Self-organizing Polynomial Neural Networks Research Articles

A new pressure and temperature dependent relative viscosity model for water-Al2O3 nanofluids using GMDH neural network

The introduction of nanoparticles into fluids have been used in various sciences such as; heat transfer, drilling mud, hydraulic fracturing, EOR, and widely in biotechnology science. The dispersion of nanoparticles in the fluid can affect significantly the viscosity of the system. In this study, a self-organizing polynomial neural network based on a group method of data handling (GMDH) is developed to investigate the viscosity of water-based nanofluids regarding temperature and especially pressure changes. The influence of high pressure has not been previously considered in any correlation. The results were estimated using the GMDH model and have higher accuracy than various theoretical models and empirical equations and show the coefficient of determination of 0.999.

A novel strength behavior prediction model of self‐compacting concrete with foundry sand and hybrid fibers

AbstractIn this paper, an Improved FireFly Optimization Algorithm (IFFOA)‐based optimal Self‐Organizing Polynomial Neural Network (SOPNN) is proposed to analyze the compressive strength, tensile strength, and flexural strength of the self‐compacting concrete (SCC) with the inclusion of hybrid fibers whenever exposed to high temperature. The SCC mixture is formed by the materials taken in this study along with the hybrid fibers. The preparation of SCC is made by adding water to powder with a proportion of 3:10 and hybrid fibers content is about 2 kg/m3. The samples are heated to a temperature of 210, 320, 530, and 790° at the duration of 7 and 28 days. Experiments are performed to analyze the loss in compressive strength, tensile strength, and flexural strength. The proposed method is used to analyze the loss functions based on the amount of cement, aggregates, temperature, additives along with the inclusion, and exclusion of hybrid fibers. Further, it is found the proposed method analyzes the loss in compressive strength, tensile strength, and flexural strength of SCC more accurately than the other methods.

PH Neutralization Process Modeling Using GA Based Self-Organizing Polynomial Neural Network

pH Neutralization Process Modeling Using GA Based Self-Organizing Polynomial Neural Network

Estimation of the viscosity of nine nanofluids using a hybrid GMDH-type neural network system

The introduction of nanoparticles into the fluids traditionally used in heat transfer processes, such as water, ethylene glycol and propylene glycol, has led to the advent of nanofluids which have become widely applicable due to their improved heat transfer properties. Dispersion of nanoparticles in base fluid affects the viscosity of system to a noticeable degree. In this regard, we developed a hybrid self-organizing polynomial neural network on the basis of group method of data handling (GMDH) to study the viscosity of nine nanofluids based on water, ethylene glycol and propylene glycol. The results show that the hybrid GMDH model can accurately predict the viscosity of nanofluids. The percentage of average absolute relative deviation (AARD%) for all systems was 2.14% with a high regression coefficient of R=0.9978. The results estimated by the hybrid GMDH model, when compared to those of various theoretical models and an empirical equation, exhibit a higher accuracy.

Optimization of self-organizing polynomial neural networks

The main disadvantage of self-organizing polynomial neural networks (SOPNN) automatically structured and trained by the group method of data handling (GMDH) algorithm is a partial optimization of model weights as the GMDH algorithm optimizes only the weights of the topmost (output) node. In order to estimate to what extent the approximation accuracy of the obtained model can be improved the particle swarm optimization (PSO) has been used for the optimization of weights of all node-polynomials. Since the PSO is generally computationally expensive and time consuming a more efficient Levenberg–Marquardt (LM) algorithm is adapted for the optimization of the SOPNN. After it has been optimized by the LM algorithm the SOPNN outperformed the corresponding models based on artificial neural networks (ANN) and support vector method (SVM). The research is based on the meta-modeling of the thermodynamic effects in fluid flow measurements with time-constraints. The outstanding characteristics of the optimized SOPNN models are also demonstrated in learning the recurrence relations of multiple superimposed oscillations (MSO).

입자화 중심 자기구성 다항식 신경 회로망의 새로운 설계

In this study, we introduce a new design methodology of a granular-oriented self-organizing polynomial neural networks (GoSOPNNs) that is based on multi-layer perceptron with Context-based Polynomial Neurons (CPNs) or Polynomial Neurons (PNs). In contrast to the typical architectures encountered in polynomial neural networks (PNN), our main objective is to develop a methodological design strategy of GoSOPNNs as follows : (a) The 1st layer of the proposed network consists of Context-based Polynomial Neuron (CPN). In here, CPN is fully reflective of the structure encountered in numeric data which are granulated with the aid of Context-based Fuzzy C-Means (C-FCM) clustering method. The context-based clustering supporting the design of information granules is completed in the space of the input data while the build of the clusters is guided by a collection of some predefined fuzzy sets (so-called contexts) defined in the output space. (b) The proposed design procedure being applied at each layer of GoSOPNN leads to the selection of preferred nodes of the network (CPNs or PNs) whose local characteristics (such as the number of contexts, the number of clusters, a collection of the specific subset of input variables, and the order of the polynomial) can be easily adjusted. These options contribute to the flexibility as well as simplicity and compactness of the resulting architecture of the network. For the evaluation of performance of the proposed GoSOPNN network, we describe a detailed characteristic of the proposed model using a well-known learning machine data(Automobile Miles Per Gallon Data, Boston Housing Data, Medical Image System Data).

Hybrid GMDH-type modeling for nonlinear systems: Synergism to intelligent identification

This paper presents a novel hybrid GMDH-type algorithm which combines neural networks (NNs) with an approximation scheme (self-organizing polynomial neural network: SOPNN). This composite structure is developed to establish a new heuristic approximation method for identification of nonlinear static systems. NNs have been widely employed to process modeling and control because of their approximation capabilities. And SOPNN is an analysis technique for identifying nonlinear relationships between the inputs and outputs of such systems and builds hierarchical polynomial regressions of required complexity. Therefore, the combined model can harmonize NNs with SOPNN and find a workable synergistic environment. Simulation results of the nonlinear static system are provided to show that the proposed method is much more accurate than other modeling methods. Thus, it can be considered for efficient system identification methodology.

Advanced self-organizing polynomial neural network

In this paper, we introduce a concept of advanced self-organizing polynomial neural network (Adv_SOPNN). The SOPNN is a flexible neural architecture whose structure is developed through a modeling process. But the SOPNN has a fatal drawback; it cannot be constructed for nonlinear systems with few input variables. To relax this limitation of the conventional SOPNN, we combine a fuzzy system and neural networks with the SOPNN. Input variables are partitioned into several subspaces by the fuzzy system or neural network, and these subspaces are utilized as new input variables to the SOPNN architecture. Two types of the advanced SOPNN are obtained by combining not only the fuzzy rules of a fuzzy system with SOPNN but also the nodes in a hidden layer of neural networks with SOPNN into one methodology. The proposed method is applied to the nonlinear system with two inputs, which cannot be identified by conventional SOPNN to show the performance of the advanced SOPNN. The results show that the proposed method is efficient for systems with limited data set and a few input variables and much more accurate than other modeling methods with respect to identification error.

Multi-layer self-organizing polynomial neural networks and their development with the use of genetic algorithms

In this paper, we introduce a new architecture of genetic algorithms (GA)-based self-organizing polynomial neural networks (SOPNN) and discuss a comprehensive design methodology. Let us recall that the design of the “conventional” PNNs uses an extended group method of data handling (GMDH) and exploits polynomials (such as linear, quadratic, and modified quadratic functions) as well as considers a fixed number of input nodes (as being selected in advance by a network designer) at polynomial neurons (or nodes) located in each layer. The proposed GA-based SOPNN gives rise to a structurally optimized structure and comes with a substantial level of flexibility in comparison to the one we encounter in conventional PNNs. The design procedure applied in the construction of each layer of a PNN deals with its structural optimization involving the selection of preferred nodes (or PNs) with specific local characteristics (such as the number of input variables, the order of the polynomial, and a collection of the specific subset of input variables) and addresses specific aspects of parametric optimization. An aggregate performance index with a weighting factor is proposed in order to achieve a sound balance between approximation and generalization (predictive) abilities of the network. To evaluate the performance of the GA-based SOPNN, the model is experimented with using chaotic time series data. A comparative analysis reveals that the proposed GA-based SOPNN exhibits higher accuracy and superb predictive capability in comparison to some previous models available in the literature.

Relation-based neurofuzzy networks with evolutionary data granulation

In this study, we introduce a concept of self-organizing neurofuzzy networks (SONFN), a hybrid modeling architecture combining relation-based neurofuzzy networks (NFN) and self-organizing polynomial neural networks (PNN). For such networks we develop a comprehensive design methodology and carry out a series of numeric experiments using data coming from the area of software engineering. The construction of SONFNs exploits fundamental technologies of computational intelligence (CI), namely fuzzy sets, neural networks, and genetic algorithms. The architecture of the SONFN results from a synergistic usage of NFN and PNN. NFN contributes to the formation of the premise part of the rule-based structure of the SONFN. The consequence part of the SONFN is designed using PNNs. We discuss two types of SONFN architectures with the taxonomy based on the NFN scheme being applied to the premise part of SONFN and propose a comprehensive learning algorithm. It is shown that this network exhibits a dynamic structure as the number of its layers as well as the number of nodes in each layer of the SONFN are not predetermined (as this is usually the case for a popular topology of a multilayer perceptron). The experimental results deal with well-known software data such as the NASA dataset concerning software cost estimation and the one describing software modules of the medical imaging system (MIS). In comparison with the previously discussed approaches, the self-organizing networks are more accurate and exhibit superb generalization capabilities.

Self-organizing polynomial neural networks based on polynomial and fuzzy polynomial neurons: analysis and design

In this study, we introduce and investigate a class of neural architectures of polynomial neural networks (PNNs), develop a comprehensive design methodology and carry out a series of numeric experiments. PNN is a flexible neural architecture whose structure (topology) is developed through learning. In particular, the number of layers of the PNN is not fixed in advance but is generated on the fly. In this sense, PNN is a self-organizing network. We distinguish between two kinds of SOPNN architectures, that is, (a) polynomial neuron (PN) based and (b) fuzzy polynomial neuron (FPN) based self-organizing networks. This taxonomy is based on the character of each neuron structure in the network. Each of them comes with two structures referred here to as basic and the modified topology. Moreover, for each topology of the SOPNN we identify two types that is a generic and advanced type. The essence of the design procedure of self-organizing polynomial neural networks (SOPNN) dwells on the group method of data handling (GMDH) (IEEE Trans. Systems Man and Cybernet. 12 (1971) 364). Each node of the PN based SOPNN exhibits a high level of flexibility and realizes a polynomial type of mapping (linear, quadratic, and cubic) between input and output variables. FPN based SOPNN dwells on the ideas of fuzzy rule-based computing and neural networks. Especially in FPN based SOPNN, the generic rules in the system assume the form “if A then y = P( x ) ” where A is a fuzzy relation in the condition space while P( x ) is a polynomial forming a conclusion part of the rule. Each FPN (processing element) consists of a series of the nonlinear inference rules. The conclusion part of the rules, especially the regression polynomial uses several types of high-order polynomials such as linear, quadratic, modified quadratic, and cubic. As the premise part of the rules, both triangular and Gaussian-like membership functions are studied. Simulations involve a series of synthetic as well as experimental data used across various neurofuzzy systems. A detailed comparative analysis is included as well.

The design of self-organizing Polynomial Neural Networks

Abstract In this study, we introduce and investigate a class of neural architectures of Polynomial Neural Networks (PNNs), discuss a comprehensive design methodology and carry out a series of numeric experiments. PNN is a flexible neural architecture whose structure (topology) is developed through learning. In particular, the number of layers of the PNN is not fixed in advance but becomes generated on the fly. In this sense, PNN is a self-organizing network. The essence of the design procedure dwells on the Group Method of Data Handling (GMDH). Each node of the PNN exhibits a high level of flexibility and realizes a polynomial type of mapping (linear, quadratic, and cubic) between input and output variables. The experimental part of the study involves two representative time series such as Box–Jenkins gas furnace data and a pH neutralization process.