Presence Of Nonlinearities Research Articles

A non-linear local active noise control with integrated virtual sensing using an adaptive hybrid spline filter

Virtual sensing technique has been a promising means for local active noise control (ANC) to surpass the design constraint of error microphone placement at a desired location. Most existing systems which use virtual sensing employ an finite impulse response (FIR) filter based adaptive filter for achieving noise cancellation. However, the effectiveness of such ANC systems deteriorate in the presence of non-linearities in the system. In this paper, an attempt has been made to develop a class of non-linear ANC systems, with integrated virtual sensing, based on adaptive spline filters. These include a Wiener model, a Hammerstein model and a sandwich Hammerstein-Wiener based hybrid model of non-linear ANC. The learning algorithms for the proposed ANC schemes have been developed and it was observed that the adaptive nature of the activation functions allow the ANC system to shift from linear to non-linear and vice versa depending on the control scenario. The simulation results demonstrate that the hybrid spline based ANC system provides an improved noise reduction performance in non-linear scenarios in comparison with other ANC schemes.

Adaptive passive fault tolerant control of DFIG-based wind turbine using a self-tuning fractional integral sliding mode control

Controlling variable wind speed turbine (VWT) system based on a doubly-fed induction generator (DFIG) is a challenging task. It requires a control law that is both adaptable and robust enough to handle the complex dynamics of the closed control loop system. Sliding mode control (SMC) is a robust control technology that has shown good performance when employed as a passive fault-tolerant control for wind energy systems. To improve the closed control loop of VWT based on DFIG with the aim of improving energy efficiency, even in presence of nonlinearities and a certain range of bounded parametric uncertainties, whether electrically or mechanically, an adaptive passive fault tolerant control (AP-FTC) based on a self-tuning fractional integral sliding mode control law (ST-FISMC) developed from a novel hyperbolic fractional surface is proposed in this paper. ST-FISMC introduces a nonlinear hyperbolic function into the sliding manifold for self-tuning adaptation of control law, while fractional integral of the control law smooths discontinuous sign function to reduce chattering. Additionally, this work introduces an adaptive observer, developed and proved based on a chosen Lyapunov function. This observer is designed to estimate variations in electrical parameters and stator flux, ensuring sensorless decoupling in indirect field- oriented control (SI-FOC) of DFIG. Lyapunov theory is also used to prove stability of states vectors in closed control loop with presence of bounded parameters uncertainties or external disturbances. Simulation results show that the proposed approach offers better performance in capturing optimal wind energy, as well as the ability to regulate active/reactive power and high resilience in presence of occurring parameter uncertainties or external disturbances.

A cloud–edge collaboration based quality-related hierarchical fault detection framework for large-scale manufacturing processes

Against the backdrop of the new-generation intelligent manufacturing and Industrial Internet of Things, manufacturing processes are evolving towards integration, large-scale operations, and complexity, and the requirements for process safety and product quality reliability are constantly improving. However, these processes are generally distinguished by multi-production sub-processes with cooperative coupling, and multi-hierarchical levels integrated automation systems, where any deviation or abnormality occurring within a sub-process or system level will lead to the extensive propagation and evolution of faults, making the comprehensive quality-related fault detection face increasing challenges in practice. In response, a novel cloud–edge collaboration-based quality-related hierarchical fault detection framework is constructed in this paper, which can facilitate interconnected communication between sub-processes and enhance collaborative interactions at different hierarchical levels to improve fault detection accuracy and reliability. First, two quality supervised training mechanisms based on minimal gated unit are introduced for capturing different scale dynamics features on the cloud side and edge side. These methods enable more adequate extraction of quality-related deep hidden features, particularly in the presence of nonlinearity and dynamics. Subsequently, a federated bi-directional knowledge distillation-based strategy is proposed, leveraging the concept of federated learning. Quality knowledge such as prediction and quality-related features from both the cloud side and edge side are integrated into the training steps of federated learning, thereby strengthening the interaction between multiple sub-processes and distinct levels. Furthermore, comprehensive quality-related fault detection strategies are formulated based on the quality-related features of the cloud side and each sub-process on the edge side, respectively. Finally, the proposed framework is deployed into a cloud–edge-device collaborative prototype system based on a real hot strip mill process to demonstrate its effectiveness and applicability.

Topological solitons in coupled Su-Schrieffer-Heeger waveguide arrays.

We investigate the formation of multipole topological solitons at the edges of two and three coupled parallel Su-Schrieffer-Heeger (SSH) waveguide arrays. We show that independent variations of waveguide spacing in the unit cells (dimers) in coupled waveguide arrays result in the emergence at their edges of several topological edge states with different internal symmetries. The number of emerging edge states is determined by how many arrays are in topologically nontrivial phase. In the presence of nonlinearity, such edge states give rise to families of multipole topological edge solitons with distinct stability properties. Our results illustrate that coupling between quasi-one-dimensional topological structures substantially enriches the variety of stable topological edge solitons existing in them.

Enhancement of virtual inertia via delay designed GADRC in hybrid microgrid with communication delay

The lowering of inertia in a hybrid microgrid caused by the incorporation of renewable sources of energy leads to an increased rate of change of frequency and frequency deviation in the system. Further, the varying load demand and the presence of communication delay adversely affect the frequency regulation. In view of this, in this paper, a modified virtual inertia control strategy is formulated and implemented through the energy storage device to enhance the overall inertia of the hybrid microgrid. Secondly, a delay-designed generalized active disturbance rejection control (DD-GADRC) technique is proposed for the secondary frequency control of the power system under varying communication delay and rapidly fluctuating load demand in the system. The effectiveness of the proposed control scheme is evaluated across multiple scenarios, including situations when there are continuous changes in solar or wind power generations. The robustness of the proposed technique is also evaluated under parametric variations and the presence of non-linearities in the system. Finally, the effectiveness of the proposed technique is analyzed and compared to various pre-existing control strategies in the literature related to the hybrid microgrid.

Macro-financial imbalances and cyclical systemic risk dynamics: understanding the factors driving the financial cycle in the presence of non-linearities

Abstract This paper develops a multivariate filter based on an unobserved component model to estimate the financial cycle. Our model features: (1) a dynamic relationship between the financial cycle and key variables; (2) time-varying shock volatility for trend and cycle components. We demonstrate that our approach not only exhibits superior early warning properties for banking crises but also outperforms commonly used indicators in terms of data fit for decomposition exercises, as evidenced by the higher marginal likelihood. We document three important properties of the financial cycle. First, the sensitivity of the financial cycle to changes in real estate valuations increased during the post-90s period. Second, the sensitivity of the cycle to changes in financial conditions displays volatility and country specificities. Finally, our reduced form estimates suggest that the banking crisis of 1988 was preceded by positive contributions from the risk appetite shock, while the primary source of vulnerabilities emanated from the housing market in the run-up to the Global Financial Crisis.

Double shooting method for FRCM reinforced systems in debonding problems

The debonding process in FRCM (Fiber Reinforced Cementitious Matrix) strengthened brittle substrates, such as concrete and masonry, is characterized by complex failure modes that include debonding at both the external and internal interfaces of the composite, as well as damage to the mortar matrix. This study addresses this problem classically as a mode-II fracture process by accounting for the one-dimensional non-linear interfacial shear stress-slip relationship combined with matrix axial non-linearity. The approach employed considers the longitudinal displacements of both the inner and outer layers of mortar, along with that of the fiber textile, as unknowns, and analytically solves the second-order ordinary differential equation (ODE) system that governs the debonding problem. Then, the boundary value problem (BVP) is transformed into an initial value problem (IVP) and a double shooting method is proposed to find displacements and stresses along the bonded length in the presence of non-linearity. The appropriate initial values of matrix layer displacements, satisfying the required boundary conditions, are efficiently determined through a two-dimensional bisection method working on rectangular and triangular patches. The softening behavior of both mortar layers and interfaces between mortar and fiber are taken into account using jagged constitutive relationships to enhance convergence. The numerical calculation speed, robustness, and key simulation parameters are thoroughly discussed. Moreover, the proposed numerical approach is compared with existing experimental data and models, on both concrete and masonry FRCM-reinforced specimens. The influence of mortar failure and interfacial strength is also explored. The model demonstrates its ability to effectively reproduce the global bond behavior observed in experimental studies, while capturing the local behavior and simulating various failure modes observed in the tests.

The derivative-based approach to nonlinear mediation models: insights and applications

Traditional mediation analysis has been developed in the context of linear models, enabling the estimation of indirect effects through the product of regression coefficients. However, in the presence of nonlinearities, defining and estimating indirect effects becomes more challenging. While nonlinear mediation models are relatively easy to address in the counterfactual-based framework, very few generalizations to nonlinear associational settings have been proposed. One of the most intuitive is the derivative-based approach that, however, seems not to be widely spread among scholars. In this paper, we deepen such an approach to nonlinear mediation models, clarifying and proposing solutions to some issues which have not been addressed by the previous literature. Specifically, we discussed discrete exposures, binary mediators and extensions of this approach to more complex settings like the multilevel one. We also propose to estimate confidence intervals for the indirect effect within a Bayesian framework and compare its performance to that of other approaches in the literature through a simulation study. Finally, a real data application is presented.

An optimal hybrid quadcopter control technique with MPC-based backstepping

Quadcopter unmanned aerial vehicle is a multivariable, coupled, unstable, and underactuated system with inherent nonlinearity. It is gaining popularity in various applications and has been the subject of numerous research studies. However, modelling and controlling a quadcopter to follow a trajectory is a challenging issue for which there is no unique solution. This study proposes an optimal hybrid quadcopter control with MPC-based backstepping control for following a reference trajectory. The outer-loop controller (backstepping controller) regulates the quadcopter’s position, whereas the inner-loop controller (Model Predictive Control) regulates its attitude. The translational and rotational dynamics of the quadcopter are analyzed utilizing the Newton-Euler method. After that, the backstepping controller (BC) is created, which is a recurrent control method according to Lyapunov’s theory that utilizes a genetic algorithm (GA) to choose the controller parameters automatically. In order to apply a linear control technique in the presence of nonlinearities in the quadcopter dynamics, Linear Parameter Varying (LPV) Model Predictive Control (MPC) structure is developed. Simulation validated the dynamic performance of the proposed optimal hybrid MPC-based backstepping controller of the quadcopter in following a given reference trajectory. The simulations demonstrate the fact that using a command control input in trajectory tracking, the proposed control algorithm offers suitable tracking over the assigned position references with maximum appropriate tracking errors of 0.1 m for the �� and �� positions and 0.15 m for the �� position.

Spatial resolution effects on the solar open flux estimates

Context. Spectropolarimetric observations used to infer the solar magnetic fields are obtained with a limited spatial resolution. The effects of this limited resolution on the inference of the open flux over the observed region have not been extensively studied. Aims. We aim to characterize the biases that arise in the inference of the mean flux density by performing an end-to-end study that involves the generation of synthetic data, its interpretation (inversion), and a comparison of the results with the original model. Methods. We synthesized polarized spectra of the two magnetically sensitive lines of neutral iron around 630 nm from a state-of-the-art numerical simulation of the solar photosphere. We then performed data degradation to simulate the effect of the telescope with a limited angular resolution and interpreted (inverted) the data using a Milne-Eddington spectropolarimetric inversion code. We then studied the dependence of the inferred parameters on the telescope resolution. Results. The results show a significant decrease in the mean magnetic flux density – related to the open flux observed at the disk center – with decreasing telescope resolution. The original net magnetic field flux is fully resolved by a 1m telescope, but a 20 cm aperture telescope yields a 30% smaller value. Even in the fully resolved case, the result is still biased due to the corrugation of the photospheric surface. Conclusions. Even the spatially averaged quantities, such as the open magnetic flux in the observed region, are underestimated when the magnetic structures are unresolved. The reason for this is the presence of nonlinearities in the magnetic field inference process. This effect might have implications for the modeling of large-scale solar magnetic fields; for example, those corresponding to the coronal holes, or the polar magnetic fields, which are relevant to our understanding of the solar cycle.

A Novel Chaotic System with Only Quadratic Nonlinearities: Analysis of Dynamical Properties and Stability

In nonlinear dynamics, there is a continuous exploration of introducing systems with evidence of chaotic behavior. The presence of nonlinearity within system equations is crucial, as it allows for the emergence of chaotic dynamics. Given that quadratic terms represent the simplest form of nonlinearity, our study focuses on introducing a novel chaotic system characterized by only quadratic nonlinearities. We conducted an extensive analysis of this system’s dynamical properties, encompassing the examination of equilibrium stability, bifurcation phenomena, Lyapunov analysis, and the system’s basin of attraction. Our investigations revealed the presence of eight unstable equilibria, the coexistence of symmetrical strange repeller(s), and the potential for multistability in the system.

A novel approach to solve hyperbolic Buckley-Leverett equation by using a transformer based physics informed neural network

Solving hyperbolic partial differential equation is a challenging task due to the non-linear feature that requires to capture the shock wave. Numerical solution relies on discretization of both spatial and temporal domain, and iterative approach like Newton's method is involved and time step size is crucial for stability and convergence in the presence of non-linearity. Physics-informed neural networks (PINNs) offer a new and versatile approach for solving partial different equations by minimizing the residual of governing equations and approaching to the initial and boundary conditions. Currently, most PINNs are built based on a simple fully connected neural network which exhibits some limitations to model complex non-linear partial differential equations. In this paper, a novel method is developed to combine Transformer model and PINNs approach (Tr-PINN) to solving a hyperbolic partial differential equation directly without any prior knowledge. Tr-PINN method is based on a series of Transformer blocks where self-attention mechanism is used to capture the non-linearity features of the solution. Unlike most PINNs models generate inputs with spatial and temporal vectors only, Tr-PINN introduces the non-linearity term mobility ratio as additional input vector. The method is tested on a classical hyperbolic problem, called Buckley-Leverett equation with non-convex flux function. We found that the Tr-PINN method can capture the water shock front effectively and provide a general solution for Buckley-Leverett equation under various mobility ratio conditions.

Comparative dynamics analysis of the environmental policy efficacy in a nonlinear Cournot duopoly with differentiated goods and emission charges

The price and the exchanged quantity volatility observed in real-world markets may be explained, according to the existing empirical literature, in terms of the endogenous fluctuations generated by the presence of nonlinearities. We then replace with a sigmoid adaptive best response mechanism the linear partial adjustment best response rule considered in Mamada and Perrings (2020), where the effect produced by quadratic emission charges on the dynamics of a Cournot duopoly model with homogeneous goods was investigated. Moreover, the sigmoid nonlinearity, in addition to being well suited to describe the bounded output variations caused by physical, historical and institutional constraints, makes the model able to generate interesting, non-divergent dynamic outcomes, despite the linearity of the demand function and of marginal costs. Additionally, following the suggestion in Mamada and Perrings (2020), we deal with the more general case of differentiated products. Beyond analytically studying the stability of the unique steady state, coinciding with the Nash equilibrium, and the effect produced by the main parameters on the stability region, we perform two comparative dynamics investigations which allow to evaluate the environmental policy efficacy when the Nash equilibrium is not stable and thus the standard comparative statics technique does not fit for the purpose. In particular, the former analysis, which is based on a comparison of emissions for different levels of charges, shows that, also in case the Nash equilibrium is not stable, the considered environmental policy may be effective both with complements and with substitutes. The latter investigation, consisting in a comparison of emissions along non-stationary trajectories and along the equilibrium path, in the proposed experiments highlights that emissions are larger along non-stationary trajectories. This gives us the opportunity to show how to act on the level of the asymptotes of the sigmoid adjustment mechanism to reduce output variations, reaching at one time a complete stabilization of the system and limiting pollution.

Generalised performance of neural network controllers for feedforward active noise control of nonlinear systems

Advances in digital technologies have allowed for the development of complex active noise and vibration control solutions that have been utilised in a wide range of applications. Such control systems are commonly designed using linear filters, which cannot fully capture the dynamics of nonlinear systems. To overcome such issues, it has been shown that replacing linear controllers with Neural Networks (NNs) can improve control performance in the presence of nonlinearities. Many real systems are subject to non-stationary disturbances where the magnitude of the system excitation time dependent. However, within the literature, the performance of single NN controllers across different excitation levels has not been thoroughly explored. In this paper, a method of training Multilayer Perceptrons (MLPs) for single-input-single-output (SISO) feedforward acoustic noise control is presented. In a simple time-discrete simulation, the performance of the trained NNs is investigated for different excitation levels. The effects of the properties of the training data and NN controller on generalised performance are explored. It is demonstrated that the generalised control performance of the MLP controllers falls as the range of magnitudes included in the training data is increased, and that this performance can be recovered by increasing the number of hidden nodes within the controller.

Event-Triggered Adaptive Control of Uncertain Strict-Feedback Nonlinear Systems Using Fully Actuated System Approach.

In most existing results, event-triggered controllers are designed based on the backstepping design approach for uncertain strict-feedback nonlinear systems (SFNSs). However, the transmitted signals in the event-triggered scheme (ETS) are discontinuous, which makes the repetitive differentiation of virtual control signals undefined. To overcome this deficiency, this article designs an event-triggered adaptive controller for uncertain SFNSs based on the fully actuated system (FAS) approach. Since the system states and the adaptive parameters are only updated at each triggering instant, the original dynamics cannot be completely removed by using the FAS approach, leading to that the asymptotic stability of the control system is difficult to be guaranteed. To handle such a problem, an ETS with the adaptive parameters is constructed based on Lyapunov method to compensate the effect of triggering. As a result, the asymptotic stability of the system can be guaranteed in the presence of nonlinearities without the global Lipschitz condition, and Zeno behavior can be avoided by using the contradiction method. Furthermore, a positive lower bound for interevent intervals can be got by adding a constant into the ETS, which ensures that the system is practically stabilizable under the bounded nonlinearities. Finally, two simulation examples are presented to demonstrate the superiority and effectiveness of the proposed approach.

Association between serum copper levels and muscle mass: results from NHANES 2011-2016.

Copper is essential for various biological processes. However, excess copper has several adverse health effects. The effects of serum copper on muscle mass are poorly understood. This study aimed to investigate the association between serum copper levels and muscle mass in the US population. We utilized National Health and Nutrition Examination Survey (NHANES) data between 2011 and 2016 for analysis. Data on serum copper, muscle mass (measured using the appendicular skeletal muscle mass index (ASMI)), and covariates were extracted and analyzed. Weighted multivariate linear regression analyses and smooth curve fittings were performed to investigate the association between serum copper levels and ASMI. Subgroup analyses stratified according to age and sex were performed. In the presence of nonlinearity, threshold effect analysis was performed using a two-piecewise linear regression model. A total of 3860 participants were included in the final analysis. Serum copper levels were negatively associated with ASMI in the fully adjusted model. Furthermore, by comparing participants in the highest and lowest tertiles of serum copper levels, we found that the ASMI decreased by 0.292 kg/m2. In the sex-stratified subgroup analysis, we observed an inverse association between serum copper levels and the ASMI in both men and women. When stratified by age, the association remained significant among participants < 40 years of age, but not among those ≥ 40 years old. Smooth curve fitting revealed a nonlinear relationship between serum copper and ASMI, with an inflection point identified at 150.6 μg/dL. Our study revealed an inverse relationship between serum copper levels and muscle mass. This finding improves the current knowledge on the impact of serum copper on muscle loss and highlights the importance of serum copper homeostasis in muscle health.

Measuring fiscal policy sustainability in developing Asia: what does the Markov Switching Augmented Dickey-Fuller Test tell us?

This paper measures fiscal sustainability in 22 developing Asian countries for the period 1999–2017. Previous literature generates conflicting results: one paper applies the usual stationarity and cointegration tests and finds that fiscal policy is sustainable but in weak form. Another paper employs a fiscal reaction function and finds that fiscal policy is unsustainable. This paper uses an expanded version of the Markov Switching Augmented Dickey-Fuller test (MS-ADF), which remedies the shortcomings of conventional stationarity tests to provide more statistical power in the presence of nonlinearities and structural breaks. The MS-ADF has never been applied to this set of countries. Results show that the majority of the countries have “uncertain” debt trajectories, not definitively sustainable or unsustainable but somewhere in-between. This is a more nuanced picture of the debt trajectories in the region relative to what is obtained using the established methods. A more nuanced assessment could lead to more suitable policy corrections.

Proper Orthogonal Decomposition-Based Surrogate Modeling Approximation for Aeroengines Nonlinear Unbalance Responses

Abstract Finite element (FE) models to simulate aeroengines rotordynamics become more and more complex thanks to the improvement of computational resources. Numerical simulations for industrial scale applications are nevertheless expensive in terms of computational effort because of their size and the presence of nonlinearities. In many-query frameworks (sensitivity or reliability analysis, model calibration, etc.), parametric studies have to be performed and the FE models are generally simplified or strongly reduced with a consequent loss of accuracy. Recent machine learning methods can be employed to build faster-to-evaluate surrogates of the original model. Nevertheless, this type of offline approach can be very demanding in terms of number of full order evaluations to reach a sufficient accuracy. The challenge is therefore to control the burden associated with the evaluation of the design of experiments (DoE) and the surrogate model training phase. This work presents a surrogate modeling technique to quickly and accurately reproduce the nonlinear unbalance responses of industrial scale rotor-dynamical models submitted to rotor–stator contact. About 20DOFs of the industrial FEM are considered in this work and a proper orthogonal decomposition (POD)-based approximation (surrogate modeling technique known as POD-SM or nonintrusive POD in the literature) of their frequency dependent unbalance response are presented. In order to analyze the modeling uncertainties of a specific shaft's support of a modern aeroengine, its dynamical parameters (stiffness, damping, nonlinear contact parameters) are studied within a specific variation range, defining the design space covered by this study.

A non-parametric algorithm for time-dependent modal analysis of civil structures and infrastructures

Vibration-based monitoring strategies have been demonstrated to be effective tools in providing – in nearly real-time – reliable information regarding the integrity of structures and infrastructure systems. However, commonly used methods for vibration analysis and modal identification are not able to capture the time variation of the modal properties during single acquisitions, hence they cannot perform dynamic identification in the presence of nonlinearities or non-stationary input excitations. To overcome this limitation, a novel non-parametric algorithm for automatic time-dependent modal analysis is hereby presented and discussed. This Enhanced Modal Identification for Long-term Integrity Assessment (EMILIA) algorithm can compute time-dependent estimations of the natural frequencies and mode shapes that can be critical to the early identification of hidden damage. The dynamic characterization of a beam-like structure in sound and damaged conditions is carried out for numerical validation purposes, allowing to evaluate the reliability of the proposed method over different scenarios and comparing its efficiency against traditional algorithms. Finally, further tests are conducted to analyse the sensitivity of the EMILIA algorithm to its main parameters and components.

Dynamic neural network switching for active noise control of nonlinear systems

Advancements in digital technologies have allowed for the development of increasingly complex active noise and vibration control solutions, with a wide range of applications. Such control systems are commonly designed using linear digital filters which cannot fully capture the dynamics of nonlinear systems. To overcome this, it has previously been shown that replacing linear controllers with neural networks (NNs) can improve control performance in the presence of nonlinearities in both the system plant and primary path. Inferring the outputs of NN controllers can, however, be computationally expensive, limiting the practicality and real-time performance of such control systems. It has been demonstrated previously that, with nonlinearity in the primary path, the range of nonlinearity over which a single NN controller can achieve significant levels of control is limited by the size of the NN. In this paper, a method of dynamically switching between multiple smaller NN controllers is presented. In a simple time-discrete simulation, the performance and computational cost of this approach is compared to that of individual fixed NN controllers, demonstrating improved computational efficiency and performance over a range of nonlinearity as the system disturbance changes over time.