A random model approach for the LASSO

The least absolute selection and shrinkage operator (LASSO) is a method of estimation for linear models similar to ridge regression. It shrinks the effect estimates, potentially shrinking some to be identically zero. The amount of shrinkage is governed by a single parameter. Using a random model formulation of the LASSO, this parameter can be specified as the ratio of dispersion parameters. These parameters are estimated using an approximation to the marginal likelihood of the observed data. The observed score equations from the approximation are biased and hence are adjusted by subtracting an empirical estimate of the expected value. After estimation, the model effects can be tested (via simulation) as the distribution of the observed data given that all model effects are zero is known. Two related simulation studies are presented that show that dispersion parameter estimation results in effect estimates that are competitive with other estimation methods (including other LASSO methods).     

Parameter estimation in general state-space models using particle methods

Particle filtering techniques are a set of powerful and versatile simulation-based methods to perform optimal state estimation in nonlinear non-Gaussian state-space models. If the model includes fixed parameters, a standard technique to perform parameter estimation consists of extending the state with the parameter to transform the problem into an optimal filtering problem. However, this approach requires the use of special particle filtering techniques which suffer from several drawbacks. We consider here an alternative approach combining particle filtering and gradient algorithms to perform batch and recursive maximum likelihood parameter estimation. An original particle method is presented to implement these approaches and their efficiency is assessed through simulation.     

波系在液体中的弹性管梁上的反射和辐射

本文研究入射波系在液体中的半无限弹性管梁的开口端的反射和辐射问题,此波系由管梁上的挠曲波和管内、管外液体中相应的表面波(声波)所组成.利用Fourier变换,将这个半无限问题严格地归结为求解Wiener-Hopf型方程.然后将液体和管梁的密度比作为小参数,用摄动法求近似解.文章着重研究了反射系数的计算,还给出了远场的辐射型式曲线.     

Robust estimation of periodic autoregressive processes in the presence of additive outliers

This paper suggests a robust estimation procedure for the parameters of the periodic AR (PAR) models when the data contains additive outliers. The proposed robust methodology is an extension of the robust scale and covariance functions given in, respectively, Rousseeuw and Croux (1993) [28], and Ma and Genton (2000) [23] to accommodate periodicity. These periodic robust functions are used in the Yule-Walker equations to obtain robust parameter estimates. The asymptotic central limit theorems of the estimators are established, and an extensive Monte Carlo experiment is conducted to evaluate the performance of the robust methodology for periodic time series with finite sample sizes. The quarterly Fraser River data was used as an example of application of the proposed robust methodology. All the results presented here give strong motivation to use the methodology in practical situations in which periodically correlated time series contain additive outliers.     

Maximum Likelihood Estimation of the Markov-Switching GARCH Model Based on a General Collapsing Procedure

The Markov-switching GARCH model allows for a GARCH structure with time-varying parameters. This flexibility is unfortunately undermined by a path dependence problem which complicates the parameter estimation process. This problem led to the development of computationally intensive estimation methods and to simpler techniques based on an approximation of the model, known as collapsing procedures. This article develops an original algorithm to conduct maximum likelihood inference in the Markov-switching GARCH model, generalizing and improving previously proposed collapsing approaches. A new relationship between particle filtering and collapsing procedures is established which reveals that this algorithm corresponds to a deterministic particle filter. Simulation and empirical studies show that the proposed method allows for a fast and accurate estimation of the model.     

AR模型辨识的稀疏结构迭代算法

模型估计是机器学习领域一个重要的研究内容,动态数据的模型估计是系统辨识和系统控制的基础.针对AR时间序列模型辨识问题,证明了在给定阶数下AR模型参数的最小二乘估计本质上也是一种矩估计.根据结构风险最小化原理,通过对模型拟合度和模型复杂度的折衷,提出了基于稀疏结构迭代的AR序列模型估计算法,并讨论了基于广义岭估计的最优正则化参数选取规则.数值结果表明,方法能以节省参数的方式有效地实现AR模型的辨识,比矩估计法结果有明显改善.     

Parameter estimation of delay differential equations: An integration-free LS-SVM approach

This paper introduces an estimation method based on Least Squares Support Vector Machines (LS-SVMs) for approximating time-varying as well as constant parameters in deterministic parameter-affine delay differential equations (DDEs). The proposed method reduces the parameter estimation problem to an algebraic optimization problem. Thus, as opposed to conventional approaches, it avoids iterative simulation of the given dynamical system and therefore a significant speedup can be achieved in the parameter estimation procedure. The solution obtained by the proposed approach can be further utilized for initialization of the conventional nonconvex optimization methods for parameter estimation of DDEs. Approximate LS-SVM based models for the state and its derivative are first estimated from the observed data. These estimates are then used for estimation of the unknown parameters of the model. Numerical results are presented and discussed for demonstrating the applicability of the proposed method.     

Optimal sensor placement for modal identification of structures using genetic algorithms—a case study: the olympic stadium in Cali,Colombia

Adequate sensor placement plays a key role in such fields as system identification, structural control, damage detection and structural health monitoring of flexible structures. In recent years, interest has increased in the development of methods for determining an arrangement of sensors suitable for characterizing the dynamic behavior of a given structure. This paper describes the implementation of genetic algorithms as a strategy for optimal placement of a predefined number of sensors. The method is based on the maximization of a fitness function that evaluates sensor positions in terms of natural frequency identification effectiveness and mode shape independence under various occupation and excitation scenarios using a custom genetic algorithm. A finite element model of the stadium was used to evaluate modal parameters used in the fitness function, and to simulate different occupation and excitation scenarios. The results obtained with the genetic algorithm strategy are compared with those obtained from applying the Effective Independence and Modal Kinetic Energy sensor placement techniques. The sensor distribution obtained from the proposed strategy will be used in a structural health monitoring system to be installed in the stadium.     

A note on maximum likelihood estimation for the complex-valued first-order autoregressive process

The maximum likelihood estimation of the parameters of a complex-valued zero-mean normal stationary first-order autoregressive process is investigated. It is shown that the likelihood function corresponding to independent replicated series is uniquely maximized at a point in the interior of the parameter space. A closed-form expression is given for the estimator.     

Optimization based on quasi-Monte Carlo sampling to design state estimators for non-linear systems

State estimation for a class of non-linear, continuous-time dynamic systems affected by disturbances is investigated. The estimator is assigned a given structure that depends on an innovation function taking on the form of a ridge computational model, with some parameters to be optimized. The behaviour of the estimation error is analysed by using input-to-state stability. The design of the estimator is reduced to the determination of the parameters in such a way as to guarantee the regional exponential stability of the estimation error in a disturbance-free setting and to minimize a cost function that measures the effectiveness of the estimation when the system is affected by disturbances. Stability is achieved by constraining the derivative of a Lyapunov function to be negative definite on a grid of points, via the penalization of the constraints that are not satisfied. Low-discrepancy sampling techniques, typical of quasi-Monte Carlo methods, are exploited in order to reduce the computational burden in finding the optimal parameters of the innovation function. Simulation results are presented to investigate the performance of the estimator in comparison with the extended Kalman filter and in dependence of the complexity of the computational model and the sampling coarseness.     

Numerical implementation and applications of a coupling algorithm for structural–acoustic models with unequal discretization and partially interfacing surfaces

The numerical implementation of a coupled finite element–boundary element algorithm for computing simultaneously the structural vibration and the associated acoustic field and a complete set of validation and application data is presented. The new developments in the coupling algorithm presented in this paper are associated with a capability for unequal mesh density between the structural and the acoustic model, division of both models into interfacing and non-interfacing zones, efficient computation of the coupling matrices, and incorporation of acoustic multiple connection constraints in the coupling computations. Applications are identified in the area of launch vehicle dynamics where a reverberant acoustic environment provides the excitation for computing either noise transmitted through flexible structures, or noise-induced vibration due to acoustic loads. Results and correlation to test data are presented for a fairing and an expansion nozzle of a rocket. Numerical results are also compared to an analytical solution for noise transmitted through a flexible cavity backed plate.     

钢筋混凝土旧工业厂房结构加固方案优选

当前人们选择旧工业厂房结构加固方案效率低下,且所考虑的因素较为片面,为了全面、高效地解决这一问题,通过综合考虑安全性、经济性、时间性、可行性和适用性等因素,以加固效果显著的工程案例为标准,以全面的18个参数为评价指标,构建了一种基于蛛网面积相似和形状相似的结构加固方案优选模型。该模型中首先运用熵权法确定18个指标权重,并将参数值归一化处理,随后运用Python计算蛛网结构相似度,检索出与目标范例最为相似的源范例。最后以结构加固效果显著的工程为例,验证了该模型能有效减少主观误差,具有较强的实用性,并以此模型优选出了某轧钢厂房结构加固方案。     

Bayesian network approach to multinomial parameter learning using data and expert judgments

One of the hardest challenges in building a realistic Bayesian Network (BN) model is to construct the node probability tables (NPTs). Even with a fixed predefined model structure and very large amounts of relevant data, machine learning methods do not consistently achieve great accuracy compared to the ground truth when learning the NPT entries (parameters). Hence, it is widely believed that incorporating expert judgments can improve the learning process. We present a multinomial parameter learning method, which can easily incorporate both expert judgments and data during the parameter learning process. This method uses an auxiliary BN model to learn the parameters of a given BN. The auxiliary BN contains continuous variables and the parameter estimation amounts to updating these variables using an iterative discretization technique. The expert judgments are provided in the form of constraints on parameters divided into two categories: linear inequality constraints and approximate equality constraints. The method is evaluated with experiments based on a number of well-known sample BN models (such as Asia, Alarm and Hailfinder) as well as a real-world software defects prediction BN model. Empirically, the new method achieves much greater learning accuracy (compared to both state-of-the-art machine learning techniques and directly competing methods) with much less data. For example, in the software defects BN for a sample size of 20 (which would be considered difficult to collect in practice) when a small number of real expert constraints are provided, our method achieves a level of accuracy in parameter estimation that can only be matched by other methods with much larger sample sizes (320 samples required for the standard machine learning method, and 105 for the directly competing method with constraints).     

Parameter estimation for generalized diffusion processes with reflected boundary

Reflected Ornstein-Uhlenbeck process is a process that returns continuously and immediately to the interior of the state space when it attains a certain boundary. It is an extended model of the traditional Ornstein-Uhlenbeck process being extensively used in finance as a one-factor short-term interest rate model. In this paper, under certain constraints, we are concerned with the problem of estimating the unknown parameter in the reflected Ornstein-Uhlenbeck processes with the general drift coefficient. The methodology of estimation is built upon the maximum likelihood approach and the method of stochastic integration. The strong consistency and asymptotic normality of estimator are derived. As a by-product of the use, we also establish Girsanov’s theorem of our model in this paper.     

Modified weighted squared error estimation procedures with special emphasis on the stable laws

Two families of parameter estimation procedures for the stablelaws based on a variant of the characteristic function are provided. The methodology which produces viable computational procedures for the stable laws is generally applicable to other families of distributions across avariety of settings. Both families of procedures may be described as a modified weighted chi-squared minimization procedure, and both explicitlytake account of constraints on the parameter space. Influence functions for and efficiencies of the estimators a r e given. If _l, x₂, ..., x_n is a random sample from an unknown distribution F, a method for determining the stable law to which F is attracted is developed. Procedures for regression and autoregression with stable error structurear e provided. A number of examples are given.     

Uniform stability for solutions of a structural acoustics PDE model with no added dissipative feedback

A rate of rational decay is obtained for smooth solutions of a PDE model, which has been used in the literature to describe structural acoustic flows. This structural acoustics model is composed of two distinct PDE systems: (i) a wave equation, to model the interior acoustic flow within the given cavity Ω and (ii) a structurally damped elastic equation, to describe time‐evolving displacements along the flexible portion Γ₀ of the cavity walls. Moreover, the extent of damping in this elastic component is quantified by parameter η∈[0,1]. The coupling between these two distinct dynamics occurs across the boundary interface Γ₀. Our main result is the derivation of uniform decay rates for classical solutions of this particular structural acoustic PDE, decay rates that are obtained without incorporating any additional boundary dissipative feedback mechanisms. In particular, in the case that full Kelvin–Voight damping is present in fourth‐order elastic dynamics, that is, the structural acoustics system as it appears in the literature, solutions that correspond to smooth initial data decay at a rate of . By way of deriving these stability results, necessary a priori inequalities for a certain static structural acoustics PDE model are generated here; these inequalities ultimately allow for an application of a recently derived resolvent criterion for rational decay. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimal observation network in geostatistics and underground hydrology

Mathematical models and algorithms for the optimal design of data collection for regionalized variables are presented. The topics considered subsume as a special case optimal drilling strategies in hydrology, the mining industries and other geostatistical applications. In these disciplines an optimal design is a critical consideration since data, can only be obtained through an expensive drilling process.The methods given here are based on the theory of regionalized variables and of kriging. The basis of the methods for locating a single additional data point, and for locating multiple points, is the theory of minimizing uncertainty in parameter estimation. That is, the possible locations of additional points must be determined on the basis of surface analysis with respect to the projected costs of obtaining this data.After a summary of basic kriging techniques, four models are discussed. The first deals with the optimal location problem for a single experimental point, and the second, third and fourth models pertain to the case of multiple additional points. (Unfortunately the repeated application of the single-point model leads only to approximations of the global optima, since the global optima are usually unobtainable as a simple sum of the partial optima.) In the second model, an optimal regular observation network is to be designed to minimize the uncertainty of the estimation process subject to either the given number of additional data, or an upper bound for the cost of the additional data. In the fourth model, the number or cost of additional points is minimized subject to bounded uncertainty conditions. Finally, a numerical example will be used to illustrate the models and algorithms.     

Constructing C1 triangular patch of degree six by the Boolean sum of an approximation operator and an interpolation operator

A new method to construct C¹ triangular patches which satisfy the given boundary curves and cross-boundary slopes is presented. The Boolean sum of an approximation operator and an interpolation operator is employed to construct the triangular patch. The approximation operator is used to construct a polynomial patch of degree six. The polynomial of degree six affords more freedoms, which makes the approximation operator not only approximate the given boundary interpolation conditions but also have a better approximation precision in the interior of the triangle, so that the triangular patch has a better precision on both the boundary and the interior of the triangular domain. The interpolation operator is utilized to build an interpolation patch which satisfies the given boundary conditions. The Boolean sum of the approximation and interpolation patches forms the triangular patch. Comparison results of the new method with other three methods are given.     

Reserve assemblage of critical areas: A zero-one programming approach

The problem of selecting land for inclusion within a protected reserve is formulated as a zero-one programming model. The model seeks to minimize the cost of delineating a reserve which protects critical habitat areas and significant biogeographic areas. As well, the provision of a buffer zone around an interior or core area is addressed, as are the spatial properties of contiguity and compactness. The model is applicable to both regular and irregular parcel systems. Two techniques that combines post-simplex branching and bounding with objective function bounding are presented for efficiently generating exact solutions. A hypothetical example demonstrates that medium-sized problems can be solved with modest computational effort.