Strong Nonlinearity Research Articles

Effect of laser chirping on third harmonic generation in anharmonic clusters with ripple on cluster density

A proposed model delves into the resonant enhancement of third harmonic generation (THG) by a short-pulse laser inside nanoclustered plasma under the influence of density ripple. An intense chirped laser pulse incident on a clustered plasma of argon gas displaces the electrons of the medium and produces a restoring force. This force is considered to vary nonlinearly with electron displacement, leading to the anharmonic response of the electron clouds of the cluster. The nonlinear current at the third harmonic frequency arises from the perturbation of the electron density of the cluster by the ponderomotive force exerted on them by the incident laser pulse. Applying ripple in cluster density and electron density of surrounding plasma enables the phase-matching criteria for THG to be satisfied, which leads to enhanced harmonic output. An anharmonic structure of clusters exhibits strong optical nonlinearities, resulting in the plasmon resonance broadening and producing harmonics with greater efficiency. Numerical analysis shows that the chirp parameter of the laser pulse and ripple on cluster density enhance system nonlinearity causing the generation of a third harmonic of enhanced amplitude. The study explores how different factors such as laser intensity, cluster size, ripple parameter, chirp parameter, and electron excursion influence the efficiency of THG.

Generation of Soliton Frequency Combs in NEMS.

In this study, we present an innovative approach leveraging combination internal resonances within a NEMS platform to generate mechanical soliton frequency combs (FCs) spanning a broad spectrum. In the time domain, the FCs take the form of a periodic train of narrow pulses, a highly coveted phenomenon within the realm of nonlinear wave-matter interactions. Our method relies on an intricate interaction among multiple vibration modes of a bracket-nanocantilever enabled by the strong nonlinearity of the electrostatic field. Through numerical simulation and experimental validation, we demonstrate that by amplifying the motions of the NEMS with the external electrostatic forcing tuned to excite the superharmonic resonance of order-n of the fundamental mode and exploiting combination internal resonances, we can generate multiple stable localized mechanical wave packets with different lobe sizes embodying soliton states I and II. This represents a significant breakthrough with profound implications for quantum computing and metrology.

An off-energy multipole kicker injection scheme designed with an acceptance analysis method for a diffraction-limited storage ring

Diffraction-limited storage rings (DLSRs) have restricted dynamic apertures (DAs) due to their ultralow emittances and very strong nonlinearity. Off-energy multipole kicker injection (MKI) scheme, in which off-energy beam is injected onto the corresponding off-energy orbit, can reduce the requirement of DAs. However, it requires relatively large energy acceptance and high dispersion bumps. For a DLSR lattice with relatively large energy acceptance and off-momentum DAs, off-energy beam can be injected into the off-momentum DA but with an additional offset from the off-energy closed orbit to increase the total offset of the injected beam from the on-energy closed orbit, which is favorable to the application of the off-energy MKI. In this paper, such an off-energy MKI is designed for a DLSR, and an acceptance analysis method based on 6D particle tracking is utilized to design and optimize this injection scheme. Detailed simulation is carried out, and the results demonstrate the feasibility of this injection scheme.

Unveiling vacuum fluctuations and nonclassical states with cavity-enhanced tripartite interactions

Enhancing and tailoring light–matter interactions offer remarkable nonlinear resources with wide-ranging applications in various scientific disciplines. In this study, strong and deterministic tripartite “beamsplitter” (“squeeze”) interactions are constructed by utilizing cavity-enhanced nonlinear anti-Stokes (Stokes) scattering within spin–photon–phonon degrees of freedom. We explore exotic dynamical and steady-state properties associated with the confined motion of a single atom within a high-finesse optical cavity. Notably, we demonstrate the direct extraction of vacuum fluctuations of photons and phonons, which are inherent in Heisenberg’s uncertainty principle, without requiring any free parameters. Moreover, our approach enables the realization of high-quality single-quanta sources with large average photon (phonon) occupancies. The underlying physical mechanisms responsible for generating the nonclassical quantum emitters are attributed to the decay-enhanced single-quanta blockade and long-lived motional phonons, resulting in strong nonlinearity. This work unveils significant opportunities for hitherto studying unexplored physical phenomena and provides novel perspectives on fundamental physics dominated by strong tripartite interactions.

Finite-time hybrid impulsive formation tracking control of multi-agent systems via aperiodic intermittent communication

This article studies the problem of formation tracking control in multi-agent systems, achieved in finite time, under challenging conditions such as strong nonlinearity, aperiodic intermittent communication, and time-delay effects, all within a hybrid impulsive framework. The impulses are categorized as either stabilizing control impulses or disruptive impulses. Furthermore, by integrating Lyapunov-based stability theory, graph theory, and the linear matrix inequality (LMI) method, new stability criteria are established. These criteria ensure finite-time intermittent formation tracking while considering weak Lyapunov inequality conditions, intermittent communication rates, and time-varying gain strengths. Additionally, the approach manages an indefinite number of impulsive moments and adjusts the control domain’s width based on the average impulsive interval and state-dependent control width. Numerical simulations are provided to validate the applicability and effectiveness of the proposed formation tracking control protocols.

EVENT-TRIGGERED CONTROL OF MILLING PHOTOELECTRIC TRACKING SERVO SYSTEMS BASED ON MULTI-INNOVATION INTEREST PARAMETER IDENTIFICATION

Given the coupling of speed and current and the nonlinearity of electronic devices, the photoelectric tracking servo system for milling machines make it difficult to determine the model parameters, and traditional proportional–integral (PI) control hardly meets the high-performance requirements of milling machine optoelectronic tracking servo systems, especially in the development of system networking. In this study, an event-triggered intelligent PI position control strategy based on a multi-innovation identification model was proposed to improve the low control accuracy and dynamic performance caused by the strong coupling and nonlinearity in the optoelectronic tracking servo system of computerized numerical control (CNC) milling machines. A discredite model of the system was established through a multi-innovation identification model, and the PI control parameter was quickly determined using an improved multiverse optimization (IMVO) algorithm. At the same time, an event-triggering mechanism was introduced, thus reducing the number of controller triggers and saving system resources while ensuring the dynamic performance of the system. Finally, experiment results were compared with typical second-order system engineering design PI (SSED-PI) control, pole placement PI (PP-PI) control, and multiverse optimization (MVO)-PI control. Results demonstrate that the proposed multi-innovation stochastic gradient identification model fully utilizes the historical turning angle information of the optoelectronic tracking servo system and has higher accuracy than traditional stochastic gradient identification (parameter accuracy improved by 6.9 times, quantization error reduced by 6.7 times). The proposed event-triggered IMVO-PI (ET-IMVO-PI) has a triggering frequency of 3.5% compared with time-triggered IMVO-PI, with an overshoot of less than 0.5%, which can meet the needs of most engineering practices (less than 5%). Compared with event-triggered SSED-PI, PP-PI, and IMVO-PI, ET-IMVO-PI has higher dynamic performance and fewer triggering times, which can effectively meet the requirements of high-performance network control. The proposed method serves a crucial theoretical guide and important reference for the upgrading and transformation of the photoelectric tracking servo system of CNC milling machines. Keywords: Event-triggered control, Multiple innovative parameter identification, Multiverse optimization PI, Optoelectronic tracking servo system

Numerical simulations of a ship sailing across pack ice area in forward motion under different drafts

Different from the existing CFD-DEM models in which the ship remains stationary, a CFD-DEM model with the ship in forward motion is proposed in this paper to simulate the process of a ship sailing across pack ice area at a forward speed under different drafts. A high-precision method for generating pack ice area on the undisturbed free surface that can be used in conjunction with the proposed model is introduced. Taking an ice-strengthened Panamax bulker as study object, the available model test results are used to verify the reliability of the proposed model, which shows that the model can effectively evaluate the resistance performance and simulate the ship-ice-water interaction. Based on the verified model, the ice resistances on different parts of the hull are first investigated, which reveals that the ice resistance of the bow is most significant, while those of the midship and stern are negligible. Then, the speed dependence of ice resistance under different drafts is studied. It shows a strong nonlinearity under shallow draft, while the nonlinearity gradually weakens as the draft increases. Finally, the proportions of ice resistance and open-water resistance in the total resistance under different drafts and ship speeds are discussed.

Powered–coasting–powered multi-phase mission reconfiguration method for launch vehicles under power system failures

For the final stage of a launch vehicle with powered–coasting–powered multi-phase flight, this paper investigates the joint reconfiguration method to determine subsequent flight trajectory and degraded orbit after power system failure in the first powered phase. While power system failures due to mass–flow–rate drop have been thoroughly studied in the existing literature, this paper focuses on the more challenging specific impulse drop failures, which result in loss of total launcher energy. This paper aims to design a fault-tolerant guidance method with onboard potential and to analyze the survivability and characteristics of the launcher in the event of such a failure. In the problem modeling, the strong nonlinearity of the orbital elements as terminal constraints is eliminated by analyzing the orbital properties in the orbital coordinate system to establish the primal trajectory optimization problem. For this multi-phase trajectory optimization problem, a joint optimization algorithm for the degradation orbit and the flight trajectory, based on convex optimization and Radau pseudospectral method, is designed to achieve autonomous mission reconfiguration. The algorithm introduces the relaxation–penalization idea, where the terminal constraints are relaxed and penalized in the performance index, allowing the algorithm to adaptively form an optimal degradation circular or elliptical orbit based on the remaining capacity of the launch vehicle. Simulation experiments demonstrate the effectiveness and superiority of the mission reconfiguration algorithm. Finally, the paper presents the first analysis of the optimal allocation of flight time between the first powered phase, the coasting phase, and the second powered phase in a propellant depletion scenario following the launcher power system failure.

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.