and albedo–cloud–flux relationships. We identify the minimal NN structure and predictor variables for accurate predictions. Then, an NN model is trained with realistic radiation flux and atmospheric variable data and is tested with respect to its predictions at different order levels: zero-order for the flux itself, first-order for radiative sensitivity (kernels), and second-order for kernel differences. This paper documents the test results and explains the NN’s ability to reproduce the complex nonlinear relationship between radiation flux and different atmospheric variables, such as surface albedo, cloud optical depth, and their coupling effects.

Coastal Compound Flood Simulation through Coupled Multidimensional Modeling Framework

Coastal watersheds are prone to compound flooding caused by heavy rainfall, storm surge, and high tide. Accurate prediction and modeling of coastal compound floods (CCF) require precise physical representation in numerical models with appropriate numerical approximation associated with multi-driver physical processes for simulating the flood dynamics. To address this, an integrated and tightly coupled modeling approach is implemented to capture the nonlinear and complex processes involved in CCF and interconnectivity among Multidimensional Hydraulics (pipe and channel), Hydrodynamics (2D overland flow), and distributed Hydrologic (MH3) models are developed. The coupled modeling framework focuses on the development of interconnected meshes of the node-link-basin using the Interconnected Channel and Pond Routing (ICPR) model. This framework effectively incorporates the complex drainage network system of tidal creeks, tidal channels, underground sewer networks, and detention ponds of the Charleston Peninsula of South Carolina (SC). The dynamics of the urbanized floodplain in the peninsula are represented using high-resolution LiDAR-derived Digital Elevation Model (DEM) and Digital Surface Model (DSM). The overland flow is simulated using energy balance, momentum balance, and diffusive wave methods. The performance of the CCF model is tested for the 2015 SC historical flood and a high tide flood event. The momentum balance-based CCF model shows 98.35% accuracy in identifying street-level flooding locations. Furthermore, the model shows that incorporating DSM processing in the current study improves the accuracy of urban flood simulation by approximately 15% to 33% compared to LiDAR DEM. It is revealed that the momentum balance method outperforms to simulate the flood dynamics. Consequently, this study contributes to the modeling of CCF by developing an integrated MH3 system that enhances the physical representation of coastal hydrology at a fine scale.

Nonlinear Optical Processes in Centrosymmetric Systems by Cavity-Induced Symmetry Breaking

Nonlinear Optical Processes in Centrosymmetric Systems by Cavity-Induced Symmetry Breaking

Intermodal effective phase matching for second harmonic generation of ultrashort pulses in high index contrast optical fibers

Second harmonic generation (SHG) in glass optical fibers calls for creating a second order susceptibility in the fiber glass and for achieving phase matching between the pump and the second harmonic signal. The latter is very challenging when using ultrashort pulses, given that the group velocities of the pump and the second harmonic should also be matched. We have shown in previous work that it is possible to achieve simultaneous modal phase matching (MPM) and group velocity matching (GVM) when the pump and the second harmonic are propagating in the LP01 and LP02 modes, respectively, in high GeO2-content double-clad optical fibers. However, simultaneous MPM and GVM can only be obtained in optical fibers with dedicated designs and within very tight geometrical tolerances. In this paper, we show that instead of considering the matching of phase and group velocities separately, we can consider a more general or “effective” phase matching approach, in which we consider all the dispersion terms up to the second order in the expressions of the propagation constants of the pump and second harmonic signals. This allows introducing the pulse duration as a controllable parameter that helps to enforce the said effective phase matching in fibers with designs that deviate by as much as 10% from the target, while providing for temporal walk-off lengths in excess of several centimeters. The impact of this finding goes beyond SHG only and can be applied to other ultrashort laser pulse-based nonlinear optical processes in fibers and waveguides.

Pharmacokinetics, absolute bioavailability, and tissue distribution of WJ-14, a novel N-methyl-d-aspartate receptor antagonist, in rats by liquid chromatography-tandem mass spectrometry.

To circumvent the limitations of current antidepressants, WJ-14, a novel N-methyl-d-aspartate receptor antagonist, was synthesized and demonstrated to have remarkable efficiency in the treatment of depression. To illustrate the pharmacokinetics, absolute bioavailability, and tissue distribution of WJ-14 in rats, a rapid and sensitive liquid chromatography-tandem mass spectrometry-based analytical method was developed and validated for the separation and detection of WJ-14 in both plasma and tissue samples. After oral administration, WJ-14 was rapidly absorbed into the blood with time to reach the maximum plasma concentration (Tmax ) within 0.28 h and quickly eliminated with clearance (Cl) exceeding 6.80L/h/kg and elimination half-life (t1/2 ) within 2.69 h. No obvious accumulation was found with mean residencetime (MRT) within 4.10 h. Tissue distribution revealed that WJ-14 was extensively distributed in the main tissues of rats, and massive amounts of WJ-14 were distributed in the liver. Extensive distribution and quick elimination led to extremely low absolute bioavailability of WJ-14 (1.91% of 8.33 mg/kg and 3.30% of 24.99 mg/kg). WJ-14 was detected in the brain only 0.083 h after oral administration, which is crucial for a rapid-onset antidepressant candidate. In addition, WJ-14 likely exhibited a non-linear pharmacokinetic process at dosages of 8.33 and 24.99 mg/kg. The findings may provide valuable information for subsequent studies on WJ-14.

On the dynamics of soliton solutions for the nonlinear fractional dynamical system: Application in ultrasound imaging

This article examines the third-order non-linear fractional Westervelt model by using a newly developed integration tool termed the new extended direct algebraic approach. The different wave structures to the considered model are secured in various forms, including bright, dark, and combo solitons. The application of wave structures is advantageous in the examination of sound wave propagation and high amplitude phenomena in the fields of medical imaging and therapy. These solutions are effective in facilitating ultrasound propagation in tissue, underwater acoustics, acoustic cavitation, acoustic levitation, and other related applications. The internal tissue of human beings can be visualized and studied through the use of ultrasound imaging technologies in the field of medicine. This technology possesses numerous uses in both industrial and medicinal sectors. There has been a growing interest in fractional nonlinear partial differential equations due to their ability to describe various complex occurrences and exhibit more dynamic architectures of localized wave solutions. On employing accurate parameter values, multiple graphical representations are generated to provide the visual depiction of the acquired results. The results of this study indicate that the chosen methodology effectively improves nonlinear dynamical processes. The findings indicate that the selected methodology demonstrates efficacy, feasibility, and versatility when applied to intricate systems across several domains, with a special emphasis on ultrasonic imaging. The findings indicate that the system exhibits a potentially significant abundance of soliton structures.

Data-model linkage prediction of tool remaining useful life based on deep feature fusion and Wiener process

Accurately predicting the tool remaining useful life (RUL) is critical for maximizing tool utilization and saving machining costs. Various physical model-based or data-driven prediction methods have been developed and successfully applied in different machining operations. However, many uncertain factors affect tool RUL during the cutting process, making it challenging to create a precise physical model to characterize the degradation of tool performance. The success of the purely data-driven technique depends on the amount and quality of the training samples, it does not consider the physical law of tool wear, and the interpretability of the prediction results is poor. This paper presents a data-model linkage approach for tool RUL prediction based on deep feature fusion and Wiener process to address the above limitations. A convolutional stacked bidirectional long short-term memory network with time-space attention mechanism (CSBLSTM-TSAM) is developed in the data-driven module to fuse the multi-sensor signals collected during the cutting process and then obtain the mapping relationship between signal features and tool wear values. In the physical modeling module, a three-stage tool RUL prediction model based on the nonlinear Wiener process is established by considering the evolution law of different wear stages and multi-layer uncertainty, and the corresponding probability density function is derived. The real-time estimated tool wear of the data-driven module is used as the observed value of the physical model, and the model parameters are dynamically updated by the weight-optimized particle filter (WOPF) algorithm under a Bayesian framework, thereby realizing the data-model linkage tool RUL prediction. Milling experiments demonstrate that the proposed method not only improves RUL prediction accuracy, but also has good generalization ability and robustness for prediction tasks under different working conditions.

Giant enhancement of optical nonlinearity from monolayer MoS2 using plasmonic nanocavity

Abstract The particle-on-mirror nanocavity, supporting multiple plasmonic resonances, provides an ideal platform to efficiently boost the nonlinear optical processes at the nanoscale. Here, we report on the enhancement of the second (SHG) and third-harmonic generations (THG) from the monolayer MoS2 using a multi-resonant Au nanosphere dimer-on-mirror nanocavity (DoMN). The strong plasmon hybridization between the dimer and underlying Au substrate leads to the emergence of two distinct cavity modes, which are intentionally aligned with the SH and TH frequencies, rendering a 15- and 68-fold enhancement for the SHG and THG of the monolayer MoS2, respectively. Further theoretical analysis yields that these remarkable nonlinearity enhancements are also ascribed to the amplification of nonlinear source because of the excellent spatial mode overlap and the high directivity of nonlinear emission enabled by the cavity modes. Our results pave the way for the implementation of low-cost, and highly efficient nonlinear photonics devices integrated with plasmonic nanocavities.

Constrained model predictive fault-tolerant control for nonlinear batch processes with time delay by integrating a LRF method and a switching strategy

To guarantee the control performance of batch processes under time delays and actuator failures, a novel iterative learning model-based predictive fault-tolerant control approach is developed. First, a two-dimensional switched model was developed by linearizing the system at multiple operating points so as to describe the actual process with and without actuator faults. Second, a switching controller with greater robustness and diminished conservativeness was developed based on this switched model. Compared to conventional fault-tolerant control methods, the switching controller has stronger fault-tolerant ability, less conservativeness, and higher energy efficiency. Third, by integrating the Lyapunov-Razumikhin function (LRF) method, sufficient conditions for system stability could be provided based on the robust positive invariant and terminal constraint sets. Solving the stability conditions could then allow us to obtain the control law gains under faulty or normal cases. Compared to the existing Lyapunov-Krasovskii function method (LKF) method, the developed stability conditions were simpler, less complex, and less conservative. Finally, the effectiveness of the proposed method is tested on a continuous stirred reactor (CSTR).

Toward generalized Milankovitch theory (GMT)

Abstract. In recent decades, numerous paleoclimate records and results of model simulations have provided strong support for the astronomical theory of Quaternary glacial cycles formulated in its modern form by Milutin Milankovitch. At the same time, new findings have revealed that the classical Milankovitch theory is unable to explain a number of important facts, such as the change in the dominant periodicity of glacial cycles from 41 to 100 kyr about 1 million years ago. This transition was also accompanied by an increase in the amplitude and asymmetry of the glacial cycles. Here, based on the results of a hierarchy of models and data analysis, a framework of the extended (generalized) version of the Milankovitch theory is presented. To illustrate the main elements of this theory, a simple conceptual model of glacial cycles was developed using the results of an Earth system model, CLIMBER-2. This conceptual model explicitly assumes the multistability of the climate–cryosphere system and the instability of the “supercritical” ice sheets. Using this model, it is shown that Quaternary glacial cycles can be successfully reproduced as the strongly nonlinear response of the Earth system to the orbital forcing, where 100 kyr cyclicity originates from the phase locking of the precession and obliquity-forced glacial cycles to the corresponding eccentricity cycle. The eccentricity influences glacial cycles solely through its amplitude modulation of the precession component of orbital forcing, while the long timescale of the late Quaternary glacial cycles is determined by the time required for ice sheets to reach their critical size. The postulates used to construct this conceptual model were justified using analysis of relevant physical and biogeochemical processes and feedbacks. In particular, the role of climate–ice sheet–carbon cycle feedback in shaping and globalization of glacial cycles is discussed. The reasons for the instability of the large northern ice sheets and the mechanisms of the Earth system escape from the “glacial trap” via a set of strongly nonlinear processes are presented. It is also shown that the transition from the 41 to the 100 kyr world about 1 million years ago can be explained by a gradual increase in the critical size of ice sheets, which in turn is related to the gradual removal of terrestrial sediments from the northern continents. The implications of this nonlinear paradigm for understanding Quaternary climate dynamics and the remaining knowledge gaps are finally discussed.

Non-linear modes of global sea surface temperature variability and their relationships with global precipitation and temperature

Sea surface temperature (SST) modes are comprised of variability that arises from inherently nonlinear processes. Historically, a limitation arises from applying linear statistics to define these modes. Accurate depiction of the complex, non-linear nature of SST modes of variability necessitates the specification of a model capable of producing nonlinear patterns. In this study, we apply an artificial neural network algorithm integrated with autoencoders to analyze the seasonal non-linear global SST modes allowing for improved characterization of the modes and their large-scale temperature and precipitation teleconnections. Our results show that during boreal summer, SST cooling over the central to eastern tropical Pacific co-occurs with the Arctic amplification. In recent decades, the negative SST trend in the central to eastern tropical Pacific, combined with the positive trend in the western tropical Pacific is linked to an increase in the amplitude of SST modes associated with the Arctic warming, resulting in warmer temperatures over large portions of the global land, particularly over Greenland. In boreal winter, El Niño Southern Oscillation (ENSO) is the prominent global SST mode. The distinct spatiotemporal patterns of ENSO modes are associated with unique effects on regional land temperature and precipitation. The central Pacific El Niño is more associated with the combination of warm and dry conditions over Western Australia, and the northern part of South America. Conversely, the central to eastern El Niño is more associated with the combination of warm and dry conditions over parts of Southern Africa, and the northern part of South America. The spatiotemporal patterns and trends in the amplitude of the analyzed non-linear global SST modes alongside their regional influences on temperature and precipitation are discussed. The broader impact of this study is on the potential of neural networks in effectively delineating non-linear global SST modes and their associations with regional climates.