Beam element modelling of vehicle body-in-white applying artificial neural network

In this study a large knowledge base is first established through numerous designs of experiments on beam elements, based on a validated finite element model of a reference vehicle body-in-white. Then a recurrent artificial neural network is applied to extract the input/output relationship between the crash dynamic characteristics and beam element features. With such established relationship, beam element features are predicted according to expected crash dynamic characteristics. Our analyses show that the predicted beam element model enables generating essential crash dynamic characteristics for concept BIW design evaluation at a reasonable level of accuracy. Last, a data assurance criterion is developed to quantitatively validate the beam element modelling.     

Mathematical modelling and optimal control of solar dryers

A mathematical model of the solar dryers designed and used in Cuba is presented and discussed. The model consists of a set of ordinary nonlinear differential equations which describe the behaviour of the main parts of the dryer. Using the model, an optimal control problem is formulated and solutions within the class of piecewise constant controls are numerically obtained. It is shown that controls which are constant over intervals of 24 hours have the best properties for application to drying plants.     

Horseshoe in a model of artificial neural network

In this paper, we study a three-dimensional general model of artificial neural network (ANN). To confirm the chaotic behavior in this neural network demonstrated in numerical studies, we consider a cross-section properly chosen for the attractor obtained and study the dynamics of the corresponding Poincaré map, and rigorously verify the existence of horseshoe by computer-assisted verification arguments.     

Approximation properties of a multilayered feedforward artificial neural network

We prove that an artificial neural network with multiple hidden layers and akth-order sigmoidal response function can be used to approximate any continuous function on any compact subset of a Euclidean space so as to achieve the Jackson rate of approximation. Moreover, if the function to be approximated has an analytic extension, then a nearly geometric rate of approximation can be achieved. We also discuss the problem of approximation of a compact subset of a Euclidean space with such networks with a classical sigmoidal response function.Dedicated to Dr. C.A. Micchelli on the occasion of his fiftieth birthday, December 1992Research supported in part by AFOSR Grant No. 226 113 and by the AvH Foundation.     

A discrete dynamical system as a model of a neural network with generalized Hebbian synapses

We study the dynamical behavior of a discrete time dynamical system which can serve as a model of a learning process. We determine fixed points of this system and basins of attraction of attracting points. This system was studied by Fernanda Botelho and James J. Jamison in [A learning rule with generalized Hebbian synapses, J. Math. Anal. Appl. 273 (2002) 529-547] but authors used its continuous counterpart to describe basins of attraction.     

Approximation by neural networks with a bounded number of nodes at each level

It is shown that the general approximation property of feed-forward multilayer perceptron networks can be achieved in networks where the number of nodes in each layer is bounded, but the number of layers grows to infinity. This is the case provided the node function is twice continuously differentiable and not linear.     

Analytic modelling of solar radiation: driven temperature variations of outdoor surfaces

An analytic model is described for the variation of surface temperature T₀(t) ofa freely evaporating or totally dry surface exposed to complicated, non-analytic variations of meteorological conditions expressed in (N + 1)-point time series form. Its basis is a parameterized, analytic representation of T₀, inserted in linearized equations describing the surface energy balance and the concurrent underlying heat conduction. Applied to diurnal variations (with N = 24) over bare soil, the model reproduces observed temperatures with a typical standard deviation less than 1K, and the daily mean within 0.1 K.

The method should find general application in modelling of storage systems subject to complicated, discretely-sampled boundary conditions, where a linear analytic equation links the latter to the storage term.     

Mathematical modelling of a diesel common-rail system

In diesel common-rail systems, the exact knowledge of the injection pressure is important to accurately control the injected diesel mass and thus the combustion process. This paper focuses on the mathematical modelling of the hydraulic and mechanical components of a common-rail system in order to describe the dynamics of the diesel rail pressure. Based on this model, an average model is derived to reduce the model complexity and to allow for a fast calculation of the mass flow into the rail for different crank shaft revolution speeds and openings of the fuel metering unit. The main purpose of this average model is to serve as a basis for a model-based (non-linear) controller design. The stationary accuracy of the models is validated by means of measurement data.     

Green's function solution of the time-dependent solar collector problem

The Green's function for the time-dependent solar collector problem is derived and examined. It is found that the influence of a point source of irradiance propagates with the speed of the heat transfer fluid. This result contradicts some earlier work.An analytical expression is derived for the output fluid temperature in terms of the irradiance as a function of position and time. Fluctuations in ambient and input fluid temperatures are also considered.     

Bifurcation of a three-unit neural network

Considered is a system of delay differential equations modeling a time-delayed connecting network of three neurons without self-feedback. Discussing the change of the number of eigenvalues with zero real part, we locate the boundary of the stability region and finally determine the largest stability region of trivial solution. We investigate the existence of bifurcation phenomena of codimension one/two of the trivial equilibrium by considering the intersections of some parameter curves, which, in the aτ-half parameter plane, correspond to zero root or pure imaginary roots. In particular, the equivariant bifurcation is studied because of the equivariance of the system. We also present numerical simulations to demonstrate the rich dynamical behavior near the equivariant Pitchfork-Hopf bifurcation points, Hopf-Hopf bifurcation points, and some higher codimension bifurcation points.     

Performance evaluation of artificial neural network approaches in forecasting reservoir inflow

This study investigates the potential of Time Lag Recurrent Neural Networks (TLRN) for modeling the daily inflow into Eleviyan reservoir, Iran. TLRN are extended with short term memory structures that have local recurrent connections, thus making them an appropriate model for processing temporal (time-varying) information. For this study, the daily inflow into Eleviyan reservoir between years 2004–2007 was considered. To compare the performance of TLRN, a back propagation neural network was used. The TLRN model with gamma memory structure, eight input layer nodes, two hidden layer and one output layer (8-2-1) was found performing best out of three different models used in forecasting daily inflow. A comparison of results with back propagation neural network suggest that neither TLRN nor back propagation approaches were good in forecasting high inflow but, both approaches perform well when used to forecast low inflow values. However, statistical test suggests that both TLRN and back propagation neural network models were able to reproduce similar basic statistics as that of the actual data.     

Encapsulation of air vessel design in a neural network

The trial and error process of calculating the characteristics of an air vessel suitable to protect a rising main against the effects of hydraulic transients has proved to be cumbersome for the design engineer. The own experience and sets of charts, which can be found in the literature, can provide some help. The aim of this paper is to present a neural network allowing instantaneous and direct calculation of air and vessel volumes from the system parameters. This neural network has been implemented in the hydraulic transient simulation package DYAGATS.     

The impact of special days in call arrivals forecasting: A neural network approach to modelling special days

A key challenge for call centres remains the forecasting of high frequency call arrivals collected in hourly or shorter time buckets. In addition to the complex intraday, intraweek and intrayear seasonal cycles, call arrival data typically contain a large number of anomalous days, driven by the occurrence of holidays, special events, promotional activities and system failures. This study evaluates the use of a variety of univariate time series forecasting methods for forecasting intraday call arrivals in the presence of such outliers. Apart from established, statistical methods, we consider artificial neural networks (ANNs). Based on the modelling flexibility of the latter, we introduce and evaluate different methods to encode the outlying periods. Using intraday arrival series from a call centre operated by one of Europe’s leading entertainment companies, we provide new insights on the impact of outliers on the performance of established forecasting methods. Results show that ANNs forecast call centre data accurately, and are capable of modelling complex outliers using relatively simple outlier modelling approaches. We argue that the relative complexity of ANNs over standard statistical models is offset by the simplicity of coding multiple and unknown effects during outlying periods.     

Optimization of operating strategies in a community solar heating system

Minimization of auxiliary energy costs is discussed for heating in a district solar heating system with effective heat storage. The minimization problem is approached by dynamic programming which gives an optimal operating strategy for the auxiliary energy system. The effects of different pricing schemes of auxiliary energy (electricity) have been studied. The results show that with an adequate heat storage capacity, the optimization of the auxiliary energy use in a community solar heating system may lead to considerable cost savings.     

Efficacy analysis of a body-mass-reduction treatment using mathematical modelling

Obesity was categorized as a chronic disease by the World Health Organization (WHO) in 1997 because the problem had reached at pandemic level and presented a serious risk factor with respect to people who have been developing type-2 diabetes, hyperdyslipidaemia and hypertension. These four risk factors tend to accelerate the development of cardiovascular diseases. As a result, obesity has also become a significant social and economic burden. An important observation with regard to the population exhibiting increased body mass is the fact that they would like to decrease their weight, although they are frequently not successful. In this paper, a modelling-and-simulation approach is used for the presentation, analysis and explanation of the reasons that have an important influence on the treatment’s efficacy. The presented modelling results are based on the observation and treatment experiences of patients in a specialized institution over a period of 15 years, where each year around 100 new patients enter the treatment programme. The introduction of the motivation principle in the model structure allows strong support for the actions of the therapeutic team in a closed-loop manner, as the checking of different scenarios for the individual patient is easily realized. The efficacy of the treatment can, in this way, be significantly improved. In the past 6 years, which mainly involved open-loop treatments, the dropout rate was 70%. After the introduction of proposed closed-loop approach, this was reduced to 27% in the past year. As a consequence, the effect on body-mass control was significantly improved.     

Development and experimental validation of a control-oriented Diesel engine model for fuel consumption and brake torque predictions

This article describes the development and experimental validation of a control-oriented, real-time capable, Diesel engine instantaneous fuel consumption and brake torque model under warmed-up conditions with only two inputs: torque request and the engine speed and no other measurements. Such a model, with the capability of reliably and computationally efficiently estimating the aforementioned variables at both steady-state and transient engine-operating conditions, can be utilized in the context of real-time control and optimization of hybrid power train systems. Although Diesel engine dynamics are highly non-linear and very complex, by considering the Diesel engine and its control system, that is, engine control unit together as an entity, it becomes possible to predict the engine instantaneous fuel consumption and torque based on only those two inputs. A synergy between different modelling methodologies including physically based grey-box and data-driven black-box approaches were integrated in the Diesel engine model. The fuelling and torque predictions have been validated by means of experimental data from a medium-duty Diesel engine at both steady-state and transient operations, including engine start-ups and shutdowns.     

Modelling and experimental validation of the deflection of a leveller for hot heavy plates

In order to successfully automate levelling processes, in particular for heavy plates, the deflection of the leveller has to be compensated based on a deflection model. In this work, a detailed mathematical deflection model of a hot leveller with bending mechanism and its experimental validation are presented. The roll intermesh profiles are calculated based on the deflection of the work rolls that are elastically supported by support rolls, frames, posts and adjustment screws. The deflection model is suited to compensate the effect of deflection on the roll intermesh and the plate flatness as well as to assess the loads of critical parts, for example the support rolls. A new experimental design to measure the deflection of a leveller is presented and successfully applied for model validation. The work roll deflection is measured directly by means of displacement sensors that are inserted in cut-outs of test plates. These test plates are modelled as linear elastic stripes. For normal load levels, the relative accuracy (repeatability) of the roll intermesh prediction of the model is better than 0.08 mm.