Strong Nonlinearity Research Articles

Input-to-state hybrid impulsive formation stabilization for multi-agent systems with impulse delays

This paper addresses the input-to-state formation stabilization problem of nonlinear multi-agent systems within a hybrid impulsive framework, considering delay-dependent impulses, strong nonlinearity, and deception attack signals. By leveraging Lyapunov functionals, impulsive comparison theory, average impulsive interval methods, and graph theory, we develop novel criteria for possessing locally input-to-state and integral input-to-state formation stabilization across different impulse sequence classes. These criteria are expressed in terms of continuous/impulsive feedback gains, time delay size, nonlinearity strength, uniform upper bound of impulsive interval, and length of average impulsive interval. Notably, the design of control impulses benefit the destabilizing continuous dynamics in the formation stabilization process. To demonstrate the effectiveness and validity of the analytical results, we provide numerical simulation examples involving various types of external attack signals.

Behavioral modeling of LMBA with different back‐off state using PSO optimized XGBoost method

AbstractIn this paper, an optimization technique based on the particle swarm optimization (PSO) algorithm is applied to the eXtreme gradient boosting (XGBoost) method for load modulated balanced amplifiers (LMBAs) modeling, taking into consideration both strong nonlinearity and memory effects. An overview of the basic principles of the proposed modeling technique is provided, as well as a detailed description of how the model is extracted. To improve the performance of the XGBoost model, the hyperparameters are optimized using the PSO algorithm. An in‐house designed LMBA was used to perform experimental validation, which demonstrated that the new PSO‐XGBoost model provided very efficient and extremely accurate predictions, especially in the case of strong nonlinearities. When compared to traditional Volterra models, canonical piecewise‐linear based models, and standard XGBoost models, the proposed PSO‐XGBoost model provides improved performance with reasonable complexity.

Quality-driven deep feature representation learning and its industrial application to soft sensors

Establishing effective soft sensors relies on feature representation that is capable of capturing critical information. Stacked AutoEncoder (SAE) is able to capture the intricate structures of data characterized by high dimensionality and strong non-linearity by extracting abstract features layer by layer, making it widely used. However, the pretraining process of SAE is unsupervised, which means the features extracted cannot leverage label information to provide more actionable insights for downstream tasks. To extract more valuable feature representation, a new quality-driven dynamic weighted SAE (QD-SAE) is proposed in this paper. By incorporating supervised information dominated by the quality variable into the learned features during the pretraining of the SAE and weighting the abstract features layer by layer, the features that are beneficial to the prediction task are thus focused. In QD-SAE, the supervised information is computed by an improved attention score. In the initial state of the supervised fine-tuning process, the weighted features compose the hidden layers of the entire network. Finally, a benchmark function case and a real complex industrial process case are used to verify the effectiveness and advantages of QD-SAE. The experimental analyses demonstrate that the soft sensor constructed by the QD-SAE can predict the output variable with high accuracy and outperforms the conventional neural networks.

Explainable AI model for predicting equivalent viscous damping in dual frame–wall resilient system

A prominent challenge in applying the direct displacement-based design (DDBD) method to the proposed dual frame–wall lateral force-resisting system lies in determining the equivalent viscous damping ratio (EVDR). However, the strong nonlinearity and complexity behind the equivalent procedure lead to limited choice, mostly trial and error based on experience, to explain and predict the EVDR in the context of traditional research. This study employs the XGBoost method to unravel intricate relationships of EVDR using over 5 million data points from nonlinear time-history (NLTH) analyses, encompassing various parameters including the fundamental period, ductility, subsystem stiffness ratios, post-yielding stiffness ratios of the subsystems and ground motion types. SHapley Additive exPlanations (SHAP) values consistently identify critical features relevant to the equivalent procedure. Comprehensive feature ablation tests further illuminate the robustness and susceptibility of each model. Additionally, the incorporation of Local Interpretable Model-agnostic Explanations (LIME) for local interpretability provides insights into the intricate decision-making mechanisms inherent in each model’s predictions. Both the predicting results from machine learning (ML) and traditional method are also compared. Findings highlight the relative importance of features for EVDR and present a refined prediction model. It underscores the pivotal role of model interpretability in reinforcing confidence in complex models and advocates for leveraging ML techniques to enhance the effectiveness and efficiency of the DDBD method in structural design.

A high-static-low-dynamic-stiffness delayed resonator vibration absorber

Delayed resonator (DR), which enables complete vibration suppression through loop delay tuning, has been extensively investigated as a linear active dynamic vibration absorber since its invention. Besides, the nonlinear high-static-low-dynamic stiffness (HSLDS) has been widely used in vibration isolators for broadband (yet incomplete) vibration reduction. This work combines the benefits of DR and the nonlinear HSLDS characteristics, thus creating a nonlinear DR (NDR). Three unexplored topics are considered: (1). To address the nonlinear dynamics that are made complicated by the introduction of delay and the nonlinearity coupled between the NDR and the primary structure; (2). To tune the control parameters to seek possible complete vibration suppression in the nonlinear case, and accordingly, to determine the operable frequency band; (3). To evaluate how the HSLDS characteristics can enhance the performance of the linear DR (LDR) and how to design an NDR to maximize its benefits. Without loss of generality, a classic nonlinear HSLDS structure with three springs and two links is considered, and mathematical tools and computational algorithms are introduced or proposed to efficiently address theoretical analysis. Using the parameters of an experimental setup, we show that a properly tuned NDR suppresses the vibrations on the primary structure to a sufficiently low level. Besides, the HSLDS characteristics extend the operable frequency band compared with the LDR, while strong nonlinearity limits such extension. The proposed analysis procedures for delay-coupled nonlinear dynamics, alongside the control parameter tuning, determination of operable frequency bands, and structural design rules, establish a basic theoretical framework for the NDR design.

Recursive identification of kernel-based hammerstein model for online energy efficiency estimation of large-scale chemical plants

Accurate energy efficiency prediction is crucial for decision-making in large-scale chemical production, especially considering energy management and environmental concerns. The complexity of chemical processes, characterized by strong nonlinearities, dynamics, and uncertainties, challenges traditional prediction methods. This paper introduces KHSM (Kernel-based Hammerstein Subspace Model), which models nonlinear static and linear dynamic processes in series by embedding kernel function-based nonlinear mapping into subspace modeling for energy efficiency estimation. KHSM identifies nonlinear process models without explicit nonlinear mapping functions, constructing dynamic models that encompass both energy input and product output variables. An adaptive KHSM variant dynamically updates the energy efficiency model, improving accuracy by iteratively selecting and excluding samples. Comparative analysis shows KHSM outperforms existing methods, achieving a coefficient of determination (R2) closest to 1 and reducing the root-mean-square error (RMSE) by up to an order of magnitude, with the smallest mean and standard deviation. Additionally, modeling efficiency increases by an order of magnitude. The developed model enables ongoing energy efficiency estimation and proactive identification of efficiency trends. Validation through mathematical and real-world ethylene process cases demonstrates KHSM's efficacy and applicability. These estimates facilitate informed adjustments to energy management strategies and optimization of production approaches in energy-intensive chemical processes.

Supercontinua from integrated gallium nitride waveguides

Supercontinua are broadband spectra that are essential to optical spectroscopy, sensing, imaging, and metrology. They are generated from ultrashort laser pulses through nonlinear frequency conversion in fibers, bulk media, and chip-integrated waveguides. For any generating platform, balancing the competing criteria of strong nonlinearity, transparency, and absence of multiphoton absorption is a key challenge. Here, we explore supercontinuum generation in integrated gallium nitride (GaN) waveguides, which combine a high Kerr nonlinearity, mid-infrared transparency, and a large bandgap that prevents two- and three-photon absorption in the technologically important telecom C-band, where compact erbium-based pump lasers exist. Using this type of laser, we demonstrate tunable dispersive waves and gap-free spectra extending to almost 4 µm in wavelength, which is relevant to functional group chemical sensing. Additionally, leveraging the material’s second-order nonlinearity, we implement on-chip f-to-2f interferometry to detect the pump laser’s carrier-envelope offset frequency, which enables precision metrology. These results demonstrate the versatility of GaN-on-sapphire as a platform for broadband nonlinear photonics.

Data-Driven Tube-Based Robust Predictive Control for Constrained Wastewater Treatment Process.

The wastewater treatment process (WWTP) is characterized by unknown nonlinearity and external disturbances, which complicates the tracking control of dissolved oxygen concentration (DOC) within operational constraints. To address this issue, a data-driven tube-based robust predictive control (DTRPC) strategy is proposed to achieve stable tracking control of DOC and satisfy the system constraints. First, a tube-based robust predictive control (TRPC) strategy is designed to deal with system constraints and external disturbances. Specifically, a nominal controller is designed to ensure that the nominal output accurately tracks the set-point under tightened constraints, while an auxiliary feedback controller is designed to suppress disturbances and restore the nominal performance of the disturbed WWTP. Second, two fuzzy neural network identifiers are employed to provide accurate predictive outputs for the control process, overcoming the challenges of modeling the WWTP with strong nonlinearity and unknown dynamics. Third, the generalized multiplier method is utilized to solve the constrained optimization problem to obtain the nominal control law, and the gradient descent algorithm is used to obtain the auxiliary control law. The implementation of this composite controller ensures the satisfaction of the system constraints and the effective suppression of disturbances. Finally, the feasibility and stability of the proposed DTRPC strategy are guaranteed through rigorous theoretical analysis, and its effectiveness is demonstrated through the simulations on the benchmark simulation model No.1.

Predesigned perovskite crystal waveguides for room-temperature exciton-polariton condensation and edge lasing.

Perovskite crystals-with their exceptional nonlinear optical properties, lasing and waveguiding capabilities-offer a promising platform for integrated photonic circuitry within the strong-coupling regime at room temperature. Here we demonstrate a versatile template-assisted method to efficiently fabricate large-scale waveguiding perovskite crystals of arbitrarily predefined geometry such as microwires, couplers and splitters. We non-resonantly stimulate a condensate of waveguided exciton-polaritons resulting in bright polariton lasing from the transverse interfaces and corners of our perovskite microstructures. Large blueshifts with excitation power and high mutual coherence between the different edge and corner lasing signals are detected in the far-field photoluminescence, implying that a spatially extended condensates of coherent polaritons has formed. The condensate polaritons are found to propagate over long distances in the wires from the excitation spot and can couple to neighbouring wires through large air gaps, making our platform promising for integrated polaritonic circuitry and on-chip optical devices with strong nonlinearities.

A novel method of vehicle height control utilizing semi-active actuator

Inspired by the physical phenomenon that the balance position of the vehicle body changes due to a suspension system with asymmetric damping, this paper presents a novel method to control the vehicle height utilizing semi-active actuators. The proposed vehicle height control method uses the asymmetric damping of the semi-active actuator to control the raising and lowering of the vehicle body, which essentially harnesses the energy from the vehicle’s driving vibrations and has the characteristics of low cost, energy saving and fast response. Aiming at the strong nonlinearity and discontinuity of the piecewise linear nonlinear system of the vehicle body vibration, the homotopy analysis method (HAM) is used to solve the high-order analytical solution, the non-smooth terms are processed through Fourier series expansion, and the iteration method is combined to treat the iteration result as the initial guess solution for the next iteration, improving the convergence accuracy of the series solution and expands the application scope of the HAM. The feasibility of the presented method is investigated from an analytical point of view and the influences of some critical parameters on the responses of the system are analyzed. Finally, the magnetorheological damper (MRD) produced by LORD company is utilized as the actuator, and the vehicle height control experiments system is established by using NI-Labview software and NI-PXI hardware platform, The experiments are performed to verify the feasibility of the proposed vehicle height control method and the system response laws. The proposed method realizes the functions of active actuators using semi-active actuators, and tries a new method and approach for vehicle height control under specific working conditions, such as short-term obstacle surmounting, high-speed steering, emergency avoidance, and rollover prevention.

Forecasting mooring tension of offshore platforms based on complete ensemble empirical mode decomposition with adaptive noise and deep learning network

The tension sequence data of offshore platforms mooring cables exhibit randomness, strong nonlinearity, and nonsmoothness. Previous studies have shown that single neural network models, such as long short-term memory (LSTM) and recurrent neural network (RNN) models, can effectively predict nonlinear data. Dealing with nonstationary data presents several challenges, nevertheless, like a noticeable delay in forecast outcomes and significant prediction errors. Aiming to address the aforementioned challenges, this article proposes an innovative hybrid prediction model named CEEMDAN-CLL for predicting mooring tension in semi-submersible platforms based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), frequency-domain analysis, convolutional neural network–long short-term memory (CNN-LSTM), and LSTM. The data used in this study are those monitored during the operation of “DeepSea One”, which is the first deepwater semi-submersible production platform in the South China Sea, is taken as the research object and cover a wide range of orientations and sea states.

A novel global modelling strategy integrated dynamic kernel canonical variate analysis for the air handling unit fault detection via considering the two-directional dynamics

As an indispensable component of air-conditioning system, the air handling unit (AHU) always exhibits strong nonlinearity and two-directional dynamics (time-wise and batch-wise dynamics). However, existing monitoring strategies cannot adequately figure out the AHU's two-directional dynamics from the nonlinear data. To boost the AHU's fault detection performance, a novel global modelling scheme integrated dynamic kernel canonical variate analysis (GDKCVA) is developed in this paper. The first contribution is to collect datasets from various days to develop a three-way training dataset and then normalize it along the batch-wise to suppress the batch-wise dynamics and variables' correlations. The second contribution is to establish the dynamic kernel CVA by integrating autoregressive moving average exogenous framework to more effectively confront the time-wise dynamics and variables' nonlinear relationships. The kernel matrices of augmented batch dataset are determined utilizing the kernel trick that transforms nonlinear data into high-dimensional linear space by leveraging kernel function. The third contribution is to propose a novel global modelling strategy to further eliminate the batch-wise dynamics by computing the total average kernel matrices from all the normal batch datasets. Finally, experiments and comparisons on the ASHRAE RP-1312 datasets are carried out to assess the suggested GDKCVA's fault detection capability. Compared with the kernel CVA (KCVA), the three-way training dataset based CVA (TCVA) and the three-way training dataset based KCVA (TKCVA), the proposed GDKCVA has the highest fault detection rates and its average fault detection rates of three monitoring statistics for eleven fault patterns reach 99.38 %, 99.15 % and 100 %, respectively.

An Improved Series 36-Pulse Rectifier Based on Dual Passive Pulse-Doubling Circuit on the System DC Side

The series-type 12-pulse rectifier generates a large amount of harmonics in the AC side current due to the strong nonlinearity of its rectifying diodes, causing serious harmonic pollution to the power grid. This article proposes a series 36-pulse rectifier based on a DC side dual passive frequency-doubling circuit to suppress the AC side current harmonics of a 12-pulse rectifier. The rectifier uses two symmetrical passive pulse multiplication circuits to regulate the circulation in the DC side circuit, increasing the output voltage and current state of the rectifier bridge, thereby increasing the number of pulses in the rectifier from 12 times to 36 times. Firstly, the working principle of the rectifier and the working mode of the dual passive frequency-doubling circuit were analyzed. Secondly, the harmonic suppression mechanism of the rectifier input current was revealed, and the frequency-doubling characteristics of the load voltage were analyzed. Finally, the correctness of the theoretical analysis was verified through a semi-physical platform. The verification and comparison results show that under the optimal conditions of the injecting transformer turns ratio, the DPPC can not only reduce the THD value of the input current by about 1/3 (from 14.87% to 4.78%) but can also increase the fluctuation frequency of the load voltage by 3 times (from 12 to 36), while improving the power quality of the AC/DC side rectifier and achieving the low harmonic operation of the rectifier. The proposed 36-pulse rectifier can effectively suppress harmonics; it has the advantages of simple structure, strong robustness, and high output voltage gain, and it is suitable for medium-voltage and high-voltage high-power rectification applications.

A Foundational Study on Rational Optimization of Damping Ratio for Accurate Dynamic Simulation with Ultra Large Displacement

The integration of dynamic simulation analysis has become widespread in general-purpose software, providing enhanced capabilities. However, accurately tracking deformations based on complete equilibrium solutions remains a significant challenge in problems characterized by strong geometric nonlinearity. This study examines the accuracy of the combined Newmark β method and Tangent stiffness method in dynamic analysis with ultra large displacements and evaluates the utility of Rayleigh proportional damping in numerical simulations compared to experimental models. An experimental model of a slender steel plate undergoing free vibrations after being released from a deformed state was created. Video footage capturing the deformation histories was compared to computational simulations to verify accuracy. The study also examines the appropriate values of the damping ratio (ζ) and the Newmark β value in the simulations. The results indicate that adjusting various damping ratio and a β value of 1/2 yield more realistic simulations with longer conservation of mechanical energy. The findings suggest that incorporating numerical damping into actual damping settings can achieve a more realistic simulation of dynamic behaviour with ultra-large displacements. Furthermore, experiments and analyses were performed to correct natural frequency by changing Young’s modulus, which is a key factor influencing natural frequencies, with observed correlations to plate thickness, setting the stage for further research under varied conditions to develop a more rational methodology for structural analysis.

A highly accurate and efficient Genocchi‐based spectral technique applied to singular fractional order boundary value problems

This article focuses on an efficient and highly accurate approximate solver for a class of generalized singular boundary value problems (SBVPs) having nonlinearity and with two‐term fractional derivatives. The involved fractional derivative operators are given in the form of Liouville–Caputo. The developed algorithm for solving the generalized SBVPs consists of two main stages. The first stage is devoted to an iterative quasilinearization method (QLM) to conquer the (strong) nonlinearity of the governing SBVPs. Secondly, we employ the generalized Genocchi polynomials (GGPs) to treat the resulting sequence of linearized SBVPs numerically. An upper error estimate for the Genocchi series solution in the norm is obtained via a rigorous error analysis. The main benefit of the presented QLM‐GGPs procedure is that the required number of iteration in the first stage is within a few steps, and an accurate polynomial solution is obtained through computer implementations in the second stage. Three widely applicable test cases are investigated to observe the efficacy as well as the high‐order accuracy of the QLM‐GGPs algorithm. The comparable accuracy and robustness of the presented algorithm are validated by doing comparisons with the results of some well‐established available computational methods. It is apparently shown that the QLM‐GGPs algorithm provides a promising tool to solve strongly nonlinear SBVPs with two‐term fractional derivatives accurately and efficiently.

Longitudinal ultrasound measurements of polyethylene oxide across dilute to concentrated aqueous solutions

Measuring the properties of polymer solutions is crucial for understanding fundamental polymer physics. The longitudinal ultrasound measurement method offers a promising technique for characterizing these properties. In this study, we develop a mathematical model to correlate longitudinal ultrasonic signals with the material properties of polyethylene oxide (PEO) from dilute to concentrated aqueous solutions. After applying reflection and diffraction corrections, the accuracy of the measurement results improves to over 97 %. Our findings reveal a positive correlation between the speed of sound, density, and longitudinal modulus with the mass concentration of PEO. Additionally, ultrasonic relaxation analysis reveals that PEO solutions exhibit at least one relaxation process in the frequency range of 3–7 MHz, independent of concentration and molecular weight. Compared to dilute solutions, the relaxation amplitude in concentrated solutions is larger and accompanied by strong nonlinearity, attributed to conformational changes caused by molecular entanglement in concentrated solutions.

Silicon‐On‐Silicon Carbide Platform for Integrated Photonics

AbstractSilicon carbide (SiC)'s nonlinear optical properties and applications to quantum information have recently brought attention to its potential as an integrated photonics platform. However, despite its many excellent material properties, such as large thermal conductivity, wide transparency window, and strong optical nonlinearities, it is generally a difficult material for microfabrication. Here, it is shown that directly bonded silicon‐on‐silicon carbide can be a high‐performing hybrid photonics platform that does not require the need to form SiC membranes or directly pattern in SiC. The optimized bonding method yields defect‐free, uniform films with minimal oxide at the silicon–silicon–carbide interface. Ring resonators are patterned into the silicon layer with standard, complimentary metal–oxide–semiconductor (CMOS) compatible (Si) fabrication and measure room‐temperature, near‐infrared quality factors exceeding 105. The corresponding propagation loss is 5.7 dB cm−1. The process offers a wafer‐scalable pathway to the integration of SiC photonics into CMOS devices.

Three-wave mixing experiments in indium–tin–oxide thin-films with no phase matching

Abstract One challenge of using nonlinear optical phenomena for practical applications is the need to perform phase-matching. Recently, epsilon-near-zero materials have been shown to demonstrate strong optical nonlinearities, in addition to their other unique properties. As suggested by their name, the permittivity of the material is close to zero for a certain wavelength range. We demonstrate that this small permittivity allows for efficient three-wave mixing interactions to take place in indium–tin–oxide thin films without the need for phase matching the pump and signal beams. The efficiency of the second-order nonlinear interactions is characterized, and cascaded three-wave mixing is demonstrated.

Characterisation of the Glare Properties of Photovoltaic Modules and PV Systems Using a Photographic Camera

With the increasing prevalence of photovoltaic (PV) installations on north-facing roofs in urban areas, the issue of glare on PV modules is becoming more significant. This paper presents a method for measuring and characterising the intensity and type of glare using a commercially available photo camera. The method utilises the fact that brightness information is inherently contained in a photograph. Due to the strong non-linearity of brightness information in an image, especially when using High Dynamic Range (HDR) functionality, an image needs to be divided into multiple sub-images with clearly defined settings, and the linear range extracted from each of them. The information obtained in this way is then assembled into a new image. The resulting luminance image describes the intensity and shape of glare, forming the basis for calculating the occurrence of glare (times and days of the year) in a simplified manner.

Meshing theory and contact analysis of double enveloping hourglass worm drive with planar generatrix

The meshing and limit equations of worm drive usually have strong nonlinearities such as multiple solutions, solution nonexistence and equation singularity. Meanwhile, the tooth surfaces of worm drive are in nonconforming line contact, which often requires mesh refinement of contact region for the loaded contact analysis. These two challenges cause that the modeling of worm drive heavily relies on manual adjustment and the loaded contact analysis of worm drive is still rare especially when edge contact and assembly error are concerned. Focusing on the double enveloping hourglass worm (DEHW) drive with planar generatrix, this work presents procedures to solve meshing and limit equations with global convergence. The instantaneous contact line, meshing limit line, curvature interference limit line and tooth surface grid discretization are adaptively generated, without manual trial or adjustment. On the basis of adaptive mesh refinement of tooth surface, the mortar virtual element method is adopted for loaded contact analysis of DEHW drive with edge contact and center distance error. Under sliding friction, the discrete system of governing equalities and inequalities is solved by semi-smooth Newton algorithm after constraint condensation. Numerical results for meshing theory and loaded contact analysis of DEHW drive with planar generatrix are discussed.