Detection of Horizontal Two-Phase Flow Patterns Through a Neural Network Model

Detection of Horizontal Two-Phase Flow Patterns Through a Neural Network Model

K. C. O. Crivelaro

P. Seleghim Jr.

NETeF – EESC - Universidade de SãoPaulo

Av. Trabalhador São Carlense, 400

13566-590 São Carlos, SP. Brazil

E. Hervieu

DTP- DRN - Commissariat à l'Energie Atomique

38054 Grenoble cedex 9France

One of the main problems related to the transport and manipulation of multiphase fluids concerns the existence of characteristic flow patterns and its strong influence on important operation parameters. A good example of this occurs in gas-liquid chemical reactors in which maximum efficiencies can be achieved by maintaining a finely dispersed bubbly flow to maximize the total interfacial area. Thus, the ability to automatically detect flow patterns is of crucial importance, especially for the adequate operation of multiphase systems. This work describes the application of a neural model to process the signals delivered by a direct imaging probe to produce a diagnostic of the corresponding flow pattern. The neural model is constituted of six independent neural modules, each of which trained to detect one of the main horizontal flow patterns, and a last winner-take-all layer responsible for resolving when two or more patterns are simultaneously detected. Experimental signals representing different bubbly, intermittent, annular and stratified flow patterns were used to validate the neural model.

Keywords: multiphase flow, flow patterns, neural networks, signal analysis

Introduction

The majority of problems arising in the design and operation of multiphase flow systems is closely related to the existence of characteristic flow patterns and its severe consequences for the hydrodynamics as well as for heat and mass transfer. Consequently, industrial applications are often designed to work under strict conditions regarding the flow pattern. This is the case in bubble reactors, for which the gas must be finely dispersed to maximize reaction rates, or some petroleum transport systems where slugging might cause dangerous mechanical stresses. Several other examples could be evoked, but the essential point is that, although prediction based on phenomenological models is fairly well developed, on-line monitoring of multiphase flow patterns is still a limiting technological problem.

The development of objective criteria for on-line detection of flow patterns has been the central subject of studies of many researchers during the past years. Probably one of the first articles to address this issue is the work Hubbard & Dukler (1966), which characterized several flow patterns based on the spectral analysis of pressure signals. Following the same line some articles can be listed: Weisman et al. (1979), Vince & Lahey (1982), Matsui (1984), Tutu (1984), Mishima and Ishii (1984), Sekoguchi et al. (1987) and many others. A complete list would be too extense, and a detailed review of the work done up to the end of the 80's can be found in Drahos & Cermak (1989). The tendency in the 90's was to investigate what less restrictive signal analysis and fractal methods would reveal. Regarding specifically the characterization of the flow patterns from its temporal aspects, Saether et al. (1990), França et al. (1991) and Lewin (1992) proposed interesting flow pattern characterization methods based on the determination of fractal dimensions. Also, Soldati et al. (1996) developed a criterion based on diffusional analysis, which was able to characterize air-oil flows.

Focusing specifically on the characterization of the transitions themselves, Seleghim and Hervieu (1994) and Hervieu and Seleghim (1998) showed that a flow pattern transition is associated with a loss of stationarity, quantified through the calculus of time-frequency covariances of void signals. This approach led to a virtually universal criterion, i.e. common to all transitions. The rationale for this is simple and starts on a reasonable assumption of what in fact is a flow pattern: eigen-trajectories in the phase state a deterministic model governing the flow. Thus, the dynamic state of a particularly established flow pattern must follow the corresponding eigen-trajectories and its description variables must exhibit a stationary behavior. A consequence of this is that, a transition flow being a non-pattern, its dynamic state will evolve freely in the phase state and the description variables will exhibit a non-stationary behavior.

From a signal analysis perspective, these ideas implie that the ability to characterize two-phase flow patterns relies firstly on taking signals which access to a minimum degree of detail the evolution of the actual dynamical states of the flow and, secondly, on implementing methods of analysis capable of resolving stationary and non- or less-stationary situations. Besides the articles referenced above, there are some reported research work that could be cast into this framework. An interesting entry is the work by Rajkovic et al. (1995) who used spatio-temporal complexities calculated from the proper orthogonal decomposition method of a set of distributed pressure sensors to characterize different flow patterns in vertical flow. Also, Delprat et al. (1999) who constructed a three-dimensional characterization space for horizontal air-water flows using signals delivered by a direct imaging probe (Seleghim and Hervieu, 1998) and coordinates accounting for frequency, angular position and shape features of the observation window.

Another interesting and promising approach that in some way follows the ideas above is based on the use of connectionist or neural model. Among many interesting mathematical properties, a neural network has associative memory capabilities that enables the projection of input patterns onto a space formed be the stored characteristic patterns. This characteristic is particularly interesting for the problem diagnosis and, in fact, has been used in a wide variety of problems (character recognition, voice identification, etc.). Probably one of the first research works in this line is the one by Mi et al., (1998) in which a neural network is used to produce flow pattern diagnoses from a few statistical moments calculated directly from void signals. Also Crivelaro et al. (1999) trained individual neural networks with single outputs that were fired when a specific horizontal flow patterns was detected. The present work is actually the continuation of the latter and has the main objective of assembling these individual dedicated neural models so as to produce a continuous diagnosis of the flow pattern in steady state as well as in transient flow situations.

Neural Network Models

A neural network can be defined as a nonlinear mapping of an input onto an output vector space. This is achieved through layers of activation functions or neurons in which the input coordinates are summed according to weighting values and bias to produce single output or firing values. In this work, we used a feed forward network for which there is no recursiveness, i.e. the input vector of a specific neuron layer is formed only by the firing values of the preceding layer (Fig. 1).

Formally, if the activation function of i-th neuron in the j-th layer is indicated by F_i,j( ^. ), its output s_i,j can be calculated from the outputs of the preceding layer s_i,j-1 and the corresponding bias b_i,j and weighting values w_i,k,j-1 (the second subscript k indicates the neuron in the (j-1)-th layer from which the connection is being established) according to the expression

The network's input and output values being denoted respectively by x_i and h_i, the mapping relation of one onto another can be calculated by successively applying (1), what for the example in Fig. 1 results

Expression (2) makes clear that the relation between x_i and h_i is unambiguously defined by choosing the activation functions and by setting the bias and weighting values. Among many, a very important characteristic of neural networks is the so-called learning potential, i.e. the possibility of adjusting the bias and weighting values through a convenient training rule so as to reproduce closely pre-assigned pairs of input/output values. The back-propagation is probably the most employed training heuristics and is particularly well adapted to feed forward architectures. It is based on the iterative application of a discrete gradient descent algorithm, computed from the first derivatives of a conveniently defined error function with respect to the parameters of the network. In general lines the basic steps of the back-propagation procedure implemented in this work are the following:

1. Initialize the parameters of the network

b_i,j

and

w_i,k,j

From a training data set with pre-assigned input/output pairs

take one in specific and form the pair

2.Calculate the error function according to the Euclidean norm

3. Calculate the derivatives of the error

e

with respect to

b_i,j

and

w_i,k,j

4. Modify the network parameters according to a steepest descent strategy and a specified learning rate a

5. Iterate from 2 to 5, successively modifying bi,j and wi,k,j , until a a defined number of learning epochs (cycles) or a convenient stopping criterion has been achieved

The performance of a neural network is profoundly affected by its internal architecture (the number hidden layers and the number of neurons in each one) and the type of interconnections (feed-forward, recursive, winner-take-all, etc.). The exact shape of the activation function has limited effects on the overall performance and is usually set according to the needs of the training heuristics (a sigmoid function in the case of back-propagation method). There is no general mathematical theory but rather a number of empirical rules to be considered when constructing such models. Regarding the problem of detecting flow patterns from signals delivered by a direct imaging probe, a problem analogous to that of recognizing characters from a scanned text for which there is a well established knowledge base, a modular architecture presents some advantages over a fully interconnected model (see for instance Cao et al., 1997). Empirical estimates indicate that the total learning time on a conventional single processor computer depends approximately on N³(the total number of interconnections to the third). Thus, the decomposition of the global network into independent modules facilitates the rapid and efficient adjustment of the weighting coefficients.

The architecture adopted in this work, depicted in Fig. 2, consists of 6 independent feed-forward modules, each one dedicated to the detection of the 6 main flow patterns in horizontal two-phase flow (stratified smooth, wavy and rugged, intermittent, bubbly and annular). Each module was trained separately to produce a single output ranging from 0 to 1, indicating a perfect flow pattern match (output=1) or mismatch (output=0). Some details are given in table 1 concerning the specific architectures, which were optimized after an extensive work by Crivelaro (1999). The number of input neurons at the input layer was fixed to 320 corresponding to (16 electrodes) x (20 samples), which defines a convenient observation window. In dimensional terms, this window exists in an angle-time space and has sides given by (16 electrodes) x (p diam./16) and (20 samples) x (1/Fs), where Fs is the rate in Hz at which data is presented to the input neurons (sub-sampling frequency). An output winner-take-all layer resolves when two or more modules produces values close to 1 indicating multiple match. This may be the case of some intermittent flows at very low flow rates (for which slugging frequency may decrease to tenths of Hertz): given that observation windows have different time lengths, independent modules may diagnose such patterns as intermittent, bubbly or stratified wavy.

Experimental Set-Up and the Direct Imaging Probe

A large number of experimental tests was performed aiming at producing a representative set of training data and to validate the pattern recognition by the neural model. The experimental facility at the CEA-Grenoble has a horizontal test section made in Plexiglas, with 30 m in length and an internal diameter of 60 mm. The air and water supply system is capable of producing all main horizontal air-water flow patterns. A computer is responsible for the simultaneous control of the flow rates according to previously stated schedules so that reproducible steady state as well as transient tests can be done. For a detailed description of the experimental circuit see Seleghim (1996).

As mentioned, the diagnosis of the flow pattern is achieved by processing the signals delivered by a direct imaging probe through a neural model. This probe, placed on the central point of the test section, consists of two stainless steel ring electrodes mounted flush inside the tube and one third of the inner diameter away from each other. A 20 kHz sinusoidal voltage is applied through the excitation ring. Independent current to voltage converters quantifies the resulting current distribution on the segmented measurement ring.

These signals are simultaneously sampled at 30 Hz through an A/D acquisition board and can be continuously displayed on the computer screen to produce on-line images of the phase distribution within the probe's sensing volume. For a detailed description of the probe see Seleghim and Hervieu (1998). A schematic representation of the experimental circuit is given in Fig. 3.

Results

After having trained the neural modules, the performance of the diagnostic system was demonstrated by means of 4 transient tests, for which the flow slowly evolved from different established flow patterns and passed by the corresponding transitions in between. More specifically, denoting Q_l and Q_g the volumetric flow rates at standard conditions of water and air respectively, these testes are the following: (A) annular to intermittent (Q_l = 2 m³/h and Q_g = 250 to 70 m³/h), (B) stratified wavy to intermittent (Q_l = 0.5 to 5 m³/h and Q_g = 40 m³/h), (C) Stratified smooth to wavy to intermittent (Q_l = 0.5 to 5 m³/h and Q_g = 10 m³/h) and (D) intermittent to bubbly (Q_l = 5 to 50 m³/h and Q_g 40 = m³/h). The corresponding trajectories are shown in the Taitel & Dukler's two-phase flow map of Fig. 4 (Taitel & Dukler, 1976), together with points indicating the steady state tests.

For each transient test the signals delivered by the probe were processed through the neural diagnosis system to obtain a continuous diagnosis binary vector, of which the only non-zero value indicates the flow pattern present in the sensing volume. These results are shown in Fig. 5(A) to 5(D) (lower box). To be able to confront the diagnosis, it is also shown the time traces of the normalized global inter-electrode impedance (box above the neural network's output box), the average spectral content (upper left box) and the modulus of the Gabor transform, from which it is possible to visualize the evolution of the instantaneous spectral content of the signal during the transient test (upper right box). The Gabor transform is particularly well suited, not only for the characterization of the flow patterns themselves, but also of the corresponding transitions (Seleghim, 1996 and Hervieu and Seleghim, 1998).

Conclusions

A neural network model has been developed to produce continuous diagnoses of two-phase flow patterns in steady state and transient flow conditions. The basic architecture of this model consists of 6 dedicated models, trained to detect specific horizontal flow patterns, and an output winner-take-all layer responsible for resolving when more than one of these modules fire simultaneously. The input signals are delivered by a direct imaging probe so that it is assured the access to information concerning geometrical and temporal features of the flow. Experimental data were collected for air-water horizontal flows produced in a test section with 60 mm internal diameter and 30m long. More specifically, the signals obtained from a series of steady state tests representative of all main horizontal patterns (Fig. 4) constituted a training data set used to adjust the weighting coefficients of the neural modules. The validation of the diagnosis was obtained by means of 4 transient tests, for which the flow slowly evolved from different established flow patterns and underwent the corresponding transitions in between. Results are shown in Fig. 5, together with the inter-electrode impedance signal and the corresponding Fourier (frequency) and Gabor (joint time-frequency) transforms, and it is clear that correct diagnoses are achieved. Future work in this topic shall include a systematic optimization of the internal architecture and the development of a dedicated hardware platform for the neural model to permit an on-line diagnosis. Also, a very interesting point which should be addressed in future work is the use of self-organizing neural networks to identify and to characterize flow patterns in generic industrial multiphase flow systems.

Acknowledgement

This work was sponsored by CNPq – Conselho Nacional de Pesquisa through scholarship to K.C.O.C. and FAPESP- Fundação de Amparo à Pesquisa do Estado de São Paulo through grant No. 92/1221-2. The support of these foundations is greatly acknowledged.

Manuscript received: July, 2001. Technical Editor: Aristeu da Silva Neto.

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Publication Dates

• Publication in this collection
  18 Sept 2002
• Date of issue
  Mar 2002

History

• Received
  July 2001