Dissertations / Theses on the topic 'Model multi strate'

J'ai utilisé une étude de 30 ans portant sur une espèce d'oiseau marin longévif (la mouette tridactyle) afin d'étudier les compromis évolutifs entre recrutement, reproduction, et survie. Mes résultats indiquent que l'âge à la première reproduction et la sélection de l'habitat sont intimement liés, et que l'âge au recrutement influence également les trajectoires de survie et de reproduction. D'autres sources d'hétérogénéité observée (investissement reproducteur) et non-observée ('frailty') agissent également sur la survie et la reproduction au cours de la vie. Les recrues d'âge intermédiaire (âge = 5) maintiennent un succès reproducteur élevé au cours de la vie et minimisent le déclin des chances de survie avec l'âge par rapport aux autres recrues. Même si les mesures de fitness individuelles indiquent que le recrutement précoce est la plus avantageuse des stratégies, les coûts associés au différé du recrutement semblent minimes
I used a 30-year study of long-lived seabirds (black-legged Kittiwakes) that breed in Brittany to study the evolution of trade-offs between early-life breeding decisions, future reproduction, and survival. I first found that recruitment age and habitat selection were intimately linked. Recruitment age further influenced breeding success and survival trajectories. Furthermore, sources of observed (reproductive covariates, experience) and unobserved heterogeneity (frailty) explained substantial amounts of variability in breeding success and survival. Overall, intermediate age recruits (age 5) seemed to maintain high breeding success over life and minimized senescence in survival compared to other recruits. Even though individual fitness showed that earlier recruitment was the most beneficial recruitment strategy, the costs associated to delayed recruitment seemed minimal

No two species can indefinitely occupy the same ecological niche according to the competitive exclusion principle. When competing strains of the same pathogen invade a homogeneous population, the strain with the largest basic reproductive ratio R0 will force the other strains to extinction. However, over 51 pathogens are documented to have multiple strains [3] coexisting, contrary to the results from homogeneous models. In reality, the world is heterogeneous with the population varying in susceptibility. As such, the study of epidemiology, and hence the problem of pathogen coexistence should entail heterogeneity. Heterogeneous models tend to capture dynamics such as resistance to infection, giving more accurate results of the epidemics. This study will focus on the behavior of multi-pathogen heterogeneous models and will try to answer the question: what are the conditions on the model parameters that lead to pathogen coexistence? The goal is to understand the mechanisms in heterogeneous populations that mediate pathogen coexistence. Using the moment closure method, Fleming et. al. [22] used a two pathogen heterogeneous model (1.9) to show that pathogen coexistence was possible between strains of the baculovirus under certain conditions. In the first part of our study, we consider the same model using the hidden keystone variable (HKV) method. We show that under some conditions, the moment closure method and the HKV method give the same results. We also show that pathogen coexistence is possible for a much wider range of parameters, and give a complete analysis of the model (1.9), and give an explanation for the observed coexistence. The host population (gypsy moth) considered in the model (1.9) has a year life span, and hence, demography was introduced to the model using a discrete time model (1.12). In the second part of our study, we will consider a multi-pathogen compartmental heterogeneous model (3.1) with continuous time demography. We show using a Lyapunov function that pathogen coexistence is possible between multiple strains of the same pathogen. We provide analytical and numerical evidence that multiple strains of the same pathogen can coexist in a heterogeneous population.

Measuring process safety performance is a challenge, and the wide variations in understanding, compliance, and implementation of process safety programs increase the challenge. Process safety can be measured in three strata: (1) measurement of process safety elements within facilities; (2) benchmarking of process safety elements among facilities; and (3) use of incident data collection from various sources for industrial safety performance assessment. The methods presently available for measurement of process safety within facilities are deficient because the results are strongly dependent on user judgment. Performance benchmarking among facilities is done within closed groups of organizations. Neither the questionnaires nor the results are available to the public. Many organizations collect data on industrial incidents. These organizations differ from each other in their interests, data collection procedures, definitions, and scope, and each of them analyzes its data to achieve its objectives. However, there have been no attempts to explore the potential of integrating data sources and harnessing these databases for industrial safety performance assessment. In this study we developed models to pursue the measurement of samples of the strata described above. The measurement methodologies employed herein overcome the disadvantages of existing methodologies and increase their capabilities.

Previous multi-strain mathematical models have elucidated that the degree of cross-protective responses between similar strains, acting as a form of immune selection, generates different behavioural states of the pathogen population. This thesis explores these multi-strain dynamic states, to examine their robustness and stability in the face of pathogenic intrinsic phenotypic variation, and the extrinsic force of immune selection. This is achieved in two main ways: Chapter 2 introduces phenotypic variation in pathogen transmissibility, testing the robustness of a stable pathogen population to the emergence of an introduced strain of higher transmission potential; and Chapter 3 introduces a new model with a possibility of immunity to both strain-specific and cross-strain (conserved) determinants, to investigate how heterogeneity in the specificity of a host immune response alters the pathogen population structure. A final investigation in Chapter 4 develops a method of reverse-pattern oriented modelling using a machine learning algorithm to determine which intrinsic properties of the pathogen, and their combinations, lead to particular disease-like population patterns. This research offers novel techniques to complement previous and ongoing work on multi-strain modelling, with direct applications to a range of infectious agents such as Plasmodium falciparum, influenza A, and rotavirus, but also with a wider potential for other multi-strain systems.

The security objectives enforce the security policy, which defines what is to be protected in a network environment. The violation of these security objectives induces security threats. We introduce an explicit notion of security objectives for a security protocol. This notion should precede the formal verification process. In the absence of such a notion, the security protocol may be proven correct despite the fact that it is not equipped to defend against all potential threats. In order to establish the correctness of security objectives, we present a formal model that provides basis for the formal verification of security protocols. We also develop the modal logic, proof based, and multi-agent approaches using the Strand Space framework. In our modal logic approach, we present the logical constructs to model a protocol's behavior in such a way that the participants can verify different security parameters by looking at their own run of the protocol. In our proof based model, we present a generic set of proofs to establish the correctness of a security protocol. We model the 802.11i protocol into our proof based system and then perform the formal verification of the authentication property. The intruder in our model is imbued with powerful capabilities and repercussions to possible attacks are evaluated. Our analysis proves that the authentication of 802.11i is not compromised in the presented model. We further demonstrate how changes in our model will yield a successful man-in-the-middle attack. Our multi-agent approach includes an explicit notion of multi-agent, which was missing in the Strand Space framework. The limitation of Strand Space framework is the assumption that all the information available to a principal is either supplied initially or is contained in messages received by that principal. However, other important information may also be available to a principal in a security setting, such as a principal may combine information from different roles played by him in a protocol to launch a powerful attack. Our presented approach models the behavior of a distributed system as a multi-agent system. The presented model captures the combined information, the formal model of knowledge, and the belief of agents over time. After building this formal model, we present a formal proof of authentication of the 4-way handshake of the 802.11i protocol.
Ph.D.
School of Electrical Engineering and Computer Science
Engineering and Computer Science
Computer Science PhD

Una caracterización precisa y completa del tejido cardíaco es esencial para el diagnóstico y tratamiento de problemas cardíacos. Para caracterizar la función cardíaca desde diferentes perspectivas, en la práctica clínica, se adquieren grandes cantidades de datos de distinta naturaleza sobre un mismo paciente, proporcionando información útil para la evaluación del corazón. Aunque los distintos datos obtenidos de cada paciente se suelen analizar por separado para evaluar la función cardíaca desde diferentes perspectivas, la combinación efectiva de esta información heterogénea podría ser útil para tener una mejor visión de la anatomía y la función cardíaca. El objetivo principal de esta tesis es el desarrollo de métodos para integrar imágenes e información de distinta naturaleza para una caracterización del tejido cardíaco más completa y precisa.
An accurate and complete cardiac tissue characterization is essential to diagnose and treat heart problems. To characterize cardiac function from different perspectives, large amounts of data of different nature from the same patient are acquired in clinical practice, providing information that is useful for heart assessment. Although the different data obtained from each patient are often analyzed separately to assess cardiac function from different perspectives, the effective combination of this heterogeneous information may be useful for a better insight into heart anatomy and function. The main objective of this thesis is to develop methods to integrate images and information of different nature for a more complete and accurate cardiac tissue characterization.

Several geotechnical processes can only be reliably interpreted by taking account of the soil-atmosphere interactions. This thesis investigates two geotechnical problems involving soil-atmosphere interactions that drive water flow through the soil skeleton in two opposite directions; Problem 1: slope failure in expansive soils induced by water infiltration, Problem 2: large strain consolidation of soft soils induced by water evaporation. Both problems are of practical interest for safe and economical design of various geotechnical infrastructures. Two major geotechnical activities in the world; namely, the construction of water transfer canal in expansive soil area in China and the deposition of oil sands and hard rock tailings in Canada can be cited as classic examples of Problems 1 and 2, respectively. In such problems, substantial zones of the domain may switch between an unsaturated and saturated condition. Therefore, rational analysis requires simultaneous modelling of both unsaturated and saturated soil behaviour. The first goal of this thesis is to investigate the influence of swelling (the most characteristic behaviour of expansive soils) on slope stability using numerical methods. Swelling of expansive soils contributes to slope instability during rainfall because of two key reasons (i) soil swelling affects the flow process that actually induces swelling, (i.e. a typical coupling phenomenon), and (ii) swelling-induced stress redistribution and displacement development. In this thesis, the first effect is studied by a coupled (mechanical-hydraulic) numerical analysis of the response of a slope to rainfall using commercial software (GeoSlope). The second effect, the swelling-induced stress redistribution and displacement development after wetting, is tracked using a newly developed numerical program. In the program strain softening behaviour is introduced into the elasto-plastic Mohr-Coulomb Model for modelling unsaturated soil. A novel stress (net stress and suction)-dependent model for moduli of elasticity, combined with the predictive model for shear strength based on Soil Water Retention Behaviour are incorporated into the numerical program to achieve a smooth transition between saturated and unsaturated states. The results show that soil swelling can decrease the factor of safety by accelerating the wetting front depth due to hydro-mechanical coupling, while changes of sliding mass geometry has a negligible influence. The change of stress regime associated with soil swelling is significant to induce plastic strain softening (swelling-induced softening) and contribute to the slope failures. The second goal of thesis is to develop a novel computer program for simulation of large strain consolidation of soft soil under both self-weight and evaporation conditions. This program is both theoretically sound and practically applicable. Several basic/advanced constitutive models for unsaturated soils, including State Surface Model (SSM), Barcelona Basic model (BBM), Glasgow Coupled model (GCM) and bounding surface water retention model, are innovatively implemented into a piece-wise linear framework solved using finite difference technique. The developed program is referred to as UNSATCON-(ML), which has been tested using (a) existing analytical/numerical solutions and (b) various laboratory and field studies for single-layer and multiple-layer deposition of hard rock and oil sands tailings. Features of UNSATCON-(ML) that are improvements over existing models typically used to analyze consolidation-desiccation in soft soils include: (i) coupling of soil large deformation with true unsaturated water flow; (ii) correct reproduction of the shrinkage behaviour of soil under evaporation-induced desiccation; (iii) smooth transition between saturated and unsaturated states despite that some selected models are established using two independent stress variables, (iv) ensuring strictly mass conservation of water, and (v) simulation of irrecoverable volume change and hydraulic hysteresis to properly analyze multilayer tailings deposition. A number of hypothetical field case analyses are carried out using UNSATCON-ML, illustrating its applicability to industry.

Les études de faisabilité concernant le stockage géologique profond des déchets radioactifs ont conduit un intérêt accru concernant la modélisation géomécanique de la roche hte. En France, une roche hte potentielle est l'argilite du Callovo-Oxfordien du site de Meuse/Haute Marne. Etant donné que le principe de stockage géologique profond repose fortement sur la capacité de confinement de la formation hte, sa faible perméabilité est d'une importance clé. La perméabilité étant dépendante de la microstructure du matériau et de son évolution sous chargement, le comportement couplé hydro-mécanique de l'argilite est important. En effet, des modifications mécaniques sont induites par le creusement de la galerie d'entreposage, générant une zone endommagée (EDZ), pouvant conduire une modification de la perméabilité dans le voisinage de la galerie. Dans les matériaux microstructure complexe comme l'argilite du Callovo-Oxfordien, le comportement macroscopique trouve son origine dans l'interaction des constituants micro-mécaniques. En plus du couplage entre le comportement hydraulique et mécanique, un couplage entre les échelles micro et macro existe. Par le biais de l'élaboration d'un cadre d'homogénéisation du couplage hydro-mécanique, une approche de modélisation deuxéchelles est développée dans ce travail, dans laquelle la relation constitutive macroscopique découle directement du comportement à l'échelle microscopique. Un modèle existant du couplage hydro-mécanique, reposant sur l'identification de grains et d'espaces poreux intergranulaires à l'échelle micro est adopté comme point de départ. Ce modèle repose sur une homogénéisation numérique du comportement à la petite échelle afin d'obtenir à l'échelle macroscopique la réponse en contrainte et de transport du fluide interstitiel. Ce modèle est basé sur un VER périodique qui permet de déduire le comportement macroscopique local de l'argilite. En réponse, en un point d'intégration macro donné, à un incrément de la déformation et du gradient de pression, la réponse du VER permet d'exprimer l'incrément de contrainte et de flux associé, constituant de fait un équivalent numérique de la relation constitutive. Les problèmes aux conditions limites macro et micro sont traités simultanément par la méthode élément fini. Pour obtenir les opérateurs tangents consistants à l'échelle macro, la méthode d'homogénéisation par condensation statique des opérateurs tangeants micro est étendu au cas avec couplage hydro-mécanique. L'implémentation du modèle double échelle et la mise en uvre des développements théoriques d'homogénéisation ont été effectués dans le code élément fini Lagamine (Université de Liège). Pour la modélisation de la localisation de la déformation à l'échelle macro, qui, dans un formalisme de milieu continu classique, souffre de la dépendance au maillage, l'approche double-échelle a été utilisée dans un formalisme de milieu enrichi de type milieu de second gradient pour matériau poreux saturé. Les capacités du modèle homogénéisé numériquement, utilisé dans un cadre de milieu de second gradient, sont ensuite démontrées par des simulations d'essais dométriques et d'essais de compression biaxiaux. L'approche se confirme être un moyen puissant pour modéliser l'anisotropie initiale et induite du comportement mécanique et du comportement hydraulique. Pour la modélisation du comportement de l'argilite du Callovo-Oxfordien, des VER sont construits en tenant compte des travaux de caractérisation de la géométrie des inclusions microscopiques et des résultats expérimentaux d'essais macroscopiques.La loi de comportement homogénéisée numériquement ainsi calibrée est utilisée dans des simulations de creusement de galerie jusqu'à des niveaux d'endommagement générant une localisation de la déformation.Ces calculs montrent à la fois la pertinence et l'applicabilité du concept double échelle pour l'évaluation du comportement hydromécanique des EDZ dans un contexte du stockage des déchets radioactifs
Feasibility studies for deep geological radioactive waste disposal facilities have led to an increased interest in the geomechanical modelling of its host rock. In France, a potential host rock is the Callovo-Oxfordian claystone. The low permeability of this material is of key importance, as the principal of deep geological disposal strongly relies on the sealing capacity of the host formation. The permeability being coupled to the mechanical material state, hydromechanical coupled behaviour of the claystone becomes important when mechanical alterations are induced by gallery excavation in the so-called excavation damaged zone (EDZ). In materials with microstructure such as the Callovo-Oxfordian claystone [Robinet et al., 2012], the macroscopic behaviour has its origin in the interaction of its mi- cromechanical constituents. In addition to the coupling between hydraulic and mech- anical behaviour, a coupling between the micro (material microstructure) and macro will be made. By means of the development of a framework of computational homo- genization for hydromechanical coupling, a doublescale modelling approach is formu- lated, for which the macroscale constitutive relations are derived from the microscale by homogenization. An existing model for the modelling of hydromechanical coupling based on the distinct definition of grains and intergranular pore space [Frey, 2010] is adopted and modified to enable the application of first order computational homogenization for obtaining macroscale stress and fluid transport responses. This model is used to constitute a periodic representative elementary volume (REV) that allows the rep- resentation of the local macroscopic behaviour of the claystone. As a response to deformation loading, the behaviour of the REV represents the numerical equivalent of a constitutive relation at the macroscale. For the required consistent tangent operators, the framework of computational homogenization by static condensation [Kouznetsova et al., 2001] is extended to hy- dromechanical coupling. The theoretical developments of this extension are imple- mented in the finite element code Lagamine (Li` ege) as an independent constitutive relation. For the modelling of localization of deformation, which in classical FE meth- ods suffers from the well-known mesh dependency, the doublescale approach of hy- dromechanical coupling is combined with a local second gradient model [Collin et al., 2006] to control the internal length scale of localized deformation. By accepting the periodic boundary conditions as a regularization of the microscale deformation, the use of the multiscale model in combination with the local second gradient model can be used for modelling localization phenomena in HM-coupled settings with material softening. The modelling capacities of the approach are demonstrated by means of simula- tions of oedometer tests and biaxial compression tests. The approach is demonstrated to be a powerful way to model anisotropy in the mechanical as well as the hydraulic behaviour of the material both in the initial material state and as an effect of hy- dromechanical alterations. For the application to the modelling of Callovo-Oxfordian claystone, microstructural REVs are calibrated to geometrical characteristics of the inclusion that form the microstructure under consideration and to macroscale ex- perimental results of the mechanical behaviour. The calibrated constitutive relation is used in the simulation of gallery excavation processes. These computations give a proof of concept of the doublescale assessment of the hydromechanical behaviour of the excavation damaged zones around galleries in the context of nuclear waste disposal

The thesis presents a novel computational method for analysing the static and dynamic behaviour of a multi-damaged beam using local and non-local elasticity theories. Most of the lumped damage beam models proposed to date are based on slender beam theory in classical (local) elasticity and are limited by inaccuracies caused by the implicit assumption of the Euler-Bernoulli beam model and by the spring model itself, which simplifies the real beam behaviour around the crack. In addition, size effects and material heterogeneity cannot be taken into account using the classical elasticity theory due to the absence of any microstructural parameter. The proposed work is based on the inhomogeneous Euler-Bernoulli beam theory in which a Dirac's delta function is added to the bending flexibility at the position of each crack: that is, the severer the damage, the larger is the resulting impulsive term. The crack is assumed to be always open, resulting in a linear system (i.e. nonlinear phenomena associated with breathing cracks are not considered). In order to provide an accurate representation of the structure's behaviour, a new multi-cracked beam element including shear effects and rotatory inertia is developed using the flexibility approach for the concentrated damage. The resulting stiffness matrix and load vector terms are evaluated by the unit-displacement method, employing the closed-form solutions for the multi-cracked beam problem. The same deformed shapes are used to derive the consistent mass matrix, also including the rotatory inertia terms. The two-node multi-damaged beam model has been validated through comparison of the results of static and dynamic analyses for two numerical examples against those provided by a commercial finite element code. The proposed model is shown to improve the computational efficiency as well as the accuracy, thanks to the inclusion of both shear deformations and rotatory inertia. The inaccuracy of the spring model, where for example for a rotational spring a finite jump appears on the rotations' profile, has been tackled by the enrichment of the elastic constitutive law with higher order stress and strain gradients. In particular, a new phenomenological approach based upon a convenient form of non-local elasticity beam theory has been presented. This hybrid non-local beam model is able to take into account the distortion on the stress/strain field around the crack as well as to include the microstructure of the material, without introducing any additional crack related parameters. The Laplace's transform method applied to the differential equation of the problem allowed deriving the static closed-form solution for the multi-cracked Euler-Bernoulli beams with hybrid non-local elasticity. The dynamic analysis has been performed using a new computational meshless method, where the equation of motions are discretised by a Galerkin-type approximation, with convenient shape functions able to ensure the same grade of approximation as the beam element for the classical elasticity. The importance of the inclusion of microstructural parameters is addressed and their effects are quantified also in comparison with those obtained using the classical elasticity theory.

The thin-tile vault is a structural system widely used in the Mediterranean area. The most spectacular development took place through modernist-style buildings designed by architects such as Antonio Gaudí o Luís Domènech and Muntaner among the others. Thin-tile vault, from a morphological standpoint, is made up of one or more leaf of thin-tile lay flat, and joined with plaster or mortar. As a particularity of this arrangement, the load is applied parallel to the face of the thin-tile as opposed to the load-bearing walls masonry, where the load is applied perpendicularly to it. Deepening the knowledge of this type of masonry is the main objective of this thesis. In masonry, normally the compressive strength of the constituent materials is used to analytically establish the compressive strength of the masonry. This thesis, and based on the experimental results on one-, two- , and three-leaf thin-tile specimens, analyse stress-strain law, failure modes, and mechanical properties and compared with those corresponding to different masonries presented in the literature
La volta catalana és un sistema estructural àmpliament utilitzat en l'àrea mediterrània. Es a través d'edificis d'estil modernista d’arquitectes com Antoni Gaudí o Lluís Domènech i Muntaner que presenta el seu màxim esplendor. La volta catalana, des d'un vessant morfològica, està constituïda per una combinació d'una o diverses fulles de rajoles col·locades planes, i unides amb guix o morter. Una particularitat d'aquesta fàbrica és l’aplicació de la càrrega paral•lela a la cara de la rajola en contraposició a la fàbrica de rajol de parets on aquesta és aplicada perpendicular. Aprofundir en el coneixement d’aquest tipus de fàbrica es el principal objectiu d’aquesta tesis. En fàbrica, habitualment la determinació analítica de la resistència a compressió es determina a partir dels materials constituents (peça i morter). La tesi, i a partir dels resultats experimentals sobre provetes de fàbrica de rajola d'una, dues i tres fulles, analitza el comportament tensió-deformació, el mode de falla i les propietats mecàniques i els compara amb diferents fàbriques presents en la literatura

The thesis is based on the use of mathematical modeling and analysis to gain insightinto the transmission dynamics of malaria in a community. A new deterministic model for assessing the role of age-structure on the disease dynamics is designed. The model undergoes backward bifurcation, a dynamic phenomenon characterized by the co-existence of a stable disease-free and an endemic equilibrium of the model when the associated reproduction number is less than unity. It is shown that adding age-structure to the basic model for malaria transmission does not alter its essential qualitative dynamics. The study is extended to incorporate the use of anti-malaria drugs. Numerical simulations of the extended model suggest that for the case when treatment does not cause drug resistance (and the reproduction number of each of the two strains exceed unity), the model undergoes competitive exclusion. The impact of various effectiveness levels of the treatment strategy is assessed.

The thesis is based on the use of mathematical modeling and analysis to gain insightinto the transmission dynamics of malaria in a community. A new deterministic model for assessing the role of age-structure on the disease dynamics is designed. The model undergoes backward bifurcation, a dynamic phenomenon characterized by the co-existence of a stable disease-free and an endemic equilibrium of the model when the associated reproduction number is less than unity. It is shown that adding age-structure to the basic model for malaria transmission does not alter its essential qualitative dynamics. The study is extended to incorporate the use of anti-malaria drugs. Numerical simulations of the extended model suggest that for the case when treatment does not cause drug resistance (and the reproduction number of each of the two strains exceed unity), the model undergoes competitive exclusion. The impact of various effectiveness levels of the treatment strategy is assessed.

碩士
國防大學理工學院
空間科學碩士班
99
The purpose of this study is verifying the feasibility of GPS/GLONASS integrated satellite system, groundwater method and geoid model used to monitor changes of strata variation in Taiwan area. First, GPS/GLONASS integrated satellite systems were used for baseline observation for 24 hours on CCIT’s (Chung Cheng Institute of Technology) G002 and G007 control points with Bernese 5.0 GPS software. Data from GPS-only and both integrated satellites systems were divided in each second and 15 seconds. Results show that baseline observations of GPS/GLONASS compared with those of GPS systems increase up to 34% ~ 81% in each 15 seconds and increase up to 94.56% to 95.93% in every 1 second. As cycle ambiguity resolutions of GPS/GLONASS compared with those of GPS increase up to 16% to 64% in each 15 seconds and increase up to 22% ~ 67% in every 1 second. The results indicate that compared GPS/GLONASS systems with GPS-only system in calculation not only reduce time of consuming but also improve accuracy of computing. Second, by collecting of three years’ GPS and GLONASS’s satellite tracking data, Kimnen point was selected in center of star –net for computing 22 points’ ellipsoid heights, and Geoid Model for determining geoid undulations of values on same points. 22 Groundwaters of the Water Resources Agency which closed to previous observed points monitor heights of water level. It is indicated that three kinds of height values at 8 locations within almost 2 km from the groundwater show a linear relationship, and the changes of Taiwan area’s strata variation can be presented effectively.

博士
國立中正大學
機械系
99
Wafer testing in the semiconductor industry is generally per-formed using a multi-layer probe card. In the present study, Castiglia-no’s second theorem is used to derive analytical formulae for the con-tact force and scrub mark length generated during the probing test. The formulations are then integrated with a multi-objective program-ming algorithm in order to optimize the probe needle parameters in such a way as to ensure a uniform contact force and a minimum scrub mark length. The validity of the analytical model is confirmed by comparing the solutions obtained for the contact force and scrub mark length with the equivalent results obtained from finite element (FE) simulations. The effectiveness of the analytical model and optimiza-tion procedure is demonstrated by optimizing the needle parameters of a commercial four-layer probe card. It is shown that the optimized probe card not only produces a more uniform contact force than the original probe card, but also yields a shorter and more uniform scrub mark length. Finally, to propose a more complete tool in design of probe card, this research found out prediction formula of probe scrub depth by using contact mechanics and experiment.