On an interval prediction of COVID-19 development based on a SEIR epidemic model

In this paper, a new version of the well-known epidemic mathematical SEIR model is used to analyze the pandemic course of COVID-19 in eight different countries. One of the proposed model’s improvements is to reflect the societal feedback on the disease and confinement features. The SEIR model parameters are allowed to be time-varying, and the ranges of their values are identified by using publicly available data for France, Italy, Spain, Germany, Brazil, Russia, New York State (US), and China. The identified model is then applied to predict the SARS-CoV-2 virus propagation under various conditions of confinement. For this purpose, an interval predictor is designed, allowing variations and uncertainties in the model parameters to be taken into account. The code and the utilized data are available on Github.     

Statistical results for system identification based on quantized observations

System identification based on quantized observations requires either approximations of the quantization noise, leading to suboptimal algorithms, or dedicated algorithms tailored to the quantization noise properties. This contribution studies fundamental issues in estimation that relate directly to the core methods in system identification. As a first contribution, results from statistical quantization theory are surveyed and applied to both moment calculations (mean, variance etc) and the likelihood function of the measured signal. In particular, the role of adding dithering noise at the sensor is studied. The overall message is that tailored dithering noise can considerably simplify the derivation of optimal estimators. The price for this is a decreased signal to noise ratio, and a second contribution is a detailed study of these effects in terms of the Cramér–Rao lower bound. The common additive uniform noise approximation of quantization is discussed, compared, and interpreted in light of the suggested approaches.     

COVID-19 epidemic control using short-term lockdowns for collective gain

While many efforts are currently devoted to vaccines development and administration, social distancing measures, including severe restrictions such as lockdowns, remain fundamental tools to contain the spread of COVID-19. A crucial point for any government is to understand, on the basis of the epidemic curve, the right temporal instant to set up a lockdown and then to remove it. Different strategies are being adopted with distinct shades of intensity. USA and Europe tend to introduce restrictions of considerable temporal length. They vary in time: a severe lockdown may be reached and then gradually relaxed. An interesting alternative is the Australian model where short and sharp responses have repeatedly tackled the virus and allowed people a return to near normalcy. After a few positive cases are detected, a lockdown is immediately set. In this paper we show that the Australian model can be generalized and given a rigorous mathematical analysis, casting strategies of the type short-term pain for collective gain in the context of sliding-mode control, an important branch of nonlinear control theory. This allows us to gain important insights regarding how to implement short-term lockdowns, obtaining a better understanding of their merits and possible limitations. Effects of vaccines administration in improving the control law’s effectiveness are also illustrated. Our model predicts the duration of the severe lockdown to be set to maintain e.g. the number of people in intensive care under a certain threshold. After tuning our strategy exploiting data collected in Italy, it turns out that COVID-19 epidemic could be e.g. controlled by alternating one or two weeks of complete lockdown with one or two months of freedom, respectively. Control strategies of this kind, where the lockdown’s duration is well circumscribed, could be important also to alleviate coronavirus impact on economy.     

Issues in sampling and estimating continuous-time models with stochastic disturbances

The standard continuous time state space model with stochastic disturbances contains the mathematical abstraction of continuous time white noise. To work with well defined, discrete time observations, it is necessary to sample the model with care. The basic issues are well known, and have been discussed in the literature. However, the consequences have not quite penetrated the practice of estimation and identification. One example is that the standard model of an observation, being a snapshot of the current state plus noise independent of the state, cannot be reconciled with this picture. Another is that estimation and identification of time continuous models require a more careful treatment of the sampling formulas. We discuss and illustrate these issues in the current contribution. An application of particular practical importance is the estimation of models based on irregularly sampled observations.     

随机鼠疫病模型的核范数子空间辨识

基于连续鼠疫病模型,通过零阶保持器得到相应的离散模型.由于随机扰动的存在,提出相应的随机鼠疫病模型.设计卡尔曼滤波器,估计随机模型的状态变量以及降低噪声影响.采用核范数最小化方法代替奇异值分解,得到输入输出投影矩阵的低秩矩阵逼近.通过交替方向乘子法求解此优化问题,得到输出变量的最优解.根据世界卫生组织的非洲人类鼠疫病数据,利用本文提出的方法得到随机鼠疫病模型.仿真研究表明提出方法的有效性和精确性.     

基于辅助模型的多新息广义增广随机梯度算法

将辅助模型辨识思想与多新息辨识理论相结合,利用系统可测信忠建立一个辅助模型.分别用辅助模型输出和噪声估计值代替辨识模型信忠向量中未知真实输出变量和不可测噪声项,并引入新忠长度扩展标量新息为新息向量,提出了Box-lenkins模型的辅助模型多新忠广义增广随机梯度辨识方法.所提出方法重复使用系统数据,能够改善参数估计精度,加快算法的收敛速度.     

Robust performance optimization based on stochastic model errors: the stable case

Robust control aims to account for model uncertainty in design. Traditional methods for robust control typically assume knowledge of hard bounds on the system frequency response. However, this does not match well with system identification procedures which typically yield statistical confidence bounds on the estimated model. This paper explores a new procedure for obtaining a better match between robust control and system identification by using stochastic confidence bounds for robust control design. Given a nominal design, we set up an optimization problem which is aimed at reducing the statistical variability, measured in a mean square sense, from the nominal sensitivity. The proposed procedure is straightforward and leads to an easily computable solution for the final robust controller in the case of a stable plant and modest plant uncertainty. An illustrative example is provided which shows the advantages of the method. Copyright © 2002 John Wiley & Sons, Ltd.     

An improved bias-compensation approach for errors-in-variables model identification

Parametric estimation of the dynamic errors-in-variables models is considered in this paper. In particular, a bias compensation approach is examined in a generalized framework. Sufficient conditions for uniqueness of the identified model are presented. Subsequently, a statistical accuracy analysis of the estimation algorithm is carried out. The asymptotic covariance matrix of the system parameter estimates depends on a user chosen filter and a certain weighting matrix. It is shown how these can be tuned to boost the estimation performance. The numerical simulation results suggest that the covariance matrix of the estimated parameter vector is very close to the Cramér-Rao lower bound for the estimation problem.     

Convex output feedback model predictive control for mitigation of COVID-19 pandemic

In this paper, a model predictive control approach is proposed for epidemic mitigation. The disease spreading dynamics is described by an 8-compartment smooth nonlinear model of the COVID-19 pandemic in Hungary known from the literature, where the manipulable control input is the stringency of the introduced non-pharmaceutical measures. It is assumed that only the number of hospitalized people is measured on-line, and the other state variables are computed using a state observer which is based on the dynamic inversion of a linear sub-system of the model. The objective function contains a measure of the direct harmful consequences of the restrictions, and the constraints refer to input bounds and to the capacity of the healthcare system. By exploiting the special properties of the model, the nonlinear optimization problem required by the control design is reformulated to convex tasks, allowing a computationally efficient solution. Two approaches are proposed: the first finds a suboptimal solution by geometric programming, while the second one further simplifies the problem and transforms it to a linear programming task. Simulations show that both suboptimal solutions fulfill the design specifications even in the presence of parameter uncertainties.     

Quantifying the accuracy of Hammerstein model estimation

This paper investigates the accuracy of the linear component that forms part of an overall Hammerstein model-structure estimate, and a key finding is that the process of estimating the non-linear element can have a strong effect on the associated estimate of the linear dynamics. Furthermore, this effect is not explained simply by way of considering how the input spectrum is changed by the non-linearity. Instead, it arises that the linear model-estimate variability may be dominated by a term that depends on the frequency response of the linear system itself. Amongst other things, the main results derived here have experiment design implications for Hammerstein system estimation.     

基于改进差分进化算法的非线性系统模型参数辨识

针对非线性模型的参数估计寻优较为困难的问题,提出一种基于改进的差分进化算法的非线性系统模型参数辨识新方法。通过引入一个自适应变异率,随着迭代的进行自适应调整缩放因子,从而在初期保持种群多样性以避免早熟,并在后期逐步降低变异率,保留优良信息,避免最优解遭到破坏。交叉概率采用动态非线性增加的方法,提高了收敛速度。为了验证算法性能,针对几类典型的非线性模型参数辨识问题进行了仿真研究,并将其应用于一类发酵动力学模型参数的估计中。结果表明改进算法的参数辨识精度高,收敛速度也比较快,有效提高了模型建立的精度与效率,为解决实际系统中参数估计问题提供了一条可行的途径。     

A review on data-driven linear parameter-varying modeling approaches: A high-purity distillation column case study

Model-based control strategies are widely used for optimal operation of chemical processes to respond to the increasing performance demands in the chemical industry. Yet, obtaining accurate models to describe the inherently nonlinear, time-varying dynamics of chemical processes remains a challenge in most model-based control applications. This paper reviews data-driven, Linear Parameter-Varying (LPV) modeling approaches for process systems by exploring and comparing various identification methods on a high-purity distillation column case study. Several LPV identification methods that utilize input–output and series expansion model structures are explored. Two LPV identification perspectives are adopted: (i) the local approach, which corresponds to the interpolation of Linear Time-Invariant (LTI) models identified at different steady-state operating points of the system and (ii) the global approach, where a parametrized LPV model structure is identified directly using a global data set with varying operating points. For the local approach, various model interpolation schemes are studied under an Output Error (OE) noise setting, whereas in the global case, a polynomial parametrization based OE prediction error minimization approach, an Orthonormal Basis Functions (OBFs) based model estimator and a Least-Square Support Vector Machine (LS-SVM) based non-parametric approach are investigated. Through extensive simulation studies, the aforementioned LPV identification approaches are analyzed in terms of the attainable model accuracy and local frequency response behavior of the obtained models. Recommendations are provided to achieve adequate choice between the methods for a particular process system at hand.     

基于神经网络的需求预测模型

零售业的销售过程中积累了大量数据,如何从这些海量数据中提取知识、建立有效的需求预测模型,为零售商提供市场和趋势分析、降低库存成本是零售行业亟待解决的问题。在传统的零售业需求预测模型——Holt-Winter模型中应用神经网络方法,使得需求预测不依赖于数学模型的精度,预测模型中的季节性影响因子等参数能够根据预测误差作相应调整,避免了传统算法中误差的累积,大大提高了预测精度。利用Excel内嵌的VBA实现了该算法,使需求预测能够根据用户需要实现,并提供可视化的结果。     

Subspace based system identification with periodic excitation signals

An identification algorithm for use with data generated by periodic inputs is presented. The algorithm is based on the geometrical properties of the resulting periodic output signal and a state-space model is derived from the signal subspace of a Hankel matrix by means of a singular value decomposition. It is shown that 2n + 1 noise-free output measurements are required to identify an nth order system. The algorithm is demonstrated to be consistent when the output measurements are corrupted by zero mean noise characterized by decaying covariances. The computational complexity of the algorithm is several orders of magnitude lower than standard methods.     

On guaranteed parameter estimation of a multiparameter linear regression process

This paper presents a sequential estimation procedure for the unknown parameters of a continuous-time stochastic linear regression process. As an example, the sequential estimation problem of two dynamic parameters in stochastic linear systems with memory and in autoregressive processes is solved. The estimation procedure is based on the least squares method with weights and yields estimators with guaranteed accuracy in the sense of the L_q-norm for fixed q≥2.The proposed procedure works in the mentioned examples for all possible values of unknown dynamic parameters on the plane R² for the autoregressive processes and on the plane R² with the exception of some lines for the linear stochastic delay equations. The asymptotic behaviour of the duration of observations is determined.The general estimation procedure is designed for two or more parametric models. It is shown that the proposed procedure can be applied to the sequential parameter estimation problem of affine stochastic delay differential equations and autoregressive processes of an arbitrary order.     

Third-order cumulants based methods for continuous-time errors-in-variables model identification

In this paper, the problem of identifying stochastic linear continuous-time systems from noisy input/output data is addressed. The input of the system is assumed to have a skewed probability density function, whereas the noises contaminating the data are assumed to be symmetrically distributed. The third-order cumulants of the input/output data are then (asymptotically) insensitive to the noises, that can be coloured and/or mutually correlated. Using this noise-cancellation property two computationally simple estimators are proposed. The usefulness of the proposed algorithms is assessed through a numerical simulation.     

基于支持向量机的税收预测模型的研究

针对税收收入预测不稳定,非线性、动态开放性的特点,提出了支持向量机(SVM)的税收收入预测方法,并将该方法用于某市国税系统的实际税收收入情况进行预测,和传统回归方法比较说明所提出的税收收入预测方法是可行和有效的.     

From SIR to SEAIRD: A novel data-driven modeling approach based on the Grey-box System Theory to predict the dynamics of COVID-19

Applied Intelligence - Common compartmental modeling for COVID-19 is based on a priori knowledge and numerous assumptions. Additionally, they do not systematically incorporate asymptomatic cases....