Design a robust sliding mode controller based on the state and parameter estimation for the nonlinear epidemiological model of Covid-19

In this research, the challenging problem of Covid-19 mitigation is looked at from an engineering point of view. At first, the behavior of coronavirus in the Iranian and Russian societies is expressed by a set of ordinary differential equations. In the proposed model, the control input signals are vaccination, social distance and facial masks, and medical treatment. The unknown parameters of the system are estimated by long short-term memory (LSTM) algorithm. In the LSTM algorithm, the problem of long-term dependency is prevented. The uncertainty and measurement noises are inherent characteristics of epidemiological models. For this reason, an extended Kalman filter (EKF) is developed to estimate the state variables of the proposed model. In continuation, a robust sliding mode controller is designed to control the spread of coronavirus under vaccination, social distance and facial masks, and medical treatment. The stability of the closed-loop system is guaranteed by the Lyapunov theorems. The official confirmed data provided by the Iranian and Russian ministries of health are employed to simulate the proposed algorithms. It is understood from simulation results that global vaccination has the potential to create herd immunity in long term. Under the proposed controller, daily Covid-19 infections and deaths become less than 500 and 10 people, respectively.

     

基于交互式多模型秩滤波的移动机器人组合导航算法

针对非结构化环境下移动机器人组合导航系统中存在的时变或非高斯噪声,将秩滤波器(rank Kalman filter,RKF)与交互式多模型算法(interactive multiple model filter,IMM)相结合,提出一种交互式多模型秩滤波算法(IMM-RKF)。秩滤波根据秩统计量相关原理确定采样点和权值,可适用于具有非高斯噪声的非线性系统;交互式多模型算法是解决结构和参数易发生变化系统中状态估计问题的重要途径,能够抑制组合导航系统中时变噪声引起的导航参数估计误差。仿真实验表明,相比于交互式多模型扩展卡尔曼滤波(IMM-EKF)和交互式多模型无迹卡尔曼滤波(IMM-UKF),提出的IMM-RKF算法能够提高组合导航系统姿态、速度和位置估计精度。     

蚁群算法求解二维拉压不同模量反问题

利用光滑函数技术对二维拉压不同模量本构关系进行光滑化处理,采用初应力方法求解二维拉压不同模量正问题的有限元方程。在此基础上,建立了基于连续域蚁群算法的二维拉压不同模量反问题的数值求解模型,考虑了区域非均质的影响,实现了对拉压弹性模量和泊松比的单一/组合识别。通过两个数值算例,对所提算法进行了数值验证,分别探讨了蚁群算法相关参数、测点分布和数据噪音等对识别结果的影响。数值验证表明,所提算法可有效地求解二维拉压不同模量反问题,并具有较好的计算精度。     

Analysis of spatially extended excitable Izhikevich neuron model near instability

The dynamic response and bifurcations of high-dimensional systems endowed with hysteretic restoring forces in all degrees of freedom are investigated. Two types of hysteresis models are considered, namely the Bouc–Wen model and a differential version of the so-called exponential model of hysteresis. The numerical technique tailored for tackling high-dimensional hysteretic systems is based on an enhanced pathfollowing approach based on the Poincaré map. In particular, a five-dof mass-spring-damper-like system, with each rheological element described by the Bouc–Wen or the exponential model of hysteresis enriched by cubic and quintic nonlinear elastic terms, is investigated and a rich variety of nonlinear responses and bifurcations is found and discussed.

     

Parameters identification for chaotic systems based on a modified Jaya algorithm

In this paper, parameters identification for chaotic systems using a modified Jaya algorithm is considered. Firstly, the objective function is formulated based on the variance rate between the responses acquired from the measurement and calculation. Then, the Jaya algorithm is put forward to solve this nonlinear optimization problem. To enhance the performance of the original Jaya, a one-step K-means clustering mechanism and a new updated equation for the best-so-far solution are introduced. To demonstrate the effectiveness of the suggested method, benchmark functions are firstly employed to conduct optimize. Afterward, numerical simulations, including a jerk circuit chaotic system, a hyper-chaotic system and a synchronized chaotic system are used to verify the present algorithm. The simulation results illustrates that the proposed algorithm for chaotic systems is a promising tool with higher identification accuracy, faster convergence rate, as well as stronger robustness.     

Online system identification using fractional-order Hammerstein model with noise cancellation

Slow convergence and low accuracy are two main drawbacks in nonlinear system identification methods. It becomes more complicated when time delay and noises are considered. In this paper, considering a fractional-order Hammerstein model, an online identification method is proposed. A combination of an evolutionary optimization method and recursive least square algorithm is used to estimate the system parameters and orders in the presence of unknown noises. Finally, simulation results are taken to prove the effectiveness of the proposed algorithm.

     

非线性最小二乘跟踪的对偶变量变分方法

最小二乘跟踪方法是近几年提出的一种计算动力系统跟踪轨迹的方法.基于最小二乘跟踪的灵敏度分析算法可以有效避免传统的非线性系统灵敏度分析方法中的病态初值问题,因此其在混沌系统灵敏度分析方面有着重要的应用.针对非线性的最小二乘跟踪问题,首先将其重新描述为带有约束的非线性最优控制问题,引入协态变量并将系统的哈密顿函数表示为关于状态变量和协态变量的函数.然后将目标函数的积分时间离散化,根据对偶变量变分原理,以离散区间两端的状态变量作为独立变量,用Lagrange插值多项式近似离散区间内的状态变量和协态变量,进而将非线性最优控制问题转化为求解非线性方程组问题.这种算法无需对原问题做线性化处理,避免了复杂的线性化过程以及可能因此造成的误差,同时为求解非线性最小二乘跟踪问题提供了新的思路.根据最小二乘方法可以得到两条设计参数有微小变化的状态轨迹,基于这两条状态轨迹可进一步计算出系统关于设计参数的灵敏度,范德波振子作为数值算例验证了该方法在求解最小二乘跟踪问题以及计算非线性系统灵敏度时的有效性.      

Effect of regularized functions on the dynamic response of a clutch system using a high-order algorithm

The main objective of this work is to propose some regularization techniques for modeling contact actions in a clutch system and to solve the obtained nonlinear dynamic problem by a high-order algorithm. This device is modeled by a discrete mechanical system with eleven degrees of freedom. In several works, the discontinuous models of the contact actions are replaced by the smoothed functions using the hyperbolic tangent. We propose, in this work, to replace the discontinuous model by a regularized model with new continuous functions that permit us to search the solution under Taylor series expansion. This regularized model approaches better the discontinuous model than the model based on the smoothing functions, especially in the vicinity of the zone of singularities. To solve the equations of motion of discrete mechanical systems, we propose to use a high-order algorithm combining a time discretization, a change of variable based on the previous time, a homotopy transformation and Taylor series expansion in the continuation process. The results obtained by this modeling are compared with those computed by the Newton–Raphson algorithm.     

Gradient-based parameter estimation for input nonlinear systems with ARMA noises based on the auxiliary model

This paper presents a gradient-based iterative identification algorithm and an auxiliary-model-based multi-innovation generalized extended stochastic gradient algorithm for input nonlinear systems with autoregressive moving average (ARMA) noises, i.e., the input nonlinear Box–Jenkins (IN–BJ) systems. The estimation errors given by the gradient-based iterative algorithm are smaller than the generalized extended stochastic gradient algorithm under same data lengths. A simulation example is provided.     

An improved nonlinear reduced-order modeling for transonic aeroelastic systems

In this study, an improved nonlinear reduced-order model composed of a linear part and a nonlinear part is explored for transonic aeroelastic systems. The linear part is identified via the eigensystem realization algorithm and the nonlinear part is obtained via the Levenberg–Marquardt algorithm. The impulsive signal is chosen as the training signal for the linear part and the sinusoidal signal is used to determine the order of the linear part. The training signal for the nonlinear part is selected as the filtered white Gaussian noise with the maximal amplitude and frequency range to be designed via the aeroelastic responses. An NACA64A010 airfoil and an NACA0012 airfoil are taken as illustrative examples to demonstrate the performance of the presented reduced-order model in modeling transonic aerodynamic forces. The aeroelastic behaviors of the two airfoils are obtained via computational fluid dynamics to solve the Euler equation and the Navier–Stokes equation, respectively. The numerical results demonstrate that the presented reduced-order model can successfully predict the nonlinear aerodynamic forces with and without viscous flows. Moreover, the presented reduced-order model is capable of capturing the flutter velocity and modeling complex aeroelastic behaviors, including limit-cycle oscillations, beat phenomena and nodal-shaped oscillations at the transonic Mach numbers with high accuracy.     

Input-output reduced-order modeling of unsteady flow over an airfoil at a high angle of attack based on dynamic mode decomposition with control

Due to the damage caused by stall flutter, the investigation and modeling of the flow over a wind turbine airfoil at high angles of attack are essential. Dynamic mode decomposition (DMD) and dynamic mode decomposition with control (DMDc) are used to analyze unsteady flow and identify the intrinsic dynamics. The DMDc algorithm is found to have an identification problem when the spatial dimension of the training data is larger than the number of snapshots. IDMDc, a variant algorithm based on reduced dimension data, is introduced to identify the precise intrinsic dynamics. DMD, DMDc and IDMDc are all used to decompose the data for unsteady flow over the S809 airfoil that are obtained by numerical simulations. The DMD results show that the dominant feature of a static airfoil is the adjacent shedding vortices in the wake. For an oscillating airfoil, the DMDc results may fail to consider the effect of the input and have an identification problem. IDMDc can alleviate this problem. The dominant IDMDc modes show that the intrinsic flow for the oscillating case is similar to the unsteady flow over the static airfoil. Moreover, the input–output model identified by IDMDc can give better predictions for different oscillating cases than the identified DMDc model.     

基于有色噪声的改进卡尔曼滤波方法

为了解决实际工程中微机械惯性测量单元加速度计数据存在有色噪声导致计算的姿态角波动异常的问题,提出一种基于有色噪声的改进卡尔曼滤波方法。通过对有色噪声的特点进行分析,建立了针对有色噪声的状态预测协方差公式、卡尔曼滤波增益公式、系统状态与动态有色噪声的协方差公式、测量值与观测有色噪声的协方差公式,推导出处理有色噪声的卡尔曼滤波公式。仿真试验表明,改进的卡尔曼滤波方法能有效解决有色噪声导致的姿态角波动异常问题,证明了基于白噪声的卡尔曼滤波是基于有色噪声卡尔曼滤波的特例。     

A highly-efficient method for stationary response of multi-degree-of-freedom nonlinear stochastic systems

Analytical and numerical studies of multi-degree-of-freedom(MDOF) nonlinear stochastic or deterministic dynamic systems have long been a technical challenge.This paper presents a highly-efficient method for determining the stationary probability density functions(PDFs) of MDOF nonlinear systems subjected to both additive and multiplicative Gaussian white noises. The proposed method takes advantages of the sufficient conditions of the reduced Fokker-Planck-Kolmogorov(FPK) equation when constructi...     

Several gradient-based iterative estimation algorithms for a class of nonlinear systems using the filtering technique

This paper considers iterative identification problems for a class of nonlinear systems with colored noises, which can be described by a linear-in-parameters output error autoregressive model. A gradient-based iterative (GI) algorithm, a filtered GI algorithm, and a filtered three-stage GI algorithm are developed using the decomposition technique and filtering technique, and their computational efficiencies are analyzed and compared. The simulation results indicate that the proposed algorithms can estimate effectively the parameters of nonlinear systems.     

Nonlinear equivalent model and its identification for a delayed absorber with magnetic action using distorted measurement

For an absorber with the magnetic action and the delayed feedback, the equivalent strongly nonlinear model of the magnet force is proposed. We develop an identification algorithm with correcting distorted output measurement to identify and estimate the relevant parameters of the equivalently nonlinear model and the time delay in the feedback loop. The detailed steps of the algorithm are given analytically. We configure an experimental device of a delayed electromechanical absorber with action of the nonlinear magnetic force. The new algorithm is employed to identify the relative parameters of the device, such as time delay, damping and nonlinear stiffness, based on data of the output measurement with distortion. The results show that it is reasonable that the magnet action may be equivalent to the cubic nonlinear force. One may also see that the new algorithm may treat the experimental distorting measurement and correct it as long as the measurement still keeps periodicity. As an important result, values of the identified parameters with the correcting distortion are closer to those of the original measurement than those without the no correcting distortion for some excitation frequencies. It means that the algorithm may correct the polluted measurement, so that the quality of the identification is greatly improved. The new algorithm may be useful for design of nonlinear electromechanical absorber with time-delayed feedback.     

Model determination for nonlinear state-based system identification

A complete methodology for robust nonlinear system identification is derived and illustrated through example. A proven state estimation algorithm is utilized in conjunction with a modified version of a stepwise regression approach to successfully determine the nonlinear dynamics in a “known” truth simulation without a priori knowledge of the system model. First, Minimum Model Error (MME) estimation is derived and illustrated through example. MME is a robust state estimation routine that provides, in addition to smooth states, an estimate of the unmodeled system dynamics is determined from noisy measurement data of known variance. Next, an Analysis of Variance (ANOVA) model correlation routine where a modified version of a forward stepwise procedure is derived and implemented. The ANOVA approach to model acceptance is well documented primarily in social science literature, but has been sparsely written about for engineering applications. This paper shows a significant improvement in nonlinear model identification when used in conjunction with MME estimation.     

Newton iterative identification for a class of output nonlinear systems with moving average noises

This paper discusses iterative identification problems for a class of output nonlinear systems (i.e., Wiener nonlinear systems) with moving average noises from input–output measurement data, based on the Newton iterative method. The basic idea is to decompose a nonlinear system into two subsystems, to replace the unknown variables in the information vectors with their corresponding estimates at the previous iteration, and to present a Newton iterative identification method using the hierarchical identification principle. The numerical simulation results indicate that the proposed algorithms are effective.     

NON-INTERIOR SMOOTHING ALGORITHM FOR FRICTIONAL CONTACT PROBLEMS

A new algorithm for solving the three-dimensional elastic contact problem with friction is presented. The algorithm is a non-interior smoothing algorithm based on an NCP-function. The parametric variational principle and parametric quadratic programming method were applied to the analysis of three-dimensional frictional contact problem. The solution of the contact problem was finally reduced to a linear complementarity problem, which was reformulated as a system of nonsmooth equations via an NCP-function. A smoothing approximation to the nonsmooth equations was given by the aggregate function. A Newton method was used to solve the resulting smoothing nonlinear equations. The algorithm presented is easy to understand and implement. The reliability and efficiency of this algorithm are demonstrated both by the numerical experiments of LCP in mathematical way and the examples of contact problems in mechanics.     

基于断面形状优化的地铁车轮减振降噪研究

以降低地铁车辆在运行中产生的轮轨接触噪声为目的,将结构动力优化方法运用于地铁车轮断面外形设计,建立了地铁车轮振动噪声最优化设计的数学模型,编制了相应的算法程序.以我国某地铁车轮为例,给出了以车轮断面外形几何参数为设计变量、车轮结构振动辐射噪声值最小为目标函数的优化计算实例,得到了车轮断面外形几何参数在可行域内的最优解.结果表明,该优化设计方法是成功的,可以有效地降低车轮因振动而产生的噪声.     

Adjoint‐based airfoil optimization with discretization error control

In this article, we develop a new airfoil shape optimization algorithm based on higher‐order adaptive DG methods with control of the discretization error. Each flow solution in the optimization loop is computed on a sequence of goal‐oriented h‐refined or hp‐refined meshes until the error estimation of the discretization error in a flow‐related target quantity (including the drag and lift coefficients) is below a prescribed tolerance. Discrete adjoint solutions are computed and employed for the multi‐target error estimation and adaptive mesh refinement. Furthermore, discrete adjoint solutions are employed for evaluating the gradients of the objective function used in the CGs optimization algorithm. Furthermore, an extension of the adjoint‐based gradient evaluation to the case of target lift flow computations is employed. The proposed algorithm is demonstrated on an inviscid transonic flow around the RAE2822, where the shape is optimized to minimize the drag at a given constant lift and airfoil thickness. The effect of the accuracy of the underlying flow solutions on the quality of the optimized airfoil shapes is investigated. Copyright © 2014 John Wiley & Sons, Ltd.