Reducing tire rolling resistance and energy loss is a topic of interest to the tire industry. Und... more Reducing tire rolling resistance and energy loss is a topic of interest to the tire industry. Understanding and modeling these phenomena are essential to approach this problem and propose robust solutions. This work suggests a reduced-order model based on the Bouc-Wen model to simulate internal variables from viscoelastic constitutive laws. Furthermore, sensitivity analysis is performed on the Bouc-Wen parameters to evaluate their influence on the system response and capture the full range of possible values that improve the predictive ability of the reduced-order model. This task is accomplished by calculating the Sobol's indices estimated from a Polynomial-Chaos expansion. Once the range of feasible model solutions is established, the reduced-order model is calibrated through Bayesian inference. Finally, the uncertainties are propagated, and the reduced-order model is validated using data of viscoelastic internal variables from the finite element approximation of a steady-rolling tire. Satisfactory results are obtained, as the reduced-order model can simulate viscoelastic internal variables with a reduced computational cost for some branches of interest. Its responses are in agreement with the experimental data.
to reduce the dynamics of interest by assuming a quasi-steady state for the electrical subsystem,... more to reduce the dynamics of interest by assuming a quasi-steady state for the electrical subsystem, eliminating the inductive term from the electrical equation. Numerical experiments help to illustrate the typical behavior of the electromechanical system, a boundary layer phenomenon near the initial dynamic state, and the validity limits of the electromechanical quasisteady-state assumption discussed here.
Parametric variability is inevitable in actual energy harvesters. It can significantly affect cru... more Parametric variability is inevitable in actual energy harvesters. It can significantly affect crucial aspects of the system performance, especially in harvesting systems that present geometric parameters, material properties, or excitation conditions that are susceptible to small perturbations. This work aims to develop an investigation to identify the most critical parameters in the dynamic behavior of asymmetric bistable energy harvesters with nonlinear piezoelectric coupling, considering the variability of their physical and excitation properties. For this purpose, a global sensitivity analysis based on orthogonal variance decomposition, employing Sobol indices, is performed to quantify the effect of the harvester parameters on the variance of the recovered power. This technique quantifies the variance concerning each parameter individ-Supplementary Information The online version contains supplementary material available at
Structural Health Monitoring An International Journal, 2022
In the present work, two issues that can complicate a damage detection process are considered: th... more In the present work, two issues that can complicate a damage detection process are considered: the uncertainties and the intrinsically nonlinear behavior. To deal with these issues, a stochastic version of the Volterra series is proposed as a baseline model, and novelty detection is applied to distinguish the condition of the structure between a reference baseline state (presumed ''healthy'') and damaged. The studied system exhibits nonlinear behavior even in the reference condition, and it is exposed to a type of damage that causes the structure to display a nonlinear behavior with a different nature than the initial one. In addition, the uncertainties associated with data variation are taken into account in the application of the methodology. The results confirm that the monitoring of nonlinear coefficients and nonlinear components of the system response enables the method to detect the presence of the damage earlier than the application of some linear-based metrics. Besides that, the stochastic treatment enables the specification of a probabilistic interval of confidence for the system response in an uncertain ambient, thus providing more robust and reliable forecasts.
Chaotic vibrations may appear in nonlinear energy harvesting systems, which can be problematic wh... more Chaotic vibrations may appear in nonlinear energy harvesting systems, which can be problematic when using the recovered power, as it may require an extra expenditure of energy to rectify the voltage signal or reduce the harvesting process efficiency when charging the battery. Both cases can derail the energy harvester's functionality. An alternative in this situation is to explore chaos control to stabilize the system dynamics so that the recovered voltage signal is regular and more suitable for use in the applications of interest. This paper address this problem employing an extended delayed feedback method that combines a displacement actuator and a digital controller to implement the control mechanism. The control strategy is mathematically formulated and tested in a bistable energy harvesting system that often operates in a chaotic regime. The controller shows itself capable of stabilizing the chaotic dynamics at a very low energetic cost.
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2022
The severe acute respiratory syndrome of coronavirus 2 spread globally very quickly, causing grea... more The severe acute respiratory syndrome of coronavirus 2 spread globally very quickly, causing great concern at the international level due to the severity of the associated respiratory disease, the so-called COVID-19. Considering Rio de Janeiro city (Brazil) as an example, the first diagnosis of this disease occurred in March 2020, but the exact moment when the local spread of the virus started is uncertain as the Brazilian epidemiological surveillance system was not widely prepared to detect suspected cases of COVID-19 at that time. Improvements in this surveillance system occurred over the pandemic, but due to the complex nature of the disease transmission process, specifying the exact moment of emergence of new community contagion outbreaks is a complicated task. This work aims to propose a general methodology to determine possible start dates for the multiple community outbreaks of COVID-19, using for this purpose a parametric statistical approach that combines surveillance data, nonlinear regression, and information criteria to obtain a statistical model capable of describing the multiple waves of contagion observed. The dynamics of COVID-19 in the city of Rio de Janeiro is taken as a case study, and the results suggest that the original strain of the virus was already circulating in Rio de Janeiro city as early as late February 2020, probably being massively disseminated in the population during the carnival festivities.
Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2022
Volterra series is a widely used tool for identifying physical systems with polynomial nonlineari... more Volterra series is a widely used tool for identifying physical systems with polynomial nonlinearities. In this approach, the Volterra kernels expanded using Kautz functions can be identified using several techniques to optimize the filters' poles. This methodology is very efficient when the system observations are not subject to high noise-induced variabilities (uncertainties). However, this optimization procedure may not be effective when the uncertainty level is increased since the optimal value might be susceptible to small perturbations. Seeking to overcome this weakness, the present work proposes a new stochastic method of identification based on the Volterra series, which does not solve an optimization problem. In this new approach, the Volterra kernels are described as stochastic processes. The parameters of Kautz filters are considered independent random variables so that their probability distribution captures the variabilities. The effectiveness of the new technique is tested experimentally in a nonlinear mechanical system. The results show that the identified stochastic Volterra kernels can reproduce the nonlinear dynamics characteristics and the data variability.
The COVID-19 pandemic has given rise to a great demand for computational models capable of descri... more The COVID-19 pandemic has given rise to a great demand for computational models capable of describing and inferring the evolution of an epidemic outbreak in the short term. In this sense, we introduce epidWaves, a package that provides a framework for fitting multi-wave epidemic models to data from actual outbreaks of COVID-19 and other infectious diseases. Code metadata Current code version v1.
The ongoing pandemic of COVID-19 has highlighted the importance of mathematical tools to understa... more The ongoing pandemic of COVID-19 has highlighted the importance of mathematical tools to understand and predict outbreaks of severe infectious diseases, including arboviruses such as Zika. To this end, we introduce ARBO, a package for simulation and analysis of arbovirus nonlinear dynamics. The implementation follows a minimalist style, and is intuitive and extensible to many settings of vector-borne disease outbreaks. This paper outlines the main tools that compose ARBO, discusses how recent research works about the Brazilian Zika outbreak have explored the package's capabilities, and describes its potential impact for future works on mathematical epidemiology.
The simulation of reactive flows is a very challenging task from the computational point of view,... more The simulation of reactive flows is a very challenging task from the computational point of view, as in addition to taking into account all the complex aspects of fluid dynamics, it requires a detailed description of the chemical kinetics involved in the process. Thus, the use of strategies to reduce simulation time is essential. Among the existing reduction techniques, the In Situ Adaptive Tabulation (ISAT) is one of the most promising since it offers a good compromise between accuracy and cost reduction. This paper presents the CRFlowLib, a computational package to simulate chemically reacting flows using ISAT algorithm Code metadata Current code version 2.0
STONEHENGE is a toolbox designed to evaluate nonlinear vibration-based energy harvesting systems,... more STONEHENGE is a toolbox designed to evaluate nonlinear vibration-based energy harvesting systems, which demand careful studies regarding their nontrivial behavior. It is composed of an ensemble of codes to study and characterize the dynamic behavior, as well as deal with varieties of physical parameters and excitation. For this, it has six modules, initial value problem, dynamic animation, nonlinear tools, sensitivity analysis, stochastic simulation, and chaos control. A bistable oscillator is used as a benchmark for a vibration harvester. We hope this toolbox can contribute to the development and improvement of old and new generations of nonlinear vibration-based energy harvesting systems.
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering, 2021
This study aims to address the question: can the structural reliability of an offshore wind turbi... more This study aims to address the question: can the structural reliability of an offshore wind turbine (OWT) under fatigue loading conditions be predicted more consistently? To respond to that question this study addresses the following specific aims: (1) to obtain a systematic approach that takes into consideration the amount of information available for the uncertainty modeling of the model input parameters and (2) to determine the impact of the most sensitive input parameters on the structural reliability of the OWT through a surrogate model. First, a coupled model to determine the fatigue life of the support structure considering the soil-structure interaction under 15 different loading conditions was developed. Second, a sensitivity scheme using two global analyses was developed to consistently establish the most and least important input parameters of the model. Third, systematic uncertainty quantification (UQ) scheme was employed to model the uncertainties of model input parameters based on their available-data-driven and physics-informed-information. Finally, the impact of the proposed UQ framework on the OWT structural reliability was evaluated through the estimation of the probability of failure of the structure based on the fatigue limit state design criterion. The results show high sensitivity for the wind speed and moderate sensitivity for parameters usually considered as deterministic values in design standards. Additionally, it is shown that applying systematic UQ not only produces a more efficient and better approximation of the fatigue life under uncertainty, but also a more accurate estimation of the structural reliability of offshore wind turbine's structure during conceptual design. Consequently, more reliable, and robust estimations of the structural designs for large offshore wind turbines with limited information may be achieved during the early stages of design.
This study aims to investigate the performance of a data-driven methodology for quantifying damag... more This study aims to investigate the performance of a data-driven methodology for quantifying damage based on the use of a metamodel obtained from the Polynomial Chaos-Kriging method. The investigation seeks to quantify the severity of the damage, described by a specific type of debonding in a wind turbine blade as a function of a damage index. The damage indexes used are computed using a data-driven vibration-based structural health monitoring methodology. The blade’s debonding damage is introduced artificially, and the blade is excited with an electromechanical actuator that introduces a mechanical impulse causing the impact on the blade. The acceleration responses’ vibrations are measured by accelerometers distributed along the trailing and the wind turbine blade. A metamodel is formerly obtained through the Polynomial Chaos-Kriging method based on the damage indexes, trained with the blade’s healthy condition and four damage conditions, and validated with the other two damage conditions. The Polynomial Chaos-Kriging manifests promising results for capturing the proper trend for the severity of the damage as a function of the damage index. This research complements the damage detection analyses previously performed on the same blade.
This work deals with the solution of a non-convex optimization problem to enhance the performance... more This work deals with the solution of a non-convex optimization problem to enhance the performance of an energy harvesting device, which involves a nonlinear objective function and a discontinuous constraint. This optimization problem, which seeks to find a suitable configuration of parameters that maximize the electrical power recovered by a bistable energy harvesting system, is formulated in terms of the dynamical system response and a binary classifier obtained from 0 to 1 test for chaos. A stochastic solution strategy that combines penalization and the cross-entropy method is proposed and numerically tested. Computational experiments are conducted to address the performance of the proposed optimization approach by comparison with a reference solution, obtained via an exhaustive search in a refined numerical mesh. The obtained results illustrate the effectiveness and robustness of the cross-entropy optimization strategy (even in the presence of noise or in moderately higher dimensions), showing that the proposed framework may be a very useful and powerful tool to solve optimization problems involving nonlinear energy harvesting dynamical systems.
Journal of Verification, Validation and Uncertainty Quantification, 2020
The advent of state-of-the-art additive manufacturing (AM) processes has facilitated the manufact... more The advent of state-of-the-art additive manufacturing (AM) processes has facilitated the manufacturing of complex orthopedic metallic implants such as femoral stems with porous portions based on lattice structures. These struts often have rough and not smooth textured surfaces, for which the irregularities may influence mechanical properties. To make robust predictions about the behavior of this kind of system, the variability effect of its parameters on the stem stiffness must be considered in the processes of modeling and design of porous femoral stems. Also, to improve the credibility of computational models used for hip implant analysis, which involves numerous uncertainties, there is a need for rigorous uncertainty quantification (UQ) framework for proper model assessment following a credible-modeling standard. This work proposes a UQ framework in the presence of sparsely characterized input parameters using the maximum entropy principle for analyzing a femoral stem implant model and thus to clarify how uncertainties impact the key properties of a porous femoral stem. In this study, uncertainties in the strut thickness, pore size, Young's modulus, and external forcing are considered. The UQ framework is validated using experimental results available from literature, following the guidelines set in an ASME standard.
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2020
Mathematical models of epidemiological systems enable investigation of and predictions about pote... more Mathematical models of epidemiological systems enable investigation of and predictions about potential disease outbreaks. However, commonly used models are often highly simplified representations of incredibly complex systems. Because of these simplifications, the model output, of say new cases of a disease over time, or when an epidemic will occur, may be inconsistent with available data. In this case, we must improve the model, especially if we plan to make decisions based on it that could affect human health and safety, but direct improvements are often beyond our reach. In this work, we explore this problem through a case study of the Zika outbreak in Brazil in 2016. We propose an embedded discrepancy operator—a modification to the model equations that requires modest information about the system and is calibrated by all relevant data. We show that the new enriched model demonstrates greatly increased consistency with real data. Moreover, the method is general enough to easily apply to many other mathematical models in epidemiology.
Structural Health Monitoring An International Journal, 2020
In the present work, two issues that can complicate a damage detection process are considered: th... more In the present work, two issues that can complicate a damage detection process are considered: the uncertainties and the intrinsically nonlinear behavior. To deal with these issues, a stochastic version of the Volterra series is proposed as a base-line model, and novelty detection is applied to distinguish the condition of the structure between a reference baseline state (presumed ''healthy'') and damaged. The studied system exhibits nonlinear behavior even in the reference condition , and it is exposed to a type of damage that causes the structure to display a nonlinear behavior with a different nature than the initial one. In addition, the uncertainties associated with data variation are taken into account in the application of the methodology. The results confirm that the monitoring of nonlinear coefficients and nonlinear components of the system response enables the method to detect the presence of the damage earlier than the application of some linear-based metrics. Besides that, the stochastic treatment enables the specification of a probabilistic interval of confidence for the system response in an uncertain ambient, thus providing more robust and reliable forecasts.
This work proposes a parametric probabilistic approach to model damage accumulation using the dou... more This work proposes a parametric probabilistic approach to model damage accumulation using the double linear damage rule (DLDR) considering the existence of limited experimental fatigue data. A probabilistic version of DLDR is developed in which the joint distribution of the knee-point coordinates is obtained as a function of the joint distribution of the DLDR model input parameters. Considering information extracted from experiments containing a limited number of data points, an uncertainty quantification framework based on the Maximum Entropy Principle and Monte Carlo simulations is proposed to determine the distribution of fatigue life. The proposed approach is validated using fatigue life experiments available in the literature.
This paper deals with nonlinear mechanics of an elevator brake system subjected to uncertainties.... more This paper deals with nonlinear mechanics of an elevator brake system subjected to uncertainties. A deterministic model that relates the braking force with uncertain parameters is deduced from mechanical equilibrium conditions. In order to take into account parameters variabilities, a parametric probabilistic approach is employed. In this stochastic formalism, the uncertain parameters are modeled as random variables, with distributions specified by the maximum entropy principle. The uncertainties are propagated by the Monte Carlo method, which provides a detailed statistical characterization of the response. This work still considers the optimum design of the brake system, formulating and solving nonlinear optimization problems, with and without the uncertainties effects.
Reducing tire rolling resistance and energy loss is a topic of interest to the tire industry. Und... more Reducing tire rolling resistance and energy loss is a topic of interest to the tire industry. Understanding and modeling these phenomena are essential to approach this problem and propose robust solutions. This work suggests a reduced-order model based on the Bouc-Wen model to simulate internal variables from viscoelastic constitutive laws. Furthermore, sensitivity analysis is performed on the Bouc-Wen parameters to evaluate their influence on the system response and capture the full range of possible values that improve the predictive ability of the reduced-order model. This task is accomplished by calculating the Sobol's indices estimated from a Polynomial-Chaos expansion. Once the range of feasible model solutions is established, the reduced-order model is calibrated through Bayesian inference. Finally, the uncertainties are propagated, and the reduced-order model is validated using data of viscoelastic internal variables from the finite element approximation of a steady-rolling tire. Satisfactory results are obtained, as the reduced-order model can simulate viscoelastic internal variables with a reduced computational cost for some branches of interest. Its responses are in agreement with the experimental data.
to reduce the dynamics of interest by assuming a quasi-steady state for the electrical subsystem,... more to reduce the dynamics of interest by assuming a quasi-steady state for the electrical subsystem, eliminating the inductive term from the electrical equation. Numerical experiments help to illustrate the typical behavior of the electromechanical system, a boundary layer phenomenon near the initial dynamic state, and the validity limits of the electromechanical quasisteady-state assumption discussed here.
Parametric variability is inevitable in actual energy harvesters. It can significantly affect cru... more Parametric variability is inevitable in actual energy harvesters. It can significantly affect crucial aspects of the system performance, especially in harvesting systems that present geometric parameters, material properties, or excitation conditions that are susceptible to small perturbations. This work aims to develop an investigation to identify the most critical parameters in the dynamic behavior of asymmetric bistable energy harvesters with nonlinear piezoelectric coupling, considering the variability of their physical and excitation properties. For this purpose, a global sensitivity analysis based on orthogonal variance decomposition, employing Sobol indices, is performed to quantify the effect of the harvester parameters on the variance of the recovered power. This technique quantifies the variance concerning each parameter individ-Supplementary Information The online version contains supplementary material available at
Structural Health Monitoring An International Journal, 2022
In the present work, two issues that can complicate a damage detection process are considered: th... more In the present work, two issues that can complicate a damage detection process are considered: the uncertainties and the intrinsically nonlinear behavior. To deal with these issues, a stochastic version of the Volterra series is proposed as a baseline model, and novelty detection is applied to distinguish the condition of the structure between a reference baseline state (presumed ''healthy'') and damaged. The studied system exhibits nonlinear behavior even in the reference condition, and it is exposed to a type of damage that causes the structure to display a nonlinear behavior with a different nature than the initial one. In addition, the uncertainties associated with data variation are taken into account in the application of the methodology. The results confirm that the monitoring of nonlinear coefficients and nonlinear components of the system response enables the method to detect the presence of the damage earlier than the application of some linear-based metrics. Besides that, the stochastic treatment enables the specification of a probabilistic interval of confidence for the system response in an uncertain ambient, thus providing more robust and reliable forecasts.
Chaotic vibrations may appear in nonlinear energy harvesting systems, which can be problematic wh... more Chaotic vibrations may appear in nonlinear energy harvesting systems, which can be problematic when using the recovered power, as it may require an extra expenditure of energy to rectify the voltage signal or reduce the harvesting process efficiency when charging the battery. Both cases can derail the energy harvester's functionality. An alternative in this situation is to explore chaos control to stabilize the system dynamics so that the recovered voltage signal is regular and more suitable for use in the applications of interest. This paper address this problem employing an extended delayed feedback method that combines a displacement actuator and a digital controller to implement the control mechanism. The control strategy is mathematically formulated and tested in a bistable energy harvesting system that often operates in a chaotic regime. The controller shows itself capable of stabilizing the chaotic dynamics at a very low energetic cost.
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2022
The severe acute respiratory syndrome of coronavirus 2 spread globally very quickly, causing grea... more The severe acute respiratory syndrome of coronavirus 2 spread globally very quickly, causing great concern at the international level due to the severity of the associated respiratory disease, the so-called COVID-19. Considering Rio de Janeiro city (Brazil) as an example, the first diagnosis of this disease occurred in March 2020, but the exact moment when the local spread of the virus started is uncertain as the Brazilian epidemiological surveillance system was not widely prepared to detect suspected cases of COVID-19 at that time. Improvements in this surveillance system occurred over the pandemic, but due to the complex nature of the disease transmission process, specifying the exact moment of emergence of new community contagion outbreaks is a complicated task. This work aims to propose a general methodology to determine possible start dates for the multiple community outbreaks of COVID-19, using for this purpose a parametric statistical approach that combines surveillance data, nonlinear regression, and information criteria to obtain a statistical model capable of describing the multiple waves of contagion observed. The dynamics of COVID-19 in the city of Rio de Janeiro is taken as a case study, and the results suggest that the original strain of the virus was already circulating in Rio de Janeiro city as early as late February 2020, probably being massively disseminated in the population during the carnival festivities.
Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2022
Volterra series is a widely used tool for identifying physical systems with polynomial nonlineari... more Volterra series is a widely used tool for identifying physical systems with polynomial nonlinearities. In this approach, the Volterra kernels expanded using Kautz functions can be identified using several techniques to optimize the filters' poles. This methodology is very efficient when the system observations are not subject to high noise-induced variabilities (uncertainties). However, this optimization procedure may not be effective when the uncertainty level is increased since the optimal value might be susceptible to small perturbations. Seeking to overcome this weakness, the present work proposes a new stochastic method of identification based on the Volterra series, which does not solve an optimization problem. In this new approach, the Volterra kernels are described as stochastic processes. The parameters of Kautz filters are considered independent random variables so that their probability distribution captures the variabilities. The effectiveness of the new technique is tested experimentally in a nonlinear mechanical system. The results show that the identified stochastic Volterra kernels can reproduce the nonlinear dynamics characteristics and the data variability.
The COVID-19 pandemic has given rise to a great demand for computational models capable of descri... more The COVID-19 pandemic has given rise to a great demand for computational models capable of describing and inferring the evolution of an epidemic outbreak in the short term. In this sense, we introduce epidWaves, a package that provides a framework for fitting multi-wave epidemic models to data from actual outbreaks of COVID-19 and other infectious diseases. Code metadata Current code version v1.
The ongoing pandemic of COVID-19 has highlighted the importance of mathematical tools to understa... more The ongoing pandemic of COVID-19 has highlighted the importance of mathematical tools to understand and predict outbreaks of severe infectious diseases, including arboviruses such as Zika. To this end, we introduce ARBO, a package for simulation and analysis of arbovirus nonlinear dynamics. The implementation follows a minimalist style, and is intuitive and extensible to many settings of vector-borne disease outbreaks. This paper outlines the main tools that compose ARBO, discusses how recent research works about the Brazilian Zika outbreak have explored the package's capabilities, and describes its potential impact for future works on mathematical epidemiology.
The simulation of reactive flows is a very challenging task from the computational point of view,... more The simulation of reactive flows is a very challenging task from the computational point of view, as in addition to taking into account all the complex aspects of fluid dynamics, it requires a detailed description of the chemical kinetics involved in the process. Thus, the use of strategies to reduce simulation time is essential. Among the existing reduction techniques, the In Situ Adaptive Tabulation (ISAT) is one of the most promising since it offers a good compromise between accuracy and cost reduction. This paper presents the CRFlowLib, a computational package to simulate chemically reacting flows using ISAT algorithm Code metadata Current code version 2.0
STONEHENGE is a toolbox designed to evaluate nonlinear vibration-based energy harvesting systems,... more STONEHENGE is a toolbox designed to evaluate nonlinear vibration-based energy harvesting systems, which demand careful studies regarding their nontrivial behavior. It is composed of an ensemble of codes to study and characterize the dynamic behavior, as well as deal with varieties of physical parameters and excitation. For this, it has six modules, initial value problem, dynamic animation, nonlinear tools, sensitivity analysis, stochastic simulation, and chaos control. A bistable oscillator is used as a benchmark for a vibration harvester. We hope this toolbox can contribute to the development and improvement of old and new generations of nonlinear vibration-based energy harvesting systems.
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering, 2021
This study aims to address the question: can the structural reliability of an offshore wind turbi... more This study aims to address the question: can the structural reliability of an offshore wind turbine (OWT) under fatigue loading conditions be predicted more consistently? To respond to that question this study addresses the following specific aims: (1) to obtain a systematic approach that takes into consideration the amount of information available for the uncertainty modeling of the model input parameters and (2) to determine the impact of the most sensitive input parameters on the structural reliability of the OWT through a surrogate model. First, a coupled model to determine the fatigue life of the support structure considering the soil-structure interaction under 15 different loading conditions was developed. Second, a sensitivity scheme using two global analyses was developed to consistently establish the most and least important input parameters of the model. Third, systematic uncertainty quantification (UQ) scheme was employed to model the uncertainties of model input parameters based on their available-data-driven and physics-informed-information. Finally, the impact of the proposed UQ framework on the OWT structural reliability was evaluated through the estimation of the probability of failure of the structure based on the fatigue limit state design criterion. The results show high sensitivity for the wind speed and moderate sensitivity for parameters usually considered as deterministic values in design standards. Additionally, it is shown that applying systematic UQ not only produces a more efficient and better approximation of the fatigue life under uncertainty, but also a more accurate estimation of the structural reliability of offshore wind turbine's structure during conceptual design. Consequently, more reliable, and robust estimations of the structural designs for large offshore wind turbines with limited information may be achieved during the early stages of design.
This study aims to investigate the performance of a data-driven methodology for quantifying damag... more This study aims to investigate the performance of a data-driven methodology for quantifying damage based on the use of a metamodel obtained from the Polynomial Chaos-Kriging method. The investigation seeks to quantify the severity of the damage, described by a specific type of debonding in a wind turbine blade as a function of a damage index. The damage indexes used are computed using a data-driven vibration-based structural health monitoring methodology. The blade’s debonding damage is introduced artificially, and the blade is excited with an electromechanical actuator that introduces a mechanical impulse causing the impact on the blade. The acceleration responses’ vibrations are measured by accelerometers distributed along the trailing and the wind turbine blade. A metamodel is formerly obtained through the Polynomial Chaos-Kriging method based on the damage indexes, trained with the blade’s healthy condition and four damage conditions, and validated with the other two damage conditions. The Polynomial Chaos-Kriging manifests promising results for capturing the proper trend for the severity of the damage as a function of the damage index. This research complements the damage detection analyses previously performed on the same blade.
This work deals with the solution of a non-convex optimization problem to enhance the performance... more This work deals with the solution of a non-convex optimization problem to enhance the performance of an energy harvesting device, which involves a nonlinear objective function and a discontinuous constraint. This optimization problem, which seeks to find a suitable configuration of parameters that maximize the electrical power recovered by a bistable energy harvesting system, is formulated in terms of the dynamical system response and a binary classifier obtained from 0 to 1 test for chaos. A stochastic solution strategy that combines penalization and the cross-entropy method is proposed and numerically tested. Computational experiments are conducted to address the performance of the proposed optimization approach by comparison with a reference solution, obtained via an exhaustive search in a refined numerical mesh. The obtained results illustrate the effectiveness and robustness of the cross-entropy optimization strategy (even in the presence of noise or in moderately higher dimensions), showing that the proposed framework may be a very useful and powerful tool to solve optimization problems involving nonlinear energy harvesting dynamical systems.
Journal of Verification, Validation and Uncertainty Quantification, 2020
The advent of state-of-the-art additive manufacturing (AM) processes has facilitated the manufact... more The advent of state-of-the-art additive manufacturing (AM) processes has facilitated the manufacturing of complex orthopedic metallic implants such as femoral stems with porous portions based on lattice structures. These struts often have rough and not smooth textured surfaces, for which the irregularities may influence mechanical properties. To make robust predictions about the behavior of this kind of system, the variability effect of its parameters on the stem stiffness must be considered in the processes of modeling and design of porous femoral stems. Also, to improve the credibility of computational models used for hip implant analysis, which involves numerous uncertainties, there is a need for rigorous uncertainty quantification (UQ) framework for proper model assessment following a credible-modeling standard. This work proposes a UQ framework in the presence of sparsely characterized input parameters using the maximum entropy principle for analyzing a femoral stem implant model and thus to clarify how uncertainties impact the key properties of a porous femoral stem. In this study, uncertainties in the strut thickness, pore size, Young's modulus, and external forcing are considered. The UQ framework is validated using experimental results available from literature, following the guidelines set in an ASME standard.
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2020
Mathematical models of epidemiological systems enable investigation of and predictions about pote... more Mathematical models of epidemiological systems enable investigation of and predictions about potential disease outbreaks. However, commonly used models are often highly simplified representations of incredibly complex systems. Because of these simplifications, the model output, of say new cases of a disease over time, or when an epidemic will occur, may be inconsistent with available data. In this case, we must improve the model, especially if we plan to make decisions based on it that could affect human health and safety, but direct improvements are often beyond our reach. In this work, we explore this problem through a case study of the Zika outbreak in Brazil in 2016. We propose an embedded discrepancy operator—a modification to the model equations that requires modest information about the system and is calibrated by all relevant data. We show that the new enriched model demonstrates greatly increased consistency with real data. Moreover, the method is general enough to easily apply to many other mathematical models in epidemiology.
Structural Health Monitoring An International Journal, 2020
In the present work, two issues that can complicate a damage detection process are considered: th... more In the present work, two issues that can complicate a damage detection process are considered: the uncertainties and the intrinsically nonlinear behavior. To deal with these issues, a stochastic version of the Volterra series is proposed as a base-line model, and novelty detection is applied to distinguish the condition of the structure between a reference baseline state (presumed ''healthy'') and damaged. The studied system exhibits nonlinear behavior even in the reference condition , and it is exposed to a type of damage that causes the structure to display a nonlinear behavior with a different nature than the initial one. In addition, the uncertainties associated with data variation are taken into account in the application of the methodology. The results confirm that the monitoring of nonlinear coefficients and nonlinear components of the system response enables the method to detect the presence of the damage earlier than the application of some linear-based metrics. Besides that, the stochastic treatment enables the specification of a probabilistic interval of confidence for the system response in an uncertain ambient, thus providing more robust and reliable forecasts.
This work proposes a parametric probabilistic approach to model damage accumulation using the dou... more This work proposes a parametric probabilistic approach to model damage accumulation using the double linear damage rule (DLDR) considering the existence of limited experimental fatigue data. A probabilistic version of DLDR is developed in which the joint distribution of the knee-point coordinates is obtained as a function of the joint distribution of the DLDR model input parameters. Considering information extracted from experiments containing a limited number of data points, an uncertainty quantification framework based on the Maximum Entropy Principle and Monte Carlo simulations is proposed to determine the distribution of fatigue life. The proposed approach is validated using fatigue life experiments available in the literature.
This paper deals with nonlinear mechanics of an elevator brake system subjected to uncertainties.... more This paper deals with nonlinear mechanics of an elevator brake system subjected to uncertainties. A deterministic model that relates the braking force with uncertain parameters is deduced from mechanical equilibrium conditions. In order to take into account parameters variabilities, a parametric probabilistic approach is employed. In this stochastic formalism, the uncertain parameters are modeled as random variables, with distributions specified by the maximum entropy principle. The uncertainties are propagated by the Monte Carlo method, which provides a detailed statistical characterization of the response. This work still considers the optimum design of the brake system, formulating and solving nonlinear optimization problems, with and without the uncertainties effects.
Vibration Engineering and Technology of Machinery, 2021
The use of fractional-order controllers to drive dynamical systems to a desired/target configurat... more The use of fractional-order controllers to drive dynamical systems to a desired/target configuration became extremely popular in the last decade, with many studies stating that they present superior performance when compared to the integer-order counterparts, especially for nonlinear systems. Following this trend, the purpose of this chapter is to verify the possibility of improving the performance of the control of an inverted cart-pendulum system using fractional-order integrators. The strategy is to employ the classical pole location linear method to calculate the gains of the controller and then to compare the performance between integer-order and fractional-order integrators, the last one that are calculated using an optimization method.
Nowadays, in addition to traditional qualitative methods, quantitative techniques are also a stan... more Nowadays, in addition to traditional qualitative methods, quantitative techniques are also a standard tool to describe biological systems behavior. An example is the broad class of mathematical models, based on differential equations, used in ecology, biochemical kinetics, epidemiology, gene regulatory networks, etc. Independent of their simplicity or complexity, all these models have in common (generally unknown a priori) parameters that need to be identified from observations (data) of the real system, usually available on the literature, obtained by specific assays or surveyed by public health offices. Before using this data to calibrate the models, a good practice is to judge the most influential parameters. That can be done with aid of the Sobol’ indices, a variance-based statistical technique for global sensitivity analysis, which measures the individual importance of each parameter, as well as their joint-effect, on the model output (a.k.a. quantity of interest). These variance-based indexes may be computed using Monte Carlo simulation but, depending on the model, this task can be very costly. An alternative approach for this scenario is the use of surrogate models to speed-up the calculations. Using simple biological models, from different areas, we develop a tutorial that illustrates how practitioners can use Sobol’ indices to quantify, in a probabilistic manner, the relevance of the parameters of their models. This tutorial describes a very robust framework to compute Sobol’ indices employing a polynomial chaos surrogate model constructed with the UQLab package.
Topics in Nonlinear Mechanics and Physics: Selected Papers from CSNDD 2018, 2019
This chapter explores the nonlinear dynamics of a bistable piezo-magneto-elastic energy harvester... more This chapter explores the nonlinear dynamics of a bistable piezo-magneto-elastic energy harvester with the objective of determining the influence of external force parameters on the system response. Time series, phase space trajectories, Poincaré maps and bifurcation diagrams are employed in order to reveal system dynamics complexity and nonlinear effects, such as chaos incidence and hysteresis.
Recent Trends in Applied Nonlinear Mechanics and Physics: Selected Papers from CSNDD 2016, 2018
In agricultural industry, the process of orchards spraying is of extreme importance to avoid loss... more In agricultural industry, the process of orchards spraying is of extreme importance to avoid losses and reduction of quality in the products. In orchards spraying process an equipment called sprayer tower is used. It consists of a reservoir and fans mounted over an articulated tower, which is supported by a vehicle suspension. Due to soil irregularities this equipment is subject to random loads, which may hamper the proper dispersion of the spraying fluid. This work presents the construction of a consistent stochastic model of uncertainties to describe the non-linear dynamics of an orchard sprayer tower. In this model, the mechanical system is described by as a multi-body with three degrees of freedom, and random loadings as a harmonic random process. Uncertainties are taken into account through a parametric probabilistic approach , where maximum entropy principle is used to specify random parameters distributions. The propagation of uncertainties through the model is computed via Monte Carlo method.
Probabilistic Prognostics and Health Management of Energy Systems, 2017
Uncertainty quantification (UQ) is a multidisciplinary area, that deals with quantitative charact... more Uncertainty quantification (UQ) is a multidisciplinary area, that deals with quantitative characterization and reduction of uncertainties in applications. It is essential to certify the quality of numerical and experimental analyses of physical systems. The present manuscript aims to provide the reader with an introductory view about modeling and quantification of uncertainties in physical systems. In this sense, the text presents some fundamental concepts in UQ, a brief review of probability basics notions, discusses, through a simplistic example, the fundamental aspects of probabilistic modeling of uncertainties in a physical system, and explains what is the uncertainty propagation problem.
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Papers by Americo Cunha Jr