Fault detection in distillation column using NARX neural network

Abstract

Fault detection in the process industries is one of the most challenging tasks. It requires timely detection of anomalies which are present with noisy measurements of a large number of variable, highly correlated data with complex interactions and fault symptoms. This study proposes the robust fault detection method for the distillation column. Fault detection and diagnosis (FDD) for process monitoring and control has been an effective field of research for two decades. This area has been used widely in sophisticated engineering design applications to ensure the proper functionality and performance diagnosis of advanced and complex technologies. Robust fault detection of the realistic faults in distillation column in dynamic condition has been considered in this study. For early detection of faults, the model is based on nonlinear autoregressive with exogenous input (NARX) network. Tapped delays lines (TDLs) have been used for the input and output sequences. A case study was carried out with three different fault scenarios, i.e., valve sticking at reflux and reboiler, and tray upset. These faults would cause the product degradation. The normal data (no fault) is used for the training of neural network in all three cases. It is shown that the proposed algorithm can be used for the detection of both internal and external faults in the distillation column for dynamic system monitoring and to predict the probability of failure.

Appendix: Dynamic model of distillation column

A binary mixture with constant relative volatility at 100% tray efficiency has been assumed. This means the simple vapor–liquid equilibrium relationship can be used [41, 50];

$$y_{n} = \frac{{\alpha x_{n} }}{{1 + \left( {\alpha - 1} \right)x_{n} }}$$

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N number of trays, F feed flow rate, Z molar composition, M liquid holdup in condenser (mol), x_D top composition, x_B bottom composition, R reflux flow rate, D distillate flow rate, B bottom flow rate, M_B liquid holdup in reboiler (mol).

The fundamental relation for component continuity for condenser and reflux drum is given as:

$$\frac{{{\text{d}}(M_{\text{D}} x_{\text{D}} )}}{{{\text{d}}t}} = Vy_{N} - \left( {R + D} \right)x_{\text{D}}$$

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The fundamental relation for component continuity for reboiler and column base is given as:

$$\frac{{{\text{d}}M_{\text{B}} }}{{{\text{d}}t}} = L_{1} - V - D$$

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The component continuity is given as:

$$\frac{{{\text{d}}(M_{\text{B}} x_{\text{B}} )}}{{{\text{d}}t}} = L_{1} x_{1} - Vy_{\text{B}} - Bx_{\text{B}}$$

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The state operation of each module comprises the following equation referred as MESH equations.

[MESH = material balance equations, efficiency relations, summation equation, and heat (enthalpy) balance equations].

Material balance equation:

$$L_{i + 1} + V_{i - 1} - L_{i} - V_{i} = 0$$

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Stage efficiency relations:

$$y_{i} - y_{i - 1} = \eta_{ij} \left[ {y_{i}^{*} \left( {x_{i} ,T_{i} , p_{i} } \right) - y_{i - 1} } \right]$$

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where $y_{i} = \frac{{v_{i} }}{{V_{i} }}$ and $x_{i} = \frac{{l_{i} }}{{L_{i} }}$.

Summation equation:

$$L_{i} = \mathop \sum \limits_{j = 1}^{\text{NC}} l_{ij}$$

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$$V_{i} = \mathop \sum \limits_{j = 1}^{\text{NC}} v_{ij}$$

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Enthalpy balance equation:

$$L_{i + 1} h_{i + 1} + V_{i - 1} h_{i - 1} - L_{i} h_{i} - V_{i} h_{i} = 0.$$

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