Complex systems composed of many substructures include various structural joints connecting the substructures together. These mechanical connections play a significant role in predicting the dynamic characteristics of the assembled systems accurately. Therefore, equivalent dynamic models of joints that consist of stiffness and damping elements should be developed and the joint parameters should be determined for an accurate vibration analysis. Since it is difficult to estimate joint parameters accurately by using a pure analytical approach, it is a general practice to use experimental measurements to model joints connecting substructures. In this study an experimental identification method is suggested. In this approach the frequency response functions (FRFs) of substructures and the coupled structure are measured and FRF decoupling method is used to identify equivalent dynamic characteristics of bolted joints. Since rotational degrees of freedom (RDOF) in connection dynamics is very important, a structural joint is modeled with translational, rotational and cross-coupling stiffness and damping terms. FRF synthesis and finite-difference formulations are used for the estimation of unmeasured FRFs and RDOF related FRFs, respectively. The validity and application of the proposed method are demonstrated both numerically and experimentally. In simulation studies, simulated experimental values are used, and it is seen that the identification results are prone to high errors due to noise in measurement and the matrix inversions in the identification equations. In order to reduce the effect of noise, it is proposed to extract the joint properties by taking the average of the results obtained at several frequencies in the frequency regions sensitive to joint parameters. Yet, it is observed in practical applications that experimental errors combine with the measurement noise and the identification results still may not be so accurate. In order to solve this problem, an update algorithm is developed. In the approach proposed, the identified dynamic parameters are used as initial estimates and then optimum dynamic parameters representing the joint are obtained by using an optimization algorithm. The application of the proposed method is performed on a bolted assembly. It is shown with experimental studies that this method is very successful in identifying bolted joint parameters. The accuracy and applicability of the identification method suggested are illustrated by using a dynamically identified bolt in a new structure, and showing that the calculated FRFs in which identified joint parameters are used, match perfectly with the measured ones for the new structure. In this study, the effects of bolt size and quality of bolts, as well as the bolt torque on the joint properties are also studied by making a series of experiments and identifying the joint parameters for each case.

<p>The field of inverse problems is an area in applied mathematics that is of great importance in several scientific and industrial applications. Since an inverse problem is typically founded on non-linear and ill-posed models it is a very difficult problem to solve. To find a regularized solution it is crucial to have <em>a priori</em> information about the solution. Therefore, general theories are not sufficient considering new applications.</p><p>In this thesis we consider the inverse problem to determine the beam bending stiffness from measurements of the transverse dynamic displacement. Of special interest is to localize parts with reduced bending stiffness. Driven by requirements in the wood-industry it is not enough considering time-efficient algorithms, the models must also be adapted to manage extremely short calculation times.</p><p>For the developing of efficient methods inverse problems based on the fourth order Euler-Bernoulli beam equation and the second order string equation are studied. Important results are the transformation of a nonlinear regularization problem to a linear one and a convex procedure for finding parts with reduced bending stiffness.</p>

In this paper we discuss the stable solvability of the inverse problem of parameter identification in a jump diffusion model. Therefore we introduce the forward operator of this inverse problem and analyze its properties. We show continuity of the forward operator and stability of the inverse problem provided that the domain is restricted in a specific manner such that techniques of compact sets can be exploited. Furthermore, we show that there is an asymptotical non-injectivity which causes instability problems whenever the jump intensity increases and the jump heights decay simultaneously.

In this note, we consider an inverse problem in a jump diffusion model. Using characteristic functions we prove the injectivity of the forward operator mapping the five parameters determining the model to the density function of the return distribution.

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Magnetic Resonance Elastography (MRE) is an emerging method for non-invasive breast cancer screening. It takes the MRI displacement data output and reconstructs the internal stiffness distribution, where cancerous tissue is approximately five to ten times stiffer than healthy breast tissue. Hence, MRE offers a high contrast solution to this diagnostic problem. Current MRE methods for reconstructing stiffness use forward simulation based optimization methods that are highly non-linear, non-convex and very heavy computationally. This research develops integral-based inverse problem solutions that reformulate the underlying differential equations in terms of integrals of MRI measured displacement data, and this transforms the problem into a linear, convex optimization. All derivative terms in the formulation are removed by special choice of integration limits, so no smoothing or filtering of the input data is required. The resulting equations can easily be solved by linear least squares requiring very minimal computation. 1D inverse algorithms were developed to provide a proof of concept of the integral-based method. Initially, the complete compressible 2D Navier's equations were used to develop the 2D inverse methods. Reasonable results were achieved with the algorithm successfully identifying a 1cm by 1cm tumour with up to 10% noise, data resolution of 20 measured points per cm and actuation frequencies of 100Hz. However, for the same input data set, a simplified incompressible 2D model was used as the basis for the final proposed inverse algorithm. This approach significantly improved results by removing ill-conditioned terms from the original formulation. For a 1cm by 1 cm tumour, accurate results were obtained with up to 40% noise, a range of actuation frequencies and very low data resolution of the order of 2 measured points per cm. These results thus indicate that more crude and less expensive data measurement systems could be used to obtain good results. The methods developed can be readily extended to 3D by applying a similar incompressible integral formulation to the 3D Navier's equations.

<p>The focus of this dissertation is on phenomena exhibited by multistable systems. Two phenomena of particular importance are chaos control and stochastic resonance. In this work, both models that can predict ordered responses and experiments in which ordered responses occur are explored. In addition, parameter identification methods are presented and improved. </p><p>Chaos control, when implemented with delays, can be an effective way to stabilize unstable periodic orbits within a multistable system experiencing a chaotic response. Delayed control is easy to implement physically but greatly increases the complexity of analyzing such systems. In this work, the spectral element method was adapted to evaluate unstable periodic orbits stabilized by feedback control implemented with delays. Examples are presented for Duffing systems in which the delay is equal to the forcing period. The spectral approach is also extended to analyze the control of chaos with arbitrary delays. Control with arbitrary delays can also be used to stabilize equilibria within the chaotic response. These methods for arbitrary delays are explored in self-excited, chaotic systems.</p><p>Stochastic resonance occurs in multistable systems when an increase in noise results in an ordered response. It is well known that noise excitation of multistable systems results in the system escaping from potential wells or switching between wells. In stochastic resonance, a small external signal is amplified due to these switching events. Methods for modeling stochastic resonance in both underdamped and overdamped systems are presented. In addition, stochastic resonance in a bistable, composite beam excited by colored noise is investigated experimentally. The experimental results are compared with analytical models, and the effect of modal masses on the analytical expressions is explored. Finally, an alternative approach for calculating the effect of colored noise excitation is proposed.</p><p>In order to implement analysis methods related to delay differential equations or stochastic resonance, the parameters of the system must be known in advance or determined experimentally. Parameter identification methods provide a natural connection between experiment and theory. In this work, the harmonic balance parameter identification method was applied to beam energy harvesters and is improved using weighting matrices. The method has been applied to a nonlinear, bistable, piezoelectric beam with a tip mass. Then, an experimental method of determining the number of restoring force coefficients necessary to accurately model the systems was demonstrated. The harmonic balance method was also applied to a bistable, beam system undergoing stochastic resonance. Finally, a new weighting strategy is presented based on the signal to noise ratio of each harmonic.</p> / Dissertation

Good process control is often critical for the economic viability of large-scale production of several commercial products. In this work, the production of biodiesel from microalgae is investigated. Successful implementation of a model-based control strategy requires the identification of a model that properly captures the biochemical dynamics of microalgae, yet is simple enough to allow its implementation for controller design. For this purpose, two model reparameterization algorithms are proposed that partition the parameter space into estimable and inestimable subspaces. Both algorithms are applied using a first principles ODE model of a microalgal bioreactor, containing 6 states and 12 unknown parameters. Based on initial simulations, the non-linear algorithm achieved better degree of output prediction when compared to the linear one at a greatly decreased computational cost. Using the parameter estimates obtained through implementation of the non-linear algorithm on experimental data from a fed-batch bioreactor, the possible improvement in volumetric productivity was recognized. / Process Control

O complexo 1,4-bis(2,6-diisopropilfenil)-acenaftenodiimina-dicloroníquel(II) (1), em combinação com metilaluminoxano (MAO) foi utilizado para polimerizar eteno utilizando altas pressões e temperaturas. Foram investigados os efeitos da pressão de eteno, da temperatura, do tempo de reação e da quantidade de catalisador bem como, as propriedades dos polietilenos sintetizados. Os polietilenos obtidos com o sistema (1)/MAO foram altamente ramificados. As ramificações variaram de metil até hexil ou até mais longas, sem adição de comonômero. Os polietilenos não apresentaram metilas isoladas, apresentando uma grande quantidade de metilas 1,4, metilas 1,5 e metilas 1,6 e cadeias longas. A presença de ramificações foi devido ao mecanismo denominado chain-walking. Os valores de ramificações nos PE foram maiores que 105 e menores que 277 ramificações/1000C. O aumento do número de ramificações foi devido ao aumento na temperatura de polimerização e uma diminuição da pressão de eteno. Os PE obtidos com o sistema (1)/MAO apresentaram peso molecular (Mw) elevado entre 44.000 e 105.000 Daltons e valores de polidispersão de 2,0 a 4,0, dependendo das condições reacionais. O peso molecular dos polímeros diminuiu com o aumento da temperatura de polimerização. / The combination of 1,4-bis(2,6-diisopropylphenyl)-acenaphthenediiminedichloronickel( II) (1) and methylaluminoxane (MAO) was highly active in ethylene polymerization under high pressures and temperatures. Herein we investigated the effects of ethylene pressure, reaction temperature, reaction time and amount of catalyst on polymer properties and reaction performance. The polyethylenes obtained with 1/MAO are highly branched. The branches goes from methyl to hexyl or even longer, and this without comonomer addition. These polyethylenes obtained do not shows isolated methyl groups, but shows 1,4-methyl, 1,5 and 1,6 methyl patterns. The branching was due to the so-called chain-walking mechanism. The branch content, which is in the range 105 to 277 branches/1000 C, increased with the temperature rising or the ethylene concentration decrease. The polyethylenes produced with these system have molecular weight between 44.000 and 105.000 Daltons and polydispersions from 2,0 to 4,0 depending on the reactions conditions. The polymer molecular weight tended to decrease with increasing polymerization temperature.