증류탑의 생산물 조성추정 방법 비교 :

PLS 와 인공신경망

신주호, 구도균, 이문용

영남대학교 화학공학부

Comparison of Two Approaches for

Product Composition Estimation in Distillation Columns :

PLS v.s. ANN

Juho Shin, Dogyun Koo, Moonyong Lee

School of Chemical Engineering and Technology

Yeungnam University

Introduction

Reliable measurement of product quality is one of the most important issues in distillation columns. So far, however, most on-line composition analyzers such as gas chromatography have many problems: low reliability, high maintenance cost, measurement delay. Although the use of single temperature measurement has been widely applied to most industries as an alternatives, it still has several critical problems especially in high purity columns and multicomponent columns. For this reason, many researchers (Joseph and Brosilow, 1978; Mejdell and Skogestad, 1991; Kresta et al., 1994) have investigated the estimator based on multiple measurements in order to overcome these drawbacks. It has been known that the estimator using the multivariate analysis methods such as  Principal Component Regression (PCR) and Partial Least Square (PLS) give good predictive power and robustness to noise and sensor failures in the somewhat small operation range. However, since the distillation columns are inherently nonlinear processes (see Fig. 1), the estimation performance of the linear estimator can be significantly degraded depending on the situation.

In this paper we compare the two representative approaches to infer the product compositions for distillation columns : PLS approach and Artificial Neural Network (ANN). The main objective of this paper is to analyze the pros and cons of the two approaches in order to provide useful guidelines for selecting the estimator type. We also proposed and evaluated a hybrid type estimator in which PLS and ANN are combined. Simulation study was performed for a high purity column and several multicomponent columns.

Linear Estimator Based on PLS

Recently, among many linear statistical methods, the PLS has become most popular in analytical chemists. This method produce latent variables which have the largest covariance with dependent variables. Based on the latent variables, we make the estimation coefficient matrix Kpls (i.e., estimator) as follows:

[eqn: bar y = theta K]                                 (1)

[eqn: K sub{PLS} = W````(P sup T W````) sup {-1} Q sup T]                      (2)

where W is generated in the PLS, P is the loading matrix for the independent variables, and Q is the loading matrix for the dependent variables. While collinearity problem in estimation can be efficiently handled with the PLS, adequate transformation and pre-processing is necessary to cope with the nonlinearity of the system.

Nonlinear Estimator Based on ANN

It is well known that ANN is a powerful tool to capture the nonlinearity without any variable transformation and pre-processing. The ANN used in this work is three layered feedforward network with conventional backpropagation learning algorithm. The inputs of the ANN can be all tray temperatures and auxiliary inputs. The output can be product and feed composition. The hypertangent function and the linear function was used in the hidden layer and the output layer, respectively as the activation function.

In order to capture the advantages of the PLS approach, we also designed hybride type nonlinear estimator in which the inputs are passed through PLS module before running in ANN module.

Case Study

Rigorous steady-state simulation was performed using PRO II for producing calibration and prediction set. Several representative cases are studied :

1) n-hexane - cyc-hexane column (high purity binary example)

2) BTX column (high purity multicomponent example)

3) depropaniser column (multicomponent example)

The operation conditions and variation ranges are listed in Table 1 and 2.

MSEP and EPV (Mejdell and Skogestad, 1991) are used for evaluating the performance of various estimators.

[eqn: MSEP(k)= { 1} over {N sub {set} } SUM from { {i }=1} to N sub {set}(bar y} sub i ``(k) - y sub i``` ) sup 2]                   (3)

[eqn: EPV(k)=100×(1- {MSEP(k) } over {MSEP (0)})]                     (4)

where MSEP(0) is the variance in the dependent variables.

Results and Conclusions

1. Binary column

In the PLS, the noise-free cases have relatively good prediction performances while the noise corrupted cases produce relatively bad results when the number of factors is used more than optimal number (3-4). In addition, the performance of Log transformation for the product composition is very poor. It shows that the relationship between the [eqn: ln ( y``/``(1-y))] and the tray temperature is not linear.

2. BTX column

In the PLS case, the [eqn: ln((T sub i - T sub {LK} sup b ``)/(T sub {HK} sup b - T sub i ``))] transformation gives very poor performance because of the non-key component effect. The EPV is similar in most cases except the [eqn: ln((T sub i - T sub {LK} sup b ``)/(T sub {HK} sup b - T sub i ``))]. The performances are almost same both for the noise-free cases and the noise corrupted cases. On the other hand, The estimation performanc of the ANN largely depends on noise.

In the binary column case, both the PLS estimator and the ANN estimator are relatively more sensitive to noise compared with the BTX case. Also, the performance of the linear estimator is almost same as that of the nonlinear estimator. It seems that the ANN does not capture the nonlinearity of the system satisfactorily while sacrificing the robustness. In spite of the noise, both of the estimators are robust in the case of the BTX column.

Acknowledgement

Financial support from the Korea Science and Engineering Foundation through the Automation Research Center at Postech. is gratefully acknowledged.

References

Weber, R. and Brosilow, C. B. (1972). The use of secondary measurements to

improve control., AIChE 18(3) : 614-623.

Joseph, B. and Brosilow, C. B. (1978). Inferential control of processes : Part I.

steady state analysis and design., AIChE 24(3) : 485-492.

Geladi, P. and Kowalski B. R. (1986). Partial least-square regression : A tutorial.,

Analytica Chemica Acta 185(3) : 1-17.

Mejdell, T. and Skogestad, S. (1991). Estimation of distillation compositions from

multiple temperature measurements using partial-least-squares regression., Ind.

Eng. Chem. Res. 30 : 2543-2555.

Kresta, J. V., Marlin, T. E. and MacGregor, J. F. (1994). Development of inferential

process models using pls., Computers chem. Eng. 18(7) : 596-611.

Table 1. Binary Column                  Table 2. BTX Column

	Base conditions	Variation ranges
F TF zF N NF P yD,LK xB,LK	2204.63 lb-moles/hr 347.11 oK 0.5 40 20 1atm 0.99 0.01	± 10% ± 10oK ± 10% constant constant ± 10% 0.97 ∼ 0.997 0.001 ∼ 0.01

	Base conditions	Variation ranges
F TF zT zX N NF P yD,HK xB,LK	275 kg-moles/hr 390.9 oK 0.45 0.45 43 22 1 atm 0.01 0.01	± 13% ± 10% ± 10% ± 10% constant constant ± 10% 0.02 ∼ 0.0001 0.02 ∼ 0.0001

(a)                                 (b)

Fig 1. Nonlinearity of the binary column example (a) Zf v.s. T , (b) yD v.s. T

(a)                                   (b)

(c)                                      (d)

Fig 2. performances of the estimators (a) BTX column using PLS, (b) binary column        using PLS, (c) BTX column using ANN, (d) binary column using ANN