Nonlinear parameter estimation through particle swarm optimization

Parameter estimation procedures are very important in the chemical engineering field for development of mathematical models, since design, optimization and advanced control of chemical processes depend on model parameter values obtained from experimental data. Model nonlinearity makes the estimation of parameter and the statistical analysis of parameter estimates more difficult and more challenging. In this work, it is shown that many of these difficulties can be overcome with the use of heuristic optimization methods, such as the particle swarm optimization (PSO) method. Parameter estimation problems are solved here with PSO and it is shown that the PSO method is efficient for both minimization and construction of the confidence region of parameter estimates. Moreover, it is shown that the elliptical approximation of confidence regions of nonlinear model parameters can be very poor sometimes and that more accurate likelihood confidence regions can be constructed with PSO, allowing for more reliable statistical analysis of the significance of parameter estimates.     

Maximum likelihood estimation of higher‐order integer‐valued autoregressive processes

Abstract. In this article, we extend the earlier work of Freeland and McCabe [Journal of time Series Analysis (2004) Vol. 25, pp. 701–722] and develop a general framework for maximum likelihood (ML) analysis of higher‐order integer‐valued autoregressive processes. Our exposition includes the case where the innovation sequence has a Poisson distribution and the thinning is binomial. A recursive representation of the transition probability of the model is proposed. Based on this transition probability, we derive expressions for the score function and the Fisher information matrix, which form the basis for ML estimation and inference. Similar to the results in Freeland and McCabe (2004) , we show that the score function and the Fisher information matrix can be neatly represented as conditional expectations. Using the INAR(2) specification with binomial thinning and Poisson innovations, we examine both the asymptotic efficiency and finite sample properties of the ML estimator in relation to the widely used conditional least squares (CLS) and Yule–Walker (YW) estimators. We conclude that, if the Poisson assumption can be justified, there are substantial gains to be had from using ML especially when the thinning parameters are large.     

基于混合差分进化算法的软测量时延参数估计

时延参数估计是系统控制与信号处理的关键问题。通过构造一个适当的适应度函数,将软测量系统的时延参数估计问题转化为一个多维非线性优化问题,然后利用混合差分进化算法的全局搜索能力求解该优化问题。对两个典型问题进行了仿真实验,仿真结果表明了混合算法的有效性和鲁棒性。以石油炼制工业中典型装置常压塔为例,对其一线航空煤油的闪点软测量进行了应用验证,结果表明,时延参数估计的引入大大提高了软测量模型的精度,证实了混合差分进化算法的有效性。     

Calibration of a hexapod machine tool using a redundant leg

Parallel configurations are recently being applied to the machine tool with the hopes of greater rigidity, stability, and accuracy than conventional multi-axis structures allow. However, the many calibration methods presently available for serial machine tools are not applicable to hexapod type structures. A calibration method is presented that uses a ball–bar or other simple length measuring device to act as an ‘extra leg,’ allowing calibration of the hexapod's true kinematic parameters. This method utilizes a total least squares minimization, does not require any special hexapod configuration or difficult six degree of freedom pose measurements, and is effective with as few as one additional length sensor. Selection of calibration pose sets is briefly discussed, as well as the influence of measurement noise on calibration accuracy. Simulations show the potential for this algorithm to significantly reduce errors to the point where machining errors are within 5–10 times the measurement errors.     

Density and viscosity of vegetable oils

A generalized method was developed to estimate the liquid density of vegetable oils and fatty acids. The correlation for vegetable oils was based on fatty acid critical properties and composition of the oil. The correlations predicted the density of vegetable oils and fatty acids with an average absolute deviation of 0.21 and 0.77%, respectively. The present method is slightly more accurate in predicting vegetable oil density and simpler than the method of Halvorsen et al. Also, a method is introduced that predicts viscosity from density data, thus relating two key properties of vegetable oils.     

Robust Estimation in Vector Autoregressive Moving-Average Models

Bustos and Yohai proposed a class of robust estimates for autoregressive moving-average (ARMA) models based on residual autocovariances (RA estimates). In this paper an affine equivariant generalization of the RA estimates for vector ARMA processes is given. These estimates are asymptotically normal and, when the innovations have an elliptical distribution, their asymptotic covariance matrix differs only by a scalar factor from the covariance matrix corresponding to the maximum likelihood estimate. A Monte Carlo study confirms that the RA estimates are efficient under normal errors and robust when the sample contains outliers. A robust multivariate goodness-of-fit test based on the RA estimates is also obtained.     

基于STFT时频谱系数收缩的信号降噪方法

针对旋转机械故障振动信号的降噪问题,提出一种基于短时Fourier变换(short time Fourier transform,简称STFT)时频谱系数收缩的信号降噪方法。先将信号进行STFT,得到其时频谱。由于谱系数为复数,故根据模值大小进行谱系数收缩,并利用步长迭代算法在0到谱系数最大模值的区间内估计最优阈值。迭代运算过程中,首先,分别采用基本的硬阈值函数和软阈值函数进行系数收缩;然后,以改进风险函数为阈值评价标准,估计最优阈值;最后,利用最优阈值重新进行谱系数收缩,对得到的新谱进行STFT逆变换,重构降噪后的时域信号。仿真信号与试验数据的处理结果表明,利用所估计的最优阈值,STFT时频谱系数硬、软阈值函数收缩方法均能够实现噪声混合信号的降噪。     

Application of principal components analysis and signal-to-noise ratio for calibration of spectrophotometric analysers of food

Spectrophotometric analysers of food, being instruments for determination of the composition of food products and ingredients, are today of growing importance for food industry, as well as for food distributors and consumers. Their metrological performance significantly depends on the numerical performance of available means for spectrophotometric data processing; in particular – the means for calibration of analysers. In this paper, a new algorithm for this purpose is proposed, viz. the algorithm using principal components analysis. It is almost as efficient as partial least squares algorithms of calibration, but much simpler. It is fully automatic, viz. the selection of the most informative components is based on the signal-to-noise ratio characterising processed measurement data. The practical effectiveness of the proposed algorithm is demonstrated on a test problem consisting in determination of the concentrations of components of trinary oil mixtures.     

A novel method for estimating the track-soil parameters based on Kalman and improved strong tracking filters

A tracked vehicle has been widely used in exploring unknown environments and military fields. In current methods for suiting soil conditions, soil parameters need to be given and the traction performance cannot always be satisfied on soft soil. To solve the problem, it is essential to estimate track-soil parameters in real-time. Therefore, a detailed mathematical model is proposed for the first time. Furthermore, a novel algorithm which is composed of Kalman filter (KF) and improved strong tracking filter (STF) is developed for online track-soil estimation and named as KF–ISTF. By this method, the KF is used to estimate slip parameters, and the ISTF is used to estimate motion states. Then the key soil parameters can be estimated by using a suitable soil model. The experimental results show that equipped with the estimation algorithm, the proposed model can be used to estimate the track-soil parameters, and make the traction performance satisfied with soil conditions.