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Yapay sinir ağları ile ulaştırma taleplerinin modellenmesi

Başlık çevirisi mevcut değil.

  1. Tez No: 66774
  2. Yazar: YUSUF KAAN DEMİR
  3. Danışmanlar: PROF. DR. HALUK GERÇEK
  4. Tez Türü: Yüksek Lisans
  5. Konular: İnşaat Mühendisliği, Civil Engineering
  6. Anahtar Kelimeler: Bulanık mantık, sinir ağları, birleşim işlemi, synaptik ve somatik işlemler. XII
  7. Yıl: 1997
  8. Dil: Türkçe
  9. Üniversite: İstanbul Teknik Üniversitesi
  10. Enstitü: Fen Bilimleri Enstitüsü
  11. Ana Bilim Dalı: Ulaştırma Ana Bilim Dalı
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: 88

Özet

ÖZET Ulaştırma planlamasının temel sorunlarından biri olan ulaşım taleplerinin tahmininde, önemli çalışmalardan birisi verilerin toplanması ve bu verilerin uygun bir şekilde işlenerek matematik bir modele oturtulmasıdır. Matematik modellemeler için verilerin gerçekte çok sağlıklı ve kesin bir şekilde toplanması gerekmektedir. Bu da planlamanın maliyetini önemli oranda arttırabildiği gibi bulunan matematik modellerin insan ve insana özgü davranışları tahmin etmede her zaman başarılı olduğu da tartışılabilmektedir. 1965 yılında L.A.Zadeh'in bulanık kümeler teorisini ortaya atmasıyla, matematiğin bir handikabı olan 'var ya da yok' mantığını esas alan klasik kümeler teorisi olmadan matematiksel modeller oluşturulabileceği görülmüştür. Bunun anlamı artık insan mantığına yakın modellerin yapılabilmesinin yanında dilsel ve kesin olmayan verilerin de işlenebileceğidir. Son on yıl zarfında biyolojik sinirlerin ve öğrenme sisteminin incelenmesi ve anlaşılması ile 'yapay sinir ağları' kavramı ortaya çıkmıştır. Artık elimizde kendi kendine uyarlama sağlayabilen ve öğrenebilen, paralel hesaplama yetenekleri sayesinde hızlı hesaplama yeteneklerine sahip bir sistem vardır. Bulanık mantık kavramı sonraları yapay sinir ağları ile entegre edilmiş ve 'bulanık sinir sistemleri 'elde edilmiştir. Ulaştırma taleplerinin tahmininde birçok verinin işlenerek model kurma amacı ile çoğu zaman çeşitli regresyon analizleri kullanılmaktadır. Analizde kullanılan verilerin çoğu zaman anketlerden elde edilmesi verilerin kesinliğini düşürmekte ve regresyon analizi ile kurulan modeller her zaman mantıklı sonuçlar vermemektedir. Bu yüksek lisans tezinde yukarıda sözü edilen bilgilerin ışığında, yapay sinir ağlarının ulaştırma planlamasında kullanılıp kullanılamayacağı araştırılacaktır. Bu amaçla önce sinir ağları kavramı, ve öğrenme algoritmaları incelenmiş, sistemler matematiksel anlamda irdelenecek, ardından ulaştırma planlamasında en önemli işlemlerden biri olan ulaşım talebinin modellenmesi konusunda hem regresyon analizi, hem de yapay sinir ağları kullanılarak üç adet uygulama yapılacak elde edilen sonuçlar karşılaştırılacaktır. Yapay sinir ağları hesapları için Propagator paket programı kullanılmıştır.

Özet (Çeviri)

SUMMARY One of the main problems of the transportation planning is the modelling of the human behaviour under the any condition. In order to establish good mathematical model a careful data and information collection process is needed. More data and details often requre more quality staff for questionnaires and it means high cost. Under this circumstances, mathematical models based on classic set theory may not be enough for complex events. The real world is complex; complexity in the world generally arises form uncertainty in the form of ambiguity. Problems featuring complexity and ambiguity have been addressed subconsciously by humans since they could think, these ubiquitous features pervade most social, technical, and economic problems faced by the human race. Fortunately this genality and ambiguity are sufficient for human comprehesion of complex systems. As the quate above from Dr.Zadeh's principle of incompatibility suggests, complexity and ambiguity (imprecision) are correlated:“the closer one looks at a real-world problem, the fuzzier becomes its solution”[Zadeh, 1973]. As we learn about the a system, its complexity decreases and our understanding increases. As complexity decreases, the precision afforded by computational methods becomes very useful in modeling system. Figure S.1 which provides a useful insight into these ideas, rekates degree of complexity of the system to the precision inherent in the models of the systems. For the systems with little complexity, hence the uncertainty, closed form mathematical expression provide precise description of the systems. For the sytems that are the little more Precision in the model Mathematical Equations Complexity of the systems Figure.S.1 Complexity of the systems complex, but for which significant data exist, model free methods, such as artificial neural networks, provide powerfuland robust means to reduce some uncertainty XIIIthrough the learning, based on patterns in the available data. Finally, for the most complex systems where few numerical data exist and where only ambiguous or imprecise information available, fuzzy reasoning provides a way to understand system behavior by allowing us to interpolate approximately between observed inputs and output situations. The imprecision in fuzzy model is therefore generally quite high. The fuzzy systems can implement crisp inputs and outputs, and in this case produce a nonlinear functional mapping just as do algorithms. All complex systems can be assesed with nonlinear equations or with fuzzy models or neural networks. All are matematical abstractions of the real physical world. The point is, however, to match the model type with character of the uncertainty exhibited in the problem. In situations where precision is apparent, for example, fuzzy systems are less efficient than the more precise algorithms in providing us with the best understanding of the problem. On the other hand, fuzzy systems can focus on modelling problems characterized by imprecise or ambiguous information.1 In transportation planning, to predict transport demand, regression is widely used generally. But this analysis does not always reflect the real relationship between the inputs and outputs, thus the regression coeficient determined can be nonsenses for the desired outputs. For example, if noted that given following data (Table S.1), there are three inputs (independent variable) and one output (dependent variable). Table S.1 1 Timothy J. Ross, Fuzzy Logic With Engineering Applications, McGraw-Hill, Inc., 1995. XIVTo these data a multiple regression analysis are applied and coeffient is written last row of the above table. As can be easily seen, normally annual revenue must have positive effect on the total trip, but according to regression anlysis it does not have. Last decade, fuzzy logic and neural network are found very attractive technic for demand analysis, system modelling. In this article, tried to answer that questions“how much this technics are effective for transport planning”.Because of that first of all definition and logic of these technics are examinated. Later a transport demand anlysis problem is solved by using these technics and compared results of it with the results of the tratidional analysis. What is the Neural Network(NN).? Firs of all, when we are talking about a neural network, we should more properly say artifical neural network(ANN). Biological neural networks are much more complicated than the mathematical models we use for ANN'S. But it is customary to be lazy and drop the“A”or the“artificial”. There is no universally accepted definition of an NN. But perhaps most people in the field would agree that an NN is a network of many simple processorsfunits“), each possibly having a small amounth of local memory. The units are connnected by comminication channels (”connnnections“) which usuallly carry numeric (as oppesed to symbolic) data, encoded by any of various means. The units operate only on their local data on the inputs they receive via the connections. The restriction to local operations is often relaxed during training. Some NNs are models of biological neural networks and some are not, but historically, much of the inspiration for the field of NNs came from the desire to produce artifical systems capable of sophisticated, perhaps ”intelegenf, computations similar to those that the human brain routinely performs, and thereby possibly to enhance our understanding of the human brain. Most NNs have some sort of“training ”rule whereby the weights of connections are adjusted on the basis of data. In other words, NNs“learn”from examples (as children learn to recognize dogs from examples of dogs) and exhibit some capability for generalization beyond the training data. NNs normally have greeat potential of parallelism.since the computtations of the components are largely independent of each other. Some people regard masssive parallelism and high connectivity to be defining characteritics of Nna, but such requirements rule out various simple models, such as simple linear regression xv( a minimal feedforward net only two units plus bias), which are usefully regarded as special cases of NNs.) [3] Here is a sampling of definitions from the books on the FAQ maintained shelf. None willl please everyone. Perhaps for that reason many NN textbooks do not expilicity define neural networks....a neural network is a sytem composed of many simple processing elements operating in parallel whose function is determined by network structure, connections strengths, and the processsing performed at computing elements or nodes [1]. A neural network is massively parallel distributed processor that has a natural propensity for storing experiential knowledge and making it available for use [2]. A neural network is technique that seeks tu build an intelligent program (to implement intelligence) using models that simulatte thhe working network of the neurons in the human brain [Yamakawa, 1992Hopfield, 1982,1986]. A neuron, Figure S.1, is made up several prostrusion called dentrites and long branch called the axon. A neuron is joinned to other neurons through the dentrities. The dentrities of different meet to form synapses, the areas where massages pass. The neurons receive the impulses via the synapses. If the total of the impulses received exceeds a certain threshold value than the neurons sends an impulse down the axon where the axon is connected to other neurons through more synapses. The synapses may be axcitatory or inhabitory in nature. An excitatory synapse adds to the total the impulses reaching the neurons, whereas an inhibitory neuron reduces the total of the impulses reaching the neuron. In global sense, a neuron receives a set of input pulses and sends out another pulse that is a function of the input pulses. This concept of how neurons work in the human brain is utilized in performing computations on computers. Researchers have long felt that the neurons are reponsible for the human capacity to learn, and it is in this sense that the physical structure is being emulated by neural network to accomplish machine learning. Each computational unit computers aome function of its inputs and passes the result to connected units in the network. The knnowledge oof the system comes out of the entire network of the neurons. Figure S.2.A simple schematic of a human neuron. XVIFigure S.2 shows the analog of a neuron as a threshold element. The variables Xux2, Xj x" are the n inputts to the tthhrreshold elementt. These are analogous to impulses arriving from the several different neurons to one neuron. The variables w^v^, Wj,wn are the weights associated with the impulses/inputs, signifying the relative importance that is associated with the path from which the input is coming. When Wj is positive, input Xj acts as an excitatory signal for the element. When w, is negative, input Xj acts as an inhibitory signal for the element. The threshold element sums the product of these inputs and their associated weights (EWjXj), compares it to a prescribed threshold value and, if the summation is greater then the threshold value, computes an output using a nonlinear functions(F). The signal ouutput y Figure S.2 is nonlinear function (F) of the diffrence between the preeceding computed summation and the threshold value and is expressed as y=F(SWiXi-t) S.1 where Xi=signnal input (1=1,2,... n) wpweight associated with the signal input xi t=threshold level predescribed by user F(s)=a nonlinear function;e.g.,sigmoid function F(s)=1+(1/exp(-s)) xn Figure S.3 A thershold element as an analog to a neuron. Figure S.3 shows a simple neural network for a system with single-input signal x and a corresponding single-output signal f(x). Layer number one has only one element that has a single input, but the element sends its ouput to four other elements in the second layer. Elements shown in the second layer are all single - input single-output elements. The third layer has only one elements that has four inputs, and it computes the output fot the sytems. This neural network is termed a (1x4x1) network. The numbers represents the number of elements in each layer of XVIIthe network. The layers other than the first (input layer) and the last (output layer) layers constitute the set of hidden layers. (Systems can have more than three layers, in which case we would have more than one hidden layer.) [4]. F(x) Figure S.4 A simple 1x4x1 neural Network XVIII

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