STATIONARY TANGENT: THE DISCRETE AND NON-SMOOTH CASE

Abstract. In Keich (2000 ),we define a stationary tangent process, or a locally optimal stationary approximation, to a real non-stationary smooth Gaussian process. This paper extends the idea by constructing a discrete tangent – a `locally' optimal stationary approximation – for a discrete time, real Gaussian process. Analogously to the smooth case, our construction relies on a generalization of the recursion formula for the orthogonal polynomials of the spectral distribution function. More precisely, we use a generalization of the Schur parameters to identify the stationary tangent. By way of discretizing, we later demonstrate how this tangent can be used to obtain `good' local stationary approximations to non-smooth continuous time, real Gaussian processes. Further, we demonstrate how, analogously to the curvatures in the smooth case, the Schur parameters can be used to determine the order of stationarity of a non-smooth process.     

Bootstrapping the Local Periodogram of Locally Stationary Processes

Abstract. Locally stationary processes are non‐stationary stochastic processes the second‐order structure of which varies smoothly over time. In this paper, we develop a method to bootstrap the local periodogram of a locally stationary process. Our method generates pseudo local periodogram ordinates by combining a parametric time and non‐parametric frequency domain bootstrap approach. We first fit locally a time varying autoregressive model so as to capture the essential characteristics of the underlying process. A locally calculated non‐parametric correction in the frequency domain is then used so as to improve upon the locally parametric autoregressive fit. As an application, we investigate theoretically the asymptotic properties of the bootstrap method proposed applied to the class of local spectral means, local ratio statistics and local spectral density estimators. Some simulations demonstrate the ability of our method to give accurate estimates of the quantities of interest in finite sample situations and an application to a real‐life data‐set is presented.     

Locally Weighted Learning

This paper surveys locally weighted learning, a form of lazy learning and memory-based learning, and focuses on locally weighted linear regression. The survey discusses distance functions, smoothing parameters, weighting functions, local model structures, regularization of the estimates and bias, assessing predictions, handling noisy data and outliers, improving the quality of predictions by tuning fit parameters, interference between old and new data, implementing locally weighted learning efficiently, and applications of locally weighted learning. A companion paper surveys how locally weighted learning can be used in robot learning and control.     

A two-stage algorithm for identification of nonlinear dynamic systems

This paper investigates the two-stage stepwise identification for a class of nonlinear dynamic systems that can be described by linear-in-the-parameters models, and the model has to be built from a very large pool of basis functions or model terms. The main objective is to improve the compactness of the model that is obtained by the forward stepwise methods, while retaining the computational efficiency. The proposed algorithm first generates an initial model using a forward stepwise procedure. The significance of each selected term is then reviewed at the second stage and all insignificant ones are replaced, resulting in an optimised compact model with significantly improved performance. The main contribution of this paper is that these two stages are performed within a well-defined regression context, leading to significantly reduced computational complexity. The efficiency of the algorithm is confirmed by the computational complexity analysis, and its effectiveness is demonstrated by the simulation results.     

局部散射源参数估计的非线性算子方法

本文利用单次快摄数据的两个非线性算子估计局部散射源中心波达方向和角扩展,与多维参数搜索和其他低复杂性的局部散射源参数估计算法不同,非线性算子方法给出了单次快摄的局部散射源参数估计的闭式解,无需进行多维搜索和子空间分解。     

一类非线性脉冲发展方程的最优反馈控制

本文考虑受控系统为Banach空间中一类G0紧半群的非线性脉冲积微分方程的最优反馈控制问题。首先证明容许控制对的存在性,进一步对Lagrange问题给出了一个新的存在性定理。     

根据波速计算多相土石地基压实度的理论模型

本文基于多相复合介质的波动传播特性，导出介质内纵、横波速的理论计算公式。通过对影响因素分析，建立了横波波速与土石复合介质的干密度之间的近似理论关系。在此基础上，推导出土石地基压实度的波速计算理论模型的近似表达式。最后进行了现场地基的波速测试和灌砂法测试，通过理论计算和灌砂法测试结果的对比分析，表明该近似模型是可行的，并且其在对非均匀土石复合地基的压实质量评价中优越于传统的密度法。     

基于局部线性嵌入和支持向量机回归的TBM施工参数预测

依托吉林引松工程开展隧道掘进机（TBM）施工参数预测研究,提出TBM施工数据分段提取算法,提取上升段前30 s的总推进力、刀盘转速、推进速度、刀盘扭矩、刀盘转速电位器设定值、推进速度电位器设定值、贯入度、贯入度指数(FPI)、扭矩切深指数(TPI)9个参数作为输入;通过局部线性嵌入（LLE）完成对上升段数据特征的降维;基于支持向量机回归（SVR）建立TBM施工控制参数（推进速度、刀盘转速）和负载参数（总推进力、刀盘扭矩）预测模型. 分析是否结合前一掘进循环的FPI、TPI指数进行预测对预测效果的影响. 结果表明,上述方法在推进速度、刀盘转速、总推进力、刀盘扭矩的预测中均取得了较好的预测效果,平均预测绝对百分比误差均小于15%,验证了该预测方法的有效性,该方法可以为TBM现场施工提供指导.     

无理数字典码的测试数据压缩方案

提出了一种无理数字典码的测试数据压缩方案,能有效地压缩芯片测试数据。方案利用无理数序列建立字典,编码时只需进行相容性检查,无需填充无关位,简化了操作步骤;同时,选择局部压缩率最大的一组数据作为最终编码结果,保证压缩效果可以达到局部最优。对ISCAS 89标准电路Mintest集的实验结果显示,该方案的压缩效果优于传统压缩方法,如Golomb码、FDR码、混合定变长码等。     

浅析水利工程中混凝土检测试验及其质量控制措施

现阶段,混凝土技术在水利工程中的应用越来越广,而水利工程的建设质量关系着人民群众的生命财产安全,因此,混凝土的质量控制对水利工程整体质量的控制具有重要意义。从混凝土检测试验的角度出发,结合水利工程施工的实际,对水利工程中混凝土检测试验及其质量控制措施进行深入的研究。