On Commutation and Conjugacy of Rational Languages and the Fixed Point Method

The research on language equations has been active during last decades. Compared to the equations on words the equations on languages are much more difficult to solve. Even very simple equations that are easy to solve for words can be very hard for languages. In this thesis we study two of such equations, namely commutation and conjugacy equations. We study these equations on some limited special cases and compare some of these results to the solutions of corresponding equations on words. For both equations we study the maximal solutions, the centralizer and the conjugator. We present a fixed point method that we can use to search these maximal solutions and analyze the reasons why this method is not successful for all languages. We give also several examples to illustrate the behaviour of this method.

Kromatografisen erotusfaasin huokoskoon karakterisointi

Työssä tutkittiin sulfonoitujen polystyreenidivinyylibentseenirunkoisten geeli-, meso- ja makrohuokoistenioninvaihtohartsien rakennetta käyttäen useita eri karakterisointimenetelmiä. Lisäksi työssä tutkittiin hartsien huokoskoon vaikutusta aminohappojen kromatografisessa erotuksessa. Työn pääpaino oli hartsien huokoskoon ja huokoisuuden määrittämisessä. Sen selvittämiseksi käytettiin hyväksi elektronimikroskopiaa, typpiadsorptiomittauksia, sekä käänteistä kokoekskluusiokromatografiaa. Parhaat tulokset saatiin käänteisellä kokoekskluusiokromatografialla, joka perustuu erikokoisten dekstraanipolymeerien käyttöön mallimolekyyleinä. Menetelmä sopii meso- ja makrohuokoisuuden tutkimiseen, mutta sen heikkoutena on erittäin pitkä mittausaika. Menetelmä antaa myös huokoskokojakauman, mutta yhden hartsin mittaaminen voi kestää viikon. Menetelmää muutettiin siten, että käytettiin määritettävää huokoskokoaluetta kuvaavien kahden dekstraanipolymeerin seosta. Kromatografiset ajo-olosuhteet optimoitiin sellaisiksi, että injektoidussa seoksessa olevien dekstraanien vastehuiput erottuivat toisistaan. Tällöin voitiin luotettavasti määrittää tutkittavan stationaarifaasin suhteellinen huokoisuus. Tätä työssä kehitettyä nopeaa käänteiseen kokoekskluusiokromatografiaan perustuvaa menetelmää kutsutaan kaksipistemenetelmäksi. Hartsien sulfonihapporyhmien määrää ja jakautumista tutkittiin määrittämällä hartsien kationinvaihtokapasiteetti sekä tutkimalla hartsin pintaa konfokaali-Raman-spektroskopian avulla. Sulfonihapporyhmien ioninvaihtokyvyn selvittämiseksi mitattiin K+-muotoon muutetusta hartsista S/K-suhde poikkileikkauspinnasta. Tulosten perusteella hartsit olivat tasaisesti sulfonoituneet ja 95 % rikkiatomeista oli toimivassa ioninvaihtoryhmässä. Aminohappojen erotuksessa malliaineina oli lysiini, seriini ja tryptofaani. Hartsi oli NH4+-muodossa ja petitilavuus oli 91 mL. Eluenttina käytettiin vettä, jonka pH oli 10. Paras tulos saatiin virtausnopeudella 0,1 mL/min, jolla kaikki kolme aminohappoa erottuivat toisistaan Finex Oy:n mesohuokoisella KEF78-hartsilla. Muilla tutkituilla hartseilla kaikki kolme aminohappoa eivät missään ajo-olosuhteissa erottuneet täysin.

Advanced chemometric methods: Applicability on industrial data

Recent years have produced great advances in the instrumentation technology. The amount of available data has been increasing due to the simplicity, speed and accuracy of current spectroscopic instruments. Most of these data are, however, meaningless without a proper analysis. This has been one of the reasons for the overgrowing success of multivariate handling of such data. Industrial data is commonly not designed data; in other words, there is no exact experimental design, but rather the data have been collected as a routine procedure during an industrial process. This makes certain demands on the multivariate modeling, as the selection of samples and variables can have an enormous effect. Common approaches in the modeling of industrial data are PCA (principal component analysis) and PLS (projection to latent structures or partial least squares) but there are also other methods that should be considered. The more advanced methods include multi block modeling and nonlinear modeling. In this thesis it is shown that the results of data analysis vary according to the modeling approach used, thus making the selection of the modeling approach dependent on the purpose of the model. If the model is intended to provide accurate predictions, the approach should be different than in the case where the purpose of modeling is mostly to obtain information about the variables and the process. For industrial applicability it is essential that the methods are robust and sufficiently simple to apply. In this way the methods and the results can be compared and an approach selected that is suitable for the intended purpose. Differences in data analysis methods are compared with data from different fields of industry in this thesis. In the first two papers, the multi block method is considered for data originating from the oil and fertilizer industries. The results are compared to those from PLS and priority PLS. The third paper considers applicability of multivariate models to process control for a reactive crystallization process. In the fourth paper, nonlinear modeling is examined with a data set from the oil industry. The response has a nonlinear relation to the descriptor matrix, and the results are compared between linear modeling, polynomial PLS and nonlinear modeling using nonlinear score vectors.

Hierarchy and Expansiveness in Two-Dimensional Subshifts of Finite Type

Subshifts are sets of configurations over an infinite grid defined by a set of forbidden patterns. In this thesis, we study two-dimensional subshifts offinite type (2D SFTs), where the underlying grid is Z2 and the set of for-bidden patterns is finite. We are mainly interested in the interplay between the computational power of 2D SFTs and their geometry, examined through the concept of expansive subdynamics. 2D SFTs with expansive directions form an interesting and natural class of subshifts that lie between dimensions 1 and 2. An SFT that has only one non-expansive direction is called extremely expansive. We prove that in many aspects, extremely expansive 2D SFTs display the totality of behaviours of general 2D SFTs. For example, we construct an aperiodic extremely expansive 2D SFT and we prove that the emptiness problem is undecidable even when restricted to the class of extremely expansive 2D SFTs. We also prove that every Medvedev class contains an extremely expansive 2D SFT and we provide a characterization of the sets of directions that can be the set of non-expansive directions of a 2D SFT. Finally, we prove that for every computable sequence of 2D SFTs with an expansive direction, there exists a universal object that simulates all of the elements of the sequence. We use the so called hierarchical, self-simulating or fixed-point method for constructing 2D SFTs which has been previously used by Ga´cs, Durand, Romashchenko and Shen.

The Design and Implementation of a SD Card File System

SD card (Secure Digital Memory Card) is widely used in portable storage medium. Currently, latest researches on SD card, are mainly SD card controller based on FPGA (Field Programmable Gate Array). Most of them are relying on API interface (Application Programming Interface), AHB bus (Advanced High performance Bus), etc. They are dedicated to the realization of ultra high speed communication between SD card and upper systems. Studies about SD card controller, really play a vital role in the field of high speed cameras and other sub-areas of expertise. This design of FPGA-based file systems and SD2.0 IP (Intellectual Property core) does not only exhibit a nice transmission rate, but also achieve the systematic management of files, while retaining a strong portability and practicality. The file system design and implementation on a SD card covers the main three IP innovation points. First, the combination and integration of file system and SD card controller, makes the overall system highly integrated and practical. The popular SD2.0 protocol is implemented for communication channels. Pure digital logic design based on VHDL (Very-High-Speed Integrated Circuit Hardware Description Language), integrates the SD card controller in hardware layer and the FAT32 file system for the entire system. Secondly, the document management system mechanism makes document processing more convenient and easy. Especially for small files in batch processing, it can ease the pressure of upper system to frequently access and process them, thereby enhancing the overall efficiency of systems. Finally, digital design ensures the superior performance. For transmission security, CRC (Cyclic Redundancy Check) algorithm is for data transmission protection. Design of each module is platform-independent of macro cells, and keeps a better portability. Custom integrated instructions and interfaces may facilitate easily to use. Finally, the actual test went through multi-platform method, Xilinx and Altera FPGA developing platforms. The timing simulation and debugging of each module was covered. Finally, Test results show that the designed FPGA-based file system IP on SD card can support SD card, TF card and Micro SD with 2.0 protocols, and the successful implementation of systematic management for stored files, and supports SD bus mode. Data read and write rates in Kingston class10 card is approximately 24.27MB/s and 16.94MB/s.

Generalized Differential Evolution for Global Multi-Objective Optimization with Constraints

The objective of this thesis work is to develop and study the Differential Evolution Algorithm for multi-objective optimization with constraints. Differential Evolution is an evolutionary algorithm that has gained in popularity because of its simplicity and good observed performance. Multi-objective evolutionary algorithms have become popular since they are able to produce a set of compromise solutions during the search process to approximate the Pareto-optimal front. The starting point for this thesis was an idea how Differential Evolution, with simple changes, could be extended for optimization with multiple constraints and objectives. This approach is implemented, experimentally studied, and further developed in the work. Development and study concentrates on the multi-objective optimization aspect. The main outcomes of the work are versions of a method called Generalized Differential Evolution. The versions aim to improve the performance of the method in multi-objective optimization. A diversity preservation technique that is effective and efficient compared to previous diversity preservation techniques is developed. The thesis also studies the influence of control parameters of Differential Evolution in multi-objective optimization. Proposals for initial control parameter value selection are given. Overall, the work contributes to the diversity preservation of solutions in multi-objective optimization.

Dual light barrier method for six degrees of freedom tool center point calibration of an industrial robot

Tool center point calibration is a known problem in industrial robotics. The major focus of academic research is to enhance the accuracy and repeatability of next generation robots. However, operators of currently available robots are working within the limits of the robot´s repeatability and require calibration methods suitable for these basic applications. This study was conducted in association with Stresstech Oy, which provides solutions for manufacturing quality control. Their sensor, based on the Barkhausen noise effect, requires accurate positioning. The accuracy requirement admits a tool center point calibration problem if measurements are executed with an industrial robot. Multiple possibilities are available in the market for automatic tool center point calibration. Manufacturers provide customized calibrators to most robot types and tools. With the handmade sensors and multiple robot types that Stresstech uses, this would require great deal of labor. This thesis introduces a calibration method that is suitable for all robots which have two digital input ports free. It functions with the traditional method of using a light barrier to detect the tool in the robot coordinate system. However, this method utilizes two parallel light barriers to simultaneously measure and detect the center axis of the tool. Rotations about two axes are defined with the center axis. The last rotation about the Z-axis is calculated for tools that have different width of X- and Y-axes. The results indicate that this method is suitable for calibrating the geometric tool center point of a Barkhausen noise sensor. In the repeatability tests, a standard deviation inside robot repeatability was acquired. The Barkhausen noise signal was also evaluated after recalibration and the results indicate correct calibration. However, future studies should be conducted using a more accurate manipulator, since the method employs the robot itself as a measuring device.

Vendor Managed Inventory: the Critical Success Factors from the Manufacturer Point of View

Yritykset ovat pakotettuja erilaisiin yhteistyömuotoihin pärjätäkseen kiristyvässä kilpailussa. Yhteistyösuhteet kulkevat eri nimillä riippuen teollisuuden alasta ja siitä, missä kohtaa toimitusketjua ne toteutuvat, mutta periaatteessa kaikki pohjautuvat samaan ideaan kuin Vendor Managed Inventory (VMI); varastoon jakysyntään liittyvä tieto jaetaan toimitusketjun eri osapuolien kesken, jotta tuotanto, jakelu ja varastonhallinta olisi mahdollista optimoida. Vendor Managed Inventory on ideana yksinkertainen, mutta vaatii onnistuakseen paljon. Perusolettamus on, että toimittajan on kyettävä hallinnoimaan asiakkaan varastoa paremmin kuin asiakas itse. Tämä ei kuitenkaan ole mahdollista ilman riittävää yhteistyötä, oikeanlaista informaatiota tai sopivia tuoteominaisuuksia. Tämän työn tarkoitus on esitellä kriittiset menestystekijät valmistajan kannalta, kun näkyvyys todelliseen kysyntään on heikko ja kyseessäolevat tuotteet ovat ominaisuuksiltaan toimintamalliin huonosti soveltuvia. VMItoimintamallin soveltuvuus matkapuhelimia valmistavan yrityksen liiketoimintaan, sekä sen vaikutus asiakasyhteistyöhön, kannattavuuteen ja toiminnan tehostamiseen on myös tutkittu.

Unlicensed Mobile Access Concept from Testing Point of View

Viime vuosikymmenien aikana kommunikaatioteknologiat ovat kehittyneet erittäin paljon. Uusia verkkoja, liityntätekniikoita, protokollia ja päätelaitteita on luotu alati kehittyvällä vauhdilla, eikä hidastumisen merkkejä ole näkyvissä. Varsinkin mobiilisovellukset ovat kasvattaneet markkinaosuuksiaan viime aikoina. Unlicensed MobileAccess (UMA) on uusi liityntätekniikka mobiilipäätelaitteille, joka mahdollistaa liitynnän GSM- runkoverkkoon WLAN- tai Bluetooth - tekniikoiden avulla. Tämä diplomityö keskittyy UMAan liittyviin teknologioihin, joita tarkastellaan lähemmin ensimmäisissä kappaleissa. Tavoitteena on esitellä, mitä UMA merkitsee, ja kuinka eri tekniikoita voidaan soveltaa sen toteutuksissa. Ennenkuin uusia teknologioita voidaan soveltaa kaupallisesti, täytyy niiden olla kokonaisvaltaisesti testattuja. Erilaisia testausmenetelmiä sovelletaan laitteistonja ohjelmiston testaukseen, mutta tavoite on kuitenkin sama, eli vähentää testattavan tuotteen epäluotettavuutta ja lisätä sen laatua. Vaikka UMA käsittääkin pääasiassa jo olemassa olevia tekniikoita, tuo se silti mukanaan uuden verkkoelementin ja kaksi uutta kommunikaatioprotokollaa. Ennen kuin mitään UMAa tukevia ratkaisuja voidaan tuoda markkinoille, monia erilaisia testausmenetelmiä on suoritettava, jotta varmistutaan uuden tuotteen oikeasta toiminnallisuudesta. Koska tämä diplomityö käsittelee uutta tekniikkaa, on myös testausmenetelmien yleisen testausteorian käsittelemiselle varattu oma kappale. Kappale esittelee erilaisia testauksen näkökulmia ja niihin perustuen rakennetaan myös testausohjelmisto. Tavoitteena on luoda ohjelmisto, jota voidaan käyttää UMA-RR protokollan toiminnan varmentamiseen kohdeympäristössä.

Conflict-based Method for Conceptual Process Synthesis

The changing business environment demands that chemical industrial processes be designed such that they enable the attainment of multi-objective requirements and the enhancement of innovativedesign activities. The requirements and key issues for conceptual process synthesis have changed and are no longer those of conventional process design; there is an increased emphasis on innovative research to develop new concepts, novel techniques and processes. A central issue, how to enhance the creativity of the design process, requires further research into methodologies. The thesis presentsa conflict-based methodology for conceptual process synthesis. The motivation of the work is to support decision-making in design and synthesis and to enhance the creativity of design activities. It deals with the multi-objective requirements and combinatorially complex nature of process synthesis. The work is carriedout based on a new concept and design paradigm adapted from Theory of InventiveProblem Solving methodology (TRIZ). TRIZ is claimed to be a `systematic creativity' framework thanks to its knowledge based and evolutionary-directed nature. The conflict concept, when applied to process synthesis, throws new lights on design problems and activities. The conflict model is proposed as a way of describing design problems and handling design information. The design tasks are represented as groups of conflicts and conflict table is built as the design tool. The general design paradigm is formulated to handle conflicts in both the early and detailed design stages. The methodology developed reflects the conflict nature of process design and synthesis. The method is implemented and verified through case studies of distillation system design, reactor/separator network design and waste minimization. Handling the various levels of conflicts evolve possible design alternatives in a systematic procedure which consists of establishing an efficient and compact solution space for the detailed design stage. The approach also provides the information to bridge the gap between the application of qualitative knowledge in the early stage and quantitative techniques in the detailed design stage. Enhancement of creativity is realized through the better understanding of the design problems gained from the conflict concept and in the improvement in engineering design practice via the systematic nature of the approach.

Studies on integrating kinematic design method with mechanical systems simulation techniques

Theultimate goal of any research in the mechanism/kinematic/design area may be called predictive design, ie the optimisation of mechanism proportions in the design stage without requiring extensive life and wear testing. This is an ambitious goal and can be realised through development and refinement of numerical (computational) technology in order to facilitate the design analysis and optimisation of complex mechanisms, mechanical components and systems. As a part of the systematic design methodology this thesis concentrates on kinematic synthesis (kinematic design and analysis) methods in the mechanism synthesis process. The main task of kinematic design is to find all possible solutions in the form of structural parameters to accomplish the desired requirements of motion. Main formulations of kinematic design can be broadly divided to exact synthesis and approximate synthesis formulations. The exact synthesis formulation is based in solving n linear or nonlinear equations in n variables and the solutions for the problem areget by adopting closed form classical or modern algebraic solution methods or using numerical solution methods based on the polynomial continuation or homotopy. The approximate synthesis formulations is based on minimising the approximation error by direct optimisation The main drawbacks of exact synthesis formulationare: (ia) limitations of number of design specifications and (iia) failure in handling design constraints- especially inequality constraints. The main drawbacks of approximate synthesis formulations are: (ib) it is difficult to choose a proper initial linkage and (iib) it is hard to find more than one solution. Recentformulations in solving the approximate synthesis problem adopts polynomial continuation providing several solutions, but it can not handle inequality const-raints. Based on the practical design needs the mixed exact-approximate position synthesis with two exact and an unlimited number of approximate positions has also been developed. The solutions space is presented as a ground pivot map but thepole between the exact positions cannot be selected as a ground pivot. In this thesis the exact synthesis problem of planar mechanism is solved by generating all possible solutions for the optimisation process ¿ including solutions in positive dimensional solution sets - within inequality constraints of structural parameters. Through the literature research it is first shown that the algebraic and numerical solution methods ¿ used in the research area of computational kinematics ¿ are capable of solving non-parametric algebraic systems of n equations inn variables and cannot handle the singularities associated with positive-dimensional solution sets. In this thesis the problem of positive-dimensional solutionsets is solved adopting the main principles from mathematical research area of algebraic geometry in solving parametric ( in the mathematical sense that all parameter values are considered ¿ including the degenerate cases ¿ for which the system is solvable ) algebraic systems of n equations and at least n+1 variables.Adopting the developed solution method in solving the dyadic equations in direct polynomial form in two- to three-precision-points it has been algebraically proved and numerically demonstrated that the map of the ground pivots is ambiguousand that the singularities associated with positive-dimensional solution sets can be solved. The positive-dimensional solution sets associated with the poles might contain physically meaningful solutions in the form of optimal defectfree mechanisms. Traditionally the mechanism optimisation of hydraulically driven boommechanisms is done at early state of the design process. This will result in optimal component design rather than optimal system level design. Modern mechanismoptimisation at system level demands integration of kinematic design methods with mechanical system simulation techniques. In this thesis a new kinematic design method for hydraulically driven boom mechanism is developed and integrated in mechanical system simulation techniques. The developed kinematic design method is based on the combinations of two-precision-point formulation and on optimisation ( with mathematical programming techniques or adopting optimisation methods based on probability and statistics ) of substructures using calculated criteria from the system level response of multidegree-of-freedom mechanisms. Eg. by adopting the mixed exact-approximate position synthesis in direct optimisation (using mathematical programming techniques) with two exact positions and an unlimitednumber of approximate positions the drawbacks of (ia)-(iib) has been cancelled.The design principles of the developed method are based on the design-tree -approach of the mechanical systems and the design method ¿ in principle ¿ is capable of capturing the interrelationship between kinematic and dynamic synthesis simultaneously when the developed kinematic design method is integrated with the mechanical system simulation techniques.

Torque vibration model of axial-flux surface-mounted permanent magnet synchronous machine

In order that the radius and thus ununiform structure of the teeth and otherelectrical and magnetic parts of the machine may be taken into consideration the calculation of an axial flux permanent magnet machine is, conventionally, doneby means of 3D FEM-methods. This calculation procedure, however, requires a lotof time and computer recourses. This study proves that also analytical methods can be applied to perform the calculation successfully. The procedure of the analytical calculation can be summarized into following steps: first the magnet is divided into slices, which makes the calculation for each section individually, and then the parts are submitted to calculation of the final results. It is obvious that using this method can save a lot of designing and calculating time. Thecalculation program is designed to model the magnetic and electrical circuits of surface mounted axial flux permanent magnet synchronous machines in such a way, that it takes into account possible magnetic saturation of the iron parts. Theresult of the calculation is the torque of the motor including the vibrations. The motor geometry and the materials and either the torque or pole angle are defined and the motor can be fed with an arbitrary shape and amplitude of three-phase currents. There are no limits for the size and number of the pole pairs nor for many other factors. The calculation steps and the number of different sections of the magnet are selectable, but the calculation time is strongly depending on this. The results are compared to the measurements of real prototypes. The permanent magnet creates part of the flux in the magnetic circuit. The form and amplitude of the flux density in the air-gap depends on the geometry and material of the magnetic circuit, on the length of the air-gap and remanence flux density of the magnet. Slotting is taken into account by using the Carter factor in the slot opening area. The calculation is simple and fast if the shape of the magnetis a square and has no skew in relation to the stator slots. With a more complicated magnet shape the calculation has to be done in several sections. It is clear that according to the increasing number of sections also the result will become more accurate. In a radial flux motor all sections of the magnets create force with a same radius. In the case of an axial flux motor, each radial section creates force with a different radius and the torque is the sum of these. The magnetic circuit of the motor, consisting of the stator iron, rotor iron, air-gap, magnet and the slot, is modelled with a reluctance net, which considers the saturation of the iron. This means, that several iterations, in which the permeability is updated, has to be done in order to get final results. The motor torque is calculated using the instantaneous linkage flux and stator currents. Flux linkage is called the part of the flux that is created by the permanent magnets and the stator currents passing through the coils in stator teeth. The angle between this flux and the phase currents define the torque created by the magnetic circuit. Due to the winding structure of the stator and in order to limit the leakage flux the slot openings of the stator are normally not made of ferromagnetic material even though, in some cases, semimagnetic slot wedges are used. In the slot opening faces the flux enters the iron almost normally (tangentially with respect to the rotor flux) creating tangential forces in the rotor. This phenomenon iscalled cogging. The flux in the slot opening area on the different sides of theopening and in the different slot openings is not equal and so these forces do not compensate each other. In the calculation it is assumed that the flux entering the left side of the opening is the component left from the geometrical centre of the slot. This torque component together with the torque component calculated using the Lorenz force make the total torque of the motor. It is easy to assume that when all the magnet edges, where the derivative component of the magnet flux density is at its highest, enter the slot openings at the same time, this will have as a result a considerable cogging torque. To reduce the cogging torquethe magnet edges can be shaped so that they are not parallel to the stator slots, which is the common way to solve the problem. In doing so, the edge may be spread along the whole slot pitch and thus also the high derivative component willbe spread to occur equally along the rotation. Besides forming the magnets theymay also be placed somewhat asymmetric on the rotor surface. The asymmetric distribution can be made in many different ways. All the magnets may have a different deflection of the symmetrical centre point or they can be for example shiftedin pairs. There are some factors that limit the deflection. The first is that the magnets cannot overlap. The magnet shape and the relative width compared to the pole define the deflection in this case. The other factor is that a shifting of the poles limits the maximum torque of the motor. If the edges of adjacent magnets are very close to each other the leakage flux from one pole to the other increases reducing thus the air-gap magnetization. The asymmetric model needs some assumptions and simplifications in order to limit the size of the model and calculation time. The reluctance net is made for symmetric distribution. If the magnets are distributed asymmetrically the flux in the different pole pairs will not be exactly the same. Therefore, the assumption that the flux flows from the edges of the model to the next pole pairs, in the calculation model from one edgeto the other, is not correct. If it were wished for that this fact should be considered in multi-pole pair machines, this would mean that all the poles, in other words the whole machine, should be modelled in reluctance net. The error resulting from this wrong assumption is, nevertheless, irrelevant.

A modified structural stress method for fatigue assessment of welded structures

Fatigue life assessment of weldedstructures is commonly based on the nominal stress method, but more flexible and accurate methods have been introduced. In general, the assessment accuracy is improved as more localized information about the weld is incorporated. The structural hot spot stress method includes the influence of macro geometric effects and structural discontinuities on the design stress but excludes the local features of the weld. In this thesis, the limitations of the structural hot spot stress method are discussed and a modified structural stress method with improved accuracy is developed and verified for selected welded details. The fatigue life of structures in the as-welded state consists mainly of crack growth from pre-existing cracks or defects. Crack growth rate depends on crack geometry and the stress state on the crack face plane. This means that the stress level and shape of the stress distribution in the assumed crack path governs thetotal fatigue life. In many structural details the stress distribution is similar and adequate fatigue life estimates can be obtained just by adjusting the stress level based on a single stress value, i.e., the structural hot spot stress. There are, however, cases for which the structural stress approach is less appropriate because the stress distribution differs significantly from the more common cases. Plate edge attachments and plates on elastic foundations are some examples of structures with this type of stress distribution. The importance of fillet weld size and weld load variation on the stress distribution is another central topic in this thesis. Structural hot spot stress determination is generally based on a procedure that involves extrapolation of plate surface stresses. Other possibilities for determining the structural hot spot stress is to extrapolate stresses through the thickness at the weld toe or to use Dong's method which includes through-thickness extrapolation at some distance from the weld toe. Both of these latter methods are less sensitive to the FE mesh used. Structural stress based on surface extrapolation is sensitive to the extrapolation points selected and to the FE mesh used near these points. Rules for proper meshing, however, are well defined and not difficult to apply. To improve the accuracy of the traditional structural hot spot stress, a multi-linear stress distribution is introduced. The magnitude of the weld toe stress after linearization is dependent on the weld size, weld load and plate thickness. Simple equations have been derived by comparing assessment results based on the local linear stress distribution and LEFM based calculations. The proposed method is called the modified structural stress method (MSHS) since the structural hot spot stress (SHS) value is corrected using information on weld size andweld load. The correction procedure is verified using fatigue test results found in the literature. Also, a test case was conducted comparing the proposed method with other local fatigue assessment methods.