Monthly river discharge prediction by wavelet fuzzy time series method

The effective use of water resources is an increasingly important problem today. The rapid increase in the world population led to a decrease in clean water resources. Water, which is the most basic source of life of human beings, needs to be constructed from an optimum source, transmitted, stored and evacuated. Many structures are built for the use of water resources. Drinking water supply, irrigation water supply and transmission, power generation, flood prevention, tourism etc. Water structures are needed for many purposes. Both these initial investment costs and operating costs are very high. For instance, structures that fill the service life too early and functionless structures cause economic losses. In addition to the economic damages, sudden deformations in water structures and building below the required dimensions cause loss of life. The chemical and physical properties of water resources need to be determined very well in order to reduce the costs and make the most efficient use of the resources. In the light of the findings, it can be decided whether the water resources can be used prospectively or not and how long they can be used. This decision making process can be calculated by the effect of physical variables. Physical-based estimation methods require many measured input data. In order to supply these data, gauging stations must be installed. All of these steps are difficult and costly processes. Lower cost models can be established by the aid of time series values. The fact that time series values contain the variability of other physical parameter makes the time series analysis methods consistent. Time series analysis methods which are known as univariate analysis can be done easily by many mathematical models. While some of these models are parametric and require necessity conditions, there are no conditions to be satisfied to set up some models. At first, researchers using classical methods conducted a prediction study with autoregressive models. These models are based on a fairly simple logic, using previous flow values and making forward-looking conclusions. The fact that models with parametric structure cannot work under any circumstances can be shown as the biggest deficiency of classical models. In order to establish a model, the time series values must have a static structure, the variance of which is constant in time, normal distribution of residual values etc. many other prerequisites must be realized. In cases where these conditions are not met, the models tried to be established do not make any statistical significance. Researchers have sought to find a method to overcome many negative features of classical methods. Inspired by biological nerve cells, the researchers established mathematical models to solve linear problems in a short time. Later on, a very important step was taken in solving non-linear problems and the scientific community was introduced to a completely different field. Although artificial neural networks give good results, they have become increasingly complex to achieve better results. Although the acceleration of computers solved this problem, researchers preferred simpler methods to adapt to their problems and achieve faster results. In 1965, the mathematician Lutfi Zadeh presented a new approach to logic to the scientific community. This system of thought, which violates the limits of classical logic, has not been able to find a lot of space at first; however, the studies of the far eastern scientists and their good results have enabled it to accept this system in the west. With this approach, which can represent almost any condition with the help of verbal variables, both problems can be solved in a simple way and time can be saved. Systems that are known as machine learning and which produce new values based on the available data are used in prediction models. Bayesian algorithm, nearest neighborhood algorithm, support vector machines solve many classification problems and they are used frequently in the solution of regression problems. The closest neighborhood algorithm has a very simple operating logic and can generate predictions in high data structures. Researchers working with time series have developed models that distinguish between time series components and make predictions using these components. Fourier series are at the top of the separation models. Foruier, who can express time series as a sum of sine and cosine waves, was able to separate time series components and add a new perspective to the modeling. The inability to use it for non-stationary series can be said to be the biggest deficiency. Due to this deficiency, researchers have worked on models that perform component separation in all conditions. The wavelet transform was also the result of this effort. Within the scope of this study, time series modeling was performed by using monthly average flow values. The models created with 456 data are divided into two parts as training and testing. The mathematical equations obtained in the training part were tested in the test section and verified their usability. The models were trained with 280 data and were tested with 186 data. While creating models, artificial neural networks, fuzzy logical close neighborhood and fuzzy time series methods were used. In addition, all models are preprocessed by one of the preprocessing methods, the wavelet transform method, to increase their performance. The results were interpreted with the help of statistical success criteria. Inclusion of time series values in the estimation models after being analyzed by wavelet transformation yielded better results than models without any conversion. In addition, the use of fuzzy time series models, which have become widespread in the literature in recent years, has been tried to be used as a preprocessing technique with wavelet transformation. The results showed that the combined models gave very good results in turbid time series models. In this respect, it is thought that the thesis study will be an important place in the literature. In the first chapter, the aim of the study is given and the previous studies in the literature are mentioned. In the second part, the physical process of the flow event is mentioned. The field of study of the data was introduced and its physical and geographical features were mentioned. It is mentioned about how flow measurements are done. The characteristics of the station from which the data is received are mentioned. The data provided in the third chapter is described and the statistical characteristics are explained. The working principles of the methods used in estimation models are explained in detail. In the fourth chapter, the results of the applied models are discussed. Forecasting models where data are used without pre-emption and models established with the pre-emption process were compared with the models with the help of wavelet transform method. Conclusions and recommendations are given in the chapter five. The applicability of the first fuzzy time series method applied in hydrology has been proven. In addition, it has been observed that the performance of the fuzzy time series models established by the wavelet transform method, which is the data preprocessing method, has increased significantly. It is thought that this part of the study will give a new breath to fuzzy time series models.