Regularized Adaptation of Fuzzy Inference Systems. Modelling the Opinion of a Medical Expert about Physical Fitness: An Application

This study presents a new approach to adaptation of Sugeno type fuzzy inference systems using regularization, since regularization improves the robustness of standard parameter estimation algorithms leading to stable fuzzy approximation. The proposed method can be used for modelling, identification and control of physical processes. A recursive method for on-line identification of fuzzy parameters employing Tikhonov regularization is suggested. The power of approach was shown by applying it to the modelling, identification, and adaptive control problems of dynamic processes. The proposed approach was used for modelling of human-decisions (experience) with a fuzzy inference system and for the fuzzy approximation of physical fitness with real world medical data.     

Mathematical modeling and trajectory planning of mobile manipulators with flexible links and joints

This paper is concerned with mathematical modeling and optimal motion designing of flexible mobile manipulators. The system is composed of a multiple flexible links and flexible revolute joints manipulator mounted on a mobile platform. First, analyzing on kinematics and dynamics of the model is carried out then; open-loop optimal control approach is presented for optimal motion designing of the system. The problem is known to be complex since combined motion of the base and manipulator, non-holonomic constraint of the base and highly non-linear and complicated dynamic equations as a result of the flexible nature of both links and joints are taken into account. In the proposed method, the generalized coordinates and additional kinematic constraints are selected in such a way that the base motion coordination along the predefined path is guaranteed while the optimal motion trajectory of the end-effector is generated. This method by using Pontryagin’s minimum principle and deriving the optimality conditions converts the optimal control problem into a two point boundary value problem. A comparative assessment of the dynamic model is validated through computer simulations, and then additional simulations are done for trajectory planning of a two-link flexible mobile manipulator to demonstrate effectiveness and capability of the proposed approach.     

Modelling on fuzzy control systems

A kind of modelling method for fuzzy control systems is first proposed here, which is called modelling method based on fuzzy inference (MMFI). It should be regarded as the third modelling method that is different from two well-known modelling methods, that is, the first modelling method, mechanism modelling method (MMM), and the second modelling method, system identification modelling method (SIMM). This method can, based on the interpolation mechanism on fuzzy logic system, transfer a group of fuzzy inference rules describing a practice system into a kind of nonlinear differential equation with variable coefficients, called HX equations, so that the mathematical model of the system can be obtained. This means that we solve the difficult problem of how to get a model represented as differential equations on a complicated or fuzzy control system.     

O.R. modelling of the deterioration and maintenance of concrete structures

This paper reports on a collaborative venture between operational researchers and civil engineers over 3 years. The main objectives were to collect and publish data on the observed rates of deterioration of particular defect types in a large number of concrete bridges, and to develop predictive mathematical models that relate inspection frequency to maintenance costs. The motivation was in part associated with the prototype modelling paper for inspection practices of major concrete structures, Christer (1988). The paper reports on the analysis of data collected and the estimation of deterioration using the concept of delay time. The two phase delay time model is extended to an extra phase in order to model the process of cracking and spalling in concrete. Maximum likelihood techniques are used to estimate modelling parameters and an appropriate test of fit is carried out. Cost based models are then formulated to predict the cost effects of maintenance and inspection decision options. The cost model is applied first to an element, and then to an aggregate number of component types to produce a cost model for maintenance of a bridge or set of bridges.     

Active damping control for an underactuated multibody system

Light-weight robots and manipulators stand out due to their very good weight-to-load ratio and a low energy consumption. Unfortunately, the light-weight design yields a lower stiffness, which results in undesired elastic deformations, especially during high-speed working motion. One way to limit these unwanted oscillations can be implemented with modifications of the command signals, e.g. by input shaping or pre-computed feed-forward control. However, a feedback control-concept has the ability to provide a fast compensation of elastic deformations due to high-speed working motions or in case of unwanted environment contact as well as in the presence of other external disturbances. In this contribution, an active damping control (ADC) for fast moving manipulators with significant structural elasticities is presented. This approach does not require additional actuators and it is suitable for a large variety of manipulators that exhibit structural vibrations. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Kinetic (cellular) models of cell progression and competition with the immune system

This paper deals with the modelling of the immune response to the evolution of progressing (corrupted) endothelial cells, i.e. cancer cells. A mathematical model is proposed, on the basis of mathematical methods of the kinetic theory for a large system of interacting cells. Then a qualitative analysis is carried out to prove the existence of the solutions of the Cauchy problem related to the model and to show some results on the asymptotic behavior. Some computational simulations complete the analysis on the asymptotic behavior of the solutions, which depending on parameters and initial conditions shows either the prevalence of progressing cells or their depletion due to the action of the immune system.     

On the modelling of heat exchangers and heat exchanger network dynamics using bond graphs

ABSTRACT

Heat exchanger networks are important systems in most thermal engineering systems and are found in applications ranging from power plants and the process industry to domestic heating. Achieving cost-effective design of heat exchanger networks relies heavily on mathematical modelling and simulation-based design. Today, stationary design calculations are carried out for all new designs, but for some special applications, the transient response of complete networks has been researched. However, simulating large heat exchanger networks poses challenges due to computational speed and stiff initial value problems when flow equations are cast in differential algebraic form. In this article, a systems approach to heat exchanger and heat exchanger network modelling is suggested. The modelling approach aims at reducing the cost of system model development by producing modular and interchangeable models. The approach also aims at improving the capability for large and complex network simulation by suggesting an explicit formulation of the network flow problem.     

FEM modelling of the time-harmonic dynamical stress field problem for a pre-stressed plate-strip resting on a rigid foundation

In this paper, the FEM modelling of the time-harmonic dynamical stress field problem for the pre-stressed plate-strip with finite length resting on a rigid foundation is developed. The mathematical formulation of the considered problem is made by the use of the equations and relations of the Three-dimensional Linearized Theory of Elastic Waves in Initially Stressed Bodies. The proposed modelling is tested on the concrete problems as an example. The numerical results testing the validity of the developed FEM modelling are presented. Moreover, the numerical results attained for the various values of the problem parameters are also presented.     

Multicriteria identification sets method

A multicriteria identification and prediction method for mathematical models of simulation type in the case of several identification criteria (error functions) is proposed. The necessity of the multicriteria formulation arises, for example, when one needs to take into account errors of completely different origins (not reducible to a single characteristic) or when there is no information on the class of noise in the data to be analyzed. An identification sets method is described based on the approximation and visualization of the multidimensional graph of the identification error function and sets of suboptimal parameters. This method allows for additional advantages of the multicriteria approach, namely, the construction and visual analysis of the frontier and the effective identification set (frontier and the Pareto set for identification criteria), various representations of the sets of Pareto effective and subeffective parameter combinations, and the corresponding predictive trajectory tubes. The approximation is based on the deep holes method, which yields metric ε-coverings with nearly optimal properties, and on multiphase approximation methods for the Edgeworth–Pareto hull. The visualization relies on the approach of interactive decision maps. With the use of the multicriteria method, multiple-choice solutions of identification and prediction problems can be produced and justified by analyzing the stability of the optimal solution not only with respect to the parameters (robustness with respect to data) but also with respect to the chosen set of identification criteria (robustness with respect to the given collection of functionals).     

Scheduling of production and logistics operations of steam production systems in food industries: a case study of the tomato processing industry

This study presents an optimization approach by mathematical modelling to support some of the main operational decisions in steam production systems with multiple industrial boilers. Decisions are related to boiler operations scheduling (start-up, warm-up and shutdown time), fuel replenishment (transportation and inventory management) and fuel composition consumed by each piece of equipment. These decisions are often taken based on practical experience of people involved, instead of any decision support tool using optimization techniques; as a consequence, unnecessary costs are likely to be incurred. The optimization approach is based on mixed integer programming and parameters experimental adjustment procedures. A case study of a large tomato processing plant in Brazil was carried out along 1 year using a 3-year database. Owing to the reasonably good outcomes achieved (annually potential savings around 10%), we consider the proposed approach as a suitable tool to support some of the key decisions in boiler scheduling and fuel logistics in steam production systems for tomato processing and other similar industries.     

Individual-based modelling and simulation of microbial processes: yeast fermentation and multi-species composting

Controlled microbial activity is the core of many industrial processes. Such dynamic microbial processes must be carefully studied to optimize their application. They are usually tackled by means of continuous mathematical modelling at the population level (top-down). An alternative approach is individual-based modelling (IbM) (bottom-up). INDISIM is a discrete and spatially explicit IbM. It sets the rules that govern each microbe and its interaction with its local environment, as well as the significant environmental processes. Then it performs simulations that include a large number of microbes, and the behaviour of the whole system emerges. The rules are changed to reproduce the behaviour of microbes depending on the system to be studied. Two adaptations of INDISIM to study yeast fermentations and multi-species composting are presented in this article (INDISIM-YEAST and INDISIM-COMP), proof of INDISIM's versatility. A few representative results are also shown.     

On the macroscopic material behaviour of textile reinforced concrete undertensile loading

This paper concerns with the development of the macroscopic material behaviour of textile reinforced concrete (TRC) using an analytical approach. Therefore the heterogeneous structure of TRC is modelled on the mesoscopic level. The overall material behaviour on the macroscopic level is obtained by means of the homogenisation technique. The analytical approach is based on the micro mechanical solution for a single inclusion according to Eshelby . In extension of this solution for multidirectional reinforced concrete an effective field approximation is used. This approach considers the interactions between the different orientated rovings and the micro cracks in an average sense. For the mechanical modelling of the bond behaviour between roving and matrix after initiating of the macro cracking a slip based bond model with a multiple linear shear stress-slip relation is used. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Operational Research and Corporate Planning in Railway Management

The current corporate planning process in Westrail is described and the roles played by operational research and mathematical modelling identified. They do not include forecasting the future. Instead of the "predict and prepare paradigm" a planning approach that tries to design the future has been adopted. The organisation is described in terms of how it has evolved, what it now is, and the key features of its environment. The three stages of planning are described-strategic, tactical and operational. These provide the means for management control of the railway. Environmental assessments linked to goal setting activities are incorporated within the planning process. The significance of operational research in planning, in particular mathematical modelling, is also described. Instead of finding problems to which existing techniques can be applied, O.R. is used to provide effective operational and planning systems as a means of assisting management to design the future for the organisation.     

On the discrete kinetic theory for active particles. Mathematical tools

This paper deals with the development of a mathematical discrete kinetic theory to model the dynamics of large systems of interacting active particles whose microscopic state includes not only geometrical and mechanical variables (typically position and velocity), but also peculiar functions, called activities, which are able to modify laws of classical mechanics. The number of the above particles is sufficiently large to describe the overall state of the system by a suitable probability distribution over the microscopic state, while the microscopic state is discrete. This paper deals with a methodological approach suitable to derive the mathematical tools and structures which can be properly used to model a variety of models in different fields of applied sciences. The last part of the paper outlines some research perspectives towards modelling.     

A class of mathematical models for alternated-current electrochemical measurements accounting for non-linear effects

The traditional approach to the modelling of alternated-current electrochemical measurements is daunted by three major drawbacks: (i) only linear behaviour of the interface investigated is accounted for; (ii) the physical meaning of many model parameters is not straightforward; and (iii) entangled inverse parameter identification problems are generated. In this paper we address these problems by defining additional mathematical models related to the Fourier expansion of a more general, physically meaningful nonlinear electrochemical kinetic reaction system. The traditional linear model is regained as the truncation at the first harmonic of the series. Analytical expressions are derived for experimental observables relating to the nonlinear electrochemical behaviour that can be measured independently during the same experiment. Eventually, we show that the higher-harmonic models can be used as a general regularization tool to reduce the number of the multiple globally optimum solutions in the nonlinear leastsquares fitting of alternated-current data, highlighted in Bozzini and Sgura [Numerical issues related to the modelling of electrochemical impedance data by nonlinear least squares, Int. J. Nonlinear Mech. 40(4) (2005) 557–570].     

Wind-excited vibrations of transmission lines: A comparison of different mathematical models

In this paper, the modelling of wind-excited vibrations of conductor cables in overhead transmission lines is discussed. Only oscillations in the frequency range from 10 Hz to 50 Hz due to vortex shedding are considered. Different mathematical models are proposed for the cables, for the aerodynamic forces and for the dampers. The models are compared and their relative merits are summarized. Finally, a relatively simple approach is proposed for the calculation of the bending strains in the cables of a transmission line with dampers. The problem is an example of how mathematical modelling at different levels combines mathematical tools with engineering insight into the physical problem.     

Assessing science students’ attitudes to mathematics: a case study on a modelling project with mathematical software

This article reports the attitudes of students towards mathematics after they had participated in an applied mathematical modelling project that was part of an Applied Mathematics course. The students were majoring in Earth Science at the National Taiwan Normal University. Twenty-six students took part in the project. It was the first time a mathematical modelling project had been incorporated into the Applied Mathematics course for such students at this University. This was also the first time the students experienced applied mathematical modelling and used the mathematical software. The main aim of this modelling project was to assess whether the students’ attitudes toward mathematics changed after participating in the project. We used two questionnaires and interviews to assess the students. The results were encouraging especially the attitude of enjoyment. Hence the approach of the modelling project seems to be an effective method for Earth Science students.     

Modelling and identification of rigid‐body dynamics of parallel kinematic structures

A new approach for modelling the dynamics of parallel kinematic (PKM) structures is presented in this paper. It leads to a formulation of the dynamic equations which is linear with respect to a dynamic parameter vector of minimal dimension. Thus, the equations can be directly used for parameter identi.cation by linear estimation techniques. The algorithm utilises Jourdain 's principle of virtual power which leads to very efficient resulting code. The parameter reduction is based on opening the kinematic loops so that analytic rules known from serial robots can be implemented. Additionally, a new approach for dynamic parameter identification is suggested. The application to modelling the PKM PaLiDa and identifying its gravitational parameters proves the capacity of the presented approaches.