Application of Fuzzy Logic in Environmental Engineering for Determination of Air Quality Index

Transcription

1 Application of Fuzzy Logic in Environmental Engineering for Determination of Air Quality Index Anaokar G.S. 1 Research Student Civil Engineering Department Sardar Vallabhbhai National Institute of Technology Surat, Gujrat, India. Abstract Fuzzy logic is a powerful problem solving methodology and mathematically it is a superset of Boolean or Crisp logic. The term "fuzzy" refers to the logic involved which can deal with concepts that cannot be expressed as the "true" or "false" but rather as "partially true" or partially false. This makes it easier to mechanize tasks that are already successfully performed by humans. Fuzzy logic has based on fuzzy set theory. Fuzzy logic is a complex mathematical method that allows solving difficult simulated problems with many inputs and output variables. In Environmental Engineering it is difficult to judge the severity of pollution by layman. A present paper focus on w1determination of air quality index by using Fuzzy Logic systems. Keywords Fuzzy, logic, variables, air quality, index. I. INTRODUCTION Fuzzy logic is a powerful problem solving methodology and mathematically it is a superset of Boolean or Crisp logic. Fuzzy logic was first proposed by Lotfi A. Zadeh of the University of California at Berkeley in a He elaborated on his ideas in a 1973 through introduction of the concept of "linguistic variables", recently considered as a fuzzy set. When way to assign some rational value to intuitive assessments of individual elements of a fuzzy set. It is essentially need to translate from human fuzziness to numbers that can be used by a computer. It is a problem-solving control system methodology that lends itself to implementation in systems ranging from simple, small, embedded micro-controllers to large, networked, multi-channel computers or workstation-based data acquisition and control systems [2]. In environmental engineering different issues need to analyzed on the basis of human interface, Determination of pollution level is one of them. As the pollution intensity is being measured through no of processes and can be interpreted by no of ways, a common index or number which could be able to Khambete A. K. 2 Associate Professor Civil Engineering Department Sardar Vallabhbhai National Institute of Technology Surat, Gujrat, India. give an idea about pollution intensity to layman will be helpful to avoid further health risks. Air quality in cities in India gets diminished due to flooded populations, day by day increasing vehicles utility, rapid industrialization and unawareness. A World Health Organization (WHO) report in 2014 had 14 Indian cities among the top 20 most polluted cities of the world. Those 14 were Delhi, Patna, Gwalior, Raipur, Ahmedabad, Lucknow, Firozabad, Kanpur, Amritsar, Ludhiana, Allahabad, Agra, Khanna and Pune. (Source: The Hindu; 16 th July 2015). The major cause of increased air pollution in Indian megacities includes unprecedented surge in the number of vehicles, the expansion of road network and increase in built-up area. The Indian Institute of Topical Meteorology (IITM) has revealed that Pune s pollution level is over twice that of the prescribed national air quality standards. Air quality index (AQI) is a number used by government agencies to communicate to the public how polluted the air currently is or how polluted it is forecast to become. As the AQI increases, an increasingly large percentage of the population is likely to experience increasingly severe adverse health effects. As this will be an indicative number, will be easily interpretable to layman. Air Quality Index is being calculated on the basis of the concentration of air pollutants like SO 2, NO 2, CO, PM 2.5, PM 10, Temperature, etc. It is necessary to bring all these parameters under single indicative number which can give an idea about air quality. The Fuzzy logic system helps to identify this unique number by considering these parameters as membership functions and applying necessary rule base. Present work is carried out with due reference of worked carried out by G.Vijayaraghavan et. all; Shah Abhishek et. all. and Bai V et. all. In this paper the air quality model for city Pune, has been 109

2 developed. The necessary data is fetched through Maharashtra Pollution Control Board and processed through the software FisPro3.5. II. FUZZY LOGIC SYSTEM A. Classic Set Theory The classical set theory is built on the fundamental concept of set of which an individual is either a member or not a member. A sharp, crisp, and unambiguous distinction exists between a member and a nonmember for any well-defined set of entities in this theory, and there is a very precise and clear boundary to indicate if an entity belongs to the set. In other words, when one asks the question Is this entity a member of that set? The answer is either yes or no. This is true for both the deterministic and the stochastic cases.[1] Let S be a nonempty set, called the universe set below, consisting of all the possible elements of concern in a particular context. Each of these elements is called a member, or an element, of S. A union of several (finite or infinite) members of S is called a subset of S. To indicate that a member s of S belongs to a subset s of S, we write s S. If s is not a member of S, we write s S. To indicate that S is a subset of S, we write S S. Usually, this notation implies that S is a strictly proper subset of S in the sense that there is at least one member x S but x S. If it can be either S S or S = S, we write S S. An empty subset is denoted by. A subset of certain members that have properties P1,..., Pn will be denoted by a capital letter, say A, as A = { a a has properties P1,..., Pn }. Thus in the classical set theory, it is not allowed that an element is in a set and not in the set at the same time.[14][16] Thus, many real-world application problems cannot be described and handled by the classical set theory, including all those involving elements with only partial membership of a set. B. Fuzzy Set Theory Fuzzy set theory accepts partial memberships, and, therefore, in a sense generalizes the classical set theory to some extent. Fuzzy sets, on the other hand, allow elements to be partially in a set. Each element is given a degree of membership in a set. This membership value can range from 0 (not an element of the set) to 1 (a member of the set). It is clear that if one only allowed the extreme membership values of 0 and 1, that this would actually be equivalent to crisp sets. 110 In order to define the characteristics of fuzzy sets; we are redefining and expanding the usual characteristics of classical sets.[14][16] A classical set might be expressed as A = {x x > 6} Fuzzy set A in X is defined as a set of ordered pairs. A = {x, µa(x) x X} µa(x) is called the membership function (or MF) of x in A. The membership function maps each element of X to a membership value between 0 and 1. C. Fuzzy Terminologies 1) The Boolean algebra: In this algebra, there are only three basic logic operations: negation, and, and or. For ease of algebraic operations, it is common to use symbols,, and +, as summarized in Table 1. [1][16] A Boolean algebraic formula can be completely described by a truth table, where all the variables appearing in the formula are listed as inputs and the value of the entire formula is the output. TABLE 1 TRUTH TABLE FOR BOOLEAN OPERATORS Name Symbol Example Meaning AND. a.b Both a and b must be true for the entire formula to be true. OR + a + b If either a or b, or both, is true then the entire formula is true. NOT - ā If a is true then the entire formula is false; if a is false then the entire formula is true. The operators need to be defined as function for all possible fuzzy values that is all real numbers from 0 to 1 inclusive. Fuzzy logic is actually a superset of bivalent logic since it includes the bivalent option (0, 1) as well as all reals in between.[4] A generalized form of these operators can be worked out as TABLE 2 TRUTH TABLE FOR FUZZY OPERATORS x AND y min (x, y) x OR y max (x, y) NOT x 1 - x 2) Fuzzy Rules: Fuzzy machines, which always tend to mimic the behavior of man, work the same way. However, the decision and the means of

3 choosing that decision are replaced by fuzzy sets and the rules are replaced by fuzzy rules. Most decisions that people make are logical decisions, they look at the situation and make a decision based on the situation. Fuzzy rules also operate using a series of if-then statements. [14] For instance, if X then A, if y then b, where A and B are all sets of X and Y. Fuzzy rules define fuzzy patches, which is the key idea in fuzzy logic. The generalized form of such a decision is called a generalized modus ponens, which is in the form: If P, then Q. P; Therefore, Q. This form of logical reasoning is fairly strict, Q can only be if P. Fuzzy logic loosens this strictness by saying that Q can mostly be if P is mostly or: If P, then Q. mostly P. Therefore, mostly Q. Where P and Q are now fuzzy numbers. The reasoning above requires a set of rules to be defined. These rules are linguistic rules to relate different fuzzy sets and numbers.[16] 3) Membership Function: The membership function is a graphical representation of the magnitude of participation of each input. It associates a weighting with each of the inputs that are processed, define functional overlap between inputs, and ultimately determines an output response. [1][16] The rules use the input membership values as weighting factors to determine their influence on the fuzzy output sets of the final output conclusion. Once the functions are inferred, scaled, and combined, they are defuzzified into a crisp output which drives the system. The Shape of the membership function used defines the fuzzy set and so the decision on which type to use is dependent on the purpose. The membership function choice is the subjective aspect of fuzzy logic, it allows the desired values to be interpreted appropriately. FIGURE 1 MEMBERSHIP FUNCTIONS 4) Linguistic variable: In 1973, Professor Lotfi Zadeh proposed the concept of linguistic or "fuzzy" variables. Think of them as linguistic objects or words, rather than numbers. The sensor input is a noun, e.g. "temperature", "displacement", "velocity", "flow", "pressure", etc. Since error is just the difference, it can be thought of the same way. The fuzzy variables themselves are adjectives that modify the variable (e.g. "large positive" error, "small positive" error,"zero" error, "small negative" error, and "large negative" error). As a minimum, one could simply have "positive", "zero", and "negative" variables for each of the parameters. [16] 5) α-cut: An α-level set of a fuzzy set A of X is a non-fuzzy set denoted by [A]α and is defined by [A]α = t X A(t) α} if α>0 cl(suppa) if α =0 where cl(suppa) denotes the closure of the support of A. 6) A fuzzy number: A fuzzy number A is a fuzzy set of the real line with a normal, (fuzzy) con- vex and continuous membership function of bounded support. The family of fuzzy numbers will be denoted by F. [14][1] D. Fuzzy Inferance System: Fuzzy inference (reasoning) is the actual process of mapping. This process starts from a given input and finishes to an output using fuzzy logic. The process involves all the pieces that we have discussed in the previous sections: membership functions, fuzzy logic operators, and if-then rules.fuzzy inference systems have been successfully applied in fields such as automatic control, data classification, decision analysis, expert systems, and computer vision. Because of its multi-disciplinary nature, the fuzzy inference system is known by a number of names, such as fuzzy-rule-based system, fuzzy expert system, fuzzy model, fuzzy associative memory, fuzzy logic controller, and simply fuzzy system. The most important two types of fuzzy inference method are Mamdani and Sugeno fuzzy inference methods, Mamdani fuzzy inference is the most commonly seen inference method. This method was introduced by Mamdani and Assilian (1975). Another well-known inference method is the socalled Sugeno or Takagi Sugeno Kang method of fuzzy inference process. This method was introduced by Sugeno (1985). This method is also called as TS method. 111

4 III. METHODOLOGY A) Crisp Data set: Air quality for the city Pune (Maharashtra State) is being monitored by Maharashtra Pollution Control Board (MPCB). TABLE 3 AIR QUALITY MONITORING DATABASE AT SWARGATE Parameters SO2 NOx RSPM Standards SPM ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST

5 The monitoring is being carried out through Indian Institute of Tropical Meteorology (IITM), Pune, a constituent under the Ministry of Earth Sciences, Government of India, is spearheading country's first major initiative named as "System of Air Quality Forecasting and Research (SAFAR)". The SAFAR provides location specific information on Air Quality in near real time and its forecast 24 hours in advance. It has capability to forecast 3 days (72hrs) in advance but 3 day s advance forecast will be issued only when there is some specific extreme event. It is complemented by the weather forecasting system designed by IMD, Pune. (Source: Air quality index has been calculated for the data obtained through MPCB. The ambient air quality monitoring was carried out at Swargate a most crowded place in Pune city throughout the day - at location terrace of Swargate police Chowky. The frequency of monitoring was maintained by twice a week from 1 January 2014 to 31 December 2014 and parameters monitored were S0 2, NO x, RSPM and SPM in μg/m 3. B) Fuzzification: The process of Fuzzification involves no. of steps including designing and applying rule base, defining membership functions, defining classes as an output etc. Rule base can be defined on the basis of the available database above. Accordingly the Air quality ranges are identified as follows: TABLE 4 INDICATIVE RANGES OF AIR QUALITY Air Quality SO2 NOx RSPM SPM Good Better Poor According to predefined air quality ranges the rules are formulized as follows TABLE 5 RULE BASE Rule SOx NOx RSPM SSPM Air Quality 1 Good Good Good Good CLass1 2 Good Good Good Better CLass1 3 Good Good Good Poor Class 2 4 Good Good Better Good CLass1 Rule SOx NOx RSPM SSPM Air Quality 5 Good Good Better Better CLass1 6 Good Good Better Poor Class 2 7 Good Good Poor Good CLass1 8 Good Good Poor Better Class 2 9 Good Good Poor Poor Class 3 10 Good Better Good Good CLass1 11 Good Better Good Better CLass1 12 Good Better Good Poor Class 2 13 Good Better Better Good CLass1 14 Good Better Better Better CLass1 15 Good Better Better Poor Class 2 16 Good Better Poor Good Class 2 17 Good Better Poor Better Class 2 18 Good Better Poor Poor Class 2 19 Good Poor Good Good Class 2 20 Good Poor Good Better Class 2 21 Good Poor Good Poor Class 3 22 Good Poor Better Good Class 2 23 Good Poor Better Better Class 2 24 Good Poor Better Poor Class 3 25 Good Poor Poor Good Class 2 26 Good Poor Poor Better Class 3 27 Good Poor Poor Poor Class 4 28 Better Good Good Good CLass1 29 Better Good Good Better CLass1 30 Better Good Good Poor Class 2 31 Better Good Better Good CLass1 32 Better Good Better Better CLass1 33 Better Good Better Poor Class 2 34 Better Good Poor Good Class 2 35 Better Good Poor Better Class 2 36 Better Good Poor Poor Class 3 37 Better Better Good Good CLass1 38 Better Better Good Better CLass1 39 Better Better Good Poor Class 2 40 Better Better Better Good CLass1 41 Better Better Better Better CLass1 42 Better Better Better Poor Class 2 43 Better Better Poor Good Class 2 44 Better Better Poor Better Class 2 45 Better Better Poor Poor class 3 113

6 Rule SOx NOx RSPM SSPM Air Quality 46 Better Poor Good Good Class 2 47 Better Poor Good Better Class 2 48 Better Poor Good Poor class 3 49 Better Poor Better Good Class 2 50 Better Poor Better Better Class 2 51 Better Poor Better Poor class 3 52 Better Poor Poor Good class 3 53 Better Poor Poor Better class 3 54 Better Poor Poor Poor class 4 55 Poor Good Good Good class 3 56 Poor Good Good Better Class 2 57 Poor Good Good Poor class 3 58 Poor Good Better Good Class 2 59 Poor Good Better Better Class 2 60 Poor Good Better Poor class 3 61 Poor Good Poor Good class 3 62 Poor Good Poor Better class 3 63 Poor Good Poor Poor class 4 64 Poor Better Good Good Class 2 65 Poor Better Good Better Class 2 66 Poor Better Good Poor class 3 67 Poor Better Better Good Class 2 68 Poor Better Better Better Class 2 69 Poor Better Better Poor class 3 70 Poor Better Poor Good Class 2 71 Poor Better Poor Better class 3 72 Poor Better Poor Poor Class 2 73 Poor Poor Good Good Class 2 74 Poor Poor Good Better class 3 75 Poor Poor Good Poor class 3 76 Poor Poor Better Good class 3 77 Poor Poor Better Better class 4 78 Poor Poor Better Poor Class 5 79 Poor Poor Poor Good Class 5 80 Poor Poor Poor Better Class 5 81 Poor Poor Poor Poor Class 5 An expert opinion is taken before applying these rules and then the Air quality index in the range from 1 to 5 has been defined. Accordingly these quality index are as follows Air Quality TABLE 6 AQI CLASSES Air Quality Index Class 1 1 Class 2 2 Class 3 3 Class 4 4 Class 5 5 C) De-Fuzzification: The process of defuzzification is carried out by using software FisPro3.5. As an input the variables were Air quality parameters that is S0 2, NO x, RSPM and SPM. The membership function for all was decided as triangular as it is a most convenient being a linear functions. The output obtained is in the area form. The desired value can be obtained by Centroidal Method. FIGURE 2 DEFUZZIFICATION AFTER SOFTWARE RUN 114

7 The output obtained is as shown in figure 2 whereas figure 3 shows the desired value of air quality index which can be calculated by Centroid Method.[8] FIGURE 3 RESULT SHOWING DESIRED VALUE This is for corresponding values of respective parameters as follows TABLE 7 DESIRED PAREMETERS WITH CORRESPONDING VALUES Parameter Random Values for Above result SO2 NOx RSPM SPM For above monitored values the air quality index will be 3 indicating class 3 quality of air. IV. CONCLUSION Fuzzy Logic has emerged as a profitable tool for the controlling and steering of systems and complex industrial processes, as well as for household and entertainment electronics, as well as for other expert systems. Many real-world application problems cannot be described and handled by the classical set theory, including all those involving elements with only partial membership of a set. On the contrary, fuzzy set theory accepts partial memberships, and, therefore, in a sense generalizes the classical set theory to some extent. Fuzzy decision making process - a crucial part of fuzzy logic systems; may be carried out by various methods. The suitability of these methods is dependent on degree of precision required, available database, clarity of data etc. Fuzzy logic approach is the basic approach towards all those softwares being used for modelling and forecasting. Fuzzy logic system has the advantages as being a more prominent way for advanced software based models. FLC is a basic tool for decision making though few limitations. In environmental modelling system Fuzzy Rule base approach can be utilized in significant way as it provides a comfortable approach while making decisions through multiple criterions. In present work, the air quality index has been calculated using Fuzzy logic system. After fuzzy analysis of data obtained by 92 stations air quality index of value 3has been obtained. The output is as shown in figure 3. This figure indicates overlaid membership functions and corresponding result. References [1] Anonymous; Fuzzy Logic Fundamentals; March 26, 2001 [2] Ashok Deshpande, D. V. Raje; Fuzzy logic applications to Environmental Management studies: Case studies [3] Babaei Semiromi, F.1, Hassani, A.H., Torabian, A., Karbassi, A.R. and Hosseinzadeh Lotfi; Water quality index development using fuzzy logic: A case study of the Karoon River of Iran; African Journal of Biotechnology Vol. 10(50), pp , 5 September, [4] Bai. V, Reinier Bouwmeester and Mohan. S, Fuzzy Logic Water Quality Index and Importance of Water Quality Parameters, Raman, Air, Soil and Water Research 2009: [5] Bezdek, J. C., Fuzzy models what are they and why editorial. IEEE Transactions on Fuzzy Sys- tems, vol.1, pp [6] Cox, E., The Fuzzy Systems Handbook. Cambridge, MA: Academic Press. [7] Dubois, D. and Prade, H., Fuzzy Sets and Systems: Theory and Applications. New York: Academic Press. [8] Franck Dernoncourt ; Introduction to fuzzy logic; Masssachusets Institute of Technology; MIT, January 2013 [9] Klir G.J, Clair, Yuan B; Fuzzy sets and Fuzzy Logic theory and Application; PHIL publisher, ISBN [10] G.Vijayaraghavan, M.Jayalakshmi; A Quick Review on Applications of Fuzzy Logic in Waste Water Treatment; International Journal for Research in Applied Science & Engineering Technology (IJRASET) Volume 3 Issue V, May 2015;ISSN: ; pp

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