Nonlinear neural network

Grossberg, S. 1988b. Nonlinear neural networks principles, mechanisms and architectures. Neural Networks, 1 17-61. 

Transfer function models are linear in nature, but chemical processes are known to exhibit nonhnear behavior. One could use the same type of optimization objective as given in Eq. (8-26) to determine parameters in nonlinear first-principle models, such as Eq. (8-3) presented earlier. Also, nonhnear empirical models, such as neural network models, have recently been proposed for process applications. The key to the use of these nonlinear empirical models is naving high-quality process data, which allows the important nonhnearities to be identified. 

Providing input/output data is available, a neural network may be used to model the dynamies of an unknown plant. There is no eonstraint as to whether the plant is linear or nonlinear, providing that the training data eovers the whole envelope of plant operation. 

Controller emulation A simple applieation in eontrol is the use of neural networks to emulate the operation of existing eontrollers. It may be that a nonlinear plant requires several tuned PID eontrollers to operate over the full range of eontrol aetions. Or again, an LQ optimal eontroller has diffieulty in running in real-time. Figure 10.28 shows how the eontrol signal from an existing eontroller may be used to train, and to finally be replaeed by, a neural network eontroller. 

Neural networks can also be classified by their neuron transfer function, which typically are either linear or nonlinear models. The earliest models used linear transfer functions wherein the output values were continuous. Linear functions are not very useful for many applications because most problems are too complex to be manipulated by simple multiplication. In a nonlinear model, the output of the neuron is a nonlinear function of the sum of the inputs. The output of a nonlinear neuron can have a very complicated relationship with the activation value. 

The second main category of neural networks is the feedforward type. In this type of network, the signals go in only one direction there are no loops in the system as shown in Fig. 3. The earliest neural network models were linear feed forward. In 1972, two simultaneous articles independently proposed the same model for an associative memory, the linear associator. J. A. Anderson [17], neurophysiologist, and Teuvo Kohonen [18], an electrical engineer, were unaware of each other s work. Today, the most commonly used neural networks are nonlinear feed-forward models. 

The proposed neural network model with the nonlinear optimization routine is similar to many nonlinear... 

Several nonlinear QSAR methods have been proposed in recent years. Most of these methods are based on either ANN or machine learning techniques. Both back-propagation (BP-ANN) and counterpropagation (CP-ANN) neural networks [33] were used in these studies. Because optimization of many parameters is involved in these techniques, the speed of the analysis is relatively slow. More recently, Hirst reported a simple and fast nonlinear QSAR method in which the activity surface was generated from the activities of training set compounds based on some predefined mathematical functions [34]. 

Kreinovich, V. Y., Arbitrary nonlinearity is sufficient to represent all functions by neural networks A theorem. Neural Networks 4, 381 (1991). 

Kramer, M. A., Nonlinear principal component analysis using autoassociative neural networks. AIChE J. 37, 233-243 (1991). 

Numerous QSAR tools have been developed [152, 154] and used in modeling physicochemical data. These vary from simple linear to more complex nonlinear models, as well as classification models. A popular approach more recently became the construction of consensus or ensemble models ( combinatorial QSAR ) combining the predictions of several individual approaches [155]. Or, alternatively, models can be built by rurming the same approach, such as a neural network of a decision tree, many times and combining the output into a single prediction. 

J. Zhang, J.-H. Jiang, P. Liu, Y.-Z. Liang and R.-Q. Yu, Multivariate nonlinear modelling of fluorescence data by neural network with hidden node pruning algorithm. Anal. Chim. Acta, 344(1997) 29 0. 

D. Domine, D. Wienke, J. Devillers and L.M.C. Buydens, A new nonlinear neural mapping technique for visual exploration of QSAR data. In Neural Networks in QSAR and Drug Design, J. Devillers (ed.). Academic Press, London, 1996, p. 223-253. 

Dong, D., and McAvoy, T. J., Nonlinear principal component analysis—based on principal curves and neural networks, Comput. Chem. Eng. 20(1), 65 (1996). 

By design, ANNs are inherently flexible (can map nonlinear relationships). They produce models well suited for classification of diverse bacteria. Examples of pattern analysis using ANNs for biochemical analysis by PyMS can be traced back to the early 1990s.4fM7 In order to better demonstrate the power of neural network analysis for pathogen ID, a brief background of artificial neural network principles is provided. In particular, backpropagation artificial neural network (backprop ANN) principles are discussed, since that is the most commonly used type of ANN. 

Neural networks are applied in analytical chemistry in many and diverse ways. Used in calibration, ANNs have especially advantages in case of nonlinear relationships, multicomponent systems and single component analysis in case of various disturbances. 

Neural networks (NN) represent, as opposed to PLS and MLR, a nonlinear statistical analysis technique [43]. As is the case for both PLS and MLR, several aspects of NN should be considered when using this type of analysis technique ... 

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