Modelling and prediction of machining errors using ARMAX and NARMAX structures

Forecasting compensatory control, which was first proposed by Wu [ASME J. Eng. Ind. 99 (1977) 708], has been successfully employed to improve the accuracy of workpieces in various machining operations. This low-cost approach is based on on-line stochastic modelling and error compensation. The degree of error improvement depends very much on the accuracy of the modelling technique, which can only be performed on-line in a real-time recursive manner. In this study, the effect of the control input (i.e. the cutting force) is considered in the development of the error models, and the formulation of recursive exogenous autoregressive moving average (ARMAX) models becomes necessary. The nonlinear ARMAX or NARMAX model is also used to represent this nonlinear process. ARMAX and NARMAX models of different autoregressive (AR), moving average (MA) and exogenous (X) orders are proposed and their identifications are based on the recursive extended least square (RELS) method and the neural network (NN) method, respectively. An analysis of the computational results has confirmed that the NARMAX model and the NN method are superior to the ARMAX model and the RELS method in forecasting future machining errors, as indicated by its higher combined coefficient of efficiency.     

Thermal behaviour prediction utilizing artificial neural networks for an open office

This study investigates a neural network-based non-linear autoregressive model with external inputs (NNARX), a non-linear autoregressive moving average model with external inputs (NNARMAX), and a non-linear output error model (NNOE) to predict the thermal behaviour of an open-plan office in a modern commercial building. External and internal climate data recorded over one summer, autumn and winter season were used to build and validate the models. The paper illustrates the potential of using these models to predict room temperature and relative humidity for different time scales ahead (30 min or 2 h ahead). The prediction performance is evaluated using the criteria of goodness of fit, coefficient of determination, mean absolute error and mean squared error between predicted model output and real measurements. To obtain an optimal network structure (avoiding overfitting) after training, a pruning algorithm called optimal brain surgeon (OBS) was used to remove unnecessary input signals, weights and hidden neurons. The results demonstrate that all models provide reasonably good predictions but the NNARX and NNARMAX models outperform the NNOE model. These models can all potentially be used for improving the performance of thermal environment control systems.     

Two-stage least squares based iterative estimation algorithm for CARARMA system modeling

For stochastic systems described by the controlled autoregressive autoregressive moving average (CARARMA) models, a new-type two-stage least squares based iterative algorithm is proposed for identifying the system model parameters and the noise model parameters. The basic idea is based on the interactive estimation theory and to estimate the parameter vectors of the system model and the noise model, respectively. The simulation results indicate that the proposed algorithm is effective.     

基于ARMA模型和自由振动提取技术的海洋平台结构参数识别

用随机减量方法提取海洋平台结构在随机环境荷载非白噪声输入下的自由振动信号和用ARMA(Auto Regressive Moving Average)模型对自由振动数据建模。为了消除平台输出信号中有色噪声的影响,在随机减量系统中加人了一个虚拟系统,并采用导通条件和前导点技术使自由振动提取过程仍在有色输人的状态下进行。同时为了消除参数识别的多值性,提出了采用MA系数修正技术识别海洋平台结构的频率和阻尼动力参数的方法,最后用该套技术对海洋平台结构试验模型进行了参数识别,结果表明该方法具有较好的效果和在线识别使用价值。     

Asymptotic properties of autoregressive integrated moving average processes

In this paper we study the asymptotic behavior of so-called autoregressive integrated moving average processes. These processes constitute a large class of stochastic difference equations which includes among many other well-known processes the simple one-dimensional random walk. They were dubbed by G.E.P. Box and G.M. Jenkins who found them to provide useful models for studying and controlling the behavior of certain economic variables and various chemical processes. We show that autoregressive integrated moving average processes are asymptotically normally distributed, and that the sample paths of such processes satisfy a law of the iterated logarithm. We also establish a law which determines the time spent by a sample path on one or the other side of the “trend line” of the process.     

Low-order self-tuner for fault-tolerant control of a class of unknown nonlinear stochastic sampled-data systems

Based on the modified state-space self-tuning control (STC) via the observer/Kalman filter identification (OKID) method, an effective low-order tuner for fault-tolerant control of a class of unknown nonlinear stochastic sampled-data systems is proposed in this paper. The OKID method is a time-domain technique that identifies a discrete input–output map by using known input–output sampled data in the general coordinate form, through an extension of the eigensystem realization algorithm (ERA). Then, the above identified model in a general coordinate form is transformed to an observer form to provide a computationally effective initialization for a low-order on-line “auto-regressive moving average process with exogenous (ARMAX) model”-based identification. Furthermore, the proposed approach uses a modified Kalman filter estimate algorithm and the current-output-based observer to repair the drawback of the system multiple failures. Thus, the fault-tolerant control (FTC) performance can be significantly improved. As a result, a low-order state-space self-tuning control (STC) is constructed. Finally, the method is applied for a three-tank system with various faults to demonstrate the effectiveness of the proposed methodology.     

Dynamically evolving Gaussian spatial fields

We discuss general non-stationary spatio-temporal surfaces that involve dynamics governed by velocity fields. The approach formalizes and expands previously used models in analysis of satellite data of significant wave heights. We start with homogeneous spatial fields. By applying an extension of the standard moving average construction we obtain models which are stationary in time. The resulting surface changes with time but is dynamically inactive since its velocities, when sampled across the field, have distributions centered at zero. We introduce a dynamical evolution to such a field by composing it with a dynamical flow governed by a given velocity field. This leads to non-stationary models. The models are extensions of the earlier discretized autoregressive models which account for a local velocity of traveling surface. We demonstrate that for such a surface its dynamics is a combination of dynamics introduced by the flow and the dynamics resulting from the covariance structure of the underlying stochastic field. We extend this approach to fields that are only locally stationary and have their parameters varying over a larger spatio-temporal horizon.     

ARMA model order and parameter estimation using genetic algorithms

A new method for simultaneously determining the order and the parameters of autoregressive moving average (ARMA) models is presented in this article. Given an ARMA (p, q) model in the absence of any information for the order, the correct order of the model (p, q) as well as the correct parameters will be simultaneously determined using genetic algorithms (GAs). These algorithms simply search the order and the parameter spaces to detect their correct values using the GA operators. The proposed method works on the principle of maximizing the GA fitness value relying on the deviation between the actual plant output, with or without an additive noise, and the estimated plant output. Simulation results show in detail the efficiency of the proposed approach. In addition to that, a practical model identification and parameter estimation is conducted in this article with results obtained as desired. The new method is compared with other well-known methods for ARMA model order and parameter estimation.     

Moving least squares based sensitivity analysis for models with dependent variables

For models with dependent input variables, sensitivity analysis is often a troublesome work and only a few methods are available. Mara and Tarantola in their paper (“Variance-based sensitivity indices for models with dependent inputs”) defined a set of variance-based sensitivity indices for models with dependent inputs. We in this paper propose a method based on moving least squares approximation to calculate these sensitivity indices. The new proposed method is adaptable to both linear and nonlinear models since the moving least squares approximation can capture severe change in scattered data. Both linear and nonlinear numerical examples are employed in this paper to demonstrate the ability of the proposed method. Then the new sensitivity analysis method is applied to a cantilever beam structure and from the results the most efficient method that can decrease the variance of model output can be determined, and the efficiency is demonstrated by exploring the dependence of output variance on the variation coefficients of input variables. At last, we apply the new method to a headless rivet model and the sensitivity indices of all inputs are calculated, and some significant conclusions are obtained from the results.     

Separation of random noise models from seasonal time series data

The autocorrelation function of seasonal time series data is shown to have peaks which occur at the correlation lags equal to the integer multiples of the fundamental period that is present in the series. This property is shown to be valid even if some of the harmonics including the fundamental are removed from the time series data. Using this property, an analytical procedure is presented for estimating the variance of the white noise generating the low frequency random walk model present in the data. The procedure is similarly extended to estimate the variance of white noise generating the autoregressive (AR) and moving average (MA) noise models. The method is validated on several seasonal time series data whose components are known a priori.     

生产安全事故宏观发展态势的计量经济学研究

为了研究工矿商贸就业人员10万人生产安全事故死亡率时间序列变化特征,基于我国行业生产安全事故死亡人数及第二、三产业就业人员数量等2方面年度统计数据,通过研究事故死亡率时间序列的自回归移动平均过程,论文构建了事故死亡率时间序列的分阶段自回归移动平均模型.研究表明:工矿商贸行业10万人事故死亡率变化趋势具有明显的分阶段波动特征,事故死亡率序列均为趋势平稳过程;序列当期观测值与滞后1期观测值具有显著的自相关性;各阶段事故率自回归移动平均模型结构不尽相同;特征描述模型为正确把握我国安全生产状况及趋势提供理论依据.     

ARMAX时间序列模型异常点及异常点斑片的估计和检测

将通常的Gibbs抽样和自适应的Gibbs抽样算法用于带有外生变量的自回归移动平均时间序列(ARMAX)模型的Bayes分析,首先采用一些方法消除ARMAX模型中输入(外生变量)序列的影响,然后在前人工作的基础上给出了一种类似的挖掘相应时间序列中的异常点及异常点斑片的方法.说明了自适应的Gibbs抽样算法也能够有效地检测ARMAX模型中孤立的附加型异常点及异常点斑片.实际的和模拟的结果也显示这些方法可以明显减少掩盖和淹没现象的发生,这是对已有工作的推广和扩充.     

Applications of information theory,genetic algorithms,and neural models to predict oil flow

This work introduces a new information-theoretic methodology for choosing variables and their time lags in a prediction setting, particularly when neural networks are used in non-linear modeling. The first contribution of this work is the Cross Entropy Function (XEF) proposed to select input variables and their lags in order to compose the input vector of black-box prediction models. The proposed XEF method is more appropriate than the usually applied Cross Correlation Function (XCF) when the relationship among the input and output signals comes from a non-linear dynamic system. The second contribution is a method that minimizes the Joint Conditional Entropy (JCE) between the input and output variables by means of a Genetic Algorithm (GA). The aim is to take into account the dependence among the input variables when selecting the most appropriate set of inputs for a prediction problem. In short, theses methods can be used to assist the selection of input training data that have the necessary information to predict the target data. The proposed methods are applied to a petroleum engineering problem; predicting oil production. Experimental results obtained with a real-world dataset are presented demonstrating the feasibility and effectiveness of the method.     

Technical efficiency estimation with multiple inputs and multiple outputs using regression analysis

Regression and linear programming provide the basis for popular techniques for estimating technical efficiency. Regression-based approaches are typically parametric and can be both deterministic or stochastic where the later allows for measurement error. In contrast, linear programming models are nonparametric and allow multiple inputs and outputs. The purported disadvantage of the regression-based models is the inability to allow multiple outputs without additional data on input prices. In this paper, deterministic cross-sectional and stochastic panel data regression models that allow multiple inputs and outputs are developed. Notably, technical efficiency can be estimated using regression models characterized by multiple input, multiple output environments without input price data. We provide multiple examples including a Monte Carlo analysis.     

Hierarchical Bayesian autoregressive models for large space–time data with applications to ozone concentration modelling

Increasingly large volumes of space–time data are collected everywhere by mobile computing applications, and in many of these cases, temporal data are obtained by registering events, for example, telecommunication or Web traffic data. Having both the spatial and temporal dimensions adds substantial complexity to data analysis and inference tasks. The computational complexity increases rapidly for fitting Bayesian hierarchical models, as such a task involves repeated inversion of large matrices. The primary focus of this paper is on developing space–time autoregressive models under the hierarchical Bayesian setup. To handle large data sets, a recently developed Gaussian predictive process approximation method is extended to include autoregressive terms of latent space–time processes. Specifically, a space–time autoregressive process, supported on a set of a smaller number of knot locations, is spatially interpolated to approximate the original space–time process. The resulting model is specified within a hierarchical Bayesian framework, and Markov chain Monte Carlo techniques are used to make inference. The proposed model is applied for analysing the daily maximum 8‐h average ground level ozone concentration data from 1997 to 2006 from a large study region in the Eastern United States. The developed methods allow accurate spatial prediction of a temporally aggregated ozone summary, known as the primary ozone standard, along with its uncertainty, at any unmonitored location during the study period. Trends in spatial patterns of many features of the posterior predictive distribution of the primary standard, such as the probability of noncompliance with respect to the standard, are obtained and illustrated. Copyright © 2012 John Wiley & Sons, Ltd.     

A generalized probabilistic edge-based smoothed finite element method for elastostatic analysis of Reissner–Mindlin plates

Probabilistic analysis is becoming more important in mechanical science and real-world engineering applications. In this work, a novel generalized stochastic edge-based smoothed finite element method is proposed for Reissner–Mindlin plate problems. The edge-based smoothing technique is applied in the standard FEM to soften the over-stiff behavior of Reissner–Mindlin plate system, aiming to improve the accuracy of predictions for deterministic response. Then, the generalized nth order stochastic perturbation technique is incorporated with the edge-based S-FEM to formulate a generalized probabilistic ES-FEM framework (GP_ES-FEM). Based upon a general order Taylor expansion with random variables of input, it is able to determine higher order probabilistic moments and characteristics of the response of Reissner–Mindlin plates. The significant feature of the proposed approach is that it not only improves the numerical accuracy of deterministic output quantities with respect to a given random variable, but also overcomes the inherent drawbacks of conventional second-order perturbation approach, which is satisfactory only for small coefficients of variation of the stochastic input field. Two numerical examples for static analysis of Reissner–Mindlin plates are presented and verified by Monte Carlo simulations to demonstrate the effectiveness of the present method.     

Spatial autoregressive and moving average Hilbertian processes

This paper addresses the introduction and study of structural properties of Hilbert-valued spatial autoregressive processes (SARH(1) processes), and Hilbert-valued spatial moving average processes (SMAH(1) processes), with innovations given by two-parameter (spatial) matingale differences. For inference purposes, the conditions under which the tensorial product of standard autoregressive Hilbertian (ARH(1)) processes (respectively, of standard moving average Hilbertian (MAH(1)) processes) is a standard SARH(1) process (respectively, it is a standard SMAH(1) process) are studied. Examples related to the spatial functional observation of two-parameter Markov and diffusion processes are provided. Some open research lines are described in relation to the formulation of SARMAH processes, as well as General Spatial Linear Processes in Functional Spaces.     

System availability behavior of some stationary dependent sequences

We consider the system availability behavior of a one-unit repairable system when the failure and the repair times are generated by a stationary dependent sequence of random variables. We obtain the general expression for the point availability, and discuss the nature of the availability measure for two time series models: a first-order exponential moving average process and a first-order exponential autoregressive process.     

Stepwise selection of variables in data envelopment analysis: Procedures and managerial perspectives

One of the most important steps in the application of modeling using data envelopment analysis (DEA) is the choice of input and output variables. In this paper, we develop a formal procedure for a “stepwise” approach to variable selection that involves sequentially maximizing (or minimizing) the average change in the efficiencies as variables are added or dropped from the analysis. After developing the stepwise procedure, applications from classic DEA studies are presented and the new managerial insights gained from the stepwise procedure are discussed. We discuss how this easy to understand and intuitively sound method yields useful managerial results and assists in identifying DEA models that include variables with the largest impact on the DEA results.     

A low-order active fault-tolerant state space self-tuner for the unknown sampled-data nonlinear singular system using OKID and modified ARMAX model-based system identification

In this paper, we present two control schemes for the unknown sampled-data nonlinear singular system. One is an observer-based digital redesign tracker with the state-feedback gain and the feed-forward gain based on off-line observer/Kalman filter identification (OKID) method. The presented control scheme is able to make the unknown sampled-data nonlinear singular system to well track the desired reference signal. The other is an active fault tolerance state-space self-tuner using the OKID method and modified autoregressive moving average with exogenous inputs (ARMAX) model-based system identification for unknown sampled-data nonlinear singular system with input faults. First, one can apply the off-line OKID method to determine the appropriate (low-) order of the unknown system order and good initial parameters of the modified ARMAX model to improve the convergent speed of recursive extended-least-squares (RELS) method. Then, based on modified ARMAX-based system identification, a corresponding adaptive digital control scheme is presented for the unknown sampled-data nonlinear singular system with immeasurable system state. Moreover, in order to overcome the interference of input fault, one can use a fault-tolerant control scheme for unknown sampled-data nonlinear singular system by modifying the conventional self-tuner control (STC). The presented method can effectively cope with partially abrupt and/or gradual system input faults. Finally, some illustrative examples including a real circuit system are given to demonstrate the effectiveness of the presented design methodologies.