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publications
Dynamical responses of airfoil models with harmonic excitation under uncertain disturbance
Published in Nonlinear Dynamics, 2017
Abstract: In this paper, we investigate nonlinear dynamical responses of two-degree-of-freedom airfoil (TDOFA) models driven by harmonic excitation under uncertain disturbance. Firstly, based on the deterministic airfoil models under the harmonic excitation, we introduce stochastic TDOFA models with the uncertain disturbance as Gaussian white noise. Subsequently, we consider the amplitude-frequency characteristic of deterministic airfoil models by the averaging method, and also the stochastic averaging method is applied to obtain the mean-square response of given stochastic TDOFA systems analytically. Then, we carry out numerical simulations to verify the effectiveness of the obtained analytic solution and the influence of harmonic force on the system response is studied. Finally, stochastic jump and bifurcation can be found through the random responses of system, and probability density function and time history diagrams can be obtained via Monte Carlo simulations directly to observe the stochastic jump and bifurcation. The results show that noise can induce the occurrence of stochastic jump and bifurcation, which will have a significant impact on the safety of aircraft.
Recommended citation: Xu Y, Liu Q, Guo G, et al. Dynamical responses of airfoil models with harmonic excitation under uncertain disturbance[J]. Nonlinear Dynamics, 2017, 89: 1579-1590. https://doi.org/10.1007/s11071-017-3536-8
Active vibration suppression of a novel airfoil model with fractional order viscoelastic constitutive relationship
Published in Journal of Sound and Vibration, 2018
Abstract: This paper aims to investigate the active vibration suppression of a fractional two-degree-of-freedom viscoelastic airfoil (TDOFVA) model with a harmonic external force by means of the sliding mode control (SMC) scheme. The viscoelastic behavior is described as a fractional-order derivative, leading to a new fractional TDOFVA model. Subsequently, an averaging technique is extended to derive the amplitude-frequency relations, and its correctness is verified by Monte Carlo simulations. In addition, effects of the system parameters on the dynamics are explored. To achieve a vibration suppression, we convert the TDOFVA system into a series of fractional-order differential equations. Then, a SMC strategy is employed, in which a fractional-order integral sliding surface is presented and asymptotical stability analysis of the SMC is performed. Several numerical results are presented to illustrate the performances of the proposed SMC scheme, which indicate that the given SMC methodology is effective to realize a vibration suppression of the TDOFVA model.
Recommended citation: Liu Q, Xu Y, Kurths J. Active vibration suppression of a novel airfoil model with fractional order viscoelastic constitutive relationship[J]. Journal of Sound and vibration, 2018, 432: 50-64. https://doi.org/10.1016/j.jsv.2018.06.022
The sliding mode control for an airfoil system driven by harmonic and colored Gaussian noise excitations
Published in Applied Mathematical Modelling, 2018
Abstract: This paper addresses a sliding mode control (SMC) for an airfoil model excited by a combination of harmonic force and colored Gaussian noise. Firstly, to reveal effects of random factors, the airfoil model with colored Gaussian noise is established. Next, via a perturbation technique and the stochastic averaging method, an analytical expression for the time-averaging mean square response is derived, which agrees well with results by Monte Carlo simulations. Additionally, we uncover that colored noise can induce a stochastic jump phenomenon, which can cause a catastrophic structural failure of the airfoil or even a disintegration of the aircraft. Subsequently, the SMC strategy is employed to design an effective controller for suppressing such a jump phenomenon of the stochastic airfoil system. In the case of the proposed stochastic airfoil system, we introduce concepts of ultimately reachability with an arbitrary small bound and a mean square practical stability to realize the reachability of the sliding mode and the stability of the system state. Finally, several numerical results are presented to demonstrate the effectiveness of the proposed SMC algorithm. We show that the jump phenomenon can be suppressed efficiently to avoid a catastrophic failure of the wing structure due to large deformation/deflection, and the energy cost is discussed to analyze the SMC approach.
Recommended citation: Liu Q, Xu Y, Xu C, et al. The sliding mode control for an airfoil system driven by harmonic and colored Gaussian noise excitations[J]. Applied Mathematical Modelling, 2018, 64: 249-264. https://doi.org/10.1016/j.apm.2018.07.032
Solving Fokker-Planck equation using deep learning
Published in Chaos: An Interdisciplinary Journal of Nonlinear Science, 2020
Abstract: The probability density function of stochastic differential equations is governed by the Fokker-Planck (FP) equation. A novel machine learning method is developed to solve the general FP equations based on deep neural networks. The proposed algorithm does not require any interpolation and coordinate transformation, which is different from the traditional numerical methods. The main novelty of this paper is that penalty factors are introduced to overcome the local optimization for the deep learning approach, and the corresponding setting rules are given. Meanwhile, we consider a normalization condition as a supervision condition to effectively avoid that the trial solution is zero. Several numerical examples are presented to illustrate performances of the proposed algorithm, including one-, two-, and three-dimensional systems. All the results suggest that the deep learning is quite feasible and effective to calculate the FP equation. Furthermore, influences of the number of hidden layers, the penalty factors, and the optimization algorithm are discussed in detail. These results indicate that the performances of the machine learning technique can be improved through constructing the neural networks appropriately.
Recommended citation: Xu Y, Zhang H, Li Y, et al. Solving Fokker-Planck equation using deep learning[J]. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2020, 30(1): 013133. https://doi.org/10.1063/1.5132840
Bistability and stochastic jumps in an airfoil system with viscoelastic material property and random fluctuations
Published in Communications in Nonlinear Science and Numerical Simulation, 2020
Abstract: The purpose of this paper is to explore analytically the influences of random fluctuations on a two-degrees-of-freedom (TDOF) airfoil model with viscoelastic terms. To begin with, a convolution integral over an exponentially decaying kernel function is employed to establish a constitutive relation of the viscoelastic material. Then the corresponding TDOF airfoil model with viscoelastic terms and random excitations is introduced. Subsequently, a theoretical analysis for the proposed airfoil model is achieved through a multiple-scale method together with a perturbation technique. All of the obtained approximate analytical solutions are verified by numerical simulation results, and a good agreement is observed. Meanwhile, we also find that both high-amplitude and low-amplitude oscillations coexist within a certain range of the excitation frequency or amplitude, which is regarded as a bi-stable behavior. In addition, effects of the viscoelastic terms and the random excitations on the system responses are investigated in detail. We uncover that the viscoelastic terms have a considerable influence on the system dynamics, which can simultaneously affect the structural damping and stiffness of the airfoil system. More interestingly, stochastic jumps between high-amplitude and low-amplitude oscillations can be induced due to random fluctuations, which are further illustrated through time history and steady-state probability density function. The jumps are considered as a transition from one probable state to another or vice versa. These results indicate that the external random fluctuations have a remarkable influence on dynamics of the TDOF airfoil model with viscoelastic material property.
Recommended citation: Liu Q, Xu Y, Kurths J. Bistability and stochastic jumps in an airfoil system with viscoelastic material property and random fluctuations[J]. Communications in Nonlinear Science and Numerical Simulation, 2020, 84: 105184. https://doi.org/10.1016/j.cnsns.2020.105184
Rate-dependent tipping-delay phenomenon in a thermoacoustic system with colored noise
Published in Science China Technological Sciences, 2020
Abstract: Tipping is a phenomenon in multistable systems where small changes in inputs cause huge changes in outputs. When the parameter varies within a certain time scale, the rate will affect the tipping behaviors. These behaviors are undesirable in thermoacoustic systems, which are widely used in aviation, power generation and other industries. Thus, this paper aims at considering the tipping behaviors of the thermoacoustic system with the time-varying parameters and the combined excitations of additive and multiplicative colored noises. Transient dynamical behaviors for the proposed thermoacoustic model are implemented through the reduced Fokker-Planck-Kolmogorov equation derived by a standard stochastic averaging method. Then, the tipping problems of the rate-dependent thermoacoustic systems with random fluctuations are studied by virtue of the obtained probability density functions. Our results show that the rate delays the value of the tipping parameter compared to the one with the quasi-steady assumption, which is called as a rate-dependent tipping-delay phenomenon. Besides, the influences of the initial values, the rate, the changing time of the parameters, and the correlation time of the noises on the rate-dependent tipping-delay phenomenon are analyzed in detail. These results are of great significance for research in related fields such as aviation and land gas turbines.
Recommended citation: Zhang X Y, Xu Y, Liu Q, et al. Rate-dependent tipping-delay phenomenon in a thermoacoustic system with colored noise[J]. Science China Technological Sciences, 2020, 63(11): 2315-2327. https://doi.org/10.1007/s11431-020-1589-x
Rate-dependent bifurcation dodging in a thermoacoustic system driven by colored noise
Published in Nonlinear Dynamics, 2021
Abstract: Tipping in multistable systems occurs usually by varying the input slightly, resulting in the output switching to an often unsatisfactory state. This phenomenon is manifested in thermoacoustic systems. The thermoacoustic instability may lead to the disintegration of rocket engines, gas turbines and aeroengines, so it is necessary to design control measures for its suppression. It was speculated that such unwanted instability states may be dodged by changing the bifurcation parameters quickly enough, and compared with the white noise discussed in [1], colored noise with nonzero correlation time is more practical and important to the system. Thus, in this work, based on a fundamental mathematical model of thermoacoustic systems driven by colored noise, the corresponding Fokker–Planck–Kolmogorov equation of the amplitude is derived by using a stochastic averaging method. A transient dynamical behavior is identified through a probability density analysis. We find that both a relatively higher rate of change of parameters and change in the correlation time of the noise are beneficial to dodge thermoacoustic instability, while a relatively large noise intensity is a disadvantageous factor. More interestingly and importantly, power-law relationships between the maximum amplitude and the noise parameters are uncovered, and the probability of successfully dodging a thermoacoustic instability is calculated. These results serve as a guidance for the design of engines and to propose an effective control strategy, which is of great significance to aerospace-related fields.
Recommended citation: Zhang X, Xu Y, Liu Q, et al. Rate-dependent bifurcation dodging in a thermoacoustic system driven by colored noise[J]. Nonlinear Dynamics, 2021, 104: 2733-2743. https://doi.org/10.1007/s11071-021-06368-5
Fixed-interval smoothing of an aeroelastic airfoil model with cubic or free-play nonlinearity in incompressible flow
Published in Acta Mechanica Sinica, 2021
Abstract: Fixed-interval smoothing, as one of the most important types of state estimation, has been concerned in many practical problems especially in the analysis of flight test data. However, the existing sequential filters and smoothers usually cannot deal with nonlinear or high-dimensional systems well. A state-of-the-art technique is employed in this study to explore the fixed-interval smoothing problem of a conceptual two-dimensional airfoil model in incompressible flow from noisy measurement data. Therein, the governing equations of the airfoil model are assumed to be known or only partially known. A single objective optimization problem is constructed with the classical Runge–Kutta scheme, and then estimations of the system states, the measurement noise and even the unknown parameters are obtained simultaneously through minimizing the objective function. Effectiveness and feasibility of the method are examined under several simulated measurement data corrupted by different measurement noises. All the obtained results indicate that the introduced algorithm is applicable for the airfoil model with cubic or free-play structural nonlinearity and leads to accurate state and parameter estimations. Besides, it is highly robust to Gaussian white and even more complex heavy-tailed measurement noises. It should be emphasized that the employed algorithm is still effective to high-dimensional nonlinear aeroelastic systems.
Recommended citation: Liu Q, Xu Y, Li Y, et al. Fixed-interval smoothing of an aeroelastic airfoil model with cubic or free-play nonlinearity in incompressible flow[J]. Acta Mechanica Sinica, 2021, 37(7): 1168-1182. https://doi.org/10.1007/s10409-021-01091-1
Response statistics of a shape memory alloy oscillator with random excitation
Published in Applied Sciences, 2021
Abstract: This paper aimed to explore analytically the influences of random excitation on a shape memory alloy (SMA) oscillator. Firstly, on the basis of the deterministic SMA model under a harmonic excitation, we introduce a stochastic SMA model with a narrow-band random excitation. Subsequently, a theoretical analysis for the proposed SMA model was achieved through a multiple-scale method coupled with a perturbation technique. All of the obtained approximate analytical solutions were verified by numerical simulation results, and good agreements were observed. Then, effects of the random excitation and the temperature value on the system responses were investigated in detail. Finally, we found that stochastic switch and bifurcation can be induced by the random fluctuation, which were further illustrated through time history and steady-state probability density function. These results indicate that the random excitation has a significant impact on dynamics of the SMA model. This research provides a certain theoretical basis for the design and vibration control of the SMA oscillator in practical application.
Recommended citation: Guo R, Liu Q, Li J, et al. Response statistics of a shape memory alloy oscillator with random excitation[J]. Applied Sciences, 2021, 11(21): 10175. https://doi.org/10.3390/app112110175
Rate-dependent tipping and early warning in a thermoacoustic system under extreme operating environment
Published in Chaos: An Interdisciplinary Journal of Nonlinear Science, 2021
Abstract: Thermoacoustic instability has been an important challenge in the development of high-performance combustion systems, as it can have catastrophic consequences. The process of a sudden change in the dynamical behavior of a thermoacoustic system from a low- to high-amplitude thermoacoustic instability actually entails as a tipping point phenomenon. It has been found that when rate-dependent parameters are considered, a tipping-delay phenomenon may arise, which helps in the control of undesirable states that give rise to thermoacoustic instabilities. This work aims at understanding rate-dependent tipping dynamics of the thermoacoustic system with both time-varying parameters and a non-Gaussian Lévy noise. The latter better describes the severe operating environment of such systems than simpler types of noise. Through numerical simulations, the tipping dynamical behavior is analyzed by considering the rate-dependent parameters coupled with the main parameters of the Lévy noise, including the stability and skewness indices and the noise intensity. In addition, we investigate the effectiveness of early warning indicators in rate-dependent systems under Lévy noise excitation and uncover a relationship between warning measures and the rate of change in the parameters. These results inform and enlighten the development and design of power combustion devices and also provide researchers and engineers with effective ideas to control thermoacoustic instability and the associated tipping dynamics.
Recommended citation: Zhang X, Xu Y, Liu Q, et al. Rate-dependent tipping and early warning in a thermoacoustic system under extreme operating environment[J]. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2021, 31(11): 113115. https://doi.org/10.1063/5.0071977
Extreme events in a class of nonlinear Duffing-type oscillators with a parametric periodic force
Published in The European Physical Journal Plus, 2022
Abstract: Extreme events happen when a system is far from the expectation and normal region, which are common in many practical problems, such as climate and engineering systems. It will affect the accuracy and damage the reliability, or even lead to a collapse of the system. In this work, extreme events are studied in a class of generalized nonlinear Duffing-type oscillators with a parametric periodic force. The occurrence mechanism, description methods and risk of extreme events are discussed. We find that the tail probability of the state response is large when extreme events occur frequently. This indicates that the dynamic structure enables the system to reach a rather far position, for which the varying of the potential function provides a possible underlying explanation for this phenomenon. In addition, the effects of the amplitude and the frequency are investigated to quantify the extreme events. With the metrics of inter-event interval (IEI), mean of IEI, survival probability function, and hazard rate function, the risk of extreme events is characterized. The obtained results not only quantitatively give the characteristics of extreme events in a class of generalized Duffing-type oscillators, but also assess the risk of extreme events, which can provide theoretical guidance for the design and fabrication of micro-electromechanical components.
Recommended citation: Zhao D, Li Y, Xu Y, et al. Extreme events in a class of nonlinear Duffing-type oscillators with a parametric periodic force[J]. The European Physical Journal Plus, 2022, 137(3): 314. https://doi.org/10.1140/epjp/s13360-022-02530-z
Early warning of noise-induced catastrophic high-amplitude oscillations in an airfoil model
Published in Chaos: An Interdisciplinary Journal of Nonlinear Science, 2022
Abstract: Noise-induced tipping from a low-amplitude oscillation state to a high-amplitude one is widespread in airfoil systems. Its occurrence may cause fatigue damage to the wing structure of an aircraft, which directly threatens its flight safety. Therefore, it is of utmost importance to predict the occurrence of noise-induced high-amplitude oscillations as the system parameters vary in airfoil systems. Taking a two-degrees-of-freedom airfoil model with random loadings as a prototype class of real systems, the prediction of noise-induced tipping from low-amplitude to high-amplitude oscillations is carried out in the present study. First, we analyze the effects of random fluctuations on the system response. The results show that noise-induced catastrophic high-amplitude oscillations take place before the bifurcation point of the corresponding deterministic airfoil model. Subsequently, the possibility that the low-amplitude oscillation state of the given noisy model jumps to the high-amplitude one is analyzed based on the escape probability. Then, the new concept of the high-risk region is defined. This is an efficient early warning indicator to approximately quantify the ranges of the system parameters where noise-induced high-amplitude oscillations may occur. Compared with the existing early warning indicators, this method is a non-local universal concept of stability. More importantly, it may provide theoretical guidance for aircraft designers to take some measures to avoid such catastrophic critical jump phenomena in practical engineering applications.
Recommended citation: Ma J, Liu Q, Xu Y, et al. Early warning of noise-induced catastrophic high-amplitude oscillations in an airfoil model[J]. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2022, 32(3): 033119. https://doi.org/10.1063/5.0084796
Solving Fokker-Planck equations using deep KD-tree with a small amount of data
Published in Nonlinear Dynamics, 2022
Abstract: The Fokker–Planck (FP) equation can deterministically describe the evolution of the probability density function, which plays an extremely significant role in the fields of stochastic dynamics. Unfortunately, the limited samples that arise from the consideration of engineering practice are inevitable, which restricts the solving of the FP equation. Accordingly, in the present study, a super-DL-FP framework is established to solve the steady-state FP equation with a small amount of data, through combining the deep KD-tree and the DL-FP approach proposed in [Chaos 30, 013133 (2020)]. It should be emphasized that the normalization condition is of great importance and has to be considered in solving the steady-state FP equation. An appropriate integral estimation for the normalization condition under non-uniform meshing can effectively improve the precision of the solution, but it is still a challenging problem, especially for the case of small data. Thus, the so-called deep KD-tree method is innovatively proposed to estimate the normalized integral with a small random dataset. The main target is to obtain the appropriate discrete integral points and corresponding integral volumes by executing multiple KD-tree segmentation based on random data on the integral region. Several numerical experiments and comparisons are implemented to illustrate the superior performance of the super-DL-FP method. The obtained results indicate that the proposed algorithm can accomplish higher accuracy in the sense of lower cost than the well-known algorithms like center difference scheme, Chebyshev spectrum algorithm, and normalized flow approach.
Recommended citation: Zhang H, Xu Y, Liu Q, et al. Solving Fokker–Planck equations using deep KD-tree with a small amount of data[J]. Nonlinear Dynamics, 2022, 108(4): 4029-4043. https://doi.org/10.1007/s11071-022-07361-2
Complex nonlinear dynamics and vibration suppression of conceptual airfoil models: A state-of-the-art overview
Published in Chaos: An Interdisciplinary Journal of Nonlinear Science, 2022
Abstract: During the past few decades, several significant progresses have been made in exploring complex nonlinear dynamics and vibration suppression of conceptual aeroelastic airfoil models. Additionally, some new challenges have arisen. To the best of the author’s knowledge, most studies are concerned with the deterministic case; however, the effects of stochasticity encountered in practical flight environments on the nonlinear dynamical behaviors of the airfoil systems are neglected. Crucially, coupling interaction of the structure nonlinearities and uncertainty fluctuations can lead to some difficulties on the airfoil models, including accurate modeling, response solving, and vibration suppression. At the same time, most of the existing studies depend mainly on a mathematical model established by physical mechanisms. Unfortunately, it is challenging and even impossible to obtain an accurate physical model of the complex wing structure in engineering practice. The emergence of data science and machine learning provides new opportunities for understanding the aeroelastic airfoil systems from the data-driven point of view, such as data-driven modeling, prediction, and control from the recorded data. Nevertheless, relevant data-driven problems of the aeroelastic airfoil systems are not addressed well up to now. This survey contributes to conducting a comprehensive overview of recent developments toward understanding complex dynamical behaviors and vibration suppression, especially for stochastic dynamics, early warning, and data-driven problems, of the conceptual two-dimensional airfoil models with different structural nonlinearities. The results on the airfoil models are summarized and discussed. Besides, several potential development directions that are worth further exploration are also highlighted.
Recommended citation: Liu Q, Xu Y, Kurths J, et al. Complex nonlinear dynamics and vibration suppression of conceptual airfoil models: A state-of-the-art overview[J]. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2022, 32(6): 062101. https://doi.org/10.1063/5.0093478
Neural network-based parameter estimation of stochastic differential equations driven by Lévy noise
Published in Physica A: Statistical Mechanics and its Applications, 2022
Abstract: In this paper, a novel parameter estimation method based on a two-stage neural network (PENN) is proposed to carry out a joint estimation of a parameterized stochastic differential equation (SDE) driven by Lévy noise from a discretely sampled trajectory. The first stage is a long short term memory neural network to extract the compact time-irrelevant deep features from the trajectory. Then a fully connected neural network refines the deep features by integrating the information of time. This neural network architecture allows our method capable of processing trajectories with variable lengths and time spans. Representative SDEs including Ornstein–Uhlenbeck process, genetic toggle switch model and bistable Duffing system are presented to determine the effectiveness of our approach. The numerical results suggest that the PENN can simultaneously estimate the parameters of the system and Lévy noise with faster speed and higher accuracy in comparison with traditional estimation methods. Moreover, the method can be easily generalized to different SDEs with flexible settings of sample observation.
Recommended citation: Wang X, Feng J, Liu Q, et al. Neural network-based parameter estimation of stochastic differential equations driven by Lévy noise[J]. Physica A: Statistical Mechanics and its Applications, 2022, 606: 128146. https://doi.org/10.1016/j.physa.2022.128146
Deep learning framework for solving Fokker-Planck equations with low-rank separation representation
Published in Engineering Applications of Artificial Intelligence, 2023
Abstract: An insightful deep learning framework is proposed to solve the well-known Fokker–Planck (FP) equations that quantify the evolution of the probability density function. It efficiently reduces the demand of training data in acquiring precise integrations of special normalization conditions via neural network (NN). Instead of all hypercubic discrete points, the inputs of each NN only require one-dimensional discrete data, and this also avoids the exponential increase in training data as the dimension increase. Without loss of generality, to solve a $d$-dimensional FP equation, $d$ NNs are employed and assembled into a low-rank separation representation. The FP equation, boundary conditions, and integral operators are then re-expressed in the sense of the separation representation. It enables the constructed loss function to perform simple vector operations, in that complicated $d$-dimensional operators are replaced by a set of one dimensional operators. A tractable strategy is presented for the selection of separation rank inspired by the potential function of the given system, although selecting an appropriate separation rank is still an open issue. Typical numerical examples reveal that the proposed algorithm is effective and superior for solving FP equations. The suggested framework could be applied and extended in various areas of engineering and applied sciences.
Recommended citation: Zhang H, Xu Y, Liu Q, et al. Deep learning framework for solving Fokker–Planck equations with low-rank separation representation[J]. Engineering Applications of Artificial Intelligence, 2023, 121: 106036. https://doi.org/10.1016/j.engappai.2023.106036
Complex dynamics of a conceptual airfoil structure with consideration of extreme flight conditions
Published in Nonlinear Dynamics, 2023
Abstract: An aircraft in practice serves under extreme flight conditions that will have a substantial impact on its flight safety. Understanding dynamics of airfoil structure of an aircraft subjected to severe load conditions is thus extremely valuable and necessary. In this study, we will explore the complicated dynamical behaviors of a conceptual airfoil excited by an external harmonic force and an extreme random load. Importantly, such an extreme random load is portrayed by a non-Gaussian Lévy noise with a heavy-tailed feature. Bistable behaviors of the deterministic airfoil system are performed firstly from amplitude–frequency response and basin of attraction. Then, the effects of the extreme random load on the airfoil system are thoroughly investigated. Interestingly, within the bistable regime, the extreme random load can lead to stochastic transition and stochastic resonance. Due to its heavy-tailed nature, the Lévy noise would increase the possibility of a highly unexpected stochastic transition behavior between desirable low-amplitude and catastrophic high-amplitude oscillations compared with the Gaussian scenario. Such vibration patterns might damage or destroy the airfoil structure, which will put an aircraft in great danger. All the findings would be helpful in ensuring the flight safety and enhancing the strength and reliability of airfoil structure operating at extreme flight conditions.
Recommended citation: Liu Q, Xu Y, Li Y. Complex dynamics of a conceptual airfoil structure with consideration of extreme flight conditions[J]. Nonlinear Dynamics, 2023, 111(16): 14991-15010. https://doi.org/10.1007/s11071-023-08636-y
Dynamic responses of a conceptual two-dimensional airfoil in hypersonic flows with random perturbations
Published in Journal of Fluids and Structures, 2023
Abstract: This paper investigates a conceptual pitch–plunge airfoil in hypersonic flows with both structural and aerodynamic nonlinearity, meanwhile the effects of irregular fluctuations in the flow and external random loads modeled as a Gaussian white noise are considered. The dynamic responses of the airfoil model especially the bifurcation behaviors are analyzed via the harmonic balance method for the deterministic case. We found the airfoil system undergo both subcritical and supercritical Hopf bifurcations. Subsequently, the effects of stochasticity on the dynamical behaviors of the hypersonic airfoil system are explored in the regimes of subcritical and supercritical Hopf bifurcations depending on the system parameters. Several interesting phenomena are triggered under random perturbations such as intermittency and stochastic transition between the low-amplitude oscillation state and the undesirable high-amplitude oscillation state. These dynamics are further characterized via the probability density function and time history. This work will provide new insights into the safety and reliability design of hypersonic aircraft.
Recommended citation: Guo W, Xu Y, Li Y, et al. Dynamic responses of a conceptual two-dimensional airfoil in hypersonic flows with random perturbations[J]. Journal of Fluids and Structures, 2023, 121: 103920. https://doi.org/10.1016/j.jfluidstructs.2023.103920
The occurrence mechanisms of extreme events in a class of nonlinear Duffing-type systems under random excitations
Published in Chaos: An Interdisciplinary Journal of Nonlinear Science, 2023
Abstract: The occurrence mechanisms of extreme events under random disturbances are relatively complex and not yet clear. In this paper, we take a class of generalized Duffing-type systems as an example to reveal three mechanisms for the occurrence of extreme events. First, it is intuitive that a very large excitation can generate extreme events, such as the Lévy noise. In such a case, extreme excitation works, while it does not require much about the systems. Second, when a system has a bifurcation structure, if the difference of the branches at the bifurcation point is large, a randomly varying bifurcation parameter can lead to extreme events. Finally, when a system has rare attractors, a random impulse excitation, such as Poisson white noise, is able to cause the system to escape from one general attractor into rare attractors. Such a kind of special regime switching behavior can lead to extreme events. These results reveal the possible mechanisms of extreme events in a class of nonlinear Duffing-type systems and provide guidance for further prediction and avoidance of extreme events.
Recommended citation: Zhao D, Li Y, Liu Q, et al. The occurrence mechanisms of extreme events in a class of nonlinear Duffing-type systems under random excitations[J]. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2023, 33(8): 083109. https://doi.org/10.1063/5.0156492
Probabilistic description of extreme oscillations and reliability analysis in rolling motion under stochastic excitation
Published in Science China Technological Sciences, 2023
Abstract: Large-amplitude rolling motions, also regarded as extreme oscillations, are a great threat to marine navigation, which may lead to capsizing in ship motion. Therefore, it is important to quantify extreme oscillations, assess reliability of ship systems, and establish a suitable indicator to characterize extreme oscillations in ship systems. In this work, extreme events are investigated in a ship model considering a complex ocean environment, described by a single-degree-of-freedom nonlinear system with stochastic harmonic excitation and colored Gaussian noise. The stationary probability density function (PDF) of the system is derived through a probabilistic decomposition-synthesis method. Based on this, we infer the classical damage rate of the system. Furthermore, a new indicator, independent of the PDF, is proposed to quantify the damage related only to the fourth-order moment of the system and the threshold for extreme events. It is more universal and easier to determine as compared with the classical damage rate. A large damping ratio, a large noise intensity, or a short correlation time can reduce the damage rate and the value of the indicator. These findings provide new insights and theoretical guidance to avoid extreme oscillations and assess the reliability of practical ship movements.
Recommended citation: Zhao D, Li Y G, Xu Y, et al. Probabilistic description of extreme oscillations and reliability analysis in rolling motion under stochastic excitation[J]. Science China Technological Sciences, 2023, 66(9): 2586-2596. https://doi.org/10.1007/s11431-022-2388-4
Deep learning-based parameter estimation of stochastic differential equations driven by fractional Brownian motions with measurement noise
Published in Communications in Nonlinear Science and Numerical Simulation, 2023
Abstract: This study proposes a general parameter estimation neural network (PENN) to jointly identify the system parameters and the noise parameters of a stochastic differential equation driven by fractional Brownian motion (FBM) from a short sample trajectory. It separately extracts deep features from the trajectory and fuses the information of sampling frequency by a two-stage neural network architecture such that the sample trajectories with variable lengths and sampling times can be properly processed. In addition, by considering additive Gaussian measurement noise in the training stage and utilizing suitable loss functions, the PENN can quantitatively estimate the level of measurement noise and reduce its negative impacts on estimating the governing parameters. Experiments on Fitzhugh–Nagumo model, Duffing oscillator and genetic toggle switch model demonstrate that the PENN can accurately estimate the system parameters, the noise intensity and Hurst exponent of the process noise as well as the signal-to-noise ratio of the measurement noise with high speed.
Recommended citation: Feng J, Wang X, Liu Q, et al. Deep learning-based parameter estimation of stochastic differential equations driven by fractional Brownian motions with measurement noise[J]. Communications in Nonlinear Science and Numerical Simulation, 2023, 127: 107589. https://doi.org/10.1016/j.cnsns.2023.107589
Shimmy dynamics in a dual-wheel nose landing gear with freeplay under stochastic wind disturbances
Published in Nonlinear Dynamics, 2024
Abstract: Shimmy dynamics of a dual-wheel nose landing gear system with torsional freeplay under stochastic lateral wind disturbances is studied. Dynamic characteristics of the deterministic case are numerically analysed, especially the shimmy of the landing gear through bifurcation analysis. Meanwhile, the influences of the freeplay nonlinearity on shimmy behaviours are examined in detail. We found that the freeplay leads to an enlargement of the shimmy area and an enhancement of the shimmy characteristics compared to the case without freeplay. Furthermore, impacts of stochastic lateral wind disturbances on the shimmy of the landing gear system are estimated via time history and recurrence plots. We find that the stochastic excitation enhances shimmy of the lateral bending direction. More interestingly, the stochastic excitation strengthens the effect of the freeplay nonlinearity, which causes random intermittent large-amplitude oscillations in the torsional direction. Our results show that the interaction between the freeplay nonlinearity and the random load induces a significant reduction in the critical shimmy velocity, which has an adverse impact on the stability of the nose landing gear of an aircraft. This work will provide an insightful guidance for the design of landing gear parameters in engineering practice.
Recommended citation: Du X, Xu Y, Liu Q, et al. Shimmy dynamics in a dual-wheel nose landing gear with freeplay under stochastic wind disturbances[J]. Nonlinear Dynamics, 2024, 112(4): 2477-2499. https://doi.org/10.1007/s11071-023-09182-3
Noise-induced alternations and data-driven parameter estimation of a stochastic perceptual model
Published in The European Physical Journal Special Topics, 2024
Abstract: Neural systems are inherently noisy and our perceptual system can be then influenced from time to time. In this paper, we considered a perceptual model perturbed by Lévy colored noise, which is much easier to be satisfied in real-world environments than the general Gaussian noise. To elucidate the mechanism underlying the alternation behaviors induced by noise, we characterized the perceptual dynamics in terms of three statistical measures: the mean dominance duration, the number of alternations and the predominance of each interpretation. Numerical simulations showed that the stability index as well as the scale factor and the correlation time of the noise can lead to distinct changes in these measures. Then, attention was paid to data-driven parameter estimation which has typically received less attention than the exploration of stochastic behaviors. A distinctive neural network was proposed to give rise to joint estimates of system parameters and noise parameters, which can also give the measurement to describe the accuracy of estimation. The good performances of our method are shown by simulation tests.
Recommended citation: Wang X, Feng J, Liu Q, et al. Noise-induced alternations and data-driven parameter estimation of a stochastic perceptual model[J]. The European Physical Journal Special Topics, 2024: 1-13. https://doi.org/10.1140/epjs/s11734-024-01162-x
Reliability of Hypersonic Airfoil with Freeplay and Stochasticity via Nonlinear Energy Sink
Published in AIAA Journal, 2024
Abstract: The reliability of a pitch-plunge hypersonic airfoil in random fluctuating flow with both cubic and freeplay nonlinearity is examined. The Hopf bifurcation and dynamic responses of the hypersonic airfoil are performed. To analyze the reliability, the effects of stochasticity on the dynamic behaviors of the hypersonic airfoil model are discussed in detail. Several unwanted phenomena that result in the failure of the airfoil structure are induced by random fluctuations. Subsequently, the reliability of the airfoil model is defined and analyzed according to the first passage failure criteria. The effects of different parameters on the reliability are investigated. Furthermore, a nonlinear energy sink is introduced to suppress the vibration of the airfoil and enhance the reliability. Two-dimensional reliability regions of the airfoil model are given to provide the safety parameter region. The results show that the reliability of the airfoil model is significantly improved with the nonlinear energy sink. This work will provide new insights into the safety design of hypersonic aircraft.
Recommended citation: Guo W, Xu Y, Liu Q, et al. Reliability of hypersonic airfoil with freeplay and stochasticity via nonlinear energy sink[J]. To appear in AIAA Journal, April 2024. https://doi.org/10.2514/1.J064048
talks
Nonlinear dynamics and vibration suppression of conceptual airfoil models with random loads
Published:
Complex dynamics and vibration suppression of conceptual airfoil models with random loadings
Published:
teaching
Teaching experience 1
Undergraduate course, University 1, Department, 2014
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Teaching experience 2
Workshop, University 1, Department, 2015
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