Genetic Algorithms Optimized Fuzzy Logic Control to Support the ...

J Control Autom Electr Syst (2014) 25:32–45 DOI 10.1007/s40313-013-0090-6

Genetic Algorithms Optimized Fuzzy Logic Control to Support the Generation of Lightning Warnings Adriel Y. S. Igarashi · Gideon V. Leandro · Gustavo H. C. Oliveira · Eduardo A. Leite

Received: 27 August 2012 / Revised: 25 May 2013 / Accepted: 14 October 2013 / Published online: 23 November 2013 © Brazilian Society for Automatics–SBA 2013

Abstract This paper presents a new method using Fuzzy Logic for generating lightning warnings. This methodology uses information about the atmospheric electric field, the lightning dynamics around the interest site, and lightning distance information. This information was combined by Fuzzy Logic which had its membership functions optimized by Genetic Algorithms. In addition, the objective function was composed by multiple performance indicators proposed in this work. The proposed methodology was tested in a case study, generating lightning warning for an oil refinery. The results were compared with other methods and it was concluded that this new method shows up to be the most effective in generating lightning warnings. Keywords

Fuzzy logic · Lightning · Warnings

1 Introduction According to National Institute for Space Research (INPE), it is estimated that between 50 and 100 Cloud-to-Ground A. Y. S. Igarashi · G. V. Leandro · G. H. C. Oliveira (B) Electrical Engineering Department, Federal University of Parana, Polytechnic Center - Jardim das Américas, Curitiba, Paraná 81531-990, Brazil e-mail: [email protected] A. Y. S. Igarashi e-mail: [email protected] G. V. Leandro e-mail: [email protected] A. Y. S. Igarashi · E. A. Leite SIMEPAR Technological Institute, Polytechnic Center - Jardim das Américas, Curitiba, Paraná 81531-990, Brazil e-mail: [email protected]

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Lightning occurs every second in the world, which means 1 to 3 billion lightning strikes every year (INPE 2012). Both due its large territorial extension and proximity to equator, Brazil has the world’s highest lightning frequency, according to INPE (Pinto 2005). It is estimated that Brazil receives between 50 and 70 million lightning strikes every year, which means two electrical discharges per second or seven times per square kilometer. Due this high lightning incidence, many accidents have occurred in Brazil causing serious social and economic harms. Power lines and electric power distribution equipment are one of the most components affected. About 70 % of interruptions in electric power transmission and 40 % in distribution are related to atmospheric electrical discharges, which causes 40 % of damages in electrical power transformers. Such problems add up losses of 500 million dollars to the Brazilian economy. In society, the loss of human lives is the most important issue, which totals on average 132 victims per year in Brazil, according to INPE (Cardoso 2011). Any atmospheric electrical discharge, reaching ground or not, occurs due to opposite charges between the atmosphere and ground (Montanya et al. 2004). The behavior of those charges creates an electrical field strong enough to exceed the dielectric strength of air and create an electric arc discharge. At this instant there is a large variation in atmospheric electric field that can be detected by special equipment developed for this purpose (Golde 1997; Malan 1963). Even at this moment, there is a large release of electromagnetic radiation in the range 10–300 kHz which can be used as input for lightning sensors. A set of these sensors are able to determine the location of this phenomenon with accuracy up to 500 m (RINDAT 2012). The same way atmospheric electrical discharges (that reach the ground or not) are detected by electric field sensors

J Control Autom Electr Syst (2014) 25:32–45

during their occurrence, it is possible to predict them through the formation of dense electron clusters called charge clusters near the clouds or on the ground (cloud electrification process). This process allows the observation of field changes before any occurrence of atmospheric electrical discharges. Therefore, it is possible to anticipate these events which may result in lightning and then generate risk warnings by observing some properties of the electric field (Murphy et al. 2008). So, by the evaluation of several electric field proprieties, it is possible to foresee the phenomenon that may result in lightning (Murphy et al. 2008). Many researches about electrical discharges relate the behavior and magnitude of electrical field with the risk of atmospheric electric discharges over sensing range (Murphy et al. 2008; Beasley et al. 2005). However, there is not yet an agreement about the electric field boundaries above which there the occurrence of lightning and, as a consequence, a generation of alert. In this context, there are few studies available in the literature that describe or develop lightning forecasting methods. Frankel et al. (1991), used variables like wind, electric field, and data from lightning to construct and train an artificial neural network to create a probability occurrence map of hazard events, such as lightning. The study was focused at Kennedy Space Center (KSC) and Cape Canaveral Air Force Station (CCAFS) in Florida. Nagae et al. (2000) developed a lightning prediction system using fuzzy logic neural network during research in Japan. The authors were able to predict discharges occurrence one hour earlier. The results prove that this tool can be efficient and easy to implement. Using the model in a limited area or mesoscale, known as MM5 (Dudhia et al. 2002), and data from correlations between electrical discharges and meteorological variables, Zepka (2005), developed a lightning predictor using artificial neural network (ANN). The meteorological variables (model outputs) were selected as input in ANN algorithm, which generates the prediction of the number of lightning occurrence that will reach the ground in future. Igarashi et al. (2009) studied about sensors applied in atmospheric electric field detection and measurement related to lightning strikes in their proximity. The behavior of the electric field prior to the first lightning was also analyzed, coming to the conclusion that it is possible to identify a default behavior of the electric field for such cases. In addition to these established relationships, the efficiency of conventional warnings those activated when the measured electric field exceeds a pre-established value was also studied. Frisbie et al. (2009), using parameters of instabilities and moisture obtained from a meteorological model, proposed the Lightning Potential Index (LPI) in order to predict the location and frequency of lightning occurrence in the city

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of Grand Junction, Colorado, EUA. The index was obtained from an empiric equation and is divided into four levels of risk: low, moderate, high, and extremely high. Despite being a useful indicator for the region where the lightning can occur, the electrical activity is underestimated in areas with strong upward movement since meteorological variables related to mechanisms for the survey are not counted in the calculation of LPI. Zepka (2011) established an methodology to predict the lightning occurrence from meteorological variables obtained from high space definition numerical simulation with mesoscale model called Weather Research and Forecasting (WRF). Two different methods were capable of qualitative evaluation of lightning occurrence, the linear and normalized methods. The second one was consider more appropriate for this purpose because it could represent the atmosphere environment during a discharge e, and because of that, obtain better accuracy determining the point of lightning strike. Igarashi et al. (2011), from atmospheric electric field data and rainfall index, noted that it is possible to minimize the warn time compared to the upper limit electric field method. But, some preliminary studies of this method were not capable of generating warnings earlier enough. This study proposes a methodology to generate lightning warning based in fuzzy system with the following input variables: electrical field upper limit, distance between different discharges focusing on the same center of the target (location that will receive the discharge warning), and lightning dynamics study, if the lightning strikes were getting closer or further away from the studied region. Note also that the location of interest (center of target) can be an oil refinery, a power electric substation, or any other installation that need this type of alert. The optimized membership functions used in fuzzy system were obtained using genetic algorithms and built with an objective function evaluated by four performance indicators, also proposed in this paper. The proposed method differs from similar papers in literature due to its application of fuzzy logic method, being based on a few meteorological information, do not need complex meteorological models such as mesoscale, and having as objective the generation of lightning warning on specific area which requires high safety control and property time of evacuation. When it comes about lightning warning in a specific zone there is a traditional warning system available. This aims to reach improvements over the traditional system. In this sense, from the point of view of the application or installation that will receive the warning, the following indices are important: • Total hours upon warning advice; • Total number of warns;

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• False alarm percentage; • Average advance time about 30 min. All methodologies presented in this paper were tested and compared using a case study with real data. The goal is to achieve a propriety lightning warning in an oil refinery and check its efficiency regarding some issues aforementioned to compare the methods. This paper is divided in four sections: mechanisms to support decision making, in this section the variety of measurement equipment and tools used in warning management system design will be studied; the methodology, which will discuss the heuristic methods developed and its techniques; the final results obtained after a case analysis; and the final remarks.

2 Supporting Tools for Decision Making One of mechanisms to support decision making tools for lightning warns is the electric field sensor, known as FieldMills. The FieldMills are responsible for instantaneous measurement of the intensity of an atmospheric electric field vertical component; in other words, the electromagnetic magnitude data collection related to lighting occurrences. Note that the FieldMills measures electric field associated to atmospheric electrical discharges that may or may not reach the ground. The operating principle of FieldMills is based on charge and discharge process of parallel plates, the operating process is similar to capacitors. The Fig. 1 shows the FieldMill main

Fig. 1 a Electrification process of FieldMill plates when shutter is open. b Discharge process of FieldMill when shutter is closed. Source (Mission Instruments 2012)

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pieces, which are: an engine, responsible by the shutter opening; a flat plate sensor, responsible by measuring the concentration of charge; and a signal amplifier. The process of estimating the intensity of the vertical atmospheric electric field can be seen in Fig. 1a where the atmospheric electric field is focusing to the flat plate sensor. This causes a concentration of electrical charges from connection between equipment and ground in flat plate sensor. In Fig. 1b, the shutter closes causing the atmospheric electric field to no longer focus to the sensor. Consequently, the previously sensor charges will be back to the original position, the ground. On its way to ground, the charges will induce a current flow proportional to the atmospheric electrical field magnitude, leaving the amplifier translate it to its actual value measured in units of volts per meter (Mission Instruments 2012). Another support mechanism is the Nation-wide Integrated Atmospheric Discharges Detection Network (RINDAT). This network provides solid information about lighting occurrences and other data as incidence hour, peak current, and position uncertainty ellipsoid. This system uses technologies called Lightning Positioning and Tracking System (LPATS) and Magnetic Direction Finder (MDF) (RINDAT 2012). This network is able to provide location information of lightning with average accuracy of 500 m. Besides that, the system operates with Global Positioning System (GPS), which can determine time occurrence of lightning with 300 nanoseconds resolution. After lightning sensing detection, its information are sent to processing centers where they are evaluated in order to obtain localization and technical features. All this informa-


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Fig. 2 Electrical Field observed in three different electrical field sensors after occurrence of electrical discharges

tion are available in real time or saved in database for future evaluations. The RINDAT has five plants in: Belém; Belo Horizonte; Curitiba; Rio de Janeiro; and São José dos Campos. The RINDAT’s signals obtained from sensors were transmitted by a dedicated communication channels to each processing plant, where data are evaluated and transmitted to observation units and data storage. In Fig. 2 it is possible to find information available from two of those tools to support lightning warning decision making. The electric field behavior measured by three FieldMill sensors is presented on top of Fig. 2. In the bottom, there are all lightning occurrences at the same region, obtained from RINDAT data. In Fig. 2, a correlation between lightning incidence and variations in electrical field magnitude measured in the region of interest can be seen.

3.1 Conventional Warning

values of electrical field in the studied region. Because of that, the conventional alerts are mathematically defined by two parameters: the limit of the module of the electric field (Lim) and the minimum residence time (TP). The Lim and TP parameters are defined by users and systems designers. The lower the Lim, the more conservative turns the system which can cause unnecessary warns (false warn). The higher the TP, the more conservative will be the system, but in this case this value impacts the economic cost, because it implies the stop of production. This kind of situation can be well understood when represented by vectors. It can be defined as a vector d that corresponds to the previous established residence time (TP). The elements of this vector are the electrical field maximum values obtained from the sensor network (FieldMills) displaced in time every minute. Doing so, the conventional warning will begin when the latest value exceeds the limit (Lim) and will stop when, within the vector, any value is greater than the upper limit. In the next figure (Fig. 3) an example of how this method works is shown: To the next minute (Fig. 4): In case of, in the first examples, a threshold value equal to 2000 V/m is adopted, it would not have any warn. However, as soon as there is a value whose magnitude is greater than the threshold, there will be an electric field occurrence (Fig. 5).

The methodology usually employed to generate warning of lightning incidence is based on electric field threshold that will suggest the input and output of the warning. This methodology will be named as conventional warning (traditional method) Igarashi et al. (2009). The conventional warning generates a signal that depends only on the atmospheric electrical field amplitude; in other words, the alert is extinguished based upon past and present

Fig. 3 Dimension value d = 30, meaning, TP = 30 min

3 Metodology In his section the conventional method of warning, based only on FieldMill is shortly described, after that the warning method based on fuzzy logic, proposed here, is presented.

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Fig. 4 Electric field vector in the first minute after start


threshold. In “2” it can be noted that the total resident time with warning is set as one by this method. It is also possible to observe the residence time (TP) in which the amplitude modules of the atmospheric electric field return to within the range of threshold values. Represented by the signal in “x” format, in red, the occurrences of electrical discharges and its distances (ordinate axis at right) regarding to the center point of interest are illustrated. 3.2 Fuzzy Logic Warning

Fig. 5 Electrical field vector with magnitude bigger than limit

In this case, there will be a warning that will last at least 30 min, meaning that, until there is no longer any field element whose magnitude is higher than 2000 V/m in the vector. The conventional warning will have a state equal one (warning on) when the electrical field magnitude at the present instant is greater than the electrical field upper limit. The warning will remain set as one at least one period equal to the residence time (TP) and only when all values became under the electrical field module and its size is equal TP, the warning will be set as zero (warning off). In case of an electrical field equipment network, the instantaneous value used in electric field will be the maximum magnitude in module among all installed equipment. This method is shown in Fig. 6. The variation of electric field can be observed through the three series that comprise the chart. The electrical field vector for each one of those series is indicated in the ordinate axis at left. In this figure the electrical field upper limit (red lines) and the resident time (TP) can be seen. In “1” it is shown that the warning was activated by one electric field value that has passed on the Fig. 6 Electrical field changes in case of electrical discharge and characteristics of a boundaries-based warning

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As already mentioned, this paper uses the theory of fuzzy sets as mathematical tool for the following reasons: work with fuzzy sets as main mathematical tool due the following reasons: the existence of some uncertainties regarding the optimal electric field level to activate a warning system; the influence of other lighting in region that has already reached the ground; and because of the lack of accurate mathematical models about meteorological event dynamics. Due to all these uncertainties, this paper proposes the following input data for the fuzzy logic model: upper absolute value of an electric field; distance between lightning occurrences and the center of the target (where the electrical discharges reach the ground); and lightning event dynamics, if the electrical discharges are approaching or moving away from the landmark. The landmark can be an oil refinery, an electric power substation, or any other place that requires this kind of warning. Each input variable was converted to linguistic variables. Those new input variables will represent the subjective knowledge about the warning of lightning occurrence; in other words, how each variable can influence in warning decision making. However, as it is an innovative approach, the intervals for each input variable were initially defined upon observations and then optimized using genetic algorithms.


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Fig. 7 Representation of electric field maximum value, in module, obtained from FieldMill sensors belonging to the area in study

The first input used the maximum electric field modulus between all sensors part of the network at an instant of time. This is the main measured variable that indicates possible occurrences of lightning due to its physical relationship to the production of this meteorological phenomenon. The Fig. 7 represents the same period used in Fig. 2, but this time it is possible to see with greater clarity the electrical field behavior during atmosphere electrification. The distance variable from the last lightning events was added in order to consider the existence of lightning near the monitored region and which can generate new incident lightning in the region. This approach has been inserted through the creation of a circle with a diameter of 200 km divided into smaller circles. In total 6 circles were created around the target with the following diameters: 20, 40, 60, 100, 140, and 200 km. The last input for the fuzzy inference system represents the event dynamics. For that, two data vectors displaced in time intervals of one minute each were created, with the first vector having the dimension of “n,” and contains the “n” most recent data, and the second dimension “m,” and contains the “m” latest data. The Fig. 8 shows these two vectors where each element “dt” represents the closest lightning occurrence distance in the time interval “t” that last one minute. The last position vector “n” will occupy the first position of the vector “m” after one time offset. From these two vectors, the event dynamics, in other words, where the discharges are moving to, can be analyzed using a solution that maximizes the variables and results in the greatest covered distance in a time period. This

Fig. 8 Component vectors of the heuristic event dynamics

relationship is easily obtained by subtracting the maximum value contained in the vector of less recent distances, and the minimum of the vectors contained in the most recent distances. The result of this approach can be negative or positive. If the difference becomes positive, it means the event (or lightning) is moving toward the target, otherwise the event is moving away from the target. The value obtained represents the longest distance between two discharges occurring within the period equivalent to the sum of the two vectors sizes, n+m min. 3.2.1 Fuzzification of Input variables The input variables used in fuzzy system are: (i) Electrical Field Amplitude; (ii) Distance of lightning incidence; (iii) Lightning event dynamic. The proposed fuzzy logic method used the fuzzification of all three input variables presented by 15 membership functions of Gaussian type, s-shape and z-shape, whose adjustments were based on information obtained in tests and also through expert knowledge. This type was chosen because it can be characterized by only two parameters, simplifying optimization procedures. The membership functions terms for electric field variable are shown in Fig. 9, divided into 3 categories. These membership functions indicate that the value of the variable input is “Low,” “Medium,” or “High,” which will allow the verification of the electric field state. These three membership functions can well express the influence of electric field in the phenomenon of lightning. “Low” is the absence of correlation with incidence of lightning, “High” a great correlation, and “Medium” a threshold value.

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Fig. 9 Membership functions for fuzzification of the electric field variable

Fig. 10 Membership functions for distance variable fuzzification

Fig. 11 Membership functions for fuzzification of the variable representing the dynamic event

The input variable electric field universe of discourse was set between 0 (zero) to 10,000 (ten thousand) V/m and describes the values of the electric field with the highest probability of lightning. In Fig. 10, the membership functions for the distance variable fuzzification process can be seen, divided into 7 categories: “Very-close (VC), Close (C), Little-close (LC), Middle (M), Little-far (LF), Far (F), and Very-far (VF).” Those categories were created in order to give greater importance to closer discharges. It is noted that the distances are not equidistant because more membership functions were placed around 30 km from the target than in more distant regions. These regions were chosen and distributed according to the observations of experts. It is also seen that the universe of discourse for this input was limited to one hundred miles, as it is considered that an event occurring beyond these limits is not capable of generating changes in the electric field and it

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will hardly course this distance in less time than the optimal advance time. For the input event dynamic variable, Fig. 11 highlights the proposed membership functions, divided into five categories: “Moving away fast (MAF),” “Moving Away (MA),” “Stopped (S),” “Approaching (A),” and “Approaching Fast (AF).” This classification was performed in order to express the main speed levels used for the event. The universe of discourse for this variable is defined as the interval between −20 and 20 km. Note that this distance is the biggest difference between two discharges occurring within a given time period. Thus, the bigger difference in the interval, the faster the displacement of the event. The smaller the difference, the slower its speed. The fuzzy logic proposed uses the defuzzification of output variable by five membership functions, as illustrated in Fig. 12. These membership functions indicate that


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Fig. 12 Membership functions for the defuzzification of the electric field variable

the output variable value is in a level “Low,” “MediumLow,” “Medium,” “Medium-High,” or “High.” It was choice equidistant levels and triangular membership functions to accentuate a linear behavior in the output variable evolution. 3.2.2 Inference Procedure The inference procedure, which is responsible for fuzzy logic development, composed of 105 rules, covers all possible circumstances of the addressed problem (Pedrycz and Gomide 1988). In this work, all the rules were established through the author’s knowledge. The 105 fuzzy inference rules relate the three system inputs with a single warning output through operators of type If premise So conclusion. The implication operator used was minimum value type, or Mamdani (Mamdani and Assilian 1975). 3.2.3 Defuzzification Since the use of the Mamdani model, it was necessary to perform the step of conversion of fuzzy values in non-fuzzy step called defuzzification. Models defuzzification should be selected according to the type of problem studied and target solutions, leaving to the experts the most suitable choice. Some models do not require defuzzification, such as Takagi–Sugeno (Takagi and Sugeno 1983) and the Tsukamoto (Tsukamoto 1979), since such models already get the values directly through the rules of inference. These models are ideal for processes where there is a mathematical function that can associate output variables. The most suitable method to the interests referred in this work was the method of central area, also called the centroid (Simões and Shaw 2007). 3.2.4 Decision Making The warning decision making followed the same procedure of conventional warning method. Defuzzificated val-

ues were inserted into a vector with predetermined size and the warning decision making method is based on a threshold defined by observations of experts or via process optimization. When a defuzzificated warning value within this vector exceeds the threshold, the alert will be activated and will last for minimum time equal to the dimension of this vector, in minutes. It will be disabled only when all component values of the vector are below the established limit. With the defuzzificated relative alert level value, it was still necessary to establish a threshold value so that the warning will remain on for a minimum period of time. This process is identical to that used in the thresholds method based only on the electric field. 3.3 Membership Function Optimization In order to verify the suitability of membership functions initially proposed, some computer tools were used in order to get the best results for the problem characteristics. The search engine used in this work is known as Genetic Algorithms. These algorithms are based on principles of natural selection, evolutionary theory, and genetics. It searches for optimization of expressed criteria using a fitness function (Goldberg 1989). In order to define the objective function in this paper four indicators are proposed that show, through numbers, the system performance. In the following sections each of these indicators is described. Therefore, we assume that these indicators are set in a time period T and related to a particular region of interest. 3.3.1 Performance Indicators Number of Warning (NA) This indicator is defined in a time period T and indirectly causes economic impacts, because each warning requires an effective lap time to work, the worker tends not to return to with the same vigor as when it came out, affecting productivity.

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Definition: NA =

T

ea

(1)

where: • ea—warning event, 1 when warning is on and 0 if is not. Warning Hours (HA) It is a key indicator for the analysis of the costs associated with the alert. This indicator is based on the amount of hours on alert during the analyzed period T. Due to its characteristics, it can cause both financial and societal impact. For the case in question, the indicator will be related to the cost of man-hour stopped, decreased production, and increased runtime of a job. Definition: HA =

NA

hai

(2)

i=1

• ti —Time of occurrence of the first lighting in the event. • t0 —Time from the start of the warning. • n—Number of times there was warning and lightning in the analyzed period. To be recorded, at least one occurrence of lightning during the alert is needed. This also assumes that (ti − t0 ) is limited to 60 min. 3.3.2 Genetic Algorithms for Optimization Several sets were used for Genetic Algorithms (GAs); however, the option that presented the highest convergence in the context of the present work was the following: • Elitist selection method; • Tournament selection between four individuals in the population; • Individual uniform mutations with rate of 20 %; • Two points Crossover with 80 % rate.

where: • ha—Total warning hours during period T. • N A—Total number of warning during period T. Percentage of Uncovered Lightning (PRD) This indicator was developed in order to estimate the percentage of lightning occurrences that were not covered by warning, what is undesirable. This indicator is particularly important because it is related to the safety and protection of human lives. This indicator is defined as follows: 100 nrd nr T

PRD =

(3)

where: • nr d—Lightning occurrences not covered by warning during T period. • nr —Total lightning occurrences during T period. Mean Time Prior the First Discharge (TMA) Temporal efficiency indicator related to advance time generates an advanced warning; it means time is measured before the first lightning occurrence in the target. Its level will directly affect the prevention of accidents, because the warning should be turned on sufficient time before to eventual decision making. It can be defined as follows: TMA =

n 1 (ti − t0 ) n i=1

where:

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(4)

The mutation with rate of 20 % was used to ensure population diversity; however, it was carefully selected in order to keep the acquired information contained in individuals during the past generations, using the elitist selection method. Furthermore, in order to limit the processing costs and match the algorithm to the problem, the optimization was divided in two steps: – The first containing only the intrinsic variables which are the 30 membership functions variables. Lower and upper bounds were also established. Knowing that there are 15 membership functions, each one is defined by two parameters (mean and variance), – The second containing extrinsic five fuzzy logic variables. The parameters “m” and “n” refer to the dynamics of the event, the time interval of the electric field, the alert threshold and its minimum residence time. The optimized genetic algorithms membership functions was first used by Karr (1991), when applying genetic algorithms to solve the control problem of the inverted pendulum. Since then, other researchers have applied this technique to several problems: Meredith et al. (1992), Araújo et al. (2003), and Arslan and Kaya (2001). Due to the great combinations possibilities between the parameters used, it was chosen to set the population’s first individual, instead of generating it randomly. Moreover, due to limitations of computational hardware, 30 population individuals were selected and as stopping criteria, a maximum of 50 generations. The objective function proposed to quantify the performance of the warning method generation equals objective


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function from AG method. A time interval T and a composition of the many performance indicators defined for the problem are set. The equation is shown below: OF = k1

|TMA − 28| PRD HA NA + k2 + k3 + k4 2 136 28 105

(5)

The denominators values were considered ideal for the analyzed period and were employed in order to obtain a result less than 1 if there is improvement, or greater than 1, if performance is considered worse than ideal for the period. The indexes of PRD, HA, and NA values considered ideal were chosen according to the warning need and the period of analysis. Such values were defined in order to adapt them to the reality and conditions required by the alert system user. The values shown in (5) are illustrated for the case of an oil refinery. Regarding TMA, an exact value of 28 min is set. The equation will “penalize” the values larger or smaller than the proposed one. Despite the ideal advance time be 30 min, 28 was chosen since the FieldMill does not have a large area of sensitivity. However, the results of this research showed that it is possible to get 30 min of TMA. The ki indexes represent the weights given to each performance index. These rates can vary depending on the problem requirements, the more important a parameter is, the greater its weight.

4 Results The methods reported in this paper were tested on an area of 10 km diameter around an oil refinery where three FieldMill are installed, where electric field data are collected. Such arrangement allows full coverage of the area and enables the increases in lead time warnings (Igarashi et al. 2009). It is important to say, based on previous studies (Lacerda et al. 2010), that the FieldMill region’s sensitivity is approximately 5 km around it, so the region of interest was fully covered by the sensing area of the equipment. The results are presented in two phases, one for optimization (training) and another for validation. Initially the process optimization through genetic algorithms was made during

2 months and 126 incident lightning occurrences in the region of interest. Validation was done by adding more 10 months, a total of 12 months of incident discharges, 285 occurrences on the area of interest. As described in the previous section, the optimization process of system variables is done. Therefore, it is assumed that the parameters of the objective function (5) are: • • • •

k1 k2 k3 k4

= 4; = 4; = 6; = 8.

The choices of indices ki were made by specialists. The main indicator used was the NA, because it sought to reduce the number of alerts and consequently avoid unnecessary evacuation of people from the region without risk. In the second place, the TMA variable was prioritized to enable an advance time high enough to promote safe egress of people. The results of the optimization process can be seen in Figs. 13 and 14, which, respectively, show the convergence of the objective function for the intrinsic and extrinsic variables. It is noted that the value obtained by intrinsic optimizing is the same as the beginning of the extrinsic optimization process since this process began with the best result of the intrinsic optimization. The convergence process brought new membership functions. Figure 15 shows the result of the optimized membership functions for electric field variable: Observing Fig. 15, it can be noted that the solution to the optimization problem may not often coincide with the proposed from a rational point of view, particularly when looking at the range between 3000 and 4000 V/m. It must be emphasized that the results do not depend only on membership functions, but also on the rules of inference and data used in the optimization. Figs. 16 and 17 show the other optimization results for distance and event dynamics variables, respectively. In Fig. 17 we observe that the optimization process led to a simplification of the membership functions, because the “stop” function is part of the function “Approaching.” So it

Fig. 13 Convergence process of the objective function for the optimization of membership functions (intrinsic optimization)

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Fig. 14 Convergence process of the objective function for the optimization of extrinsic functions

Fig. 15 Optimization process result for membership functions of the electric field variable

Fig. 16 Results of the optimization process for membership functions of the distance variable

Fig. 17 Results of the optimization process for membership functions of the event dynamics variable

can be eliminated, along with its rules of inference, without prejudice to the system. After membership functions optimization, it has the following indicators results (Table 1): The validation process was done by extending the analysis period to 12 months. Table 2 shows the results obtained for that period.

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It is observed that the validation period is 6 times larger than the optimization. However, there are several months (especially during winter) in which the occurrence of lightning is practically nonexistent, which explains the disproportion of the values in Tables 1 and 2. The same optimization algorithm was applied to the extrinsic variables. In this case the results of intrinsic opti-


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Table 1 Results of the intrinsic optimization process via Genetic Algorithms for the period of 2 months (optimization) HA NA PRD TMA OF Fuzzy Warning optimized intrinsically 80

79

0.8

29

10.3

Table 2 Results of the intrinsic optimization process via Genetic Algorithms for the period of 12 months (validation) HA NA PRD TMA OF Fuzzy Warning optimized intrinsically 190 180 4.5

31

29.1

Table 3 Results of the extrinsic optimization process via Genetic Algorithms for the period of 2 months (optimization)

Fuzzy Warning optimized intrinsically and extrinsically

HA

NA

PRD

TMA

OF

91

52

0.8

29

8.4

Table 4 Results of the extrinsic optimization process via Genetic Algorithms for the period of 12 months (validation)


HA

NA

PRD

TMA

OF

217

121

3.1

32

22.8

Table 5 Comparison between warning systems presented in this work HA NA PRD TMA OF Conventional Warning

345 217 4.5

Fuzzy Warning without optimization

164 135 9

32

36.7

29

33

Fuzzy Warning optimized intrinsically 190 180 4.5

31

29.1


32

22.8

217 121 3.1

Observe that, from the objective function point of view, the use of optimized Fuzzy Logic with intrinsically and extrinsically membership functions were more effective than the other methods. This approach achieved better results in the percentage of lightning prediction (PRD) and number of alerts (NA). But, due to the reduction of the PRD, the warning hours (HA) were increased. It is noticed that these two indicators are antagonistic, because to obtain a lower PRD it is necessary to increase the HA. This fact can be verified by the method of fuzzy warning generation without optimization, which had the lowest number of HA, but a PRD above the ideal. The NA is related to the period of analysis and has little influence on the other indexes. The Fig. 18 shows the comparison between the obtained objective functions, it is known that the smaller the function, the better the result. After analyzing the results, the difficulty of choosing a more important indicator is clear. It can be verified that there was no Fuzzy system to present an improvement in all index performance. A low value of NA, combined with a suitable PRD, which is directly related to protection of individuals and plants in region of interest, is indicated in order to reduce unnecessary evacuation of workers and, finally, it is essential to obtain appropriate advance time to promote safe egress and allocation in proper time, estimated to be about 30 min. After all, the number of warning hours is significant due its economic impact. The cost is caused by the amount of hours while employees will be prevented from carrying out their activities. Thus, the solution to this problem cannot be based only in one performance indicator and it is through the objective function that such choice is done. Based on it, the Fuzzy Logic warning system with intrinsic and extrinsic Genetic Algorithms optimization presented the best combination of results; which indicates a great progress compared to pasts researches (Igarashi et al. 2011).

The best result among all systems is in bold format

5 Conclusions mization were used as a starting point which means that the system had optimized membership functions, and in this step the external parameters will be optimized to it. Likewise, the optimization was made for a period of 2 months and validation for 12 months. The results for both processes, optimization and validation, are shown in Tables 3 and 4. In order to demonstrate the improvement of the Genetic Algorithms optimized Fuzzy system, proposed in this paper, a comparison was made between conventional alerts based only on the electric field with a threshold equal to 2000 V/m and a Fuzzy system without optimization. The results can be seen in Table 5.

This work showed that the lightning warning incidence based on Fuzzy Logic can be more efficient than the conventional warnings based only on the electric field. The use of other sources of information, such as the event dynamics and the distance of occurrence, when properly associated by Fuzzy Logic, made a lightning occurrence to become more predictable, causing an increase in mean advance time prior the first discharge and also reducing the warning hours when compared to conventional warning system. Furthermore, the optimization of such systems proved to be feasible for the problem at hand. Through this study, the use of real weather data showed that, despite the greater number of hours over all systems based on Fuzzy Logic, the intrinsic and extrinsic

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Fig. 18 Comparison of the objective final results functions for the validation period

optimized system is quite effective to protect human life in view of fewer amount of lightning occurrences not alerted and total number of warning. Acknowledgments This work was supported by the Technological Institute SIMEPAR, through which the necessary financing to carry out activities relating to this paper was obtained. Moreover, due to SIMEPAR the assignment of the data used in this paper was possible, and due to CNPq and SETI/Araucaria Foundation the granting of scholarships to developing study as well new technologies concerned in this work was possible. The third author acknowledges the support of CNPq and Araucaria Foundation.

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