Behavior Of System Research Articles

Fluidized bed reactor for 4-chlorophenol photodegradation via solar and visible radiation using ZnO/g-C3N4/carbon xerogel as a photocatalyst

This study investigates the feasibility of employing a fluidized bed reactor for the degradation of 4-chlorophenol (4CP), considering multiple operational parameters (type of radiation, fresh inlet flow rate and recycle flow rate). The selection of the ZnO/g-C3N4/carbon xerogel as photocatalyst, a choice motivated by the improved charge transfer and increased catalyst activity under visible radiation provided by the presence of carbon xerogel and g-C3N4, was previously determined through tests conducted in a jacketed batch reactor under visible radiation, in which the ternary material efficiency was compared to their constituting counterpart materials. The semiconductors constituting the unary, binary, and ternary materials were chosen based on considerations of availability, sustainability, and abundance in nature. The use of the proposed fluidized bed reactor brings advantages in scalability, distribution of irradiated light and overall costs when compared to commonly used batch reactors, whereas the investigation of the flow parameters involved in such process is of great importance to understand and optimize the efficiency of the pollutant degradation process. Regarding the ternary photocatalyst, X-ray diffractometry (XRD) revealed the presence of zinc oxide's hexagonal crystalline structure. Moreover, additional characterization using Raman spectroscopy, Fourier-transform infrared spectroscopy (FT-IR), scanning electron microscopy (SEM), transmission electron microscopy (TEM), and energy-dispersive spectroscopy (EDS) confirmed the presence not only of ZnO but also of carbon xerogel and g-C3N4 in the composite. From the photodegradation experiments, it was determined that the optimal fresh inlet flow rate to achieve the best degradation, as well as the recycle flow rate for this purpose, were 0.07 and 25 L h−1, respectively. Mathematical simulations described that the model that best fits the system's behavior considers the specific reaction rate as dependent on the concentration of the catalyst in the medium.

Relationship between learners’ L2 Motivational Self System and parental investment behavior in learners’ English learning

Students’ motivation and learning behavior are significantly impacted by parents’ participation and investment. It has been demonstrated that parental investment behavior could exert a direct effect on students’ L2 Motivational Self System (L2MSS) mediated by parental investment belief. Nevertheless, the relationship between components of parental investment behavior and students’ language learning motivation remains a topic necessitating further scholarly investigation. In response to this gap, we conducted a quantitative study involving a survey of 900 high school students to explore the relationship between students’ English learning motivation, as conceptualized by the L2 Motivational Self System and parental investment behavior based on a four-component model. The findings in this study indicated that high school students exhibited moderate levels of L2MSS and relatively low levels of parental investment behavior. Moreover, students’ L2MSS was found to have a significant positive correlation with the global parental investment behavior, with parental emotional investment behavior emerging as a positive predictor of high school students’ L2MSS. These results underscore the importance of parental provision of sufficient economic, relationship, knowledge, and emotional support in cultivating a nurturing and supportive familial context conducive to the development of students’ positive future selves.

A novel approach to runway overrun risk assessment using FRAM and flight data monitoring

Abstract Runway overruns (ROs) are the result of an aircraft rolling beyond the end of a runway, which is one of the accident’s types that most frequently occurs on aviation. The risk of an RO arises from the synergistic effect among its precursors, such as unstable approaches, long touchdowns and inadequate use of deceleration devices. To analyse this complex socio-technical system, the current work proposes a customised functional resonance analysis method, called FRAM-FDM, as traditional techniques of risk and safety assessment do not identify the interactions and couplings between the various functional aspects of the system itself, especially regarding human and organisational components. Basically, FRAM-FDM is the coupling of a traditional FRAM with flight data monitoring (FDM) techniques, used here to quantify the variabilities of the flight crew performance while executing the required activity (i.e. the landing). In this proposal, these variabilities (i.e. the FRAM functions aspects) are aggregated by the addend of a logistic regression, resulting in a model to evaluate the flare operations and the brake application profile effect on the remaining distance to the end of the runway, used as a reference to classify the landing as acceptable or not. The present application of the FRAM-FDM assesses the operational risk of a sample fleet in overrunning the runway during landing, highlighting the brake pedal application profile as the most relevant contributor. The model improves the knowledge about the system behaviour, being useful to direct flight crew training.

An Integrated Dimension Theory and Modulation Signal Bispectrum Technique for Analyzing Bearing Fault in Industrial Fibrizer

Abstract This study investigates the dynamics of roller bearings by utilizing the dimension theory technique to diagnose the bearing clearance faults of revolving machines. The generation of local defects in rotating machines is closely related to the clearance behaviour of the rotor-bearing system. A dynamic model of bearing with dimension theory by matrix method (DTMM) is developed for characteristics of bearing clearance considering the influence of local defects on the inner and outer bearings races. The characteristics of bearing internal radial clearance considering the impact of the defect on the bearing are analyzed. An experimental study has been performed under various operational conditions. The noisy signal is subsequently eliminated using the Modulation Signal Bispectrum (MSB). The efficiency and reliability of the stated approach are evaluated using a specialized bearing test and a run-to-failure fibrizer test. As a result, this technology offers a significant opportunity to execute more cost-effective maintenance work to eliminate the breakdown of machinery.

Response prediction and probabilistic analysis of the vehicle-ballasted track system considering track irregularity based on long-short term memory neural network

It is necessary to efficiently and accurately predict the dynamic behavior of the train-track system subjected to massive random track geometric excitations for system evaluation and maintenance. This paper proposed an engineering practical approach for the train-track system behavior prediction by integrating the deep learning surrogate model-based long-short term memory (LSTM) and physical model of the train-ballasted track interaction (TBTI) system, and then the generalized probability density evolution method (GPDEM) is introduced to achieve the probabilistic assessment of the TBTI system under limited track irregularities, where the track irregularity probability model (TIPM) coupled with generalized-F discrepancy points sets is employed to compress the track irregularity sets to reduce the number of system responses (as training target) but without loss of the responses completeness, therefore, it can promote the efficiency and accuracy of training model. The prediction performance of the surrogate model is illustrated by comparing the time-frequency domain information, mean and standard deviation of the responses obtained by the physical model and surrogate model. The results indicated the proposed method can accurately predict the system response, especially the low and medium frequency response below 50 Hz, and improve the efficiency of stochastic analysis for the TBTI system by approximately 20 times. Furthermore, the applicability of the proposed method is further examined by investigating the influence of probability levels of track irregularity and train speeds on train performance. Its extended model is also implemented to predict the response of systems induced by any measured track irregularity in real-time, which promotes the generalization capability of the proposed surrogate model.

A long-horizon move-blocking based direct power model predictive control for dynamic enhancement of DC microgrids

This research paper presents a novel long-horizon move-blocking based direct power model predictive control (DPMPC) strategy, uniquely designed to enhance the dynamic performance of boost converters in the grid-connected mode within DC microgrids. A precise dynamic model is developed considering a boost converter connected to a DC-link supplying constant power and resistive loads. To predict the system's dynamic behavior over an extended interval and enhance its performance in the presence of constant power loads, the long-horizon based finite control set model predictive control (FCS-MPC) method is introduced. To address the computational complexity associated with the conventional long-horizon DPMPC approach, a move-blocking (MB) strategy is incorporated into FCS-MPC, reducing the computational burden while improving the dynamic performance of the boost converter. Unlike recent studies that utilize DPMPC with short prediction interval, this paper presents evidence that a longer prediction interval is crucial for maintaining system stable and enhancing the dynamic response and also utilizing MB to make the control implementable in the real-time. The simulation results conducted using MATLAB/Simulink demonstrate the effective performance of the proposed strategy across various operating conditions of the boost converter. Experimental results further validate the strategy's capability to enhance the dynamic performance of the boost converter. Importantly, the experimental findings confirm the feasibility of implementing the proposed long-horizon move-blocking DPMPC strategy in real-time applications.

An Improved Positive Displacement Pump Model Accounting for Suction Cavitation

Abstract Positive displacement (PD) pumps are widely employed in industrial settings due to their inherent simplicity and reliability, serving a diverse range of applications from slurry transport to jet washing. Although their operational principles are straightforward, the fluid dynamics of the pumped medium exhibit non-trivial characteristics, including intricate transient phenomena. Consequently, a comprehensive fluid dynamic description, such as a three-dimensional RANS analysis, presents challenges due to its demanding computational requirements. While simpler analytical PD pump models are available, they often fail to adequately represent the primary system behaviors, particularly when dealing with cavitation. Motivated by these challenges, this study aims to develop a novel one-dimensional model for PD pumps, offering a representation of essential fluid phenomena without imposing significant computational burdens. After assessing the relative importance of the fluid dynamic behaviors that the model must capture, we construct a pump model based on a one-dimensional fluid description and solve it using a second-order in time and space MUSCL-TVD scheme. The model's validity is confirmed by its application to both single-chamber and three-chamber diaphragm PD pumps, which are instrumented for experimental validation. The results of the one-dimensional model exhibit strong agreement with physical experiments, both in controlled laboratory environments and field conditions. This success suggests a promising approach for industrial applications.

Dual-function of energy harvesting and vibration isolation via quasi-zero stiffness piezoelectric mechanism

Industry 4.0 realizes intelligent interconnection through the sensor group of the Internet of Things. A key challenge is to achieve the self-powering of sensors and stable operation of precision instruments. This paper introduces a dual-functional structure (VIPEH) integrating energy harvesting (EH) and vibration isolation (VI) based on the quasi-zero stiffness (QZS) piezoelectric mechanism. The paper analyzes the nonlinear statics of piezoelectric flexible beams under large deformations and conducts parametric analysis. A nonlinear dynamic model with electromechanical coupling was developed to investigate the impact of mechanical and electrical parameters on the system's dynamic bifurcation behavior, EH, and VI performance. Finally, an experimental setup is created to evaluate the VIPEH's characteristics. Sweep frequency excitation experiments demonstrate that the initial isolation frequency of VIPEH is lower than 1.4 Hz. The important thing is that VIPEH can still power the sensor based on the isolation frequency, and the output power of a single piezoelectric material can reach 3.19 mW. This not only enables the isolation of low-frequency vibrations but also presents a highly promising application for achieving self-powering in sensor clusters within the context of Industry 4.0 and the IoTs.

Abundant New Optical Soliton Solutions to the Biswas–Milovic Equation with Sensitivity Analysis for Optimization

This study extensively explores the Biswas–Milovic equation (BME) with Kerr and power law nonlinearity to extract the unique characteristics of optical soliton solutions. These optical soliton solutions have different applications in the field of precision in optical switching, applications in waveguide design, exploration of nonlinear optical effects, imaging precision, reduced intensity fluctuations, suitability for optical signal processing in optical physics, etc. Through the powerful (G′/G, 1/G)-expansion analytical method, a variety of soliton solutions are expressed in three distinct forms: trigonometric, hyperbolic, and rational expressions. Rigorous validation using Mathematica software ensures precision, while dynamic visual representations vividly portray various soliton patterns such as kink, anti-kink, singular soliton, hyperbolic, dark soliton, and periodic bright soliton solutions. Indeed, a sensitivity analysis was conducted to assess how changes in parameters affect the exact solutions, aiding in the understanding of system behavior and informing decision-making, especially in accurately designing or analyzing real-world optical phenomena. This investigation reveals the significant influence of parameters λ, τ, c, B, and Κ on the precise solutions in Kerr and power law nonlinearities within the BME. Notably, parameter λ exhibits consistently high sensitivity across all scenarios, while parameters τ and c demonstrate pronounced sensitivity in scenario III. The outcomes derived from this method are distinctive and carry significant implications for the dynamics of optical fibers and wave phenomena across various optical systems.

Markov Chains and Kinetic Theory: A Possible Application to Socio-Economic Problems

A very important class of models widely used nowadays to describe and predict, at least in stochastic terms, the behavior of many-particle systems (where the word “particle” is not meant in the purely mechanical sense: particles can be cells of a living tissue, or cars in a traffic flow, or even members of an animal or human population) is the Kinetic Theory for Active Particles, i.e., a scheme of possible generalizations and re-interpretations of the Boltzmann equation. Now, though in the literature on the subject this point is systematically disregarded, this scheme is based on Markov Chains, which are special stochastic processes with important properties they share with many natural processes. This circumstance is here carefully discussed not only to suggest the different ways in which Markov Chains can intervene in equations describing the stochastic behavior of any many-particle system, but also, as a preliminary methodological step, to point out the way in which the notion of a Markov Chain can be suitably generalized to this aim. As a final result of the discussion, we find how to develop new very plausible and likely ways to take into account possible effects of the external world on a non-isolated many-particle system, with particular attention paid to socio-economic problems.

Tracking states and transitions in semiarid rangelands: A spatiotemporal archetypal analysis of productivity dynamics using wavelets

Climate change poses challenges in classifying ecosystem dynamics, as they are influenced by shifting dynamics resulting from changes in climate forces and meteorological variables, including temperature and water availability. To address this, our study presents a novel approach using Continuous Wavelet Transform (CWT) and power spectrum analysis to classify vegetation dynamics, considering the time-dependent variability of ecosystem frequencies. We applied our method to centred and standardized MODIS NDVI time series for the period 2000–2021, using an experimental field station in northern Patagonia as a case study. By performing a continuous wavelet transform on the data for each pixel, we obtained instantaneous power spectra, capturing variability across different dates and pixels. These spectrums were then consolidated into a comprehensive database, and subsequently classified using archetypal analysis. We identified a convex combination of archetypal spectrums that best represented the entire power spectrum database. Mapping the resulting archetypes and their weights in both space and time allowed us to explore pixels' variations in archetype weights in relation to factors such as time, topography, and climate. In addition, to examine the potential relationship between the NDVI time series and climate drivers, we computed the Average Cross-Wavelet Power Spectrum (ACWPS) to different climatic indices. Three archetypes were sufficient to explain the majority of power spectrum variability in the study area. These archetypes exhibited distinctive characteristics: 1) medium-frequency variability (2–4 years), 2) low-frequency variability (>4 years), and 3) an annual (i.e. seasonal) cycle with low-frequency variability. Spatially, the first two archetypes were predominantly observed in highland steppes, while the third archetype prevailed in lowland areas associated with meadows. At the beginning of the studied period, Archetypes 1 and 3 dominated, but after the Puyehue-Cordón Caulle Volcanic Complex eruption in 2011 their prominence diminished, and Archetype 2 became more prevalent in the whole study area. Finally, all three NDVI series representative of archetypes showed a relative peak at approximately four years, which could be linked to the Indian Ocean Dipole variability. These results highlight an abrupt shift in the system's behaviour, primarily related to changes in variability distribution rather than mean values. This disturbance-induced transition aligns with the theory of state and transitions in ecological system dynamics. We propose that the states in this model are not fixed but represent alternative dynamic behaviours, akin to different types of limit cycles. Consequently, employing a wavelet analysis-based classification method provides a robust means of studying and understanding such variability and transitions, thereby offering clarity and comprehension of ecosystem states. Notably, this methodology proves particularly effective for large databases of detailed time series.

Preferential Solvation Phenomena as Solute-Induced Structure-Making/Breaking Processes: Linking Thermodynamic Preferential Interaction Parameters to Fundamental Structure Making/Breaking Functions.

In this work, we identify the explicit macroscopic-to-microscopic rigorous links between existing thermodynamic preferential interaction parameters and microstructural descriptors based on total correlation function integrals, leading to their unambiguous characterization in terms of fundamental structure making/breaking functions . First, we provide the statistics mechanical framework to identify a universal molecular-based signature for the preferential solvation phenomenon involving solutes at infinite dilution in mixed-solvent environments and discuss its fundamental properties. Then, we characterize the functions relevant to the process, identify the microscopic markers for the existing preferential interaction parameters in terms of the functions, and test their compliance with a pair of essential microstructural constraints linked to the properties of the universal signature. Moreover, we illustrate the analysis by probing the behavior of a representative ternary system comprising the solubility of methane in aqueous 1,4-dioxane mixed-solvent environments under ambient conditions. Finally, we discuss some relevant issues surrounding the statistical mechanical (microstructural) interpretation of the thermodynamic (macroscopic) preferential interaction parameters, review some pitfalls in their evaluation from molecular simulation, and provide an outlook.

Transient analysis of a bulk stream queue with arbitrarily distributed arrival intervals

We study the classical infinite buffer single server queueing model with renewal input of customers in batches of random size, having arbitrarily distributed arrival intervals and exponentially distributed service times. Using the technique of supplementary variable and shift operator we derive closed form expression of the time dependent system content distribution in terms of its Laplace transform. The analysis is mainly based on the root-finding technique of the non-linear characteristic equation in terms of the Laplace transform variable. Additionally, using asymptotic properties of Laplace transform, we deduce the corresponding steady-state distribution. We discuss some special cases of the model, thus providing an alternative approach in deriving the transient distribution. We further evaluate certain performance measures and present extensive numerical examples in tabular and graphical form to illustrate the applicability of our theoretical work. The effect of system parameters, interarrival time distribution and traffic intensity on the system behavior is also demonstrated.

The Presence of Chaos in a Viscoelastic Harmonically Forced Von Mises Truss

Abstract This work investigates how viscoelasticity affects the dynamic behavior of a lumped-parameter model of a bistable von Mises truss. The system is controlled by a linear first-order equation and a second-order nonlinear Duffing equation with a quadratic nonlinearity that governs mechanical behavior. The second-order equation controls mechanical oscillations, while the linear first-order equation controls viscoelastic force evolution. Combined, the two equations form a third-order jerk equation that controls system dynamics. Viscoelasticity adds time scales and degrees-of-freedom to material behavior, distinguishing it from viscosity-only systems. Due to harmonic excitation, the system exhibits varied dynamic responses, from periodic to quasi-periodic to chaotic. We explore the dynamics of a harmonically forced von Mises truss with viscous damping to address this purpose. We demonstrate this system's rich dynamic behavior due to driving amplitude changes. This helps explain viscoelastic system behavior. A viscoelastic unit replaces the viscous damper, and we show that, although viscous damping merely changes how fast the trajectory decays to an attractor, viscoelasticity modifies both the energy landscape and the rate of decay. In a conventional linear solid model, three viscoelastic parameters control the system's behavior instead of one, as in pure viscous damping. This adds degrees-of-freedom that affect system dynamics. We present the parameter space for chaotic behavior and the shift from regular to irregular motion. Finally, Melnikov's criteria identify the regular-chaotic threshold. The system's viscous and elastic components affect the chaotic threshold amplitude

Multiscale Effects of Predator–Prey Systems with Holling-III Functional Response

In this paper, we proposed a Holling-III predator–prey model considering the perturbation of slow-varying, carrying capacity parameters. The study aims to address how the slow changes in carrying capacity influence the dynamics of the model. Based on the bifurcation theory and the slow–fast analysis method, the existence and the equilibrium of the autonomous system are explored, and then, the critical condition of Hopf bifurcation and transcritical bifurcation is established for the autonomous system. The slow–fast coupled nonautonomous system has quasiperiodic oscillations, single Hopf bursting oscillations, and transcritical–Hopf bursting oscillations within a certain range of perturbation amplitude variation if the carrying capacity perturbation amplitude crosses some critical values, such that the predator–prey management is challenging for the extinction of predator populations under the critical value. The motion pattern of the nonautonomous system is closely related to the transcritical bifurcation, Hopf bifurcation and attractor type of the autonomous system. Finally, the effects of changes in parameters related to predator aggressiveness on system behavior are investigated. These results show how crucial the predator–prey control is for varying carrying capacities.

Pressure Changes Across a Membrane Formed by Coacervation of Oppositely Charged Polymer-Surfactant Systems.

We investigate the mass transfer and membrane growth processes during capsule formation by the interaction of the biopolymer xanthan gum with CnTAB surfactants. When a drop of xanthan gum polymer solution is added to the surfactant solution, a membrane is formed by coacervation. It encapsulates the polymer drop in the surfactant solution. The underlying mechanisms and dynamic processes during capsule formation are not yet understood in detail. Therefore, we characterized the polymer-surfactant complex formation during coacervation by measuring the surface tension and surface elasticity at the solution-air interface for different surfactant chain lengths and concentrations. The adsorption behavior of the mixed polymer-surfactant system at the solution-air interface supports the understanding of observed trends during the capsule formation. We further measured the change in capsule pressure over time and simultaneously imaged the membrane growth via confocal microscopy. The cross-linking and shrinkage during the membrane formation by coacervation leads to an increasing tensile stress in the elastic membrane, resulting in a rapid pressure rise. Afterward, the pressure gradually decreases and the capsule shrinks as water diffuses out. This is not only due to the initial capsule overpressure but also due to osmosis caused by the higher ionic strength of the surfactant solution outside the capsule compared to the polymer solution inside the capsule. The influence of polymer concentration and surfactant type and concentration on the pressure changes and the membrane structure are studied in this work, providing detailed insights into the dynamic membrane formation process by coacervation. This knowledge can be used to produce capsules with tailored membrane properties and to develop a suitable encapsulation protocol in technological applications. The obtained insights into the mass transfer of water across the capsule membrane are important for future usage in separation techniques and the food industry and allow us to better predict the capsule time stability.

Investigating the Dynamic Behavior of Integer and Noninteger Order System of Predation with Holling’s Response

The paper’s primary objective is to examine the dynamic behavior of an integer and noninteger predator–prey system with a Holling type IV functional response in the Caputo sense. Our focus is on understanding how harvesting influences the stability, equilibria, bifurcations, and limit cycles within this system. We employ qualitative and quantitative analysis methods rooted in bifurcation theory, dynamical theory, and numerical simulation. We also delve into studying the boundedness of solutions and investigating the stability and existence of equilibrium points within the system. Leveraging Sotomayor’s theorem, we establish the presence of both the saddle-node and transcritical bifurcations. The analysis of the Hopf bifurcation is carried out using the normal form theorem. The model under consideration is extended to the fractional reaction–diffusion model which captures non-local and long-range effects more accurately than integer-order derivatives. This makes fractional reaction–diffusion systems suitable for modeling phenomena with anomalous diffusion or memory effects, improving the fidelity of simulations in turn. An adaptable numerical technique for solving this class of differential equations is also suggested. Through simulation results, we observe that one of the Lyapunov exponents has a negative value, indicating the potential for the emergence of a stable-limit cycle via bifurcation as well as chaotic and complex spatiotemporal distributions. We supplement our analytical investigations with numerical simulations to provide a comprehensive understanding of the system’s behavior. It was discovered that both the prey and predator populations will continue to coexist and be permanent, regardless of the choice of fractional parameter.

Fast switching hydrogen gas leakage identification using FPGA

Hydrogen will play a key part in the decarbonization of the global energy supply as the wealth of hydrogen continues to rise. However, applying hydrogen knowledge necessitates the installation of strong safety protocols, including the use of reliable hydrogen gas-detecting devices. Gas detection and monitoring at a large scale in industries need programmable electronic systems that can provide fast response and switching. The objective of the research work is to analyze the hydrogen gas detection system using a field programmable gate array (FPGA). The system is integrated with the gas sensor module, temperature control module, buzzer for alarm, liquid crystal display (LCD) and light-emitting diode (LED) for information display, and global system for mobile communication (GSM) for wireless message communication to the mobile. The temperatures module works on the sampling of the heater resistance using a voltage divider and inbuilt analog-to-digital converter (ADC), which depend on the output voltage of the digital-to-analog converter (DAC). The comparator module compares the gas concentration with the pre-decided threshold limit and acknowledges the buzzer accordingly. The system behavior for monitoring and gas concentration detection is simulated in Xilinx Vivado design suite 2020.1. The functionality of the chip is also verified in the Modelsim 10.0 waveform simulator. for the testbench tata sand samples used. LCD (16x2) displays the messages whether hydrogen gas is detected or not and the same message is delivered on mobile. The novelty of the work is that the system is applicable for faster switching in industrial applications and the designed system supported 550 MHz frequency in our simulation and synthesis.

Introduction of Local Resonators to a Nonlinear Metamaterial With Topological Features

Abstract Recent work in nonlinear topological metamaterials has revealed many useful properties such as amplitude dependent localized vibration modes and nonreciprocal wave propagation. However, thus far, there have not been any studies to include the use of local resonators in these systems. This work seeks to fill that gap through investigating a nonlinear quasi-periodic metamaterial with periodic local resonator attachments. We model a one-dimensional metamaterial lattice as a spring-mass chain with coupled local resonators. Quasi-periodic modulation in the nonlinear connecting springs is utilized to achieve topological features. For comparison, a similar system without local resonators is also modeled. Both analytical and numerical methods are used to study this system. The dispersion relation of the infinite chain of the proposed system is determined analytically through the perturbation method of multiple scales. This analytical solution is compared to the finite chain response, estimated using the method of harmonic balance and solved numerically. The resulting band structures and mode shapes are used to study the effects of quasi-periodic parameters and excitation amplitude on the system behavior both with and without the presence of local resonators. Specifically, the impact of local resonators on topological features such as edge modes is established, demonstrating the appearance of a trivial bandgap and multiple localized edge states for both main cells and local resonators. These results highlight the interplay between local resonance and nonlinearity in a topological metamaterial demonstrating for the first time the presence of an amplitude invariant bandgap alongside amplitude dependent topological bandgaps.

Data-Driven Initial Gap Identification of Piecewise-Linear Systems Using Sparse Regression and Universal Approximation Theorem

Abstract This paper proposes a method for identifying an initial gap in piecewise-linear (PWL) systems from data. Piecewise-linear systems appear in many engineered systems such as degraded mechanical systems and infrastructures and are known to show strong nonlinearities. To analyze the behavior of such piecewise-linear systems, it is necessary to identify the initial gap, at which the system behavior switches. The proposed method identifies the initial gap by discovering the governing equations using sparse regression and calculating the gap based on the universal approximation theorem. A key step to achieve this is to approximate a piecewise-linear function by a finite sum of piecewise-linear functions in sparse regression. The equivalent gap is then calculated from the coefficients of the multiple piecewise-linear functions and their respective switching points in the obtained equation. The proposed method is first applied to a numerical model to confirm its applicability to piecewise-linear systems. Experimental validation of the proposed method has then been conducted with a simple mass-spring-hopping system, where the method successfully identifies the initial gap in the system with high accuracy.