Research Of Water Quality Analyzer Based On Fuzzy Interpolation

Since American scientist L.A.Zadeh published famous thesis " Fuzzy Sets " in 1965, this is the marking of the birth of fuzzy mathematics. In a short period of 40 years, this theory has been developed rapidly, and has showed its strong application ability combining with new theory constantly.Fuzzy theory breaks through the limit of the classical two value theory , and widens " this or that " to " either-or " nature. The more important thing is that fuzzy theory provides one theory and method of the fuzzy message, and under the fuzzy inference and fuzzy subordination function, it can turn the theory and method into the things that machine can "understand" and accept. Through this bridge of fuzzy mathematics, it gets up fuzzy ration description of human thinking, and it can use computer to deal with mankind fuzzy experience, so it becomes the focal point that fifth generation of intelligent computer studies. This thesis discusses the technology of filtering ,interpolation and approximation based on fuzzy theory, and tries to incorporate fuzzy theory into the algorithm of traditional signal progressing.It makes the treatment of the algorithm not only on the mathematics descriptive ration of the sample data, but also on the combination of the fuzzy rule and fuzzy reasoning , so it introduces " intelligence " among them.In the field of interpolation and approximation , the research of the fuzzy theory has very strong practicability, because the essence of fuzzy control is the fuzzy interpolation and the fuzzy approximation. This thesis discusses the general structure method of the fuzzy interpolation on the basis ofintroducing classics interpolation briefly. The traditional interpolation is often superposed from the formal weighting interpolation function. In the essence of fuzzy interpolation, its interpolation function is a group of "IF-THEN " fuzzy rules. And through the fuzzy subornation and fuzzy reasoning, it makes these rules have quantitative description method on mathematics. It is obvious that the fuzzy interpolation method not only uses the date information but also introduce human fuzzy thinking among them ,so it can improve the intelligent and precision of the interpolation.In this paper, in-depth study of the fuzzy mathematics theory and interpolation based on the ideas put forward its own algorithm for fuzzy interpolation.That is, the interpolation of fuzzy mathematics and fuzzy interpolation algorithm applied to the theory, the classical mathematical methods of interpolation of linear interpolation, spline interpolation, Newton interpolation,which the theory of interpolation method is already quite mature, but classical mathematics as a result of the accuracy and uncertainty, these interpolation methods have some shortcomings. For example, linear interpolation at the nodes of the first order derivative is not continuous,in accordance with the conventional thinking of people, near the interpolation nodes is the most valuable information, and linear interpolation in this method there are inherent error. Although spline interpolation for the first derivative, but the spline curve compared jitter intense, particularly in the border more visible, which makes the results of the interpolation error is relatively large. Interpolation of fuzzy thinking completely out of the interpolation of the classic ideas of mathematics, fuzzy theory and its people based on habits of mind, you can better achieve the desired objective. In the setting of fuzzy rules, the papers are given control of their own rules, based on fuzzy mathematics "IF-THEN" reasoning rules derived transfer matrix R. Control rules are determined by man-made, it is the core of fuzzy systems, so how to set up fuzzy rules to become a key issue. In the fuzzy input, the membership function mainly triangular, trapezoidal, distribution, etc., the paper against the actual situation, construct a membership function, and through continuous feedback experiment of its modifications, and ultimately be a relatively appropriate membership. The main methods of precision have the greatest membership degree method, the median and center of gravity method. In this paper, a center of gravity method, center of gravity method, also known as moment method, it is the result of fuzzy reasoning to strike a focus of all the elements of the method element. In essence, the center of gravity method is commonly referred to as the weighted average method, the use of center of gravity method to determine the fuzzy quantity can reflect the whole fuzzy value in the information accurate, this process is similar to the theory of probability for the process of mathematical expectation.In the simulation and mapping,the use of Matlab software, it is a functional, efficient and easy to carry out scientific and engineering computing interactive package. These include: the general numerical analysis, matrix computation, digital signal processing, modeling, and system control and optimization applications, and collect applications and graphics in a easy-to-use integrated environment. Simulation of the process through drawing, we can see that the control rules and set the quality of membership, through feedback control rules and membership being perfected. In this paper, the water quality of the measurement data analyzer is a series of irregular points, the determination of its function curve interpolation method is adopted in a number of points on the solution of the measurement data, and then do the interpolation points, fuzzy interpolation value function, this function instead of the actual function approximation. Interpolation of the actual data shows that the results of fuzzy interpolation is superior to the classical mathematical interpolation algorithm. With the ever-increasing control rules, the effect of interpolation will become better and better, but the limited knowledge I have, not the more in-depth research, how to improve the accuracy of fuzzy interpolation, a more reasonable set of control rules and membership functions, are worthy of research.Mathematical Theory of the fuzzy interpolation algorithm used is the inevitable result of continuous development of fuzzy theory.Fuzzy mathematics is bound to improve the continuous development of its great development potentials.But we also have to see the fact that while the overall introduction of fuzzy theory and technical application system is not perfect, the future remains to be further studied. But the potential of fuzzy math's powerful development in control theory is not in question, it's obvious advantage in engineering studies will certainly become a powerful tool.