Nonlinear total least-squares variance component estimation for GM(1,1)model

The solution of the grey model(GM(1,1)model)generally involves equal-precision observations,and the(co)variance matrix is established from the prior information.However,the data are generally available with unequal-precision measurements in reality.To deal with the errors of all observations for GM(1,1)model with errors-in-variables(EIV)structure,we exploit the total least-squares(TLS)algorithm to estimate the parameters of GM(1,1)model in this paper.Ignoring that the effect of the improper prior stochastic model and the homologous observations may degrade the accuracy of parameter estimation,we further present a nonlinear total least-squares variance component estimation approach for GM(1,1)model,which resorts to the minimum norm quadratic unbiased estimation(MINQUE).The practical and simulative experiments indicate that the presented approach has significant merits in improving the predictive accuracy in comparison with control methods.

Composition Estimation of Reactive Batch Distillation by Using Adaptive Neuro-Fuzzy Inference System

Composition estimation plays very important role in plant operation and control.Extended Kalman filter(EKF) is one of the most common estimators,which has been used in composition estimation of reactive batch distillation,but its performance is heavily dependent on the thermodynamic modeling of vapor-liquid equilibrium,which is difficult to initialize and tune.In this paper an inferential state estimation scheme based on adaptive neuro-fuzzy inference system(ANFIS) ,which is a model base estimator,is employed for composition estimation by using temperature measurements in multicomponent reactive batch distillation.The state estimator is supported by data from a complete dynamic model that includes component and energy balance equations accompanied with thermodynamic relations and reaction kinetics.The mathematical model is verified by pilot plant data.The simulation results show that the ANFIS estimator provides reliable and accurate estimation for component concentrations in reactive batch distillation.The estimated states form a basis for improving the performance of reactive batch distillation either through decision making of an operator or through an automatic closed-loop control scheme.

NEW EFFICIENT ORDER-RECURSIVE LEAST-SQUARES ALGORITHMS

Order-recursive least-squares(ORLS)algorithms are applied to the prob-lems of estimation and identification of FIR or ARMA system parameters where a fixedset of input signal samples is available and the desired order of the underlying model isunknown.On the basis of several universal formulae for updating nonsymmetric projec-tion operators,this paper presents three kinds of LS algorithms,called nonsymmetric,symmetric and square root normalized fast ORLS algorithms,respectively.As to the au-thors’ knowledge,the first and the third have not been so far provided,and the second isone of those which have the lowest computational requirement.Several simplified versionsof the algorithms are also considered.

A Real-time Updated Model Predictive Control Strategy for Batch Processes Based on State Estimation

Nonlinear model predictive control(NMPC) is an appealing control technique for improving the performance of batch processes, but its implementation in industry is not always possible due to its heavy on-line computation. To facilitate the implementation of NMPC in batch processes, we propose a real-time updated model predictive control method based on state estimation. The method includes two strategies: a multiple model building strategy and a real-time model updated strategy. The multiple model building strategy is to produce a series of sim-plified models to reduce the on-line computational complexity of NMPC. The real-time model updated strategy is to update the simplified models to keep the accuracy of the models describing dynamic process behavior. The me-thod is validated with a typical batch reactor. Simulation studies show that the new method is efficient and robust with respect to model mismatch and changes in process parameters.

LEAST-SQUARES MIXED FINITE ELEMENT METHOD FOR A CLASS OF STOKES EQUATION

A least-squares mixed finite element method was formulated for a class of Stokes equations in two dimensional domains. The steady state and the time-dependent Stokes' equations were considered. For the stationary equation, optimal H-t and L-2-error estimates are derived under the standard regularity assumption on the finite element partition ( the LBB-condition is not required). Far the evolutionary equation, optimal L-2 estimates are derived under the conventional Raviart-Thomas spaces.

面向飞机装配批架次完工时间的仿真预测方法

针对传统离散事件仿真方法缺乏对产品间差异化分析的局限性,提出一种面向飞机装配批架次作业过程的仿真预测方法。围绕飞机架次标签,研究对批架次装配作业过程中各类基本要素与交互关系的形式化定义,由此完成站位、整线仿真模型的构建;研究支持产品差异化分析的仿真推进框架与执行机制;以仿真结果数据为基础,提出基于区间估计法的架次完工时间预测方法。实验结果表明:该方法能准确地输出各架次预计完工时间的置信区间,为现场提供可靠的评估依据。

Online LS-SVM for function estimation and classification

An online algorithm for training LS-SVM (Least Square Support VectorMachines) was proposed for the application of function estimation and classification. Online LS-SVMmeans that LS-SVM can be trained in an incremental way, and can be pruned to get sparseapproximation in a decremental way. When a SV (Support Vector) is added or removed, the onlinealgorithm avoids computing large-scale matrix inverse. Thus the computation cost is reduced. Onlinealgorithm is especially useful to realistic function estimation problem such as systemidentification. The experiments with benchmark function estimation problem and classificationproblem show the validity of this online algorithm.

THE SUPERIORITY OF EMPIRICAL BAYES ESTIMATION OF PARAMETERS IN PARTITIONED NORMAL LINEAR MODEL

In this article,the empirical Bayes（EB）estimators are constructed for the estimable functions of the parameters in partitioned normal linear model.The superiorities of the EB estimators over ordinary least-squares（LS）estimator are investigated under mean square error matrix（MSEM）criterion.

Hybrid Differential Evolution for Estimation of Kinetic Parameters for Biochemical Systems

Determination of the optimal model parameters for biochemical systems is a time consuming iterative process. In this study, a novel hybrid differential evolution （DE） algorithm based on the differential evolution technique and a local search strategy is developed for solving kinetic parameter estimation problems. By combining the merits of DE with Gauss-Newton method, the proposed hybrid approach employs a DE algorithm for identifying promising regions of the solution space followed by use of Gauss-Newton method to determine the optimum in the identified regions. Some well-known benchmark estimation problems are utilized to test the efficiency and the robustness of the proposed algorithm compared to other methods in literature. The comparison indicates that the present hybrid algorithm outperforms other estimation techniques in terms of the global searching ability and the con- vergence speed. Additionally, the estimation of kinetic model parameters for a feed batch fermentor is carried out to test the applicability of the proposed algorithm. The result suggests that the method can be used to estimate suitable values of model oarameters for a comolex mathematical model.

Novel channel estimation model for OFDM in time-varying channel

A new channel estimation method for orthogonal frequency division multiplexing （OFDM） system with large subcarriers and serious intercarrier interference （ICI） is proposed. The channel frequency-domain （ CFD ） matrix of each delay path is factorized to the product of a diagonal delay matrix and a circular ICI matrix in this model. To reduce the coefficient number, the circular ICI ma- trix is squeezed by using Hamming-window as the reshaping pulse in the transmitter. Meanwhile, the elements of the diagonal delay matrix are approximated with a discrete prolate spheroidal basis ex- pansion model （DPS-BEM）. A least-square （LS） estimator is used to estimate the reduced channel coefficients. The proposed method is theoretically derived and simulated. The simulation results in- dicate that the model has good performance and is appropriate for various channel environments. The method also has low complexity and good spectral efficiency.

Crystallization Kinetics of Batch Spontaneous Nucleation of Potassium Nitrate

The batch cooling crystallization initiated from spontaneous nucleation for aqueous solution of potassium nitrate was studied. The concentration and transmittance data were acquired on line throughout the operation.Based on solute mass transfer in both liquid and solid phases, a kinetic model was deduced by assuming that the late period of primary nucleation resembles the initial period of the secondary nucleation. Nucleation and crystal growth stages were identified. Kinetic parameters were estimated piecewise from online experimental data and compared with those in literature. The estimated kinetic parameters for stages without apparent primary nucleation agreed well with those in literature. Further, a simulated concentration curve was also drawn from the estimated kinetic parameters and it matched well with that in experiment.

A Control Algorithm for the Optimization of Batch Reactor-Based Processes

Levenberg-Marquardt(LM)algorithm is applied for the optimization of the heat transfer of a batch reactor.The validity of the approach is verified through comparison with experimental results.It is found that the mathematical model can properly describe the heat transfer relationships characterizing the considered system,with the error being kept within±2℃.Indeed,the difference between the actual measured values and the model calculated value curve is within±1.5℃,which is in agreement with the model assumptions and demonstrates the reliability and effectiveness of the algorithm applied to the batch reactor heat transfer model.Therefore,the present work provides a theoretical reference for the conversion of practical problems in the field of chemical production into mathematical models.

Estimation of a Linear Model in Terms of Intra-Class Correlations of the Residual Error and the Regressors

Objectives: The objective is to analyze the interaction of the correlation structure and values of the regressor variables in the estimation of a linear model when there is a constant, possibly negative, intra-class correlation of residual errors and the group sizes are equal. Specifically: 1) How does the variance of the generalized least squares (GLS) estimator (GLSE) depend on the regressor values? 2) What is the bias in estimated variances when ordinary least squares (OLS) estimator is used? 3) In what cases are OLS and GLS equivalent. 4) How can the best linear unbiased estimator (BLUE) be constructed when the covariance matrix is singular? The purpose is to make general matrix results understandable. Results: The effects of the regressor values can be expressed in terms of the intra-class correlations of the regressors. If the intra-class correlation of residuals is large, then it is beneficial to have small intra-class correlations of the regressors, and vice versa. The algebraic presentation of GLS shows how the GLSE gives different weight to the between-group effects and the within-group effects, in what cases OLSE is equal to GLSE, and how BLUE can be constructed when the residual covariance matrix is singular. Different situations arise when the intra-class correlations of the regressors get their extreme values or intermediate values. The derivations lead to BLUE combining OLS and GLS weighting in an estimator, which can be obtained also using general matrix theory. It is indicated how the analysis can be generalized to non-equal group sizes. The analysis gives insight to models where between-group effects and within-group effects are used as separate regressors.

轧机轧制力的改进训练策略深度神经网络预测

为了提高双机架炉卷轧机的轧制力预测精度,提出了具有快速而高效训练策略的深度神经网络预测方法。介绍了双机架炉卷轧机的工作原理,分析了轧制力影响参数。在深度神经网络基础上,使用随机小批量的样本选取法,提高深度神经网络训练速度;提出自适应矩估计梯度优化算法,用于解决传统训练方法陷入局部极值的问题,从而给出了改进训练策略的深度神经网络轧制力预测方法。经轧制实验验证,改进深度神经网络的训练时间为226.15s,而传统网络的训练时间为862.93s;改进网络的预测误差绝大部分控制在3%以内,而传统网络的预测误差绝大部分控制在5%以内。以上数据表明,改进深度神经网络的训练速度和预测精度均远优于传统深度神经网络。

The mathematical weighting of GNSS observations based on different types of receivers/antennas and environmental conditions

Stochastic models play an important role in achieving high accuracy in positioning,the ideal estimator in the least-squares(LS)can be obtained only by using the suitable stochastic model.This study investigates the role of variance component estimation(VCE)in the LS method for Precise Point Positioning(PPP).This estimation is performed by considering the ionospheric-free(IF)functional model for code and the phase observation of Global Positioning System(GPS).The strategy for estimating the accuracy of these observations was evaluated to check the effect of the stochastic model in four modes:a)antenna type,b)receiver type,c)the tropospheric effect,and d)the ionosphere effect.The results show that using empirical variance for code and phase observations in some cases caused erroneous estimation of unknown components in the PPP model.This is because a constant empirical variance may not be suitable for various receivers and antennas under different conditions.Coordinates were compared in two cases using the stochastic model of nominal weight and weight estimated by LS-VCE.The position error difference for the east-west,north-south,and height components was 1.5 cm,4 mm,and 1.8 cm,respectively.Therefore,weight estimation with LS-VCE can provide more appropriate results.Eventually,the convergence time based on four elevation-dependent models was evaluated using nominal weight and LS-VCE weight.According to the results,the LS-VCE has a higher convergence rate than the nominal weight.The weight estimation using LS-VCE improves the convergence time in four elevation-dependent models by 11,13,12,and 9 min,respectively.

高斯变分推理的无人机状态与轨迹估计方法

针对目前的状态估计算法在面对非线性大批量状态时,存在的误差过大、算法迭代次数过多等问题,通过引入变分推断方法,提出了无人机轨迹的高斯变分推断(gaussian variational inference,GVI)精确估计方法.该方法首先通过提出基于高斯变分推断的损失函数,将状态估计问题转化为利用数据对后验进行近似的问题.然后,采用牛顿式更新以及梯度下降法的思想对损失函数、均值以及协方差矩阵进行优化迭代.使用该算法对无人机的状态以及轨迹进行估计,仿真结果表明,本算法精度较高.同时,本算法与最大后验估计(maximum a posteriori,MAP)算法相比,能够有效降低损失函数值,提高轨迹估计的精确性.

基于自适应加权的多传感器实时数据特征值提取

为实现监测数据的特征值提取,对传感器数据的预处理、时间维及空间维融合方法开展了研究。建立了实时数据融合模型,提出了基于3σ-grubbs检验的异常数据预处理方法,兼顾了异常数据剔除的速度与精度,能很好地消除疏失误差;对单个传感器数据采用分批估计原理进行融合,得到了特征估计值,实现了数据在时间维上的融合;通过对多个传感器的特征估计值采用自适应加权方法进行赋权,实现了数据在空间上的融合,并提出了考虑传感器精度的算法修正。实例计算表明,数据经3σ-grubbs方法处理后方差减小了20%~54%,与传统的算术平均滤波方法相比,分批估计自适应加权融合算法的数据融合方差明显更小,考虑传感器精度后的融合结果更接近高精度传感器值,特征值提取结果更加准确、可靠。

Comparison of different pseudo-linear estimators for vision-based target motion estimation

Vision-based target motion estimation based Kalman filtering or least-squares estimators is an important problem in many tasks such as vision-based swarming or vision-based target pursuit.In this paper,we focus on a problem that is very specific yet we believe important.That is,from the vision measurements,we can formulate various measurements.Which and how the measurements should be used?These problems are very fundamental,but we notice that practitioners usually do not pay special attention to them and often make mistakes.Motivated by this,we formulate three pseudo-linear measurements based on the bearing and angle measurements,which are standard vision measurements that can be obtained.Different estimators based on Kalman filtering and least-squares estimation are established and compared based on numerical experiments.It is revealed that correctly analyzing the covariance noises is critical for the Kalman filtering-based estimators.When the variance of the original measurement noise is unknown,the pseudo-linear least-squares estimator that has the smallest magnitude of the transformed noise can be a good choice.

A PRIORI ERROR ESTIMATES FOR LEAST-SQUARES MIXED FINITE ELEMENT APPROXIMATION OF ELLIPTIC OPTIMAL CONTROL PROBLEMS

In this paper, a constrained distributed optimal control problem governed by a first- order elliptic system is considered. Least-squares mixed finite element methods, which are not subject to the Ladyzhenkaya-Babuska-Brezzi consistency condition, are used for solving the elliptic system with two unknown state variables. By adopting the Lagrange multiplier approach, continuous and discrete optimality systems including a primal state equation, an adjoint state equation, and a variational inequality for the optimal control are derived, respectively. Both the discrete state equation and discrete adjoint state equation yield a symmetric and positive definite linear algebraic system. Thus, the popular solvers such as preconditioned conjugate gradient （PCG） and algebraic multi-grid （AMG） can be used for rapid solution. Optimal a priori error estimates are obtained, respectively, for the control function in L2 （Ω）-norm, for the original state and adjoint state in H1 （Ω）-norm, and for the flux state and adjoint flux state in H（div; Ω）-norm. Finally, we use one numerical example to validate the theoretical findings.

基于高分辨率网络的轻量型人体姿态估计方法

在高分辨率网络(HRNet)的基础上,提出一种融合Ghost卷积的轻量型高分辨率网络(GLHRNet)。首先使用Ghost卷积模块和极化自注意力(PSA)模块在HRNet中构建新的残差块结构,新的残差块结构可以在减少网络模型参数量和计算量的同时,建模高分辨率图像的长距离依赖关系。接着在新网络模型中引入IBN-Net的设计思想,在新网络模型的浅层同时使用批量归一化和实例归一化,为网络模型引入外观不变性,减小光照变化问题对模型的影响。算法在COCO人体姿态估计数据集上的实验结果表明,与HRNet相比新网络模型的参数量降低了36.1%,计算量降低了35.2%,人体姿态估计的平均准确率提高了1.4个百分点。