The Master’s thesis analyses the production planning in chosen company. Theoretical part focuses on terms, which are necessary to understand to deal with the issue of production planning. The practical part contains an analysis of the current state of production planning in the company, designs and their benefits to improve in this area.

Aircraft engines are one of the most heavily instrumented parts of an aircraft, and the data from various types of instrumentation across these engines are continuously monitored both offline and online for potential anomalies. Vibration monitoring in aircraft engines is traditionally performed using an order tracking methodology. Currently, there are no representative and efficient physics-based models with the adequate fidelity to perform vibration predictions in aircraft engines, given various parametric dependencies existing among different attributes such as temperature, pressure, and external conditions. This gap in research is primarily attributed to the limited understanding of mutual interactions of different variables and the nonlinear nature of engine vibrations. The objective of the current study is three-fold: (i) to present a preliminary investigation of tracked order vibrations in aircraft engines and statistically analyze them in the context of their operating environment, (ii) to develop data-driven modeling methodology to approximate a dynamical system from input-output data, and (iii) to leverage these data-driven modeling methodologies to develop highly accurate models for tracked order vibration in a turbo-fan engine valid over a wide range of operating conditions. Off-the-shelf data-driven modeling techniques, such as machine learning methods (eg., regression, neural networks), have several drawbacks including lack of interpretability and limited scope, when applying them to a complex multiscale multi-physical dynamical system. Moreover, for dynamical systems with external forcing, the identified model should not only be suitable for a specific forcing function, but should also generally approximate the input-output behavior of the data source. The author proposes a novel methodology known as Wavelet-based Dynamic Mode Decomposition (WDMD). The methodology entails using wavelets in conjunction with input-output dynamic mode decomposition (ioDMD). Similar to time-delay embedded DMD (Delay-DMD), WDMD builds on the ioDMD framework without the restrictive assumption of full state measurements. The author demonstrates the present methodology's applicability by modeling the input-output response of an Euler-Bernoulli finite element beam model, followed by an experimental investigation. As a first step towards modeling the tracked order vibration amplitudes of turbofan engines, the interdependencies and cross-correlation structure between various thermo-mechanical variables and tracked order vibration are analyzed. The order amplitudes are further contextualized in terms of their operating regime, and exploratory data analyses are performed to quantify the variability within each operating condition (OC). The understanding of complex correlation structures is leveraged and subsequently utilized to model tracked order vibrations. Switching linear dynamical system (SLDS) models are developed using individual data-driven models constructed using WDMD, and its performance in approximating the dynamics of the $1^{st}$ order amplitudes are compared with the state-of-the-art time-delay embedded dynamic mode decomposition (Delay-DMD) and Lasso regression. A parametric approach is proposed to improve the model further by leveraging previously developed WDMD and Delay-DMD methods and a parametric interpolation scheme. In particular, a recently developed pole-residue interpolation scheme is adopted to interpolate between several linear, data-driven reduced-order models (ROMs), constructed using WDMD and Delay-DMD surrogates, at known parameter samples. The parametric modeling approach is demonstrated by modeling the transverse vibration of an axially loaded finite element (FE) beam, where the axial loading is the parameter. Finally, a parametric modeling strategy for tracked order amplitudes is presented by constructing locally valid ROMs at different parametric samples corresponding to each pass-off test. The performance of the parametric-ROM is quantified and compared with the previous frameworks. This work was supported by the Rolls-Royce Fellowship, sponsored by the College of Engineering, Virginia Tech. / Doctor of Philosophy / Vibrations in commercial aircraft engines are of utmost importance as they directly translate to aviation health and safety, and hence are continuously monitored both online and offline for potential abnormalities. Notably, this is of increased interest with the abundance of air transportation in today's world. However, there is limited understanding of the complex higher vibration in aircraft engines. Vibration engineers often face ambiguity when interpreting higher vibrations. This can often lead to a lengthy investigative process resulting in longer downtime and increased testbed occupancy, ultimately leading to revenue loss. It is often hypothesized that prior engine running conditions such as shutdown/cooling time between one engine run to another engine run affect the vibration profile. Nonetheless, there exists a gap in understanding tying together various historical operational conditions, temperature, pressures, and current operational conditions with the expected vibration in the engine. This study aims to fill some of these gaps in our understanding by proposing a data-driven strategy to model the vibrations in commercial aircraft engines. Subsequently, this data-driven model can serve as a baseline model to compare the observed vibrations with the model predicted vibration and supplement physics-based models. The data for the present study is generated by operating a commercial turbofan engine in a testbed. With the advent of machine learning and data fusion, various data-driven techniques exist to model dynamical systems. However, the complexity of the turbofan engine vibrations calls for developing new techniques applicable towards modeling the vibration characteristics of a turbofan engine. Specifically, this dissertation details the development of a novel methodology called Wavelet-based Dynamic Mode Decomposition (WDMD) and applies the technique to model input-output characteristics of various dynamical systems ranging from a numerical finite element (FE) beam to an experimental free-free beam to shaft vibrations in a turbofan engine. The study finally presents an improved modeling framework by incorporating the existing techniques with parametric dependencies. This enables the existing method to consider slight differences existing from one engine run to another, such as the history of the engine, the shutdown time, and the outside environmental parameters.

Dentro da prática de verificação e projeto de estruturas metálicas, o cálculo de instabilidade exerce papel importante, já que o aço, por sua elevada resistência, incentiva o uso de colunas significativamente esbeltas. É comum na verificação da instabilidade de pórticos metálicos de andares múltiplos a utilização do conhecido fator K, que define, para a coluna, um comprimento efetivo. Tal fator é usualmente obtido em ábacos construídos a partir de duas hipóteses distintas para o mecanismo de instabilidade: a de flambagem por deslocamento lateral do andar e a de flambagem com esse deslocamento impedido. Essa divisão, e os modelos usualmente utilizados para tratá-la, se mostram incompletos para o caso de pórticos que se distanciem das hipóteses simplificadoras adotadas, e podem induzir a confusões e mal-entendido no uso do fator K. Neste trabalho, serão mostrados modelos alternativos para a determinação desse fator, buscando-se maior generalidade, assim como tentativas de esclarecer algumas possíveis ambiguidades no seu uso; além disso, esses modelos serão aplicados a alguns exemplos particulares. Como complemento ao trabalho, foi criado um programa de computador para determinar deslocamentos e esforços em segunda ordem para esse tipo de edificação, assim como ábacos alternativos. Os resultados obtidos nos exemplos serão contrastados com os fornecidos pelo programa e pelos ábacos. / In the practice of analysis and design of steel structures, instability calculations is a very important feature, since steel, for its high strength, motivates the use of significantly slender columns. It is usual in the analysis of multi-storey steel plane frames, the use of the K factor, that defines, for a column, an effective length. Such factor is usually obtained from nomograms, based on two different hypothesis for the instability mode: one with a side-way mode and the other with no lateral displacements. That division, and the models usually used to deal with, are incomplete to treat frames for which behaviour go away from the adopted hypothesis and simplifications, and they can induce to confusions and misunderstanding in the use of the K factor. In this work, alternative models will be shown for the determination of the K factor, looking for a larger generality, as well as attempting to clear ambiguities in its use; a series of examples will be then presented as applications of the models. As a complement, a computer program was created to determine first and second order nodal displacements and member forces, as well alternative nomograms; the results obtained from the models will be contrasted with those obtained from the program and the nomograms.

This research investigates the application of the AISC Direct Analysis Method for stability bracing design of columns, beams, beam-columns and frames. Emphasis is placed on out-of-plane flange bracing design in metal building frame systems. Potential improvements and extensions to the 2005 AISC Appendix 6 stability bracing provisions are studied and evaluated. The structural attributes considered include various general conditions encountered in practical metal building design: unequal brace spacing, unequal brace stiffness, nonprismatic member geometry, variable axial load or bending moment along the member length, cross-section double or single symmetry, combined bending and axial load, combined torsional and lateral bracing from girts/purlins with or without diagonal braces from these components to the inside flanges, load height, cross-section distortion, and non-rigid end boundary conditions. The research addresses both the simplification to basic bracing design rules as well as direct computation for more complex cases. The primary goal is improved assessment of the demands on flange bracing systems in metal building frames.

Dentro da prática de verificação e projeto de estruturas metálicas, o cálculo de instabilidade exerce papel importante, já que o aço, por sua elevada resistência, incentiva o uso de colunas significativamente esbeltas. É comum na verificação da instabilidade de pórticos metálicos de andares múltiplos a utilização do conhecido fator K, que define, para a coluna, um comprimento efetivo. Tal fator é usualmente obtido em ábacos construídos a partir de duas hipóteses distintas para o mecanismo de instabilidade: a de flambagem por deslocamento lateral do andar e a de flambagem com esse deslocamento impedido. Essa divisão, e os modelos usualmente utilizados para tratá-la, se mostram incompletos para o caso de pórticos que se distanciem das hipóteses simplificadoras adotadas, e podem induzir a confusões e mal-entendido no uso do fator K. Neste trabalho, serão mostrados modelos alternativos para a determinação desse fator, buscando-se maior generalidade, assim como tentativas de esclarecer algumas possíveis ambiguidades no seu uso; além disso, esses modelos serão aplicados a alguns exemplos particulares. Como complemento ao trabalho, foi criado um programa de computador para determinar deslocamentos e esforços em segunda ordem para esse tipo de edificação, assim como ábacos alternativos. Os resultados obtidos nos exemplos serão contrastados com os fornecidos pelo programa e pelos ábacos. / In the practice of analysis and design of steel structures, instability calculations is a very important feature, since steel, for its high strength, motivates the use of significantly slender columns. It is usual in the analysis of multi-storey steel plane frames, the use of the K factor, that defines, for a column, an effective length. Such factor is usually obtained from nomograms, based on two different hypothesis for the instability mode: one with a side-way mode and the other with no lateral displacements. That division, and the models usually used to deal with, are incomplete to treat frames for which behaviour go away from the adopted hypothesis and simplifications, and they can induce to confusions and misunderstanding in the use of the K factor. In this work, alternative models will be shown for the determination of the K factor, looking for a larger generality, as well as attempting to clear ambiguities in its use; a series of examples will be then presented as applications of the models. As a complement, a computer program was created to determine first and second order nodal displacements and member forces, as well alternative nomograms; the results obtained from the models will be contrasted with those obtained from the program and the nomograms.

Assessing the impact of inlet flow distortion in turbomachinery is desired early in the design cycle. This thesis introduces and validates the use of methods based on the Proper Orthogonal Decomposition (POD) to analyze clean and 1/rev static pressure distortion simulation results at design and near stall operating condition. The value of POD comes in its ability to efficiently extract both quantitative and qualitative information about dominant spatial flow structures as well as information about temporal fluctuations in flow properties. Observation of the modes allowed qualitative identification of shock waves as well as quantification of their location and range of motion. Modal coefficients revealed the location of the passage shock at a given angular location. Distortion amplification and attenuation between rotors was also identified. A relationship was identified between how distortion manifests itself based on downstream conditions. POD provides an efficient means for extracting the most meaningful information from large CFD simulation data. Static pressure and axial velocity were analyzed to explore the flow physics of 3 rotors of a compressor with a distorted inlet. Based on the results of the analysis of static pressure using the POD modes, it was concluded that there was a decreased range of motion in passage shock oscillation. Analysis of axial velocity POD modes revealed the presence of a separated region on the low pressure surface of the blade which was most dynamic in rotor 1. The thickness of this structure decreased in the near stall operating condition. The general conclusion is made that as the fan approaches stall the apparent effects of distortion are lessened which leads to less variation in the operating condition. This is due to the change in operating condition placing the fan at a different position on the speedline such that distortion effects are less pronounced. POD modes of entropy flux were used to identify three distinct levels of entropy flux in the blade row passage. The separated region was the region with the highest entropy due to the irreversibilities associated with separation.

Made available in DSpace on 2015-03-26T13:28:04Z (GMT). No. of bitstreams: 1 texto completo.pdf: 6612372 bytes, checksum: b13d5987ee6587979e4a1d61f6ce7737 (MD5) Previous issue date: 2011-03-01 / Fundação de Amparo a Pesquisa do Estado de Minas Gerais / This work presents the assessment of the application of second-order analysis to currents steel structures. Aspects related to the structural analysis, structural stability and design, are discussed according to the requirements of ABNT NBR8800:1986 and ABNT NBR8800:2008. The first-order analysis and the effective length approach are compared with the second-order analysis considering the initial imperfections proposed by ABNT NBR8800:2008. The results of the second-order analysis performed with a computer program are compared with the results obtained with the Notional Load Approach (MAES), regarded in the Annex D of ABNT NBR8800:2008. Eight case studies are presented in order to compare the responses of the different types of analysis carried out and to compare the results of the ultimate load-carrying capacity of structural members according to the methodology proposed by ABNT NBR8800:1986 and ABNT NBR8800:2008. It was found out that the results obtained with MAES were very close to those obtained with an approximated second-order analysis (ASO) performed with SAP2000. Moreover, it was noted a close proximity between the results of normal force, shear force and bending moment for the different types of analysis performed (APO, ASO and ASO-MAES), confirming the hypothesis that to "non-sway" frames the influence of second-order effects is not relevant. Regarding the ultimate load-carrying capacity verification of columns, it was found that the ABNT NBR8800:2008 interaction equation led, systematically, to a more economical design. On the other hand, the ABNT NBR8800:1986 approach, using the effective length concept, was always conservative. / Neste trabalho apresenta-se uma avaliação da aplicabilidade da análise de segunda ordem a estruturas de aço correntes. Aspectos relacionados à análise estrutural, à estabilidade estrutural e ao dimensionamento, são discutidos segundo as prescrições da ABNT NBR8800:1986 e da ABNT NBR8800:2008. A análise de primeira ordem e o método do coeficiente de flambagem (K) são avaliados e confrontados com a análise de segunda ordem e a consideração das imperfeições iniciais proposto pela ABNT NBR8800:2008. Os resultados das análises realizadas de acordo com as normas citadas anteriormente, obtidos com auxílio de um programa computacional, são comparados com os resultados obtidos por meio da aplicação do Método de Amplificação dos Esforços Solicitantes (MAES), previsto no Anexo D da ABNT NBR8800:2008. São apresentados oito estudos de caso com o intuito de comparar as respostas dos diferentes tipos de análise e comparar os resultados da verificação da capacidade última de elementos estruturais, segundo a metodologia proposta pela ABNT NBR8800:1986 e pela ABNT NBR8800:2008. Os resultados obtidos por meio do MAES foram muito próximos daqueles obtidos por meio da análise de segunda ordem aproximada (ASO), realizada com auxílio do programa computacional SAP 2000. Notou-se uma grande proximidade entre os resultados de esforços normal, cortante e momento fletor para os diferentes tipos de análise realizados (APO, ASO e ASO-MAES), confirmando a premissa de que em estruturas de pequena deslocabilidade a influência dos efeitos de segunda ordem não é relevante, ou seja, não há um aumento considerável dos esforços internos solicitantes. Com relação às verificações da capacidade última dos pilares, observou-se que a metodologia da ABNT NBR8800:2008 conduziu, sistematicamente, a um dimensionamento mais econômico. Por outro lado, a metodologia prevista na ABNT NBR8800:1986, que utiliza o conceito do comprimento efetivo de flambagem, mostrou-se sempre a favor da segurança.

This master thesis is focused on the diagnostics of vibrations and noise of an internal combustion engine. The work also includes a summary of the current state of knowledge in which the quantities used, transmission paths, measuring devices and the possibilities of performing frequency analysis are analysed. As part of the technical experiment on which this work is based, vibrations and noise on the tractor engine are measured. The obtained data are then further processed using the BK Connect program. Subsequently, a frequency analysis is performed, specifically an order analysis. The conclusion of the analysis consists of an evaluation of individual orders that cause excitation that occur in the investigated motor.

This thesis deals with a vibration diagnostics of objects, structures and machines. The theoretical part is divided into three chapters according to type of the measurement. The first part called Modal Analysis discusses the basis of vibration, methods of measurement, relevant technical equipment and principle of experimental modal analysis. The second and third chapters of the thesis are focused on the diagnosis of defects. Each chapter mentioned above describes diagnosed defects, used methods and procedure for the diagnosis. Another part of the thesis summarizes practical issues and results gained in the laboratory experiments. It begins with discovering parameters of the measured object using technical diagnostics – experimental modal analysis. In the next step the hardware concept design was created, including custom measuring application programmed in LabVIEW. One part of the design is the laboratory model which includes a structure for free mounting and a possibility of excitation by an electrodynamic exciter. The application is also modified to enable measurements with shaker excitation. Finally, applications cooperating with professional software ModalVIEW and BK Connect were developed in order to simplify the operation and increase the comfort.

Este trabalho apresenta uma análise comparativa de diferentes sistemas estruturais para um edifício de 20 pavimentos. Cada um dos modelos foi dimensionado através dos princípios do método da análise direta, presente na ABNT NBR 8800:2008. O método da amplificação dos esforços solicitantes (MAES) foi usado para se obter de forma simplificada os esforços atuantes nos elementos do edifício considerando os efeitos locais e globais de segunda ordem. A incidência do vento foi simulada de duas formas diferentes. Na primeira, chamada de uniforme, o vento foi aplicado sem excentricidade, gerando apenas o efeito de tombamento nas estruturas. Na segunda hipótese, considerou-se uma excentricidade devida aos efeitos de vizinhança, prescrita pela ABNT NBR 6123:1988, responsável por ocasionar o tombamento e a torção dos edifícios. Todas as análises numéricas foram repetidas fazendo o uso de outro método simplificado de segunda ordem, conhecido como P-Delta. Por meio dos resultados obtidos, constatou-se que a possibilidade de se reduzir a sobrecarga para o dimensionamento de pilares proporciona uma economia de material, mas, por outro lado, tem como consequência o aumento do tempo de análise, pois exige a utilização de diferentes combinações de cálculo para o dimensionamento de vigas e pilares. A estratégia utilizada para simular os efeitos de vizinhança mostrou-se satisfatória, pois permitiu introduzir de maneira fácil e prática a torção ocasionada pela incidência excêntrica do vento. Observou-se também que esses efeitos ocasionaram o aumento dos momentos fletores e dos deslocamentos das estruturas analisadas. Em relação à avaliação dos efeitos de segunda ordem, comprovou-se que, para a classificação da deslocabilidade, a combinação de cálculo crítica é aquela que possui o maior carregamento gravitacional. Entretanto, para o dimensionamento dos elementos, foi constatado que outras hipóteses de cálculo, principalmente aquelas em que o vento é a ação variável principal, podem ser determinantes. Por fim, foi observado que os resultados obtidos pelo método P-Delta ficaram bastante semelhantes àqueles calculados pelo MAES, com desvios desprezíveis. O MAES, por sua vez, mostrou-se bastante trabalhoso, pois exige a modelagem de diferentes tipos de estruturas para a determinação dos esforços. / This work presents a comparative analysis of different structural systems for a 20-storey building. Each model has been designed using the principles of the direct analysis method (DAM), present in the ABNT NBR 8800:2008. The first-order amplification method (FOAM) was used to obtain, in a simplified manner, the forces acting on the building elements, including local and global second-order effects. The incidence of the wind was simulated in two different ways. In the first case, named uniform, the wind was applied without eccentricity, generating only structure overturning. In the second case, it was considered an eccentricity due to vicinity effects, prescribed by the ABNT NBR 6123:1988, responsible for causing twisting and building overturning. All numerical analysis were carried out a simplified second-order method known as P-Delta. From the results obtained it was found that the reduction of live loads in the design of columns provides material economy, but on the other hand, increases analysis time, since it requires different combinations for beams and columns. The strategy used to simulate the vicinity effects was satisfactory, because it allowed, in an easy and practical way, the consideration of the torsion produced by the wind eccentric impact. It was also observed that these effects increased the bending moments and the displacements of the structures. About the second-order effects, it was shown that, for sway or non-sway classification, the critical combination is one with greatest gravitational loading. However, for the design of the elements, it was observed that other loading conditions can be critical, especially those in which the wind is the main live load. Finally, the results obtained by the P-Delta method were very similar to those calculated by the first-order amplification method. The FOAM was, in turn, very laborious, because it requires the modeling of different types of structures for the determination of the forces.