This page lists short abstracts of research projects undertaken by the staff of the Department of Engineering Mathematics, over the past few years.

Fast, scalable, high performance algorithms
Chamila Walgampaya

CatBoost is an algorithm for gradient boosting on decision trees. It is developed by Yandex researchers and engineers, and is used for search, recommendation systems, personal assistant, self-driving cars, weather prediction and many other tasks at Yandex and in other companies, including CERN, Cloudflare, Careem taxi. It is in open-source and can be used by anyone. We at the dept of engmath works on large datasets with CatBoost and many other gradient boosting algorithms. If you interested in this work write to us at ckw AT pdn.ac.lk.

Financial time series forecasting
Chamila Walgampaya

Every country would like to maintain the government domestic debt at a sustainable level. Domestic debt taken from the banking sector cause inflation and non banking sector debt cause to crowding out effect on private sector investors. It leads to increase the government expenditure of each and every year with the government debt service payments. That should be repaid, not only by the present generation but also by the future generation basically with their tax payments. However it is important to know, the effect of economic growth on the government domestic debt of the country, before reducing the level of the government domestic debts. We at dept of engmath study investigate the co-integration relationship between economic growth and the government total debt of Sri Lanka. If you are interested to work on this let us know by writing to ckw AT pdn.ac.lk.

Class imbalance problem in streaming data
Chamila Walgampaya

Processing of real time data demand lot of time and effort due to many reasons. One such event is the data imbalance problem. For example in real time data streams where there are two types of candidates (fraudulent and genuine) where fraudulent clicks are too small compared to that of genuine. This kind of data set is referred to as an imbalanced data set in the machine learning domain where predictive models mislead the final results due to this class imbalance problem. We at the dept of engmath work on new ways to handle the class imbalance problem. If you are interested to work on this let us know by writing to ckw AT pdn.ac.lk.

Combating click fraud in mobile advertising
Chamila Walgampaya

Online advertising has become a multi millionaire industry and more than fifty percent of the market share is dominated by mobile advertising nowadays since the excessive usage of mobile phones and tablets all around the world. Due to the large sum of money involve in this industry people are trying to jeopardize the online advertising eco system by various means. One such approach is ad fraud. The term ad fraud is referred to as any kind of fraudulent activities that are executed by fraudulent users either a human or an automated script with the intention of making illegal revenue or exhausting the advertiser budget. The academics and industry experts have conducted various kinds of research and have introduced a number of methodologies and tools in the context of ad fraud detection and prevention. We at the dept of engmath also have proposed novel approaches to combat the ad fraud. If you are interested to work on this let us know by writing to ckw AT pdn.ac.lk.

Seismic performance of rectangular-shaped columns
Susantha, K. A. S., and Aoki, T. (Aichi Institute of Technology,Japan)

The effects of web to flange aspect ratio of rectangular-shaped columns on strength and ductility were examined by means of test and finite element analyses. Recommendations for optimum aspect ratio with respect to the seismic resisting capacity were made.

Bridge piers under multi-directional cyclic loads
Susantha, K.A.S., Usami, T. (Nagoya University, Japan), Aoki, T.(Aichi Institute of Technology, Japan)

A project aimed at investigating the effects of behavior of bridge columns subjected to multi-directional cyclic loads. Extensive experimental and numerical works have been carried out.

Ductility improvement of steel columns with low-yield (LY) strength steel plates at the base
Susantha, K. A. S., and Aoki, T. (Aichi Institute of Technology, Japan)

The use of low-yield strength steel in bridge piers was introduced to achieve improved energy absorption capacity. Design recommendation for the location, dimensions and thickness of LY steel plates were made based on experimental results.

New technique for high performance steel bridge piers under earthquake loads
Susantha, K. A. S., and Aoki, T. (Aichi Institute of Technology,Japan)

New design method has been introduced for bridge piers subjected to extremely high earthquake loads. The method includes conventional box or circular section bridge piers equipped with pre-compressed concrete-filled steel tube that acts as a special axial load bearing member.

Innovative use of thickness tapered steel plates in beam columns and rigid-frame bridge piers
Susantha, K. A. S, Fukumoto, Y. (Fukuyama University, Japan), Takaku, T. (TOKO Consultant Co., Tokyo, and Aoki, T. (Aichi Institute of Technology, Japan)

A project carried out with collaboration with TOKO Consultants Ltd., Tokyo, and Fukuyama University, Japan. A design rule for the limit state strain for tapered plate columns in rigid-frame bridge piers was developed. Design rule for the use of tapered plate in bridge columns has also been developed.

Capacity and demand prediction methodology for partially concrete-filled steel bridge piers subjected to severe earthquakes
Susantha, K. A. S, Ge H. B., Usami T. (Nagoya University, Japan)

A seismic design procedure for partially concrete-filled steel columns was developed using pushover analysis. A new failure criterion based on the average strain at critical sections was adopted to determine the ultimate state of columns. New material model for confined concrete was also proposed and used in the analyses.

Development of Automatic Sensors for Environmental Factors
Thusitha Abayarathna, Kirthi Walgama, and the Tea Research Institute

Data on environmental factors such as wind speed, wind direction, solar radiation, air temperature, ground temperature, humidity and rainfall are of paramount importance in modeling and prediction of natural phenomena (eg: tea production). Manual sensors are available for data collection, but possess the disadvantages of being time-consuming, repetitive, error-prone and limited in scope, since they cannot take rapid or repeated measurements easily. It has become necessary therefore to develop automatic sensors to collect such data. This project uses PC based instrumentation to develop self-operating data collecting stations. A careful calibration process is required; data sets are collected and analyzed, and suitable corrections are made to the sensors to minimize errors. The electronic components of the sensors currently available are not tropicalized, and hence periodic replacement has become necessary. It is hoped that this project can be extended by establishing a research laboratory expressly dedicated to developing automatic sensors.

A Finite Element Mesh Refinement based on Arbitrary Lagrangian Eulerian Description
Sunil Munasinghe & Worsak Kanok-Nukulchai (AIT, Thailand)

Finite element methods based on pure Lagrangian or pure Eulerian approaches encounter some difficulties when analysing fluid problems with large free surface oscillations. The Lagrangian description, often used to analyse solids, suffers severe mesh distortions when analysing fluid problems with large free surface motions. Furthermore, stability problems often arise due to large bulk modulus and negligible shear modulus. On the other hand, the Eulerian description, though very effective in analysing fluid problems with fixed boundaries, also has difficulties when the free surface oscillations are large. To overcome the difficulties in both methods, the arbitrary-Lagrangian description is proposed, and implemented in finite element code to analyse problems with large free surface oscillations. This formulation leads to an easy and accurate treatment of fluid-structure interaction, and its mesh remeshing and rezoning permits large fluid sloshing without producing excessive distortion of the fluid finite element mesh.

Optimistic/Pessimistic Behaviour of Heterogeneous Bodies with Statistically Varying Material Characteristics
Sunil Munasinghe & M. Hori (Tokyo Univ., Japan)

In general, natural geo-materials such as soils and rocks are highly heterogeneous. However in analysis, they are often modelled with some effective properties that govern their overall behaviour. Therefore, a precise prediction of the effective material properties is essential for more accurate analysis. When the variation of data on heterogeneity is large, the effective material properties take values in a wider range. For practical purposes, it is desirable to predict the range of all possible effective properties as well as a single value which is the most likely to be realised. A limit state of optimistic or pessimistic behaviour of heterogeneous materials could be obtained if extreme values are used in analysis. The upper and lower bounds for material properties were proposed by combining given statistical distributions of heterogeneity with formal bounds proposed by Hashin-Shtrikman for heterogeneous materials.

Surface Deformation due to Differential Movement of Earthquake Faults
Sunil Munasinghe & M. Hori (Tokyo Univ., Japan)

An accurate computation of propagation of earthquake faults is essential in predicting surface deformation due to differential movement of active faults. In continuum mechanics, this phenomenon can be described as a formation of a narrow shear band due to differential movement of the bottom crust, and as a result a relative sliding of two portions of the crust occurs along the shear band. The computation of initiation and propagation of the shear band is the key issue in this finite element analysis. A non-linear numerical algorithm was developed, by modifying the Newton-Raphson technique. This algorithm is capable of computing stress resultants of both softening and hardening materials.

Approximation of a Switched Linear System by a Nonswitched Homogeneous Polynomial System
P.C.Perera, W.P.Dayawansa(TTU)

It is shown that given a switched linear control system which satisfy the controllability rank condition, it is possible to construct a non-switched homogeneous polynomial control system in such a way that the trajectories of the latter may be arbitrarily well approximated norm on finite time intervals.

Converging Towards a Comprehensive and Coherent Global Engineering Education System (CCGEES)
P.C.Perera, Sanjaya Senadheera (TTU)

Globalization is rapidly changing the way both developed and developing countries do business. In addition, the information and communication revolution has forced countries to rewrite the way they operate and plan for the future. Aggressive growth in many countries has also created a dearth of engineering talent worldwide. These challenges and opportunities have forced countries to develop and adopt new approaches for engineering education. The importance of technology literacy in the modern world has and the diversity of the profession has thrust the engineering profession to a more prominent leadership position in the society. This is changing the paradigms of engineering education around the world, both in terms of curricula and delivery methods.There are stark differences between developed and developing countries in the way engineers are educated and utilized. Developed countries enjoy robust political and economic systems, but have a smaller fraction of high school graduates entering the engineering profession. In the developing world, engineering and economic systems are not as robust, and a larger fraction of high school graduates enter the engineering profession. The high demand for engineering talent worldwide has allowed engineers are trained in developing countries to secure employees in developed countries. This "brain-drain" has opened huge gaps in the experienced engineering talent base in developing countries, and radical new approaches are needed to create a more equitable global engineering landscape. Converging towards a comprehensive and coherent global engineering education system (CCGEES) may be needed for smooth functioning of all world economies. The CCGEES must be developed based on a common foundation that require all countries to agree on what engineering is, the engineer's role in the global economy and the accreditation systems while providing flexibility for countries to be creative in meeting their own needs and allowing their engineers to be marketable globally. In this paper, the authors, one from a developing country currently working as an engineering educator in a developed country, and the other, trained in a developed country currently working as an engineering educator in a developing country, will bring together their unique perspectives to develop a framework for a CCGEES. The authors look at how engineers are educated and how they progress professionally in the countries they currently reside. Particular attention will be given to the way engineering talent is identified for admission to degree programs, the course curricula used, assessment techniques and accreditation schemes. The framework that authors developed also highlights the desired skills for engineers to be effective in the global marketplace. The authors focused on methods aimed at encouraging more diversity and flexibility in the engineering programs while maintaining a desired level of compatibility between them. This may lead to a curriculum structure that would make the engineering education systems in all countries more accessible to students worldwide. It will also promote cooperation and exchange programs between niversities and facilitate free and seamless movement of engineering talent across borders. More importantly, it has the potential to benefit both developing and developed countries.

A Sufficient Condition for Controllability of a Special Class of Polynomial Switched Systems
P.C. Perera

In this endeavor, a direct approach has been taken to establish a sufficient condition for controllability of switched systems consisting of time-invariant odd-degree polynomial subsystems. Control design for nonlinear switched control systems is known to be a nontrivial problem. The aforementioned direct approach that has been taken in this work, will hopefully lead to establish a sufficient condition for controllability of a broader class of nonlinear switched systems.

A faster algorithm to solve a certain class of linear programming problems
B.M.R.K. Basnayake, S.P.C. Perera.

Despite the ubiquitous usages of interior point algorithms in the context of solving linear programming problems, the importance of simplex method cannot be undermined. In this endeavor, the attention is focused to seek an algorithm which is faster than the simplex method for certain class of linear programming problems. It is attempted to devise the algorithm while identifying the class of linear programming problem for which this proposed method works better than the simplex method. The two methods are compared in terms of computational complexity and speed.

Improved Matched Pole Zero Mapping Method for Design of Discrete Controllers
B. U. Athukorala, P. C. Perera

Out of available methods for design of digital controllers, the method of discrete equivalent of analog controllers is most commonly used. One major step involved in this method is the discretizing of the analog controller. It turns out that the optimum method employed in discretizing the controller is plant dependent. In this endeavor, the attention is focused in determining the optimum method of discretizing an analog controller in the context of controlling an armature controlled-d.c.motor in the process of achieving desired performance.

Topological Structure of a Special Class of Linear Switched Systems
P. C. Perera

Switched control systems deserve investigation for both theoretical and practical reasons since switching based control strategies can result in algorithms that offer significant performance improvements over traditional linear control. A fundamental requirement for the design of feedback control systems is the knowledge of structural roperties of the switched system under consideration. Structural properties of a switched system are closely related to the generic counterparts such as controllability and observability. The knowledge on topological structure of switched systems consisting of continuous-time time-invariant linear subsystems can be used to clarify certain issues related to controllability as well as structural properties of such control systems. This work is mainly aimed at laying the groundwork of identifying the topological structure of the class of supervisory-based controllable switched systems consisting of continuous-time time-invariant linear subsystems

Canonical Forms and Switching Laws for Linear Switched Systems
P. C. Perera

The class of continuous-time time-invariant controllable linear systems can be stabilized by the use of controller canonical forms. Such canonical forms are not known in the context of switched control systems since a simultaneous transformation of two or more linear systems is not trivial and straightforward. Here, the attention is focused in developing such canonical forms for controllable switched systems consisting of two continuous-time time-invariant linear subsystems by constructing the simultaneous transformation matrices by arranging the suitably chosen basis vectors of the state space of the system of our interest as columns. These canonical forms are then used to devise switching strategies to control any arbitrary initial state to the origin by switching among the subsystems of the switched system of our interest.

Controllability of Polynomial Switched Systems and Their Switching Laws
P. C. Perera

A fundamental requirement for the design of feedback control systems is the knowledge of structural properties of the plant under consideration. These properties are closely related to the generic properties such as controllability. A sufficient condition for controllability of polynomial switched systems is established here. Control design for nonlinear switched control systems is known to be a nontrivial problem. In this endeavor, an indirect approach is taken to resolve the control design problem pertaining to polynomial switched systems satisfying the aforementioned sufficient condition for controllability; it is shown that trajectories of a related controllable polynomial system can be approximated arbitrarily closely by those of the polynomial switched control system of our inter.

Case Studies in Persistence of Invariant Sets under Noise
Mihirini Wagarachchi (IFS) & Sanjeeva Balasuriya

The stability of invariant sets of a map, in the sense of persisting under the inclusion of noise, is investigated for specific case studies. Both numerical and analytical methods are used in this study. Numerically: an average lifetime expectancy is computed by considering a large number of trajectories beginning at the same initial condition within the invariant set. Analytically: some established perturbative results are used to compute quantities related to set persistence. A comparison of the numerical and analytical results is attempted. More general case studies are considered, with the intention of furthering our understanding of these established analytical results, and providing an impetus for additional analytical definitions and investigations.

Stability of Sets in Almost Deterministric Maps
Sanjeeva Balasuriya

Deterministic mappings may possess different types of invariant sets, such as periodic orbits, basins of attractions of strange attractors, etc. However, in modeling a natural system with a deterministic map, many effects are ignored. A natural extension would be to include these effects as a stochastic perturbation on the deterministic map. Thus, it is of interest to know whether certain invariant sets persist under stochastic perturbations; if not, the behaviour of the invariant sets as predicted through the deterministic model is inappropriate for the natural system. An approach to analyzing the stability of these invariant sets under stochastic perturbations is being attempted both generally, and by using a formal perturbative expansion. The stability in this sense is defined through an expected lifetime of trajectories within the set.

Viscosity Induced Transport in Oceanic Jets
Sanjeeva Balasuriya, Chris Jones (Brown Univ., USA) & Bjoern Sandstede (Univ. Berlin, Germany)

Many barotropic models exist for oceanic jets (such as the Gulf Stream), and numerical investigations of arbitrary perturbations imposed on these models appear to generate chaotic motion, seemingly consistent with observed trajectories in the Gulf Stream. These models suffer the shortcoming of being only linearised solutions to the governing partial differential equations. Thus, it is important to develop a theory valid for genuine nonlinear solutions which are general rather than specific, and also to justify the cause for the imposed perturbations. A purely analytic approach is adopted for perturbations resulting directly from the inclusion of viscosity. Whether chaotic, or other forms of transport results is under analysis.

Melnikov Theory for Non-Autonomous Flows
Sanjeeva Balasuriya & Chris Jones (Brown Univ., USA)

A Melnikov theory exists for perturbations imposed on an autonomous two-dimensional flow. This provides information on the transverse crossing of stable and unstable manifolds, and hence the possibility of chaos. This projects extends the theory to the case where (a) the unperturbed flow is non-autonomous, and (b) the perturbed flow is 'close' to the unperturbed flow only in a weak functional analytical sense.

Vanishing Viscosity in the Barotropic Beta-Plane
Sanjeeva Balasuriya

Oceanic jets are expected to obey the conservation of barotropic potential vorticity to a good approximation, since viscous (dissipative) forces are negligible in the open ocean. Of interest is the legitimacy of ignoring dissipation, i.e., determining in which sense the dissipative velocity is close to that computed via inviscid dynamics. This is being investigated rigorously, with the help of powerful tools such as Sobolev's Embedding Theorem.

Exact Barotropic Models in Geophysical Fluids
Sanjeeva Balasuriya & Rohan Muthunayake

The dynamics of geophysical fluids are governed in some inviscid instances by the conservation of a quantity called the potential vorticity. Such a conservation law is derived by considering the effect of the earth's rotation and sphericity in the appropriate Navier-Stokes type equation. Additional considerations lead to the barotropic approximation, effectively reducing the flow to two-dimensions on the so-called Beta-plane. The conservation of (barotropic) potential vorticity then translates to a highly nonlinear partial differential equation for the streamfunction of the flow. Exact solutions to this equation which possess the qualitative kinematics observable in real geophysical flows are extremely difficult to find; researchers often take recourse to linearised solutions. This study attempts to determine such exact solutions to the governing equation, which have the relevant flow characteristics.

Application of Taguchi Technique for Optimization of Die Corner Radius in Sheet Metal Stamping
P.W.G.N.S. Jayasena, Kanthi Perera, Manjula Nanayakkara.

One of the most important, yet simplest deep-drawing operations on a flat blank of sheet metal is the production of a cylindrical cup. The mechanics of forming are quite complicated and there are many different factors affecting the successful drawing of a blank. Due to the some factors at the bending edge, the drawn object is not accurate. To obtain good quality product, the optimum level of Die corner radius and drawing speed that gives the optimum contact pressure and thickness strain in the deep-drawing of galvanized steel strips of 0.8 mm thickness are found. For that purpose, a series of steel strips is bent in different experiments by varying desired factors at different levels. The experiments are designed by using orthogonal arrays defined in Taguchi technique. At each experiment, contact pressure and thickness strain is calculated.
Since there are several number of factor levels, the Taguchi technique is used to analyze the observed data. According to the definitions in the Taguchi technique, this problem is analyzed as a Continuous-Continuous dynamic problem. Because the quality characteristics that are optimized don’t have exact target values and they are continuous functions, this problem fall into that category of dynamic problems.

Asymptotic Properties of the Estimators of a Sine Wave whose Frequency Changes Linearly with Time
Kanthi Perera

A sine wave whose frequency changes linearly with time and perturbed by random noise is considered, leading to the model where is random noise with variance . If the process is discretely sampled, the estimation of the parameters A, B, C, and has been completed. The study of the asymptotic properties of these estimators is being continued.

Mathematical Modelling Of Carbon Dioxide Emission Stemming From Energy Consumption As A Function Of Technological & Economic Development & Oil Price
Chalani Premarathne, Kanthi Perera, Kirthi Walgama, R. Shanthini.

Man, the most developed and one who has been taken the power of controlling the world with his new inventions, is in never-ending struggle for his well-being. Rapid economic and technological development that directly support the betterment of human lives, indirectly contaminate the environment for example via climate changes due to global warming. Global warming caused by greenhouse gases, in particular by the carbon dioxide emission stemming from energy consumption.

An effective framework is thus needed at both national and international levels to protect the environment by harm of Carbon. It is found that only chance of success is the allocation of equal carbon rations or allowances per person, which must decrease over time. Everyone must realize their responsibility for climate change, and take steps to reduce their burden on the planet. Therefore forecasting CO2 emission is important to implement new strategies for the protection of the environment.

Biophysical Modelling of Brain Dynamics
P.A.J. Gunatilake, Kirthi Walgama

One of the most exciting areas of scientific research is the study of the principles and mechanisms underlying brain function. Mathematical modeling of this brain function will support immensely in future developments of artificial intelligence and also in predicting unrevealed brain function principles.
This project mainly focuses on biophysical modeling of brain dynamics in large scale as opposed to neural network modeling in which individual neurons are modeled. Since, underlying neurophysiology and anatomy behind electroencephalograms (EEGs) is poorly understood, the project tries to build a mathematical model to analyze EEGs and underlying neurophysiology, including cortical and subcortical electrical activity of the brain. In addition, this study attempts to build a diagnostic tool that can be used to predict diseases, analyzing changes in the parameters of the model.

Development of a Mathematical Modelling Laboratory Unit
Kirthi Walgama, E. Devendra & Sanjeeva Maithripala

The aim of this project is to develop the necessary hardware and the software environment for a mathematical modeling laboratory. Basically, a desktop double tank lab unit and the necessary sensor and actuator electronics are constructed and interfaced to a computer via a process interface unit, for data acquisition, on-line and off-line model development and control. Currently, the real-time processes are implemented using the REGSIM real-time kernel; however, investigations are underway to see how a Linux real-time kernel can be incorporated. This unit will be of use in undergraduate and postgraduate courses on mathematical modeling, estimation and control, and also for serious research work in the same topics.

Modelling and Control of Active Magnetic Bearing Actuators
Kirthi Walgama, Sanath Alahakoon (Dept. of Elec. Eng.), M. Leksell & Chandur Sadarangani (Royal Inst. of Tech., Sweden)

The main aim of this project is to design and implement a control system to an Active Magnetic Bearing (AMB) actuator which can be used for the eccentric positioning of a motor shaft to study the effect of magnetic noise in the motor. To achieve this objective, we have carried out the mathematical modelling of the AMB system using system identification techniques and have designed a suitable control system first to elevate the shaft, and then to position it at a desired eccentric position. Although this basic control system is capable of maintaining the desired eccentric position when the shaft is still, rotation results in whirling. We have successfully implemented an adaptive periodic disturbance cancellation control to achieve significant reduction in the whirling. This is part of the project "Capacity Building in Electrical Engineering," funded by SIDA.

Time Varying and Adaptive Tuned (Notch) Filters
T. Kirubarajan (Dept. of Comp. Sci.) & Kirthi Walgama

The "tuned filter" is a narrow bandpass filter used to enhance a sinusoidal signal embedded in noise, while a "filter" is a narrow bandstop filter which filters out the sinusoidal signal that is corrupting a useful signal. These filters are very useful, for example in controller designs for periodic disturbance rejection, and in removing periodic trends and vibrational disturbances in the input-output data for mathematical modeling of dynamical systems. The objective of this project is to investigate performance issues in time varying tuned (notch) filters which are employed when the transient rejection in the filter needs to be speeded up, and in adaptive tuned (notch) filters which are needed when the frequency of the sinusoidal signal is not known.

Control Strategies for Bioreactors
Kirthi Walgama & D.G.G.P. Karunaratne (Dept. of Chem. Eng.)

Biological reactors are classical examples of nonlinear systems. Although they can be described by simple nonlinear dynamical equations, they exhibit very complex behaviour such as multiple steady states, bifurcation characteristics and chaos. Operating such dynamical processes at unstable steady states posed challenging problems to the control engineers.The objective of this research is to investigate suitable control system designs to operate two types of biological processes at the unstable steady states, especially when the nutrient input flow is constrained. We have investigated both linear and nonlinear control systems, and investigated the role of Anti-Windup Compensators in achieving the stability of the closed loop system.

Automatic Tuning of PID Controllers
Namal Jayatilake & Kirthi Walgama

Tuning parameters of a PID regulator is an important issue in control engineering. The techniques to auto-tune simple PID regulators based on phase and amplitude margin design criteria, Ziegler-Nichols method and refined Zeigler-Nichols method, are being studied. The amplitude and frequency of a sinusoidal signal are found by parameter estimation using different methods, with a comparison of the relative advantages of these methods.

Controller Designs for Periodic Disturbances
Kirthi Walgama, Sanath Alahakoon (Dept. of Electrical & Electronic Eng.) & R. Ratnayake (Tandon Lanka Ltd)

Periodic disturbances are often encountered in process control like rotary machines with eccentricities, reristaltic pumps used in medical devices, whirling in an active magnetic bearing system, to mention only a few. In this research, we have investigated feedforward controller designs for measurable periodic disturbances and pseudo-feedforward controllers when disturbances are not measurable. Time varying tuned filters have been introduced to deal with the performance degradation in the presence of noise. Recently, we have used adaptive disturbance canceling control systems for an Active Magnetic Bearing System, and were successful in reducing the whirling in the bearing shaft significantly. Currently, we are investigating various implementation issues involved in introducing time varying and adaptive tuned filters into the adaptive control system.

Modelling and Control of the Electrodialyser used for Black Liquor Treatment
Kirthi Walgama, R. Shanthini (Dept. of Chem. Eng.) & Janaka Ekanayake (Dept. of Electrical & Electronic Eng.)

Black liquor, the liquid affluent of the Embilipitiya pulp mill, is a severe pollutant. This soda processed black liquor has successfully been converted into a colourless liquid by processing it in the laboratory scale electrodialyser unit developed at the Dept. of Chemical Engineering.To scale up this unit to a pilot plant scale, it is necessary to carry out an extensive parametric study and to model the dynamics of the unit. This demands that the temperature and current of the electrodialyser could be controlled as designed. The objectives of this multidisciplinary project are (a) development of the necessary sensor and actuator electronics for the unit, (b) development of the PC based digital control system for current and temperature control, and (c) mathematical modeling of the dynamics of the unit.

Anti-Windup Compensators
Sanjeeva Maithripala & Kirthi Walgama

The anti-windup compensators are techniques that are used to avoid the anti-windup phenomenon in the poorly behaved control modes when the actuator gets saturated. Though there is a large number of different AWCs proposed in the literature, most of these methods can be unified as special cases of the Generalized Anti-Windup Compensator (GAWC). Investigations with the GAWC have revealed that it does not have sufficient parameterization to deal with some control systems and hence to overcome these limitations, extensions have been proposed for the GAWC and the Conditioning technique. Although these extensions have given sufficient parameterization to improve the performance, they have problems in dealing with different setpoints. Another shortcoming of these methods is the lack of proper guidelines to tune them. The objectives of the current research are to investigate the possibility of using numerical optimization for tuning the Anti-Windup Compensators and to modify the present schemes to handle different setpoints. We have successfully implemented these AWCs in real time digital control of DC motor position and velocity control systems and in active Magnetic Bearing Control Systems.

Floorplanning in VLSI Circuits
D.M.G.M.K. Dissanayake, Sarath Siyambalapitiya

Floorplanning is important in VLSI (Very Large Scale Integrated circuit) design automation.VLSI is the process of creating integrated circuits by combining thousands of transistor-based circuits into a single chip. The VLSI design automation is one of the most computational expensive and complicated processes with significant impact into computer chips manufacturing. Given a set of circuit components, or modules, and net list specifying interconnections between the modules, VLSI floorplanning is to find a floorplan for the modules such that the area of the chip and the interconnections between the modules are minimized. Even though the modules in a chip can take different shapes here we consider only the modules with rectangular shapes.Our aim is to try to develop a fast and better algorithm to solve this problem.

Task Scheduling for Multi-Processors
R.M.N.P. Rathnayake, Sarath Siyambalapitiya

Efficient scheduling techniques of computing resources are essential for achieving satisfactory performance for users, as computer systems and their applications become more and more complex. Two main goals of the task scheduling problem are meeting deadlines and achieving high resource utilization. We try to schedule all tasks so that deadlines, priority etc. are satisfied. At the moment, efficient algorithms are not available to solve this problem. Our attempt is to try to design an improved algorithm to solve this problem.

Dynamic Memory Allocation for Computer Processors
Lakmali Weerasena, Sarath Siyambalapitiya

Memory allocation is a fundamental part of any computer system and here we try to allocate computer memory in order to minimize the fragmentation of memory blocks there by minimizing the wasted space. The available algorithms to solve this problem are not very satisfactory. Our objective is to develop a more efficient algorithm to allocate memory which would try to minimize the fragmentation.

Educational Management: Timetable Scheduling Algorithms
Sarath Siyambalapitiya

Timetable scheduling is a problem faced by the management of educational institutions all over the world. In many educational institutions timetable scheduling is carried out manually and in most cases a trial and error approach is adopted.Attempts have been made to develop computer software to handle these activities. However, the results are not very encouraging due to the inherent complexity of the problem. In this study, we draw attention to the current approaches of solution to this problem and the need to look for new directions.

An Ant Algorithm for the Channel Assignment in Cellular Mobile Networks
Sarath Siyambalapitiya

Demand for mobile telephone services are growing rapidly all over the world. At the same time, the electromagnetic spectrum or frequencies allocated for this purpose are severly limited. The channel assignment problem involves efficiently assigning channels or frequencies to each radio cell in the cellular radio network, while satisfying the electromagnetic compatibility constraints. No known optimal algorithm exists for this problem. An attempt is being made to develop an efficient algorithm to solve this problem.

Assignment Problem with Preferences
Sarath Siyambalapitiya

Some areas in a country are considered congenial while others are considered difficult due to lack of facilities. Congenial areas have more educational and other facilities, and the population is comparatively higher in these areas. As a result, more educated people originate from these areas compared to difficult areas. If we consider the educational sector, there will be more qualified teachers coming from these areas, and all of them cannot be employed within the respective areas. On the other hand, there is a shortage of teachers in remote areas. Therefore, authorities will have to impose a condition saying that every teacher should serve a minimum specified period in difficult areas. This has created problems for many teachers, as they find if difficult to move to remote areas with their families due to many reasons. This situation has adversely affected their motivation and productivity. It is assumed that teachers in a particular category are requested to apply for vacancies in difficult areas according to their preferences. Selection will be based on a marking scheme where each teacher is assigned a mark based on qualifications, experience, etc. An attempt is being made to develop an efficient algorithm to assign teachers to schools in different areas. The objective is to devise a method in which each teacher is given a school according to his first choice as far as possible, while the number of teachers assigned outside their own district is minimized. This problem may have applications in other sectors where a solution of similar type is needed.

A New Algorithm for the One-dimensional Cutting Stock Problem
Sarath Siyambalapitiya
The stock cutting problem is the cutting of pieces of various sizes and shapes from a given stock piece, while minimizing the wastage of the stock material. This problem arises in many situations in the industry. Some of them are cutting steel or glass sheets into required stock sizes, cutting wooden plates to make furniture, cutting paper board to make boxes, placing advertisements on the pages of newspapers, etc. Also, the unrestricted form of this problem arises in the textile industry. In the paper manufacturing industry, ‘jumbo’ reels of paper are to be cut into narrower ‘customer’ reels according to specifications. This is to be done to minimize the wasted paper. In this study, we consider the one-dimensional cutting stock problem which is a special case of the general cutting stock problem.

Algorithms for Three-dimensional Industry Packing Problem
Sarath Siyambalapitiya & Himali Ekanayake

In many industrial applications of packing, solving the problem of efficiently dividing a large volume into many smaller volumes of various shapes consumes a lot of time. The results obtained in most cases are far from satisfactory due to unutilised volume left, which is very expensive. Some of the situations in which this problem arises exist in cargo loading, pallet packing, shipping containers and warehouse loading. Even in a single industrial organisation, this packing problem can arise under several different situations. For example, in the ceramics industry this problem arises when packing items into pallets of kiln cars to be transported for firing. In the manufacturing area of the factory, when transferring items from one stage to the next stage, the method of loading pallets helps to increase the efficiency. Additionally, a similar problem occurs in storing finished goods in warehouses. The general 3-D packing problem is an NP hard problem for which no known efficient optimal solution procedure exists. We confine our study here to only rectangular shaped objects in order to simplify the problem. Even for this problem, most of the available methods are unsatisfactory due to the high computational time involved. Our aim is to try to construct a fast and efficient solution algorithm which gives satisfactory results.

Matrix Chain Multiplication
Sarath Siyambalapitiya & Rathnamali Palamakumbura

Although the multiplication of matrices follows the associative law, there is a vast difference in the number of multiplications required for different orders for sequences of matrices. Therefore, to minimize the number of computations, it is necessary to find the best splitting order. This problem has important applications in queueing theory, markov chains and other areas. Usually, a dynamic programming algorithm is used for this purpose. Even though this method gives an optimum solution, the number of computations increases rapidly with the increase in size of the problem. We are trying to obtain a more efficient algorithm using some characteristics of the best splitting order.

Teaching Mathematics to Engineering Undergraduates: Need for a Change in Policy
Sarath Siyambalapitiya

It has been observed that the abilities in mathematics of students entering universities in Sri Lanka are on the decline in recent years. There is additionally a school of thought in engineering education, which cultivates the belief that it is sufficient to teach mathematics only as a tool, to the extent that it can be used for certain computations arising in their work. This trend, and its repercussions, are critically analysed, in relation to the experience gained at the Faculty of Engineering, University of Peradeniya.

Optimizing the ordering of Raw Material for Pharmaceutical Products
T. Tharmasoruban (Postgraduate Institute of Science), Sarath Siyambalapitiya

For the local production of pharmaceuticals, it is necessary to import variuos categories of raw material. These will have to be imported in sufficient quantities well in advance to avoid interruption in production schedules. However, keeping them in storage for extended periods of time is also not desirable due to heavy warehouse costs and the expiry dates of raw materials . Another problem is that, most of the raw material need air-conditioned storage facilities.
There are other constraints too. Some suppliers insist on minimum order quantities. Due to expiry dates, the manufacturer is forced to use them for production within the stipulated period. Due to the cash flow problems, there will be limitations on quantities that could be ordered at a time. As raw material is ordered from various suppliers in different countries, different lead times can occur. Therefore, sufficient time for delivery, custom clearance and any other delays should be allowed. At the same time, bulk orders may carry special discounts which will tempt the manufacturer to order in large quantities. Hence, it can be seen that there are several conflicts occuring in this problem which makes it very difficult to propose a general solution procedure. Therefore, what we propose to do here is to take into consideration the requirements of a particular local manufacturer of pharmaceuticals. An attempt is made to develop an algorithm to construct an ordering schedule for raw material related to this manufacturer.

An Algorithm for the Machine Layout Problem
Sarath Siyambalapitiya, N.M.D. Navaratne

Machine layout problem is concerned with the arranging of machines and other facilities in factories and workshops in order to allow smooth flow of workers and material among machines. This in effect, will reduce the wastage of time and costs and contribute to reaching the optimum production levels. An attempt is being made to develop an efficient algorithm to solve this problem considering a specific industrial situation.

Consequences of the use of the Private Coaching System to Enter Universities: a study in Sri Lanka
Sarath Siyambalapitiya

In Sri Lanka, conducting the secondary education system is considered the responsibility of the government. The Department of Examinations in Sri Lanka conducts two general qualifying examinations annually, known as the General Certificate of Education (G.C.E.), at the Ordinary and Advanced Levels, which are conducted after 11 and 13 years of schooling respectively. The latter examination is considered the university preliminary examination in Sri Lanka. A parallel system of private coaching thrives throughout the country, to prepare students for the G.C.E. (Advanced Level) examination, due to the severe competition to enter universities. The reasons behind this disturbing trend, and its repercussions, are examined. The problem is considered in relation to the intake to the Faculty of Engineering, University of Peradeniya, and some long term measures to alleviate this problem are proposed.

Importance of Algorithmic approach for Engineering Mathematics Courses
Sarath Siyambalapitiya

There is a wide disparity among approaches for teaching mathematics in engineering schools throughout the world. Some universities have mathematics departments within faculties of engineering while in others common mathematics courses are conduted, which are attended by engineering students as well. As a result, some courses try to teach mathematics only as a tool while others tend to be more theoretical in nature. Hence, the question arises : what is the best way of teaching mathematics to engineering undergraduates ? This study attempts to answer this question.

Development of an Interpreter for Petri Nets using C++
K.W.D.M.Chanrdasiri, Sarath Siyambalapitiya, D.S.Devapriya

Petri net is a general purpose mathematical tool for describing relations between conditions and events. They provide an extremely versatile tool for modelling, simulating, controlling and evaluating event driven systems like manufacturing systems , communicating systems , computer networks etc. The proposed interpreter once completed would provide the possibility of converting the informal specification of a given event driven system, into an elegant mathematical model for carrying out the tasks mentioned above. This tool is supported by a very expressive graphical formalism.

Surface Modelling and Optimization for Contour Machining
Sherin Ahamed, Sarath Siyambalapitiy, S..D.Pathirana
Cutting tools of CNC machines move over a series of contours in order to machine and generate the desired surfaces. In machining complex surface geometries, the need arises to define the axes system for defining the geometry, in such a way to minimize the machining time. Different possible axes orientations have to be evaluated in estimating the machining time, and the optimum has to be determined . At this stage, geometrical shapes generated by AutoCAD will be evaluated to achieve the best performance during machining.

Higher Education in Sri Lanka: Need for a change in attitudes
Sarath Siyambalapitiya

A private tutory system has been operating in Sri Lanka for several years to supplement the public school system . As a result of the increasing number of failure rates at universities , the funds allocated for higher education is wasted to some extent. This study concentrates on the need for a change in attitudes with respect to higher education in order to overcome this situation.

Impact of Changing University Admission Criteria on Engineering Education in Sri Lanka
Sarath Siyambalapitiya

The number of subjects to be offered for the G.C.E.(Advanced Level) Examination for university admission in Sri Lanka is to be reduced to three from four. This means that effectively, one subject has to be dropped from the present set of subjects. There has been much debate regarding which subject is to be dropped. At the same time, a new set of subjects are being introduced, and a revision of existing syllabi is also taking place. The impact of different possible decisions in this regard, with respect to admission to the Faculties of Engineering in Sri Lanka, is critically analysed.

Reducing High Failure Rates at Universities in Sri Lanka
Sarath Siyambalapitiya

High failure rates have been recorded at the examinations in Sri Lankan universities in recent years. The main reasons behind this phenomenon are analysed. The gravity of the situation is highlighted using the output of engineering graduates from the University of Peradeniya for the last ten years. Some long term measures to overcome this situation are proposed.

Need for Remedial Teaching at the University Level
Sarath Siyambalapitiya

The weak areas in Mathematics of the new entrants to the Faculty of Engineering, University of Peradeniya, is identified using a 'ranking test' conducted at the entry point. It is observed that students are weak in some topics in spite of their presence in the G.C.E.(Advanced Level) Examination syllabus for many years. This project tries to identify some of the main reasons for this weakness, and analyse the need for an organised programme of remedial teaching at the University, to solve this problem.

Harmonic Analysis of 15-Minute Solar Radiation Data
T.D.M.A. Samuel & Dushmantha Kannangara

The aim of this study is to identify the role of the distribution of solar radiation in agricultural and engineering sciences; in particular, in the tea industry. Fifteen minute data has been collected from three Agro-Met stations located in tea plantations in the highlands of Sri Lanka. Fourier transform methods (including the Fast Fourier Transform, or FFT) are used to analyse this data. The amplitudes and phases of different frequencies present in the radiation data are being determined.

A Dynamic and Holistic Approach to the Tea Industry in Sri Lanka
T.D.M.A. Samuel, in collaboration with the TRI, and Dept. of Agric. Eng. and Physics, Wageningen Agric. Univ.

A working paper is in progress, fuelled by discussions with the Director, Tea Research Institute and the Head, Dept. of Agricultural Engineering and Physics, Wageningen Agricultural University, The Netherlands.

Simulation of the Ecophysiological process of Tea Growth in Sri Lanka
T.D.M.A. Samuel, and collaborators

Also initiated in 1992, this is a collaborative project between (i) the Dept. of Engineering Maths., Univ. of Peradeniya, (ii) the Institute of Meteorology and Physics, Agric. Univ. of Vienna, and (iii) the Tea Research Institute of Sri Lanka. The objective is to increase the efficiency of management of tea plantations and undertake appropriate research specific to the physiology of tea in order to remain competitive in the world market. Three Agro-Met stations have been set up in strategic locations in the tea plantations of Sri Lanka. Data is shared by the collaborating institutions. Work is under way to statistically analyze the data, with a view of generating synthetic data for modeling and simulation of the tea production and processing in Sri Lanka.

Solar Energy for Tea Processing in Sri Lanka
T.D.M.A. Samuel, in collaboration with the Institute of Meteorology and Physics, Agricultural Univ. of Vienna, Austria.

Initiated in 1992, this project has the objective of developing a Solar Thermal System which can reduce the use of timber and imported oil. An M.Phil. on the subject is in the process of being examined. A project proposal has been submitted to the European Commission for funding for further development of this area.

Solar Radiation Estimation for Sri Lanka
T.D.M.A. Samuel, Thusitha Abayarathna, Tea Research Institute & the Institute of Meteorology and Physics, Agric. Univ. of Vienna, Austria

Begun in 1980, this project involves data collection, numerical modeling and computation. Initially, the various numerical models available for total radiation estimation were compared with available data and a method of total radiation estimation for Sri Lanka was developed. Monthly and annual isoradiation maps were drawn. Estimating global radiation has been completed, and work is in progress to estimate the diffusion radiation and the clear sky radiation. The measurement of the total and diffuse radiation, and the hours of sunshine is to be carried out.