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Infinite-Dimensional Dynamical Systems in Mechanics and Physics (Roger Temam)

Abstract Neural networks become very popular as a tool for modeling of numerous systems, including technological, economical, sociological, psychological, and even political ones. On the contrary, neural networks are models of neural structures and neural processes observed in a real brain. However, for modeling of real neural structures and real neural processes occurring in a living brain, neural networks are too simplified and too primitive. Nevertheless, neural networks can be used for modeling the behavior of many biological systems and structures. Such models are not useful for explanation, taking into account the biological systems and processes, but can be very useful for the analysis of such system behavior, including the prognosis of future results of selected activities (e.g. the prognosis of results of different therapies for modeled illnesses). In this paper, selected examples of such models and their applications are presented.

Neural networks as a tool for modeling of biological systems

An accurate thermal model for building enables the heating system (HS) to work efficiently as well as save energy. Thermal modelling often requires physical parameters of the building, which are difficult to be accurately determined. The aim of this work is to develop an optimal thermal model for better understanding of thermal dynamics with the goal of using this to estimate temperature variation in a few hours ahead within building. Based on the characteristics of thermal motion, a conventional physics-based (PB) model for building temperature estimation is introduced first. Afterwards, in order to refine the model and improve the actual performance, we propose an innovative semi-blind (SB) model based on data-driven approaches. Additionally, the methodologies including self-adaptive algorithms (SAAs) and grey prediction technique (GPT) have been applied in dealing with the integrated parameters estimation (IPE) process to ensure the practicability of the implemented model. The proposed model schema is validated by testing in a laboratory. The results indicate that the proposed approach achieves much higher accuracy in estimating temperature variation than the conventional PB model, with only limited knowledge of the building characteristics. The root mean square deviation (RMSD) of SB model and PB model are 0.18 and 0.43, respectively. According to the results, it can be concluded that the proposed SB model is able to appropriately estimate the internal temperature values and great improvement has been achieved comparing with the original thermal model.

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A Semi-blind Model with Parameter Identification for Building Temperature Estimation

Local public fiscal revenue (PFR) is an important indicator to measure the level of local economic development. Accurate prediction of local public fiscal revenue can provide theoretical support for governments and relevant departments to make scientific decisions. Firstly, we use the principal component analysis to reduce the dimensions of variables. Secondly, we predict Harbin public fiscal revenue by using hybrid genetic algorithm (GA) and support vector machine (SVM) model. Then we compare the results with a back propagation neural network model and a gray neural network model optimized with the genetic algorithm. The results show that the hybrid genetic algorithm and support vector machine model is more effective for forecasting Harbin public fiscal revenue.

Hybrid Genetic Algorithm and Support Vector Machine Performance in Public Fiscal Revenue Prediction

Introduction: Firms’ production strategy consists of interrelated strategic decisions, including pricing, demand forecasting and demand response planning, capacity planning, capital and cost structure. Production strategy is also the most important factor affecting the overall return of companies. Companies must estimate future situations in order to maintain their current position. Nowadays, with the developing technology, companies contain a wide variety of data. With various data analytics and optimization methods and tools, the data that can help the decision making process of companies can be made meaningful and usable. Objective: For companies like sanitary wares with large number of product variants, product groups based on estimated requirements will emerge. The ceramic sanitary ware sector, where the product variety is very high, shows seasonal effects in itself and seasonal and trend effects in its products. This situation makes it difficult to make estimations in the ceramic sector. The aim of this study is to increase the accuracy rate of demand estimation ratio by more than 70%. Methods: First of all, k-means clustering algorithm is used to obtain product groups. Then, an artificial Neural Networks model is used to estimate demands of product groups. Results: The obtained estimation error ratios are compared with those which are obtained by exponential smoothing and moving average methods in time series methods. It is observed that the most suitable method is Artificial Neural Networks (ANNs) for obtaining best results. Conclusion: The results prove the efficiency of the applying ANNs to clustered products as a nature-inspired method for demand estimation problem.

Demand Forecasting with Clustering and Artificial Neural Networks Methods: An Application for Stock Keeping Units

Back propagation (BP) neural network has been widely used for various data predictions in application. One of the challenging issues in various applications of BP neural network is how to improve its reliability as well as its stability. In this paper, by using a prototype for the forecast of atmospheric radiation and atmospheric ozone concentration in the state of Ohio, USA, we show that a direct use of the BP neural network may lead to the loss of forecast reliability during its evolutionary process. Under the framework of Verhulst biological model with embedding cognitive computation, we show that one can effectively reduce the dispersion of pure randomness of data sets in BP neural network and improve the prediction of future data by incorporating accumulation generation operation (AGO) into the system. We demonstrate that the integration of a modified gray model and the AGO can offer a more desirable BP neural network algorithm, and both stability and reliability become much improved compared to the direct use of BP neural network reported in current literature.

Exploiting a Modified Gray Model in Back Propagation Neural Networks for Enhanced Forecasting

Instability phenomena occurred in aeroengines are certainly very undesirable. The unstable flow not only causes a drastic reduction in the performance of the compressor but also can damage to engine's components during operations. Thus it is necessary and critical to employ various feedback control mechanism to stabilize the system. Current all proposed feedback controllers in literature require the full information of the disturbance at the duct entrance, which is an infinite-dimensional quantity and thus is impossible for a direct on-line measurement in reality. In this paper, we construct a local state observer which can deliver the full information of the disturbance by only sensing on an arbitrarily small area at the duct entrance. The approach relies on the semigroup theory as well as operator spectrum analysis. Numerical simulations are provided to illustrate the effectiveness of the proposed observer by demonstrating different types of flow situations for the aeroengine compressors.

Xuejun Gao

Papers

Exploiting a Modified Gray Model in Back Propagation Neural Networks for Enhanced Forecasting

Local observer for axial flow aeroengine compressors

Observer Design for Axial Flow Compressor