Artificial neural network approach for flow regime classification in gas–liquid–fiber flows based on frequency domain analysis of pressure signals

Abstract

The feasibility of a transportable artificial neural network (ANN)-based technique for the classification of flow regimes in three phase gas/liquid/pulp fiber systems by using pressure signals as input was examined. Experimental data obtained in a vertical, circular column $\text{1.8}\text{m}$ in height and $\text{5.08}\text{cm}$ in diameter, with air/water/Kraft softwood paper pulp, were used. The pulp consistency (weight percent of dry pulp in the pulp–water mixture) was varied in the 0.0–1.5% range. Local pressure fluctuations were recorded at three different stations along the column using three independent but principally similar transducers. An ANN was designed, trained and tested for the classification of the flow regimes using as input some density characteristics of the power spectrum for one of the normalized pressure signals (from Sensor 1), and was shown to predict the flow regimes with good accuracy. A voting scheme was also examined in which the three sensors fed separately trained ANNs, and a correct flow regime would require a vote from at least two of the three ANNs. This scheme improved the agreement between the model predictions and the data.

The ANN trained and tested for Sensor 1 predicted the flow regimes reasonably well when applied directly to the normalized pressure power spectrum density characteristics of the other two sensors, indicating a good deal of transportability. For further improvement of transportability, an ANN-based method was also developed, whereby the power spectrum density characteristics of other sensors were adjusted before they were used as input to the ANN that was based on Sensor 1 alone. The method was shown to improve the accuracy of the flow regime predictions. This method requires in practice, that the “replacement” sensor to which regime identification is transported will be, for some while, in simultaneous use with the sensor to be replaced; then the training of the “input-adjusting” ANN would be possible in industry practice. Such a situation is realistic for sensitive processes, where redundant sensors are implemented for fault tolerance.

Introduction

Objective flow regime identification in multi-phase flow process systems using minimally intrusive sensors is of great interest to various branches of industry. In paper making and recycling, in particular, opaque gas–liquid–pulp fiber three-phase mixtures are encountered in large delignification, bleaching, and deinking devices. An objective and minimally intrusive regime classification technique can help the development of online diagnostic or control methods for such systems. Hydrodynamic characteristics of gas–liquid–pulp fiber slurry flows have been investigated in the past (Duffy and Titchener, 1975; Duffy et al., 1976; Bennington et al., 1995; etc), and more recently their flow regimes and gas holdup characteristics have been studied (Lindsay et al., 1995; Reese et al., 1996; Heindel, 1999; Heindel and Garner, 1999; Xie 2003a, Xie 2003b). Brief reviews of the recent studies can be found in Xie 2003a, Xie 2003b).

Attempts at the characterization of two-phase flow patterns based on a combination of subjective judgments and objective methods have also been made in the past (Hubbard and Dukler, 1966; Mandhane et al., 1974; Jones and Zuber, 1975; Merilo et al., 1977; Weisman et al., 1979; Taitel et al., 1980; Mishima and Ishii, 1983; Matsumi, 1984; Lin and Hanratty, 1986; Fang et al., 1986; Franca et al., 1991; Drahos et al., 1991; Spedding and Spence, 1993; Lindsay et al., 1995; Cai et al., 1996; Zhang et al., 1997; Heindel and Monefeldt, 1997; Shim and Jo, 2000). Pressure fluctuations that result from the passage of gas and liquid pockets, and their statistical characteristics, are particularly attractive for objective characterization of flow regimes because the required sensors are robust, inexpensive and relatively well-developed, and therefore more likely to be applied in the industrial systems (Drahos et al., 1991). Power spectral density (PSD) and probability density function (PDF) of pressure drop fluctuations recorded by two pressure transducers were studied by Franca et al. (1991), and more recently by Shim and Jo (2000), for regime identification in gas–liquid two-phase flows. Based on the analysis of experimental data in a horizontal tube, Franca et al. (1991) noted that, although PSD and PDF could not easily be used for regime identification, objective discrimination between separated and intermittent regimes might be possible by fractal techniques. Based on PSD and PDF analyses, Shim and Jo could characterize bubbly, churn, and slug flow patterns in low-flow experiments in a vertical tube. At high flow rates, however, their technique could only distinguish the bubbly flow regime.

To avoid subjective judgment, artificial neural network (ANN) modeling and frequency estimation methods have been employed to implement non-linear mappings from measurable physical parameters to flow regimes (Cai et al., 1994; Mi et al., 1998; Mi et al., 2001). Artificial neural networks are analytical tools that imitate the neural aspect of the human brain, whereby learning is based on experience and repetition rather than the application of rule-based principles and formulas. An ANN (in its most typical form, so-called feed-forward network) consists of a layered network of neurons (nodes), with each neuron connected to a large number of others. The input signal to the network is passed among the neurons, with each neuron calculating its own output using weighting associated with connections. Learning is achieved by the adjustment of the weights associated with inter-neuron connections. ANNs provide capabilities such as learning, self-organization, generalization (response to new problems using incomplete information), and training; and are excellent for pattern recognition and trend prediction for processes that are non-linear, poorly-understood, and/or too complex for accurate first-principle mathematical modeling. They seem ideal for applications to multiphase flow systems, and when properly designed and trained, can potentially improve on-line monitoring and diagnostics.

ANNs have recently been applied for the prediction of complex thermal systems rather extensively. Although the application of neural networks to multiphase flow problems has started only recently, the published studies have clearly demonstrated their enormous potential. Mi 1998, Mi 2001 applied a neural network for two-phase flow regime identification in a vertical channel using signals from electric capacitance probes with excellent results. Gupta et al. (1999) successfully applied a hybrid method based on four neural networks along with simple first-principle models (the latter intended to render the model independent of specific device geometry), for prediction of the attachment rate constant in flotation columns.

This paper follows our previous investigations (Xie 2003a, Xie 2003b). Xie et al. (2003a) reported on a detailed investigation of the flow patterns and gas holdup of gas–water–pulp three-phase flows in a vertical, upward column. The range of pulp consistency (i.e., weight fraction of dry pulp in the pulp-water mixture) in the experiments was varied in the 0.0–1.5% range, which represents the low consistency (LC) pulp suspension range. The aforementioned test facility, with some modifications, was subsequently used (Xie et al., 2003b), whereby local pressure fluctuations recorded by a single high-sensitivity pressure transducer at a particular location on the test section wall ($\text{1.2}\text{m}$ above the test section inlet) were measured and utilized for the development of an ANN-based method for flow regime identification. Two feed-forward back-propagation ANNs were developed, each having a single hidden layer, and they were shown to predict the flow regimes well using inputs based on the pressure signal: the standard deviation, coefficients of skewness and kurtosis, and several time shift autocorrelations of normalized signals.

Although the aforementioned studies have shown that ANNs are capable of learning to recognize flow regimes based on pressure fluctuation and some other flow-induced signals, a number of important issues need to be resolved before they can find widespread industrial applications. Practical functional transportability of trained ANNs is among these crucial issues. This transportability is defined here as the capability of a single ANN to function with several sensors in the following sense: trained with a sensor, and/or a scaled-down system, it performs acceptably with another reasonably similar sensor and/or a prototypical-scale system. The ANN must then use somewhat sensor-independent, invariant characteristics of the input signal; we will help it along by preprocessing these signals to promote such invariance in the inputs.

In this paper, using the data obtained with the aforementioned test facility (Xie et al., 2003b), the transportability of an ANN trained for regime classification, between pressure signals from three separate but in principle similar sensors, is addressed. The sensors represent different observation points in flow that is not fully developed, and their signal characteristics are therefore somewhat different in addition to differences in calibration (zero, gain, and linearity)—also minor differences in the physical installation of the sensors can affect their signals. Transportability with respect to multiple similar sensors applied to the same system scale (i.e., no scale-change difference) is considered here. This type of transportability is important since small differences among similar sensors (caused by sensor drift, for example) are often inevitable. An ANN is developed that uses the power spectral characteristics of the normalized pressure fluctuations as input, and is shown to have good transportability. An ANN-based method is furthermore developed that enhances the transportability of the aforementioned ANNs. While a redundant system with multiple sensors is an obvious target application, such robustness of algorithms that provides transportability will also contribute to performance with a single sensor, shielding against effects of calibration changes or sensor replacements.