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Accurate prediction of remaining useful life (RUL) under creep conditions is crucial for the design and maintenance of industrial equipment operating at high temperatures. Traditional deterministic methods often overlook significant variability in experimental data, leading to unreliable predictions. This study introduces a probabilistic framework to address uncertainties in predicting creep rupture time. We utilize robust regression methods to minimize the influence of outliers and enhance model estimates. Sobol indices-based global sensitivity analysis identifies the most influential parameters, followed by Monte Carlo simulations to determine the probability distribution of the material's RUL. Model selection techniques, including the Akaike and Bayesian information criteria, ensure the optimal predictive model. This probabilistic approach allows for the delineation of safe operational limits with quantifiable confidence levels, thereby improving the reliability and safety of high-temperature applications. The framework's versatility also allows integration with various mathematical models, offering a comprehensive understanding of creep behavior.

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. 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.

The damage detection problem in mechanical systems, using vibration measurements, is commonly called Structural Health Monitoring (SHM). Many tools are able to detect damages by changes in the vibration pattern, mainly, when damages induce nonlinear behavior. However, a more difficult problem is to detect structural variation associated with damage, when the mechanical system has nonlinear behavior even in the reference condition. In these cases, more sophisticated methods are required to detect if the changes in the response are based on some structural variation or changes in the vibration regime, because both can generate nonlinearities. Among the many ways to solve this problem, the use of the Volterra series has several favorable points, because they are a generalization of the linear convolution, allowing the separation of linear and nonlinear contributions by input filtering through the Volterra kernels. On the other hand, the presence of uncertainties in mechanical systems, due to noise, geometric imperfections, manufacturing irregularities, environmental conditions, and others, can also change the responses, becoming more difficult the damage detection procedure. An approach based on a stochastic version of Volterra series is proposed to be used in the detection of a breathing crack in a beam vibrating in a nonlinear regime of motion, even in reference condition (without crack). The system uncertainties are simulated by the variation imposed in the linear stiffness and damping coefficient. The results show, that the nonlinear analysis done, considering the high order Volterra kernels, allows the approach to detect the crack with a small propagation and probability confidence, even in the presence of uncertainties.

The damage detection problem becomes a more difficult task when the intrinsically nonlinear behavior of the structures and the natural data variation are considered in the analysis because both phenomena can be confused with damage if linear and deterministic approaches are implemented. Therefore, this work aims the experimental application of a stochastic version of the Volterra series combined with a novelty detection approach to detect damage in an initially nonlinear system taking into account the measured data variation, caused by the presence of uncertainties. The experimental setup is composed by a cantilever beam operating in a nonlinear regime of motion, even in the healthy condition, induced by the presence of a magnet near to the free extremity. The damage associated with mass changes in a bolted connection (nuts loosed) is detected based on the comparison between linear and nonlinear contributions of the stochastic Volterra kernels in the total response, estimated in the reference and damaged conditions. The experimental measurements were performed on different days to add natural variation to the data measured. The results obtained through the stochastic proposed approach are compared with those obtained by the deterministic version of the Volterra series, showing the advantage of the stochastic model use when we consider the experimental data variation with the capability to detect the presence of the damage with statistical confidence. Besides, the nonlinear metric used presented a higher sensitivity to the occurrence of the damage compared with the linear one, justifying the application of a nonlinear metric when the system exhibits intrinsically nonlinear behavior.

This paper introduces CEopt (https://ceopt.org), a MATLAB tool leveraging the Cross-Entropy method for non-convex optimization. Due to the relative simplicity of the algorithm, it provides a kind of transparent ``gray-box'' optimization solver, with intuitive control parameters. Unique in its approach, CEopt effectively handles both equality and inequality constraints using an augmented Lagrangian method, offering robustness and scalability for moderately sized complex problems. Through select case studies, the package's applicability and effectiveness in various optimization scenarios are showcased, marking CEopt as a practical addition to optimization research and application toolsets.

This paper analyzes the impact of parametric uncertainties on the dynamics of bistable energy harvesters, focusing on obtaining statistical information about how each parameter's variability affects the energy harvesting process. To model the parametric uncertainties, we use a probability distribution derived from the maximum entropy principle, while polynomial chaos is employed to propagate uncertainty. Conditional probabilities and probability maps are obtained to investigate the effect of uncertainty on harvesting energy. We consider different models of bistable energy harvesters that account for nonlinear piezoelectric coupling and asymmetries. Our findings suggest a higher probability of increasing harvested power in the intrawell motion regime as the excitation frequency increases. In contrast, increasing the excitation amplitude and piezoelectric coupling are more likely to increase power in the chaotic and interwell motion regimes, respectively. An illustrative example is presented to emphasize the importance of investigating the influence when all parameters vary simultaneously.

The paper investigates asymmetries effects over a nonlinear vibration energy harvester dynamics. The asymmetric system performance is compared with symmetric ones. Different asymmetry levels on restoring force and gravity action are investigated from a system-sloping angle variation. Bifurcation diagrams and basins of attraction are used to examine the local and global characteristics underlying dynamical systems under different excitation energy. The results show the adverse effects of asymmetries on system dynamics. They also reveal ways to overcome them by canceling asymmetric influence from optimal sloping angle values and improving asymmetric system performance over symmetrical ones. This comprehensive numerical study provides novel valuable insights into asymmetrical energy harvester dynamics, a wide and still less explored topic.

This paper proposes a data-driven approximate Bayesian computation framework for parameter estimation and uncertainty quantification of epidemic models, which incorporates two novelties: (i) the identification of the initial conditions by using plausible dynamic states that are compatible with observational data; (ii) learning of an informative prior distribution for the model parameters via the cross-entropy method. The new methodology's effectiveness is illustrated with the aid of actual data from the COVID-19 epidemic in Rio de Janeiro city in Brazil, employing an ordinary differential equation-based model with a generalized SEIR mechanistic structure that includes time-dependent transmission rate, asymptomatics, and hospitalizations. A minimization problem with two cost terms (number of hospitalizations and deaths) is formulated, and twelve parameters are identified. The calibrated model provides a consistent description of the available data, able to extrapolate forecasts over a few weeks, making the proposed methodology very appealing for real-time epidemic modeling.

The present work revisits the reduction of the nonlinear dynamics of an electromechanical system through a quasi-steady state hypothesis, discussing the fundamental aspects of this type of approach and clarifying some confusing points found in the literature. Expressions for the characteristic time scales of dynamics are deduced from a physical analysis that establishes an analogy between electromechanical dynamics and the kinetics of a chemical reaction. It provides a physical justification, supplemented by non-dimensionalization and scaling of the equations, 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 quasi-steady-state assumption discussed here.

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.

This work presents the estimation of the parameters of an experimental setup, which is modeled as a system with three degrees of freedom, composed by a shaft, two rotors, and a DC motor, that emulates a drilling process. A Bayesian technique is used in the estimation process, to take into account the uncertainties and variabilities intrinsic to the measurement taken, which are modeled as a noise of Gaussian nature. With this procedure it is expected to check the reliability of the nominal values of the physical parameters of the test rig. An estimation process assuming that nine parameters of the experimental apparatus are unknown is conducted, and the results show that for some quantities the relative deviation with respect to the nominal values is very high. This deviation evidentiates a strong deficiency in the mathematical model used to describe the dynamic behavior of the experimental apparatus.

This work studies the dynamics of a one dimensional elastic bar with random elastic modulus and prescribed boundary conditions, say, fixed at one end, and attached to a lumped mass and two springs (one linear and another nonlinear) on the other extreme. The system analysis assumes that the elastic modulus has gamma probability distribution and uses Monte Carlo simulations to compute the propagation of uncertainty in this continuous--discrete system. After describing the deterministic and the stochastic modeling of the system, some configurations of the model are analyzed in order to characterize the effect of the lumped mass in the overall behavior of this dynamical system., Comment: arXiv admin note: text overlap with arXiv:2105.10084

This paper deals with the applications of stochastic spectral methods for structural topology optimization in the presence of uncertainties. A non-intrusive polynomial chaos expansion is integrated into a topology optimization algorithm to calculate low-order statistical moments of the mechanical-mathematical model response. This procedure, known as robust topology optimization, can optimize the mean of the compliance while simultaneously minimizing its standard deviation. In order to address possible variabilities in the loads applied to the mechanical system of interest, magnitude and direction of the external forces are assumed to be uncertain. In this probabilistic framework, forces are described as a random field or a set of random variables. Representation of the random objects and propagation of load uncertainties through the model are efficiently done through Karhunen-Lo\`{e}ve and polynomial chaos expansions. We take advantage of using polygonal elements, which have been shown to be effective in suppressing checkerboard patterns and reducing mesh dependency in the solution of topology optimization problems. Accuracy and applicability of the proposed methodology are demonstrated by means of several topology optimization examples. The obtained results, which are in excellent agreement with reference solutions computed via Monte Carlo method, show that load uncertainties play an important role in optimal design of structural systems, so that they must be taken into account to ensure a reliable optimization process.

This paper deals with the nonlinear stochastic dynamics of an orchard tower sprayer subjected to random excitations due to soil irregularities. A consistent stochastic model of uncertainties is constructed to describe random loadings and to predict variabilities in mechanical system response. The dynamics is addressed in time and frequency domains. Monte Carlo method is employed to compute the propagation of uncertainties through the stochastic model. Numerical simulations reveals a very rich dynamics, which is able to produce chaos. This numerical study also indicates that lateral vibrations follow a direct energy cascade law. A probabilistic analysis reveals the possibility of large lateral vibrations during the equipment operation.

This paper deals with the nonlinear stochastic dynamics of a piezoelectric energy harvesting system subjected to a harmonic external excitation disturbed by Gaussian colored noise. A parametric analysis is conducted, where the effects of the standard deviation and the correlation time of colored noise on the system response are investigated. The numerical results suggest a strong influence of noise on the system response for higher values of correlation time and standard deviation, and a low (noise level independent) influence for low values of correlation time.

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 individually and collectively regarding the total variation of the model. The results indicate that the frequency and amplitude of excitation, asymmetric terms and electrical proprieties of the piezoelectric coupling are the most critical parameters that affect the mean power harvested. It is also shown that the order of importance of the parameters can change according to the stability of the harvester's dynamic response. In this way, a better understanding of the system under analysis is obtained since the study allows the identification of vital parameters that rule the change of dynamic behavior and therefore constitutes a powerful tool in the robust design, optimization, and response prediction of nonlinear harvesters.

The development of computational models for the numerical simulation of chemically reacting flows operating in the turbulent regime requires the solution of partial differential equations that represent the balance of mass, linear momentum, chemical species, and energy. The chemical reactions of the model may involve detailed reaction mechanisms for the description of the physicochemical phenomena. One of the biggest challenges is the stiffness of the numerical simulation of these models and the nonlinear nature of species rate of reaction. This work presents a study of in situ adaptive tabulation (ISAT) technique, focusing on the accuracy, efficiency, and memory usage in the simulation of homogeneous stirred reactor models using simple and complex reaction mechanisms. The combustion of carbon monoxide with oxygen and methane with air mixtures are considered, using detailed reaction mechanisms with 4 and 53 species, 3 and 325 reactions, respectively. The results of these simulations indicate that the developed implementation of ISAT technique has a absolute global error smaller than 1 %. Moreover, ISAT technique provides gains, in terms of computational time, of up to 80% when compared with the direct integration of the full chemical kinetics. However, in terms of memory usage the present implementation of ISAT technique is found to be excessively demanding.

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.

This work intends to analyze the nonlinear stochastic dynamics of drillstrings in horizontal configuration. For this purpose, it considers a beam theory, with effects of rotatory inertia and shear deformation, which is capable of reproducing the large displacements that the beam undergoes. The friction and shock effects, due to beam/borehole wall transversal impacts, as well as the force and torque induced by bit-rock interaction, are also considered in the model. Uncertainties of bit-rock interaction model are taken into account using a parametric probabilistic approach. Numerical simulations have shown that the mechanical system of interest has a very rich nonlinear stochastic dynamics, which generate phenomena such as bit-bounce, stick-slip, and transverse impacts. A study aiming to maximize the drilling process efficiency, varying drillstring velocities of translation and rotation is presented. Also, the work presents the definition and solution of two optimizations problems, one deterministic and one robust, where the objective is to maximize drillstring rate of penetration into the soil respecting its structural limits.

This paper presents a theoretical study on the influence of a discrete element in the nonlinear dynamics of a continuous mechanical system subject to randomness in the model parameters. This system is composed by an elastic bar, attached to springs and a lumped mass, with a random elastic modulus and subjected to a Gaussian white-noise distributed external force. One can note that the dynamic behavior of the bar is significantly altered when the lumped mass is varied, becoming, on the right extreme and for large values of the concentrated mass, similar to a mass-spring system. It is also observed that the system response is more influenced by the randomness for small values of the lumped mass. The study conducted also show an irregular distribution of energy through the spectrum of frequencies, asymmetries and multimodal behavior in the probability distributions of the lumped mass velocity.

Multiple instances of Zika virus epidemic have been reported around the world in the last two decades, turning the related illness into an international concern. In this context the use of mathematical models for epidemics is of great importance, since they are useful tools to study the underlying outbreak numbers and allow one to test the effectiveness of different strategies used to combat the associated diseases. This work deals with the development and calibration of an epidemic model to describe the 2016 outbreak of Zika virus in Brazil. A system of 8 differential equations with 8 parameters is employed to model the evolution of the infection through two populations. Nominal values for the model parameters are estimated from the literature. An inverse problem is formulated and solved by comparing the system response to real data from the outbreak. The calibrated results presents realistic parameters and returns reasonable descriptions, with the curve shape similar to the outbreak evolution and peak value close to the highest number of infected people during 2016. Considerations about the lack of data for some initial conditions are also made through an analysis over the response behavior according to their change in value.

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., Comment: 9 pages, 7 figures