Framework For Stability Analysis Research Articles

The Stability of a Predator–Prey Model with Cross-Dispersal in a Multi-Patch Environment

This paper investigates the stability of predator–prey models within multi-patch environments, with a particular focus on the influence of cross-dispersion across patches. We apply Kirchhoff’s matrix tree theorem and Liapunov’s method to derive criteria related to the cross-dispersion topology, thus solving the challenge of determining global asymptotic stability conditions. The method incorporates realistic ecological interactions and spatial heterogeneity, offering a framework for stability analysis. Our findings demonstrate that an appropriate level of cross-dispersion can effectively mitigate oscillations and foster convergence toward equilibrium. Two numerical examples validate these theoretical results and demonstrate the feasibility and effectiveness of the model across multiple patches.

Mechanism of airfoil stall flutter: New insights from global linear stability analysis

Stall flutter is a self-excited aeroelastic vibration phenomenon that occurs in lifting systems near the stall angle of attack, characterized by the distinct single-degree-of-freedom behavior. Despite its significance, this phenomenon remains not fully understood and is often vaguely attributed to nonlinear effects. To address this gap, the present study aims to reveal the underlying fluid–structure interaction mechanisms of stall flutter through global linear stability analysis (LSA). For this purpose, a reduced-order model (ROM)-based aeroelastic stability analysis framework is established using the autoregressive with exogenous input method. The ROM-based aeroelastic model provides a low-order representation of the coupled dynamics near the equilibrium steady state and can accurately capture the stability characteristics of the fluid-elastic system. It is found that as the angle of attack approaches the static stall angle, a low-frequency weakly stable fluid mode emerges, whose frequency is sufficiently lower than that of the von Kármán vortex shedding. The interaction between this fluid mode and the structure mode ultimately leads to the instability of the aeroelastic system at high reduced velocities, which is the fundamental cause of stall flutter. Moreover, dynamic mode decomposition is employed to successfully extract the spatial coherent structures and frequency characteristics of this low-frequency fluid mode, thereby confirming the validity of the LSA results. Further analysis indicates that, as the angle of attack decreases, this low-frequency fluid mode gradually weakens and eventually degenerates into more stable non-oscillatory fluid modes, resulting in structural stabilization and the cessation of stall flutter. Overall, the linear dynamic model accurately predicts the onset of instability and the vibration frequency of the airfoil, which challenges the traditional nonlinear perspectives and supports the feasibility of using linear control theory for stall flutter suppression in future research.

Global stability analysis of flow-induced-vibration problems using an immersed boundary method

In this work, a numerical framework for global stability analysis of rigid-body-motion fluid–structure-interaction problems is presented. The Jacobian matrices which arise in the linearization procedure are derived numerically via the first-order finite difference scheme. The linearized fluid–structure coupled equations are solved using an immersed boundary method. The linear stability solver is first tested on two canonical cases, i.e., the flow past a stationary cylinder and the flow past an isolated elastically mounted cylinder. An excellent agreement between the results obtained here and those from available published research is achieved. The solver is then used to study the linear stability of the flow past two elastically mounted cylinders in tandem arrangement. The variations in growth rate and frequency of two leading modes with reduced velocity are examined. The mechanisms of lock-in and galloping phenomena observed in nonlinear simulation are elucidated from the perspective of linear instabilities in the leading modes.

A Line-Search-Based Algorithm for Multiphase Flash Calculations with CO2-Hydrocarbon System.

Multiphase flash calculations are pivotal in compositional simulation, necessitating a robust and efficient computational algorithm. In this work, we have developed a line-search-based algorithm framework for stability analysis and multiphase flash calculations. This algorithm is rooted in the modified Newton step and line-search method. The modified Newton step, derived from modified Cholesky factorization, ensures a descent direction, while the line search determines the degree of decrease. This combination facilitates convergence even in challenging regions for phase stability analysis and multiphase flash calculations, exhibiting superlinear convergence speed. Unlike traditional approaches that rely on successive substitution iteration and may resort to Newton iteration only if the Hessian matrix is positive definite, our algorithm incorporates modification via modified Cholesky factorization upon encountering a nonpositive definite Hessian matrix. We tested our algorithm with several classical fluids, demonstrating its efficiency and robustness. Furthermore, we assessed the algorithm's performance by computing the pressure-composition diagram for the CO2-hydrocarbon system, where all calculations achieved rapid convergence without failure. This newly developed algorithm for phase stability analysis and multiphase flash calculations represents a significant advancement for compositional or chemical process simulations.

Multistability of segmented rings by programming natural curvature

Multistable structures have widespread applications in the design of deployable aerospace systems, mechanical metamaterials, flexible electronics, and multimodal soft robotics due to their capability of shape reconfiguration between multiple stable states. Recently, the snap-folding of rings, often in the form of circles or polygons, has shown the capability of inducing diverse stable configurations. The natural curvature of the rod segment (curvature in its stress-free state) plays an important role in the elastic stability of these rings, determining the number and form of their stable configurations during folding. Here, we develop a general theoretical framework for the elastic stability analysis of segmented rings (e.g., polygons) based on an energy variational approach. Combining this framework with finite element simulations, we map out all planar stable configurations of various segmented rings and determine the natural curvature ranges of their multistable states. The theoretical and numerical results are validated through experiments, which demonstrate that a segmented ring with a rectangular cross-section can show up to six distinct planar stable states. The results also reveal that, by rationally designing the segment number and natural curvature of the segmented ring, its one- or multiloop configuration can store more strain energy than a circular ring of the same total length. We envision that the proposed strategy for achieving multistability in the current work will aid in the design of multifunctional, reconfigurable, and deployable structures.

Predictive stability study of poverty trend in Uganda using selected indicators

This study investigates poverty dynamics in Uganda, employing an extensive stability analysis of different socioeconomic indicators to understand long-term trends and likely drivers of poverty. An eighteen years yearly secondary data from 1992 to 2020 on poverty rates for the selected indicators under review sourced from World Bank site was utilized for all the data analysis. Outcomes from extensive data analysis shows considerable reductions in poverty rates over time, especially in outlying areas of eastern and northern Uganda despite increasing income inequality as suggested by the increasing Gini coefficient. All the metrics have a significant impact on Uganda's poverty rates, with the exception of the poverty headcount ratio, which stands at USD 6.85 per day (2017 PPP) as a percentage of the population. Particularly, the forecasted values also show a fluctuating trend movement, both downward and upward, suggesting possible variability in future poverty rates in Uganda. The necessity to carefully evaluate as well as monitor poverty dynamics to guide policy interventions aimed at reducing poverty is underlined by this information. Additionally, the stability analysis framework suggested in this research provides insights into the viability as well as resilience of Uganda's socioeconomic system in tackling poverty, enabling evidence based policies and interventions in poverty reduction. The study suggests more examination of various other dimensions of poverty and non-monetary indicators of well-being to better our understanding and support better poverty alleviation methods in Uganda along with other similar settings.

An enhanced looped-functional framework for stability analysis of sampled-data systems

This paper enhances the looped-functional framework for sampled-data systems by using continuous Lyapunov functionals instead of xT(t)Px(t). The continuous Lyapunov functionals exploit the maximum allowable sampling interval compared with the traditional Lyapunov function xT(t)Px(t) in the conventional looped-functional framework. The enhanced looped-functional framework ensures the negativeness of the continuous Lyapunov functionals concerning the sampling instants and guarantees the stability of the sampled-data systems. Based on these continuous Lyapunov functionals, this paper constructs novel Lyapunov functionals with the looped-functional which not only exploits all available vectors related to sampling intervals but also introduces an additional interval which is zero at t=tk+1. Also, this paper proposes the stability criteria based on the enhanced looped-functional framework for the sampled-data systems with the asynchronous and synchronous samplings, respectively. The numerical examples show the effectiveness of the proposed framework.

Linear internal stability for mixed traffic flow of CAVs with different automation levels

With the development of autonomous driving and vehicle-to-infrastructure technologies, connected automated vehicles (CAVs) will gradually replace human-driven vehicles (HDVs). However, during the widespread adoption of CAVs, the roads will experience a new type of mixed traffic flow composed of vehicles with different automation levels for an extended period. To analyze the impact of different automation levels on mixed traffic flow, this paper proposes a stability analysis framework for mixed traffic flow that considers different automation levels. The influence of automation level classification on the composition of mixed traffic flow is analyzed first, and the degradation of CAVs in mixed traffic flow is further explored. Then, a stability analysis framework for mixed traffic flow considering different automation levels is proposed, and the impact of key parameters on the stability is analyzed. Finally, simulation experiments are designed to validate the theoretical analysis results. The research findings indicate that (1) the stability of mixed traffic flow improves with the increase in steady-state speed. When vehicle speed exceeds 20 m/s, mixed traffic flow remains stable. (2) When the CAV penetration rate is low, the stability of mixed traffic flow is poor due to the degradation of CAVs. However, with the increase in the penetration rate and automation level of CAVs, mixed traffic flow rapidly tends toward a stable state. (3) Numerous factors influence the stability of mixed traffic flow, with the order of importance being the CAV penetration rate, automation level, headway, and maximum acceleration. Therefore, this study can provide theoretical support for managing and controlling mixed traffic flow with different automation levels in the future.

On the string stability of neural network-based car-following models: A generic analysis framework

String stability plays a crucial role in regulating traffic flow, as traffic oscillation can be triggered by string instability in the car-following (CF) behavior. Although studies over the past decades have provided various methods for analyzing string stability of analytical CF models, no studies have focused on neural network (NN) based CF models despite the fact that these models have exhibited remarkable performance in learning realistic driving behavior in the recent literature. This paper fills this gap by proposing a generic theoretical framework for analyzing the string stability of NN-based CF models through an Estimation-Approximation-Derivation-Calculation process (referred to as EADC framework). Within the framework, we first estimate the steady states of NN-based CF models by solving the corresponding optimization model and obtain the smooth approximation of the NN-based models for linearization, based on which the transfer function is constructed. We then derive the general stability criteria for two commonly used classes of NN in CF modeling, i.e., feedforward NN-based CF models with basic input and recurrent NN-based CF models with multi-step historical information. The string stability is thus obtained by calculating the partial derivatives through the automatic differentiation method. As two case studies, we apply the proposed stability analysis framework on two typical NN-based CF models, the Mo-MLP model (Mo et al., 2021) and the Huang-LSTM model (Huang et al., 2018), and obtained the complete consistency between the theoretical results and the simulation results for both models, which demonstrates the soundness of the proposed EADC framework. Moreover, we discuss the applicability of the proposed EADC stability analysis framework in the emerging era of connected and autonomous vehicles and artificial intelligence.

Slope stability analysis with a hypoplastic constitutive model: Investigating a stochastic anisotropy model and a hydro‐mechanical coupled simulation

AbstractA reliable constitutive model is essential for accurately predicting slope deformation in numerical analysis, which includes assessing slope stability as an integral component. However, calculating slope stability in numerical models can be challenging due to complex boundary conditions and advanced constitutive models, especially when probabilistic and hydro‐mechanical coupled simulations are required. In this paper, we use a vector‐sum method‐based framework for slope stability analysis that incorporates a critical state hypoplastic constitutive model. The rationality and accuracy of the stability results are initially verified through critical slip surface analysis and a factor of safety evaluation. Subsequently, we investigate the probability‐based slope stability and failure characteristics by incorporating the spatial variability of strength parameters into the hypoplastic model. Finally, the Baishuihe landslide in the Three Gorges Reservoir Region is examined as a case study, where hydro‐mechanical coupled simulations are conducted under actual water level and rainfall conditions. The time‐varying stability and deformation characteristics of the landslide are analyzed and compared with the results obtained from the Mohr‐Coulomb model. The analysis results demonstrate the practicality and efficiency of using a hypoplastic model for probabilistic and time‐varying slope stability calculations. Furthermore, it highlights the superior ability of the hypoplastic model to accurately describe reservoir landslide deformation processes.

Data-driven analysis of structural instabilities in electroactive polymer bilayers based on a variational saddle-point principle

In this work, we use a data-driven approach to model the onset of wrinkling in composite dielectric elastomer (DE) bilayer structures that are subjected to combined electro-mechanical loading conditions. Specifically, the critical surface-charge density required to activate wrinkling and the resulting number of half-waves are determined as functions of the tunable geometrical and material features of the DE bilayer using supervised machine learning (ML) models. The required data for the ML surrogates is generated using a finite-element-based framework for structural stability analysis of the DE bilayer, which is rooted in a variational saddle-point formulation for non-linear electro-elastostatics. Within the considered broad design space for the DE bilayer, the data points are sampled according to a Latin-hypercube-type design, following which training and test datasets containing the values of the target variables for the sampled input-feature vectors are generated using the adopted finite-element framework. Subsequently, we implement and compare the capabilities of different ML models to capture accurately the non-linear dependence of the wrinkling characteristics on the tunable features of the DE bilayer.

Enhancing buckling analysis of functionally graded plates using unified and generalized higher-order shear deformation theories

This paper introduces a comprehensive framework for stability analysis of functionally graded plates under diverse in-plane loading conditions while employing higher-order shear deformation theories. For this purpose, a unified model, including all shear deformation kinematics, has been proposed. This unified model incorporates any number or type of shear transverse functions, encompassing all existing plate shear deformation theories. This inclusivity is achieved through the introduction of a unique parameter, denoted by ”n” representing the number of shear deformation functions in the displacement model. Such a unified model allows great flexibility in choosing among higher order theories when modeling the behavior of plates subjected to shear deformation, making it a valuable tool for applications in engineering and materials science. Besides, this allowed us to easily introduce a fifth-order theory used for the first time in the buckling analysis of FGM plates. The critical buckling loads expressions corresponding to the employed kinematics were derived and the calculated values are compared to those computed using the numerical solver. The comparison demonstrates the effectiveness and accuracy of the formulated expressions in predicting critical buckling loads under uniaxial and biaxial loading conditions.

A Modeling Framework for Stability and Dynamic Analysis of Marine Hybrid Electric Powertrains

A Modeling Framework for Stability and Dynamic Analysis of Marine Hybrid Electric Powertrains

Adaptive dynamic surface control of MIMO nonlinear systems: A hybrid event triggering mechanism

SummaryThis paper addresses the event‐triggered stabilization control for multi‐input and multi‐output (MIMO) nonlinear systems. To handle the “explosion of complexity”, the dynamic surface control (DSC) technology is introduced to the proposed control scheme. In addition, the event‐driven idea is adopted to mitigate the data transmission pressure in sensor‐to‐controller and controller‐to‐actuator channels. Considering that the non‐derivable virtual controllers are commonly constructed in the event‐triggered control schemes aiming at saving dual‐channel resources, in this paper, a hybrid event‐triggering mechanism with multiple event detectors is developed to obtain differentiable virtual control signals, thereby providing a suitable application environment for the DSC technology. Meanwhile, an output‐based adaptive threshold is designed to obtain more communication benefits compared with the fixed threshold strategy. Finally, all signals in the closed‐loop system are ensured to be bounded under a standard Lyapunov stability analysis framework, and the effectiveness of the proposed control scheme is validated by a simulation example.

A general framework for the exact stability analysis of love dynamics with four independent time delays

We investigate the asymptotic stability of a linear love model with four independent time delays to mimic the complicated human emotions more precisely compared with the classic Strogatz model. These four delays stem from the perception of their own past emotions and their partner's past emotions for both individuals. The central idea is to exactly ascertain the stability switching boundaries where the emotions of these two individuals change in the domain of delays. For this, we propose a general stability analysis framework synthesizing the Dixon resultant theory, the frequency sweeping technique, and the cluster treatment of characteristic roots (CTCR) paradigm. We then present a detailed procedure of this framework to particularly study how one partner reacts to the other. Finally, we demonstrate the effectiveness of this framework through a case study and then provide some suggestions for the couple to achieve a sweet love relationship.

Event-Triggered Quantized Stabilization of Markov Jump Systems under Deception Attacks

This paper focuses on the event-triggered quantized control for Markov jump systems with deception attacks. First, we design an event-triggered scheme relying on dwell time and end instants of attacks. It can limit the number of switches within the triggered intervals and the lower bound of triggered instants. Second, the quantization rules and the increasing/decreasing rate of Lyapunov function are obtained for different cases. Next, combined with the increasing/decreasing rate, the lower bound of triggered instants, and the probability of switches occurring, the upper bound of Lyapunov function at the triggered instants is provided. On this basis, sufficient conditions ensuring the exponential convergence in the mean sense of the closed-loop system are given. Finally, atwo-tank system is provided to verify the effectiveness of the proposed stability analysis framework for Markov jump systems.

A quantitative analysis procedure for solving safety factor of tunnel preliminary support considering the equivalence between Hoek–Brown and Mohr–Coulomb criteria

There is a development trend from qualitative towards quantitative analysis for tunnel stability. The widely accepted convergence-confinement method (CCM) provides a quantitative framework for tunnel stability analysis, while the conventional CCM based on closed-form functions is essentially an ideal model without considering the tunnel section shape and rock weight in plastic zone. Herein, based on the CCM framework, a quantitative analysis procedure formulated through numerical simulations for more practical situations was systematically proposed to calculate the safety factor of spray-anchor support system in non-circular tunnel. Besides, similarities and differences between the most widely used Hoek-Brown (HB) and equivalent Mohr-Coulomb (EMC) criteria were considered for practical reference. The proposed method was utilized to conduct quantitative analysis of LDPs, mechanical responses of surrounding rock and safety factors for four typical tunnels, and the consistency between tunnels based on HB criterion (TBHBC) and EMC criterion (TBEMCC) was analyzed. The results indicated that the maximum radial convergence of LDP, plastic zone area, and safety factor of TBEMCC were 34.54%, 37.29%, and 47.71% lower than those of TBHBC respectively. The reasons for differences between results were revealed. The spatial effect induced by the face excavation of TBEMCC was weakened as compared to TBHBC, leading to a drop of LDP. Consequently, the safety factor was underestimated. The method systematically provided an effective tool for quantitative stability analysis and design optimization of support system for an underground excavation.

A numerical framework for linear stability analysis of two-phase stratified pipe flows

A numerical framework for linear stability analysis of two-phase stratified pipe flows

Framework for global stability analysis of dynamical systems.

Dynamical systems that are used to model power grids, the brain, and other physical systems can exhibit coexisting stable states known as attractors. A powerful tool to understand such systems, as well as to better predict when they may "tip" from one stable state to the other, is global stability analysis. It involves identifying the initial conditions that converge to each attractor, known as the basins of attraction, measuring the relative volume of these basins in state space, and quantifying how these fractions change as a system parameter evolves. By improving existing approaches, we present a comprehensive framework that allows for global stability analysis of dynamical systems. Notably, our framework enables the analysis to be made efficiently and conveniently over a parameter range. As such, it becomes an essential tool for stability analysis of dynamical systems that goes beyond local stability analysis offered by alternative frameworks. We demonstrate the effectiveness of our approach on a variety of models, including climate, power grids, ecosystems, and more. Our framework is available as simple-to-use open-source code as part of the DynamicalSystems.jl library.

Stability analysis framework for isolated microgrids with energy resources integrated using voltage source converters

Integrating distributed energy resources (DERs) enables the development of microgrids, which opens up a broad field of study. However, the dynamic behaviour of these energy resources presents challenges in these new electric systems. The stability of systems with high penetration of DERs is a developing research topic, where enhancement strategies are typically focused on specific issues, while general approaches often present several challenges without testing scenarios. In this document, an analysis of several stability issues is presented and tested in an islanded system based on the CIGRE low voltage benchmark. The conclusions obtained are noteworthy and propose further discussion and research, to enhance the understanding and future study of islanded microgrid stability with only converter-integrated energy resources.