134 resultados para Non-Linear Analytical Systems
Resumo:
This paper presents an approach, based on Lean production philosophy, for rationalising the processes involved in the production of specification documents for construction projects. Current construction literature erroneously depicts the process for the creation of construction specifications as a linear one. This traditional understanding of the specification process often culminates in process-wastes. On the contrary, the evidence suggests that though generalised, the activities involved in producing specification documents are nonlinear. Drawing on the outcome of participant observation, this paper presents an optimised approach for representing construction specifications. Consequently, the actors typically involved in producing specification documents are identified, the processes suitable for automation are highlighted and the central role of tacit knowledge is integrated into a conceptual template of construction specifications. By applying the transformation, flow, value (TFV) theory of Lean production the paper argues that value creation can be realised by eliminating the wastes associated with the traditional preparation of specification documents with a view to integrating specifications in digital models such as Building Information Models (BIM). Therefore, the paper presents an approach for rationalising the TFV theory as a method for optimising current approaches for generating construction specifications based on a revised specification writing model.
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Dynamic Bayesian Networks (DBNs) provide a versatile platform for predicting and analysing the behaviour of complex systems. As such, they are well suited to the prediction of complex ecosystem population trajectories under anthropogenic disturbances such as the dredging of marine seagrass ecosystems. However, DBNs assume a homogeneous Markov chain whereas a key characteristics of complex ecosystems is the presence of feedback loops, path dependencies and regime changes whereby the behaviour of the system can vary based on past states. This paper develops a method based on the small world structure of complex systems networks to modularise a non-homogeneous DBN and enable the computation of posterior marginal probabilities given evidence in forwards inference. It also provides an approach for an approximate solution for backwards inference as convergence is not guaranteed for a path dependent system. When applied to the seagrass dredging problem, the incorporation of path dependency can implement conditional absorption and allows release from the zero state in line with environmental and ecological observations. As dredging has a marked global impact on seagrass and other marine ecosystems of high environmental and economic value, using such a complex systems model to develop practical ways to meet the needs of conservation and industry through enhancing resistance and/or recovery is of paramount importance.
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During the past three decades, the subject of fractional calculus (that is, calculus of integrals and derivatives of arbitrary order) has gained considerable popularity and importance, mainly due to its demonstrated applications in numerous diverse and widespread fields in science and engineering. For example, fractional calculus has been successfully applied to problems in system biology, physics, chemistry and biochemistry, hydrology, medicine, and finance. In many cases these new fractional-order models are more adequate than the previously used integer-order models, because fractional derivatives and integrals enable the description of the memory and hereditary properties inherent in various materials and processes that are governed by anomalous diffusion. Hence, there is a growing need to find the solution behaviour of these fractional differential equations. However, the analytic solutions of most fractional differential equations generally cannot be obtained. As a consequence, approximate and numerical techniques are playing an important role in identifying the solution behaviour of such fractional equations and exploring their applications. The main objective of this thesis is to develop new effective numerical methods and supporting analysis, based on the finite difference and finite element methods, for solving time, space and time-space fractional dynamical systems involving fractional derivatives in one and two spatial dimensions. A series of five published papers and one manuscript in preparation will be presented on the solution of the space fractional diffusion equation, space fractional advectiondispersion equation, time and space fractional diffusion equation, time and space fractional Fokker-Planck equation with a linear or non-linear source term, and fractional cable equation involving two time fractional derivatives, respectively. One important contribution of this thesis is the demonstration of how to choose different approximation techniques for different fractional derivatives. Special attention has been paid to the Riesz space fractional derivative, due to its important application in the field of groundwater flow, system biology and finance. We present three numerical methods to approximate the Riesz space fractional derivative, namely the L1/ L2-approximation method, the standard/shifted Gr¨unwald method, and the matrix transform method (MTM). The first two methods are based on the finite difference method, while the MTM allows discretisation in space using either the finite difference or finite element methods. Furthermore, we prove the equivalence of the Riesz fractional derivative and the fractional Laplacian operator under homogeneous Dirichlet boundary conditions – a result that had not previously been established. This result justifies the aforementioned use of the MTM to approximate the Riesz fractional derivative. After spatial discretisation, the time-space fractional partial differential equation is transformed into a system of fractional-in-time differential equations. We then investigate numerical methods to handle time fractional derivatives, be they Caputo type or Riemann-Liouville type. This leads to new methods utilising either finite difference strategies or the Laplace transform method for advancing the solution in time. The stability and convergence of our proposed numerical methods are also investigated. Numerical experiments are carried out in support of our theoretical analysis. We also emphasise that the numerical methods we develop are applicable for many other types of fractional partial differential equations.
Resumo:
During the past decade, a significant amount of research has been conducted internationally with the aim of developing, implementing, and verifying "advanced analysis" methods suitable for non-linear analysis and design of steel frame structures. Application of these methods permits comprehensive assessment of the actual failure modes and ultimate strengths of structural systems in practical design situations, without resort to simplified elastic methods of analysis and semi-empirical specification equations. Advanced analysis has the potential to extend the creativity of structural engineers and simplify the design process, while ensuring greater economy and more uniform safety with respect to the ultimate limit state. The application of advanced analysis methods has previously been restricted to steel frames comprising only members with compact cross-sections that are not subject to the effects of local buckling. This precluded the use of advanced analysis from the design of steel frames comprising a significant proportion of the most commonly used Australian sections, which are non-compact and subject to the effects of local buckling. This thesis contains a detailed description of research conducted over the past three years in an attempt to extend the scope of advanced analysis by developing methods that include the effects of local buckling in a non-linear analysis formulation, suitable for practical design of steel frames comprising non-compact sections. Two alternative concentrated plasticity formulations are presented in this thesis: the refined plastic hinge method and the pseudo plastic zone method. Both methods implicitly account for the effects of gradual cross-sectional yielding, longitudinal spread of plasticity, initial geometric imperfections, residual stresses, and local buckling. The accuracy and precision of the methods for the analysis of steel frames comprising non-compact sections has been established by comparison with a comprehensive range of analytical benchmark frame solutions. Both the refined plastic hinge and pseudo plastic zone methods are more accurate and precise than the conventional individual member design methods based on elastic analysis and specification equations. For example, the pseudo plastic zone method predicts the ultimate strength of the analytical benchmark frames with an average conservative error of less than one percent, and has an acceptable maximum unconservati_ve error of less than five percent. The pseudo plastic zone model can allow the design capacity to be increased by up to 30 percent for simple frames, mainly due to the consideration of inelastic redistribution. The benefits may be even more significant for complex frames with significant redundancy, which provides greater scope for inelastic redistribution. The analytical benchmark frame solutions were obtained using a distributed plasticity shell finite element model. A detailed description of this model and the results of all the 120 benchmark analyses are provided. The model explicitly accounts for the effects of gradual cross-sectional yielding, longitudinal spread of plasticity, initial geometric imperfections, residual stresses, and local buckling. Its accuracy was verified by comparison with a variety of analytical solutions and the results of three large-scale experimental tests of steel frames comprising non-compact sections. A description of the experimental method and test results is also provided.
Resumo:
In the long term, with development of skill, knowledge, exposure and confidence within the engineering profession, rigorous analysis techniques have the potential to become a reliable and far more comprehensive method for design and verification of the structural adequacy of OPS, write Nimal J Perera, David P Thambiratnam and Brian Clark. This paper explores the potential to enhance operator safety of self-propelled mechanical plant subjected to roll over and impact of falling objects using the non-linear and dynamic response simulation capabilities of analytical processes to supplement quasi-static testing methods prescribed in International and Australian Codes of Practice for bolt on Operator Protection Systems (OPS) that are post fitted. The paper is based on research work carried out by the authors at the Queensland University of Technology (QUT) over a period of three years by instrumentation of prototype tests, scale model tests in the laboratory and rigorous analysis using validated Finite Element (FE) Models. The FE codes used were ABAQUS for implicit analysis and LSDYNA for explicit analysis. The rigorous analysis and dynamic simulation technique described in the paper can be used to investigate the structural response due to accident scenarios such as multiple roll over, impact of multiple objects and combinations of such events and thereby enhance the safety and performance of Roll Over and Falling Object Protection Systems (ROPS and FOPS). The analytical techniques are based on sound engineering principles and well established practice for investigation of dynamic impact on all self propelled vehicles. They are used for many other similar applications where experimental techniques are not feasible.
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This chapter represents the analytical solution of two-dimensional linear stretching sheet problem involving a non-Newtonian liquid and suction by (a) invoking the boundary layer approximation and (b) using this result to solve the stretching sheet problem without using boundary layer approximation. The basic boundary layer equations for momentum, which are non-linear partial differential equations, are converted into non-linear ordinary differential equations by means of similarity transformation. The results reveal a new analytical procedure for solving the boundary layer equations arising in a linear stretching sheet problem involving a non-Newtonian liquid (Walters’ liquid B). The present study throws light on the analytical solution of a class of boundary layer equations arising in the stretching sheet problem.
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In recent years considerable attention has been paid to the numerical solution of stochastic ordinary differential equations (SODEs), as SODEs are often more appropriate than their deterministic counterparts in many modelling situations. However, unlike the deterministic case numerical methods for SODEs are considerably less sophisticated due to the difficulty in representing the (possibly large number of) random variable approximations to the stochastic integrals. Although Burrage and Burrage [High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations, Applied Numerical Mathematics 22 (1996) 81-101] were able to construct strong local order 1.5 stochastic Runge-Kutta methods for certain cases, it is known that all extant stochastic Runge-Kutta methods suffer an order reduction down to strong order 0.5 if there is non-commutativity between the functions associated with the multiple Wiener processes. This order reduction down to that of the Euler-Maruyama method imposes severe difficulties in obtaining meaningful solutions in a reasonable time frame and this paper attempts to circumvent these difficulties by some new techniques. An additional difficulty in solving SODEs arises even in the Linear case since it is not possible to write the solution analytically in terms of matrix exponentials unless there is a commutativity property between the functions associated with the multiple Wiener processes. Thus in this present paper first the work of Magnus [On the exponential solution of differential equations for a linear operator, Communications on Pure and Applied Mathematics 7 (1954) 649-673] (applied to deterministic non-commutative Linear problems) will be applied to non-commutative linear SODEs and methods of strong order 1.5 for arbitrary, linear, non-commutative SODE systems will be constructed - hence giving an accurate approximation to the general linear problem. Secondly, for general nonlinear non-commutative systems with an arbitrary number (d) of Wiener processes it is shown that strong local order I Runge-Kutta methods with d + 1 stages can be constructed by evaluated a set of Lie brackets as well as the standard function evaluations. A method is then constructed which can be efficiently implemented in a parallel environment for this arbitrary number of Wiener processes. Finally some numerical results are presented which illustrate the efficacy of these approaches. (C) 1999 Elsevier Science B.V. All rights reserved.
Resumo:
The aim of this paper is to show how principles of ecological psychology and dynamical systems theory can underpin a philosophy of coaching practice in a nonlinear pedagogy. Nonlinear pedagogy is based on a view of the human movement system as a nonlinear dynamical system. We demonstrate how this perspective of the human movement system can aid understanding of skill acquisition processes and underpin practice for sports coaches. We provide a description of nonlinear pedagogy followed by a consideration of some of the fundamental principles of ecological psychology and dynamical systems theory that underpin it as a coaching philosophy. We illustrate how each principle impacts on nonlinear pedagogical coaching practice, demonstrating how each principle can substantiate a framework for the coaching process.
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The purpose of this paper is threefold. First, we propose a systemic view of communication based in autopoiesis, the theory of living systems formulated by Maturana & Varela (1980, 1987). Second, we show the links between the underpinning assumptions of autopoiesis and the sociolinguistic approaches of Halliday (1978), Fairclough (1989, 1992, 1995) and Lemke (1995, 1994). Third, we propose a theoretical and analytical synthesis of autopoiesis and sociolinguistics for the study of organisational communication. In proposing a systemic theory for organisational communication, we argue that traditional approaches to communication, information, and the role of language in human organisations have, to date, been placed in teleological constraints because of an inverted focus on organisational purpose-the generally perceived role of an organisation within society-that obscure, rather than clarify, the role of language within human organisations. We argue that human social systems are, according to the criteria defined by Maturana and Varela, third-order, non-organismic living systems constituted in language. We further propose that sociolinguistics provides an appropriate analytical tool which is both compatible and penetrating in synthesis with the systemic framework provided by an autopoietic understanding of social organisation.
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High density development has been seen as a contribution to sustainable development. However, a number of engineering issues play a crucial role in the sustainable construction of high rise buildings. Non linear deformation of concrete has an adverse impact on high-rise buildings with complex geometries, due to differential axial shortening. These adverse effects are caused by time dependent behaviour resulting in volume change known as ‘shrinkage’, ‘creep’ and ‘elastic’ deformation. These three phenomena govern the behaviour and performance of all concrete elements, during and after construction. Reinforcement content, variable concrete modulus, volume to surface area ratio of the elements, environmental conditions, and construction quality and sequence influence on the performance of concrete elements and differential axial shortening will occur in all structural systems. Its detrimental effects escalate with increasing height and non vertical load paths resulting from geometric complexity. The magnitude of these effects has a significant impact on building envelopes, building services, secondary systems, and lifetime serviceability and performance. Analytical and test procedures available to quantify the magnitude of these effects are limited to a very few parameters and are not adequately rigorous to capture the complexity of true time dependent material response. With this in mind, a research project has been undertaken to develop an accurate numerical procedure to quantify the differential axial shortening of structural elements. The procedure has been successfully applied to quantify the differential axial shortening of a high rise building, and the important capabilities available in the procedure have been discussed. A new practical concept, based on the variation of vibration characteristic of structure during and after construction and used to quantify the axial shortening and assess the performance of structure, is presented.
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This paper considers the question of designing a fully image based visual servo control for a dynamic system. The work is motivated by the ongoing development of image based visual servo control of small aerial robotic vehicles. The observed targets considered are coloured blobs on a flat surface to which the normal direction is known. The theoretical framework is directly applicable to the case of markings on a horizontal floor or landing field. The image features used are a first order spherical moment for position and an image flow measurement for velocity. A fully non-linear adaptive control design is provided that ensures global stability of the closed-loop system. © 2005 IEEE.
Resumo:
Inverse problems based on using experimental data to estimate unknown parameters of a system often arise in biological and chaotic systems. In this paper, we consider parameter estimation in systems biology involving linear and non-linear complex dynamical models, including the Michaelis–Menten enzyme kinetic system, a dynamical model of competence induction in Bacillus subtilis bacteria and a model of feedback bypass in B. subtilis bacteria. We propose some novel techniques for inverse problems. Firstly, we establish an approximation of a non-linear differential algebraic equation that corresponds to the given biological systems. Secondly, we use the Picard contraction mapping, collage methods and numerical integration techniques to convert the parameter estimation into a minimization problem of the parameters. We propose two optimization techniques: a grid approximation method and a modified hybrid Nelder–Mead simplex search and particle swarm optimization (MH-NMSS-PSO) for non-linear parameter estimation. The two techniques are used for parameter estimation in a model of competence induction in B. subtilis bacteria with noisy data. The MH-NMSS-PSO scheme is applied to a dynamical model of competence induction in B. subtilis bacteria based on experimental data and the model for feedback bypass. Numerical results demonstrate the effectiveness of our approach.
Resumo:
Concrete is commonly used as a primary construction material for tall building construction. Load bearing components such as columns and walls in concrete buildings are subjected to instantaneous and long term axial shortening caused by the time dependent effects of "shrinkage", "creep" and "elastic" deformations. Reinforcing steel content, variable concrete modulus, volume to surface area ratio of the elements and environmental conditions govern axial shortening. The impact of differential axial shortening among columns and core shear walls escalate with increasing building height. Differential axial shortening of gravity loaded elements in geometrically complex and irregular buildings result in permanent distortion and deflection of the structural frame which have a significant impact on building envelopes, building services, secondary systems and the life time serviceability and performance of a building. Existing numerical methods commonly used in design to quantify axial shortening are mainly based on elastic analytical techniques and therefore unable to capture the complexity of non-linear time dependent effect. Ambient measurements of axial shortening using vibrating wire, external mechanical strain, and electronic strain gauges are methods that are available to verify pre-estimated values from the design stage. Installing these gauges permanently embedded in or on the surface of concrete components for continuous measurements during and after construction with adequate protection is uneconomical, inconvenient and unreliable. Therefore such methods are rarely if ever used in actual practice of building construction. This research project has developed a rigorous numerical procedure that encompasses linear and non-linear time dependent phenomena for prediction of axial shortening of reinforced concrete structural components at design stage. This procedure takes into consideration (i) construction sequence, (ii) time varying values of Young's Modulus of reinforced concrete and (iii) creep and shrinkage models that account for variability resulting from environmental effects. The capabilities of the procedure are illustrated through examples. In order to update previous predictions of axial shortening during the construction and service stages of the building, this research has also developed a vibration based procedure using ambient measurements. This procedure takes into consideration the changes in vibration characteristic of structure during and after construction. The application of this procedure is illustrated through numerical examples which also highlight the features. The vibration based procedure can also be used as a tool to assess structural health/performance of key structural components in the building during construction and service life.
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This paper proposes a new approach for state estimation of angles and frequencies of equivalent areas in large power systems with synchronized phasor measurement units. Defining coherent generators and their correspondent areas, generators are aggregated and system reduction is performed in each area of inter-connected power systems. The structure of the reduced system is obtained based on the characteristics of the reduced linear model and measurement data to form the non-linear model of the reduced system. Then a Kalman estimator is designed for the reduced system to provide an equivalent dynamic system state estimation using the synchronized phasor measurement data. The method is simulated on two test systems to evaluate the feasibility of the proposed method.
Resumo:
In the past few years, remarkable progress has been made in unveiling novel and unique optical properties of strongly coupled plasmonic nanostructures. However, application of such plasmonic nanostructures in biomedicine remains challenging due to the lack of facile and robust assembly methods for producing stable nanostructures. Previous attempts to achieve plasmonic nano-assemblies using molecular ligands were limited due to the lack of flexibility that could be exercised in forming them. Here, we report the utilization of tailor-made hyperbranched polymers (HBP) as linkers to assemble gold nanoparticles (NPs) into nano-assemblies. The ease and flexibility in tuning the particle size and number of branch ends of a HBP makes it an ideal candidate as a linker, as opposed to DNA, small organic molecules and linear or dendrimeric polymers. We report a strong correlation of polymer (HBP) concentration with the size of the hybrid nano-assemblies and “hot-spot” density. We have shown that such solutions of stable HBP-gold nano-assemblies can be barcoded with various Raman tags to provide improved surface-enhanced Raman scattering (SERS) compared with non-aggregated NP systems. These Raman barcoded hybrid nano-assemblies, with further optimization of NP shape, size and “hot-spot” density, may find application as diagnostic tools in nanomedicine.