Lijie Zhao

On-line principal component analysis with application to process modeling

Principal component analysis (PCA) has been widely applied in process monitoring and modeling. The time-varying property of industrial processes requires the adaptive ability of the PCA. This paper introduces a novel PCA algorithm, named on-line PCA (OLPCA). It updates the PCA model according to the process status. The approximate linear dependence (ALD) condition is used to check each new sample. A recursive algorithm is proposed to reconstruct the PCA model with selected samples. Three types of experiments, a synthetic data, a benchmark problem, and a ball mill load experimental data, are used to illustrate our modeling method. The results show that the proposed OLPCA is computationally faster, and the modeling accuracy is higher than conventional moving window PCA (MWPCA) and recursive PCA (RPCA) for time-varying process modeling.

Modeling Load Parameters of Ball Mill in Grinding Process Based on Selective Ensemble Multisensor Information

Due to complex dynamic characteristics of the ball mill system, it is difficult to measure load parameters inside the ball mill. It has been noticed that the traditional single-model and ensemble-model based soft sensor approaches demonstrate weak generalization power. Also, mill motor current, feature subsets of the shell vibration and acoustical frequency spectra contain different useful information. To achieve better solutions and overcome these problems mentioned above, a selective ensemble multisource information approach is proposed in this paper. Only the useful feature subsets of vibration and acoustical frequency spectra are portioned and selected. Some modeling techniques, such as fast Fourier transform (FFT), mutual information (MI), kernel partial least square (KPLS), brand and band (BB), and adaptive weighting fusion (AWF), are combined effectively to model the mill load parameters. The simulation is conducted using real data from a laboratory-scale ball mill. The results show that our proposed approach can effectively fusion the shell vibration, acoustical and mill motor current signals with improved model generalization.

Soft sensor for parameters of mill load based on multi-spectral segments PLS sub-models and on-line adaptive weighted fusion algorithm

The parameters of mill load (ML) not only represent the load of the ball mill, but also determine the grinding production ratio (GPR) of the grinding process. In this paper, a novel soft sensor approach based on multi-spectral segments partial least square (PLS) model and on-line adaptive weighted fusion algorithm is proposed to estimate the ML parameters. At first, frequency spectrums of the shell vibration acceleration signals are obtained. Then the PLS sub-models are constructed with the low, medium and high frequency spectral segments. At last, the PLS sub-models are fused together with a new on-line adaptive weighted fusion algorithm to obtain the final soft sensor models. This soft sensor approach has been successfully applied in a laboratory-scale wet ball mill grinding process.

Soft Sensor Modeling of Ball Mill Load via Principal Component Analysis and Support Vector Machines

In wet ball mill, measurement accuracy of mill load (ML) is very important. It affects production capacity and energy efficiency. A soft sensor method is proposed to estimate the mill load in this paper. Vibration signal of mill shell in time domain is first transformed into power spectral density (PSD) using fast Fourier transform (FFT), such that the relative amplitudes of different frequencies contain mill load information directly. Feature variables at low, medium and high frequency bands are extracted through principal component analysis (PCA), which selects input as a preprocessing procedure to improve the modeling performance. Three support vector machine (SVM) models are built to predict the mill operating parameters. A case study shows that proposed soft sensor method has higher accuracy and better predictive performance than the other normal approaches.

Modeling of operating parameters for wet ball mill by modified GA-KPLS

Load of the ball mill affects the productivity, quality and energy consumption of the grinding process. But sensors are not available for the direct measurement of the key parameters for mill load (ML). A new soft sensor approach based on the shell vibration signals to measure the operating parameters is proposed in this paper. Vibration signal is first transformed into power spectral density (PSD) via fast Fourier transform (FFT), such that the relative amplitudes of different frequencies could contain information about operating parameters. As the spectral curve consists of a set of small peaks, the masses and the central frequencies of the peaks are extracted as the spectral features, then the kernel partial least square (KPLS) is used to built the soft sensor model. The kernel parameters, the input variables of the models including the masses and the central frequencies of the peaks are selected by Genetic algorithm (GA). At last, a new approach for the updating of the KPLS model is proposed. Experimental results show that proposed method has higher accuracy and better predictive performance than the other approaches.

KPCA based multi-spectral segments feature extraction and GA based Combinatorial optimization for frequency spectrum data modeling

Mill load (ML) estimation plays a major role in improving the grinding production rate (GPR) and the product quality of the grinding process. The ML parameters, such as mineral to ball volume ratio (MBVR), pulp density (PD) and charge volume ratio (CVR), reflect the load inside the ball mill accurately. The relative amplitudes of the high-dimensional frequency spectrum of shell vibration signals contain the information about the ML parameters. In this paper, a kernel principal component analysis (KPCA) based multi-spectral segments feature extraction and genetic algorithm (GA) based Combinatorial optimization method is proposed to estimate the ML parameters. Spectral peak clustering algorithm based knowledge is first used to partition the spectrum into several segments with their physical meaning. Then, the spectral principal components (PCs) of different segments are extracted using KPCA. The candidate input features are serial combinated with mill power. At last, GA with Akaikes information criteria (AIC) is used to select the input features and the parameters for the least square-support vector machine (LS-SVM) simultaneously. Experimental results show that the proposed approach has higher accuracy and better predictive performance than the other normal approaches.

Feature selection of frequency spectrum for modeling difficulty to measure process parameters

Some difficulty to measure process parameters can be obtained using the vibration and acoustical frequency spectra. The dimension of the frequency spectrum is very large. This poses a difficulty in selecting effective frequency band for modeling. In this paper, the partial least squares (PLS) algorithm is used to analyze the sensitivity of the frequency spectrum to these parameters. A sphere criterion is used to select different frequency bands from vibration and acoustical spectrum. The soft sensor model is constructed using the selected vibration and acoustical frequency band. The results show that the proposed approach has higher accuracy and better predictive performance than existing approaches.

Multi-class classification with one-against-one using probabilistic extreme learning machine

Probabilistic extreme learning machine (PELM) is a binary classification method, which can improve the computational speed, generalization performance and computational cost. In this work we extend the binary PELM to resolve multi-class classification problems by using one-against-one (OAO) and winner-takes-all strategy. The strategy one-against-one (OAO) involves C(C-1)/2 binary PELM models. A reliability for each sample is calculated from each binary PELM model, and the sample is assigned to the class with the largest combined reliability by using the winner-takes-all strategy. The proposed method is verified with the operational conditions classification of an industrial wastewater treatment plant. Experimental results show the good performance on classification accuracy and computational expense.

Selective ensemble modeling parameters of mill load based on shell vibration signal

Load parameters inside the ball mill have direct relationships with the optimal operation of grinding process. This paper aims to develop a selective ensemble modeling approach to estimate these parameters. At first, the original vibration signal is decomposed into a number of intrinsic mode functions (IMFs) using empirical mode decomposition (EMD) adaptively. Then, frequency spectra of these IMFs are obtained via fast Fourier transform (FFT), and a serial of kernel partial least squares (KPLS) sub-models are constructed based on these frequency spectra. At last, the ensemble models are obtained by integrating the branch and band (BB) algorithm and the information entropy-based weighting algorithm. Experimental results based on a laboratory scale ball mill indicate that the propose approach not only has better prediction accuracy, but also can interpret the vibration signal more deeply.

Spectral Kernel Principal Component Selection Based on Empirical Mode Decomposition and Genetic Algorithm for Modeling Parameters of Ball Mill Load

Parameters of ball mill load (ML) affects production capacity and energy consumption of the grinding process, which have stronger correlation with shell vibration spectrum. A novel spectral features extraction and selection approach combined with empirical mode decomposition(EMD), power spectral density(PSD), kernel principal component analysis(KPCA), genetic algorithms(GA) and partial least square(PLS) was proposed in this paper. At first, shell vibration signals were decomposed into a number of intrinsic mode functions (IMFs) based on the EMD. Secondly, the PSD of each IMF was obtained. At last, the mainly spectral KPCs extracted from the PSD were integrated together as the candidate features set. GA was used to optimize spectral KPCs as the selected features subset, which was used to construct ML parameters soft sensor models based on PLS algorithm. The experimental result shows that the proposed approach has higher accuracy and better predictive performance than other normal approaches.