THE FUZZY SYSTEM FOR RECOGNITION AND CONTROL OF THE TWO PHASE GAS-LIQUID FLOWS

. In this article the fuzzy system for the two phase gas-liquid flows recognition based on the 3D tomography data and the research facility context information is described., The system is also specialized to control the research facility in basis of the fuzzy algorithms and generated diagnostics signals.


Introduction
The two phase gas-liquid flows (example two phase gas-liquid flow is presented in figure 1). recognition still determines the growing trend in the various branches of the industry. The knowledge about the flow regime in the research or industrial set-up has a great importance in a biotechnology, liquid engineering, power plant facilities, heating industry etc.
The recognition of the two phase gas-liquid flows is a wellknown problem in a computer science. There are various recognition methods for based on the pattern recognition [6], image processing [2], image reconstruction [8] and even artificial intelligence [4]. Despite of the severity of the above methods, the human expert opinion is still the most important part of the two phase gas liquid flows recognition process. Hence, the use of fuzzy logic which in its concepts imitates the human expert inference process. The methodology described in this paper is an innovative solution considering the raw 3D ECT (Electrical Capacitance Tomography) data [1,5] and the flow context information combined into common fuzzy inference.
In the second part of the paper there is also a description of the fuzzy control module dedicated to the two phase gas-liquid flow installations. The control module allows to set a particular flow regime on demand and the automatic transmission from one flow type into another. The wide description of the flow similarity determination based on the raw 3D ECT data can be found in the authors previous publication [3]. Shortly, the flow similarity is a result of the fuzzy c-means algorithm that describes the level of the similarity of the investigated flow to the pattern flows.
The gas and the liquid flow rate are the values obtained from the research installation measurement system. Due to the relatively low accuracy of the measuring system and the frequent oscillations, these values can't be threaten as a crisp values. To reduce the impact of the mentioned factors for the final recognition results the authors decided to threat the input values of the gas flow rate and the liquid flow rate as a fuzzy number [10]. The fuzzy number that describes the input value can be interpreted as "about the value", and it is expressed by the following membership functions:  For the gas flow rate (values expressed in m 3 /h): where: is an average value of the gas flow rate measured during 15-second period;  For the liquid flow rate (values expressed in m 3 /h): where: is an average value of the liquid flow rate measured during 15 seconds.    1 → = 0,7 −5 + 4,5 → ∈ (0,7; 0, 9) 0 → ≥ 0,9 ℎ ′ ( ) = { 0 → ≤ 0,7 5 − 3,5 → ∈ (0,7; 0, 9) 1 → ≥ 0,9 The membership functions of the gas and the liquid flow rate preliminary shapes were determined due to the set of test data presented in figure 7 clustering. The final shapes were determined due to the human expert comments consideration. The final shapes of the gas and the liquid flow rates are presented in the figure 5 and figure 6. The gas and the liquid flow rates fuzzy variables were divided into four terms:  low flow rate,  medium low flow rate,  medium high flow rate,  high flow rate.
The function shape for a parameter equals 1 and 10 was also consulted and approved by the human expert in the two phase gasliquid flows recognition.

Recognition process
The recognition inference is conditioned by the standard if..then formulas. All of them used in the inference schema look as follows:

If
Gas flow rate is low/medium low/medium/medium high/ high

And
Analyzed flow is deferent from/low similar to/medium similar to/high similar to/identical to plug/slug/transitional flow

Then
Analyzed flow is plug/slug/ transitional All fuzzy recognition rules used in the studies are presented in table 1.
The fuzzy rules as well as the membership functions shapes were designed that in the worst case, the inference results are two types of flow types in different degrees of realization [7,9] while using most common Zadeh implication (28) (the realization level of the particular fuzzy rule is determined by the fuzzyfication of the input signal).

Data preparation
In the fuzzy inference for the control module there are four input values:  gas flow rate,  liquid flow rate,  current flow type,  given flow type.
The gas flow rate and the liquid flow rate values are fuzzyficated exactly the same as the input signals in recognition module, applying the membership functions presented in the fig. 5 and 6. The current flow and the given flow types have crisp values, where the current flow type is the defuzzyficated result of the recognition module and the given flow is the system user assessment.

Control process
The fuzzy rules used in the control module look as follows:  The output values are translated to the crisp values with the center of sums defuzzyfication method, expressed by the following formula: where: yvalue of each point covered by the output fuzzy set expressed in m 3 /h Finally, the two parameters are produced on the control module output:  the setting of the gas flow rate expressed in m 3 /h,  the setting of the liquid flow rate expressed in m 3 /h.

Research results
The results of the recognition process correctness was validated with 45 test flows. In the first step, each test flow type was recognized both by the human expert and the presented system. The results for each from three flow type are presented in table 3. The results of the control process are presented in table 4.
In table 3 the flows types are marked by the following symbols:  Pfor the plug flow,  Tfor the transitional flow,  Sfor the slug flow.
The flows recognized by the presented system were validated by the human expert. The differences in the flows recognition results were marked in red color. As it can be noticed there were only 3 differences in 45 test flows (2 in plug flow recognition and one in transitional flow recognition) which should be threaten as an excellent result. These differences occurs due to the different expert opinion used. Opinion of the first expert was used during the membership functions designing and the opinion of the second expert was used in the validation process. This situation confirms the authors assumptions of necessity to provide the access to manipulation of the membership functions shape by the system user. After changing the a parameter value for the gas flow rate membership function there were no differences in the recognition results between the human expert and the presented system.
In table 4  The validation routine was as follows:  The human expert set the flow parameters (the gas flow rate and the liquid flow rate);  If the presented system recognition results was equal to the expert opinion, the expert set the desired flow type in the system user panel;  After 30 seconds the recognition of new flow type was made by the system and the expert. Recognition results of the starting and the output flow was placed in table 4.
As it can be noticed there was only one difference in the recognition of the output flow (flow number 4). The reason of that difference was the same as in the recognition process (results in table 3). When the shapes of the membership functions of the gas flow rate were adjusted due to the human expert opinion there was no differences between the presented system and the expert recognition of the output flows results.  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45   Expert recognition  T  T  T  T  T  T  T  T  T  T  T  T  T  T  T   Fuzzy system recognition  T  T  T  T  T  P  T  T  T  T  T  T  T  T  T   Table 4. Control process results

Conclusions
The methods of the two phase gas-liquid flows recognition and the research installation control presented in this paper are innovative solution in this field. The fuzzy logic based algorithms allow to imitate the human expert decision and give the proper recognition results for such dynamic process as the two phase gas-liquid flows. Also the research installation control algorithms can be very useful in the industry. All presented in this paper algorithms and solutions are easy scalable and may be applied to any installations equipped with the ECT diagnostic system and the basic measurement equipment.