Jian Tang

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.

Multi-frequency signal modeling using empirical mode decomposition and PCA with application to mill load estimation

Abstract Multi-frequency signals consist of different time-scale components which have different physical interpretations. Normal principal component analysis (PCA) methods and frequency spectrum feature selection techniques do not work well in a multi-scale domain. This paper combines empirical mode decomposition (EMD), PCA, and an optimal feature extraction method to extract, select and model different scale frequency signals. We successfully apply this approach to a laboratory scale wet ball mill. The shell vibration signal produced by the ball mill of the grinding process is used for modeling the mill load. The experimental results demonstrate that this novel approach is effective compared with the other existing methods.

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.

A Comparative Study That Measures Ball Mill Load Parameters Through Different Single-Scale and Multiscale Frequency Spectra-Based Approaches

Data-driven modeling based on the shell vibration and acoustic signals of ball mills is normally applied to overcome the subjective errors of human inference. Many previously proposed selective ensemble (SEN) modeling approaches are based on “the manipulation of input features” from the multiinformation fusion perspective, which cannot selectively and jointly fuse the information hidden in multiscale spectral features and under several operating conditions (training samples). Therefore, this study suggests a new soft measuring procedure based on ensemble empirical mode decomposition (EEMD) and SEN. An improved kernel partial least-squares algorithm for SEN that is based on “subsample training samples” is utilized to construct a soft measuring model with the selected features and training samples. This study compares such data-driven soft measuring methods. The comparative results of bootstrap-based prediction performance estimation show that different methods have specific advantages in terms of simplicity, prediction accuracy, and interpretability. The industrial application of the EEMD-SEN method is discussed in this paper, and a new virtual sample generation method is proposed to address the modeling problem based on small sample spectral data.

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.

Kernel latent features adaptive extraction and selection method for multi-component non-stationary signal of industrial mechanical device

Heavy key mechanical devices relate to production quality and quantity of complex industrial process directly. It is necessary to estimate some difficulty-to-measure process parameters inside these devices. Multi-component and non-stationary mechanical signals, such as vibration and acoustic ones, are always employed to model these process parameters indirectly. How to effective extract and select interesting information from these signals is the key step to build effective soft sensor model. In this paper, a new kernel latent features adaptive extraction and selection method is proposed. Ensemble empirical mode decomposition (EEMD) is used to decompose these mechanical signals into multiple time scales sub-signals with different physical interpretations. These sub-signals are transformed to frequency spectra, and then kernel partial least squares (KPLS) algorithm is used to extract their kernel features. Integrated with mutual information (MI)-based feature selection method, a new define index is exploited to select the important sub-signals and their latent features adaptively. The shell vibration and acoustic signals of an experimental laboratory-scale ball mill in the mineral grinding process are used to validate the proposed approach.

Modeling parameters of mill load based on dual layer selective ensemble learning strategy

Different frequency spectral feature sub-sets of mill shell vibration and acoustical signals contain different information for modeling parameters of mill load. Selective ensemble modeling based on manipulate training samples can improve generalization performance of soft sensor model. Based on the former studies, we proposed a new dual layer selective ensemble learning strategy. At first, vibration and acoustical frequency spectral feature sub-sets are extracted and selected by the methods in literature [15]. Then, selective ensemble modeling method based on genetic algorithm and kernel partial least squares (GASEN-KPLS) is used to construct the first layer selective ensemble model for every feature sub-set. Finally, brand and band (BB) and adaptive weighting fusion (AWF) algorithm is use to select and combine the outputs of the first layer models to construct the second layer selective ensemble model. Results indicate that the proposed approach can perform reasonably well on estimate mill load parameters of a laboratory ball mill grinding process.