Multivariate statistical projection analysis based on wavelet transform denoising and its application in chemical process monitoring

One of the important features of chemical process data is that it is seriously polluted by noise, which seriously affects the effect of process information processing and analysis. For example, in the process of chemical process monitoring using multivariate statistical process control (MSPC), the use of these contaminated measurement information directly to analyze the process will inevitably lead to greater errors and reduce confidence in the results. For process fault diagnosis, there is a high rate of false alarms or false negatives. In order to solve this problem, people use the wavelet transform to denoise the measurement signal, improve the confidence of the signal and achieve a good application effect. However, the usual wavelet transform denoising is to directly divide the frequency of the process measurement signal. Denoising does not take into account the correlation between signals, so this processing method cannot remove the process noise more effectively and can easily lead to the loss of real information in the process. In this paper, the independent source analysis (ICA) method is used to extract the process blind source signal first, and the revised draft is received from the perspective of the process source source 07*14.

Fund Project: National High-Tech Research and Development Plan (No. Chen Guojin et al.: Multivariate statistical projection analysis based on wavelet transform denoising and its application in chemical process monitoring 1479 Wavelet transform to denoise process information in order to achieve better Noise effect, thus reducing the loss of process real information, the specific steps are as follows: using wavelet transform and blind source signal processing methods to denoise the process steady-state signal, extract the principal element, and then build statistics to monitor the process. Compared with the traditional statistical process control, this article also made a corresponding comparative study.

1 Multivariate Statistical Projection Analysis Method Based on Wavelet Transform Denoising The proposed multivariate projection analysis process based on wavelet transform denoising is composed of the following steps: using wavelet transform to coarse filter the process data, extract the process blind source signal, and reuse The wavelet transform filters out high-frequency noise, reconstructs the process observation signal, conducts principal component analysis (PCA) to test the normality of distribution of the main plant, and finally constructs process statistics.

1.1 The wavelet transform denoising analysis value, often taking S = 2a2lnN, is the standard deviation of the process noise, 6745) estimation, m is the median of the absolute deviation of the finest scale wavelet coefficients, N is the length of the sequence, ci is the signal decomposition Wavelet coefficients. After wavelet coefficients of each frequency band are selected, wavelet inverse transformation and combination are performed, and the information after process noise removal can be obtained.

1.2 blind source signal extraction method In the multivariable industrial process, there are a variety of complex cells, there is a certain link between these cells, the process signal is preprocessed and extracted according to the maximum negative entropy criterion Processes that are as independent as possible are blind to the source signal.

For the steady-state signal after rough filtering by wavelet transform S = (si, s, ..., s, *) 6R "Xm (n is the number of samples, m is the number of process variables, assuming has been standardized processing) can establish the PCA process model as Cå±®= is said to be slave t) as the fundamental wavelet or mother wavelet, *Kw) is the Fourier transform of */(), and the basic wavelet is scaled and translated to obtain the wavelet function for any signal / () 612 ( (0, its wavelet transform pair can use the wavelet function to decompose the signal into adjacent sub-signals in each frequency band. Once the signal is decomposed once, the resolution of the signal in the frequency domain is strong once. Usually the noise signal has a wider frequency domain and Mixed with the signal, but if you choose an appropriate wavelet function to transform, then in most bands, most of the noise signal wavelet transform coefficients are smaller than the signal wavelet transform coefficients, so you can use the threshold to select the wavelet coefficients in each frequency band In order to achieve the purpose of process denoising, the selection of wavelet transform coefficients in each frequency band can be performed according to Equation 121, where k is the principal element signal matrix and the load matrix, k is the main arity, and E6R is the XmS principal component residual matrix. Standard T Shows transpose of a matrix or vector.

By the covariance matrix 2 = singular value decomposition of the signal S, the principal element signal matrix T and the payload matrix P satisfy the inverse matrix (or pseudo-inverse matrix), and h is the number of process blind source signals.

6RhXm is called process mixing matrix. The key to the blind source signal extraction process is the determination of the process mixing matrix W.

It is known from information theory that a random quantity that obeys a normal distribution has the largest differential entropy. In addition, it can be seen that the more random signal probability distributions deviate from the normal distribution, the stronger the independence of the signals, so that the independence of the signals can be measured by the size of the random signal differential entropy.

The differential entropy of the lishi number y can be defined as the chemical engineering journal setting yg as a Gaussian random signal with the same covariance matrix as y, then the negative entropy of the random signal y can be defined as (8), a single blind source signal It can be expressed as /C, = wST, where w. is the ith row vector of W. By formula () and normalizing the blind source signal (ie, let /G112 = 1), we can obtain the estimated wi of w. as the signal, and the function G is a non-quadratic type function. The selection method can be