應用訊息熵在數據校正

由於在程序變數的量測訊號中，包含了隨機性誤差以及非隨機性誤差因此在程序分析中，量測數據是非常重要的。數據校正是估計量測數據中的正確值，使得正確值能滿足系統模式的限制條件。在過去文獻中，為了方便計算出估計值，數據中的隨機誤差大多假設為高斯分佈。但如果數據中含有異常誤差的存在時，大部分的M估計不容易移除。本研究提出以Correntropy為基礎的估測器，藉AIC調整核寬度下，能有效處理當數據含有異常誤差的問題。由於Correntropy是根據數據與數據間的關係所定義出的目標函數，因此容易識別出異常值以及調整異常的數據，使得估計後的數據能符合系統的限制條件。當隨機誤差在非高斯分布以及數據含有異常值存在時， Correntropy依然能有效的處理，根據這些優點將其延伸至流量及組成的雙線性系統。為了降低線性及雙線性系統，在數據較多時，疊代計算的計算速度緩慢的問題，提出將Correntropy應用在自相關人工神經網絡（AANN）。在Correntropy-AANN的結構下，AANN可以處理模式中的隨機誤差，而Correntropy可以解決異常值的問題。為驗證所提方法的有效性，應用所提的方法於三個模擬問題，常壓塔和空氣分離過程以及金屬加工廠程序。

關鍵字

數據校正

並列摘要

Measured data validation plays an important role in process operation analysis and enhancement since measured signals of process variables are often contaminated by measurement errors that include random and nonrandom errors. Data reconciliation is a method that estimates the true values of measurements. The estimates can satisfy model constraints and deviate as little as possible from the measured values. In conventional methods, the random noise in measurements, which is often presumed to follow Gaussian distribution, can be easily reduced by filtering or smoothing, but it may not be true in the unmeasured disturbances distributions. Moreover, most of the large gross errors with non-random are not easily removed by a robust M estimator. A new robust estimator based on correntropy is proposed to handle the above problems. With Akaike information criterion, the parameters of the kernel window can be properly defined. As correntropy has a generalized similarity measure, it is easy to identify outliers and reconcile them without performing any exploratory data analysis on the residuals of regression. The benefits are further extended to the bilinear system, which considers the concentrations as well as the flow rates. However, the above procedures are not good for real-time process applications, because the measured values must iteratively go through the optimization procedures and cannot be estimated timely. To reduce the computational load of on-line applications, the integrated auto-associative artificial neural network (AANN) with model constraints under the correntropy training criterion, is also proposed, called correntropy-AANN. Under this correntropy-AANN structure, AANN can handle model balance information while correntropy can solve the outlier problem. The importance of correntropy-AANN is more striking in bilinear system reconciliation which is a nonlinear problem with high computational load. Studies on two simulated problems, including an atmospheric tower and an air separation process are used to demonstrate the effectiveness of the proposed method.

並列關鍵字

Robust estimator ； Correntropy ； data reconciliation

參考文獻

1 Arora, N. & Biegler, L. T. Redescending Estimators for Data Reconciliation and Parameter Estimation. Computers and Chemical Engineering 25, 1585-1599 (2001).

3 Crowe, C. M., Campos, Y. A. G. & Hrymak, A. Reconciliation of Process Flow Rates by Matrix Projection. Part I: Linear Case. AIChE Journal 29, 881-888 (1983).

4 Crowe, C. M. Reconciliation of Process Flow Rates by Matrix Projection Part II: The Nonlinear Case. AIChE Journal 32, 616-623 (1986).

5 Crowe, C. M. The Maximum-Power Test for Gross Errors in the Original Constraints in Data Reconciliation. AIChE Journal 70, 1030-1036 (1992).

6 Du, Y. & Hodouin, D. Use of a Novel Autoassociative Neural Network for Nonlinear Steady-State Data Reconciliation. AIChE Journal 43, 1785-1796 (1997).

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應用訊息熵在數據校正

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