Accepted Manuscripts

Giuseppina Autuori, Federico Cluni, Vittorio Gusella and Patrizia Pucci
ASME J. Risk Uncertainty Part B   doi: 10.1115/1.4036806
In this note we yield with a nonlocal elastic rod problem, widely studied in the last decades. The main purpose of the paper is to investigate the effects of the statistic variability of the fractional operator order $s$ on the displacements $u$ of the rod. The rod is supposed to be subjected to external distributed forces, and the displacement field $u$ is obtained by means of numerical procedure. The attention is particularly focused on the parameter $s$, which influences the response in a nonlinear fashion. The effects of the uncertainty of $s$ on the response at different locations of the rod is investigated by the Monte Carlo simulations. The results obtained highlight the importance of $s$ in the probabilistic feature of the response. In particular, it is found that for a small coefficient of variation of $s$ the probability density function of the response has a unique well identifiable mode. On the other hand, for a high coefficient of variation of $s$ the probability density function of the response decreases monotonically. Finally, the coefficient of variation, and, to a small extent, the mean of the response tend to increase as the coefficient of variation of $s$ increases.
TOPICS: Density, Simulation, Engineering simulation, Displacement, Probability, Uncertainty, Risk
Gioacchino Alotta, Giuseppe Failla and Francesco Paolo Pinnola
ASME J. Risk Uncertainty Part B   doi: 10.1115/1.4036702
Recently, a displacement-based non-local bar model has been developed. The model is based on the assumption that non-local forces can be modeled as viscoelastic long-range interactions mutually exerted by non-adjacent bar segments due to their relative motion; the classical local stress resultants are also present in the model. A finite element (FE) formulation with closed-form expressions of the elastic and viscoelastic matrices has also been obtained. Specifically, Caputo's fractional derivative has been used in order to model viscoelastic long-range interaction. The static and quasi-static response has been already investigated. This work investigates the stochastic response of the non-local fractional viscoelastic bar introduced in previous papers, discretized with the FEM, forced by a Gaussian white noise. Since the bar is forced by a Gaussian white noise, dynamical effects cannot be neglected. The system of coupled fractional differential equations ruling the bar motion can be decoupled only by means of the fractional order state variable expansion. It is shown that following this approach Monte Carlo simulation can be performed very efficiently. For simplicity, here the work is limited to the axial response, but can be easily extended to transverse motion.
TOPICS: White noise, Risk, Simulation, Stress, Finite element methods, Differential equations, Finite element analysis, Displacement, Finite element model
Alberto Di Matteo and Antonina Pirrotta
ASME J. Risk Uncertainty Part B   doi: 10.1115/1.4036703
In this paper the probabilistic response of nonlinear systems driven by alpha-stable Lévy white noises is considered. The Path Integral solution is adopted for determining the evolution of the probability density function of nonlinear oscillators. Specifically, based on the properties of alpha-stable random variables and processes, Path Integral solution is extended to deal with Lévy white noises input with any value of the stability index alpha. It is shown that at the limit when the time increments tend to zero, the Einstein-Smoluchowsky equation, governing the evolution of the response probability density function, is fully restored. Application to linear and nonlinear systems under different values of alpha is reported. Comparisons with pertinent Monte Carlo simulation data and analytical solutions (when available) demonstrate the accuracy of the results.
TOPICS: Path integrals, Nonlinear systems, White noise, Risk, Probability, Noise (Sound), Density, Stability, Simulation
Gioacchino Alotta and Natalia Colinas-Armijo
ASME J. Risk Uncertainty Part B   doi: 10.1115/1.4036704
It is well known that mechanical parameters of polymeric materials, as for example epoxy resin, are strongly influenced by the temperature. On the other hand in many applications the temperature is not known exactly during the design process and this introduce uncertainties in the prevision of the behaviour also when the loads are deterministic. For this reason, in this paper, the mechanical behaviour of an epoxy resin is characterized by means of a fractional viscoelastic model at different temperatures; then a simple method to characterize the response of the fractional viscoelastic material at different temperatures modeled as a random variable with assigned probability density function subjected to deterministic loads is presented. It is found that first- and second-order statistical moments of the response can be easily evaluated only by the knowledge of the probability density function of the temperature and the behaviour of the parameters with the temperature. Comparison with Monte Carlo simulations are also performed in order to assess the accuracy and the reliability of the method.
TOPICS: Temperature, Viscoelastic materials, Risk, Density, Probability, Stress, Epoxy resins, Reliability, Simulation, Design, Engineering simulation, Mechanical behavior, Uncertainty
Giulio Cottone and Roberta Santoro
ASME J. Risk Uncertainty Part B   doi: 10.1115/1.4036705
In this paper, interval fractional derivative are presented. We consider uncertainty in both the order and the argument of the fractional differentiation. The approach proposed takes advantage of the property of Fourier and Laplace transforms with respect to the translation operator, in order to first define integral transform of interval functions. Subsequently, the main interval fractional integrals and derivatives, such as the Riemann-Liouville, Caputo and Riesz, are defined based on their properties with respect to integral transform. Moreover, uncertain-but-bounded linear fractional dynamical systems, relevant in modeling fractional viscoelasticity, excited by zero-mean stationary Gaussian forces are considered. Within the interval analysis framework, either exact or approximate bounds of the variance of the stationary response are proposed in case of interval stiffness or interval fractional damping, respectively.
TOPICS: Viscoelasticity, Damping, Dynamic systems, Modeling, Laplace transforms, Stiffness, Uncertainty, Risk
Dawei Zhang and Shengyang Zhu
ASME J. Risk Uncertainty Part B   doi: 10.1115/1.4036706
The paper presents a nonlinear rubber spring model for the primary suspension of the railway vehicle, which can effectively describe the amplitude dependency and the frequency dependency of the rubber spring, by taking the elastic force, the fractional derivative viscous force and nonlinear friction force into account. An improved two-dimensional vehicle-track coupled system is developed based on the nonlinear rubber spring model of the primary suspension. Nonlinear Hertz theory is used to couple the vehicle and track subsystems. The railway vehicle subsystem is regarded as a multi-body system with 10 degrees of freedom and the track subsystem is treated as finite Euler-Bernoulli beams supported on a discrete-elastic foundation. Mechanical characteristic of the rubber spring due to harmonic excitations is analyzed to clarify the stiffness and damping dependencies on the excitation frequency and the displacement amplitude. Dynamic responses of the vehicle-track coupled dynamics system induced by the welded joint irregularity and random track irregularity have been performed to illustrate the difference between the Kelvin-Voigt model and the proposed model in the time and frequency domain.
TOPICS: Rubber, Dynamics (Mechanics), Springs, Railway vehicles, Risk, Vehicles, Excitation, Stiffness, Displacement, Dynamic response, Friction, Welded joints, Mechanical properties, Degrees of freedom, Damping
Guest Editorial  
Mario Di Paola and Francesco Paolo Pinnola
ASME J. Risk Uncertainty Part B   doi: 10.1115/1.4036707
This Special Issue aims to provide advanced developments in the applications of fractional calculus in various problems of stochastic mechanics with emphasis on risk evaluation and uncertainty quantification. It is composed of eight papers written by researchers and academics from China, Germany, Italy, Spain and United Kingdom. The papers cover theoretical issues, computational methods and modeling techniques of structures and external agencies in order to refine the actual methods used in practical engineering problems, with particular regards to the stochastic mechanics context. In particular, there are some new results about the solution of barrier problem of noisy dynamical system embedded with fractional derivative, the estimation of the random temperature effects in the viscoelastic behavior of hereditary materials, the parametric study of stochastic variation of the fractional Laplacian order in the non-local structural element, the exact evaluation of response fractional spectral moments of linear fractional oscillators excited by a white noise, the path integral method for non-linear system under Levy white noise, the use of fractional operators in the interval analysis, the stochastic dynamical analysis of primary suspension in railway vehicle modeled by fractional operators, and the analysis of non-local viscoelastic nano-rod forced by Gaussian noise.
TOPICS: Structural elements (Construction), Viscoelasticity, Path integrals, Noise (Sound), Temperature effects, Dynamic systems, Modeling, Nonlinear systems, China, Nanorods, Risk assessment, White noise, Railway vehicles, Computational methods, Risk, Uncertainty quantification
Valeria Artale, Giacomo Navarra, Angela Ricciardello and Giorgio Barone
ASME J. Risk Uncertainty Part B   doi: 10.1115/1.4036700
In the last decades the research community has shown an increasing interest in the engineering applications of fractional calculus, which allows to accurately characterize the static and dynamic behaviour of many complex mechanical systems, e.g. the non-local or non-viscous constitutive law. In particular, fractional calculus has gained considerable importance in the random vibration analysis of engineering structures provided with viscoelastic damping. In this case, the evaluation of the dynamic response in the frequency domain presents significant advantages, once a probabilistic characterization of the input is provided. On the other hand, closed-form expression for the response statistics of dynamical fractional systems are not available even for the simplest cases. Taking advantage of the Residue Theorem, in this paper the exact expressions of the spectral moments of integer and complex order (i.e. fractional spectral moments) of linear fractional oscillators driven by acceleration time histories obtained as samples of stationary Gaussian white noise processes are determined.
TOPICS: White noise, Risk, Statistics as topic, Theorems (Mathematics), Structures, Constitutive equations, Damping, Engineering systems and industry applications, Random vibration, Dynamic response
Daniil Yurchenko, Andrea Burlon, Mario Di Paola, Giuseppe Failla and Antonina Pirrotta
ASME J. Risk Uncertainty Part B   doi: 10.1115/1.4036701
The paper deals with the stochastic dynamics of a vibroimpact single degree-of-freedom system under a Gaussian white noise. The system is assumed to have a hard type impact against a one-sided motionless barrier, located at the system's equilibrium. The system is endowed with a fractional derivative element. An analytical expression for the system's mean squared response amplitude is presented and compared with results of numerical simulations.
TOPICS: Dynamics (Mechanics), Computer simulation, Equilibrium (Physics), Degrees of freedom, Damping, Stochastic systems, White noise, Risk
Takao Kakizaki, Jiro Urii and Mitsuru Endo
ASME J. Risk Uncertainty Part B   doi: 10.1115/1.4036662
A 3D mass evacuation simulation using precise kinematic digital human (KDH) models and an experimental study are discussed. The flooding associated with the large tsunami caused by the Great East Japan Earthquake on March 11, 2011 was responsible for more than 90% of the disaster casualties. Unfortunately, it is expected that other huge tsunamis could occur in Japan coastal areas if an earth-quake with magnitude greater than 8 occurs along the Nankai Trough. Therefore, recent disaster prevention plans should include evacuation to higher buildings, elevated ground, and constructed tsunami evacuation towers. In this study, evacuation simulations with 500 KDHs were conducted. The simulations consisted of several subgroups of KDHs. It is shown that the possible evacuation path of each group should be carefully determined to minimize the evacuation time. Several properties such as evacuee motion characteristics of KDHs, number of evacuees, exit gates, and number of injured persons were carefully considered in the simulations. Evacuee motion was also experimentally investigated by using a multi-storied building to replicate the structure of an actual tsunami evacuation tower that could accommodate approximately 120 evacuees. The experimental results suggest that an appropriately divided group population could effectively reduce the overall group evacuation time. The results also suggest that fatigue due to walking during evacuation adversely affects the total evacuation time, especially in the ascent of stairways. The experimental data can be used to obtain more accurate simulations of mass evacuation.
TOPICS: Simulation, Evacuations, Risk, Tsunamis, Earthquakes, Floods, Shorelines, Emergency management, Disasters, Kinematics, Fatigue, Structures
Tae-uk Kim, JeongWoo Shin and Sang Wook Lee
ASME J. Risk Uncertainty Part B   doi: 10.1115/1.4036663
The development of a crashworthy landing gear is presented based on the civil regulations and the military specifications. For this, two representative crashworthy requirements are applied to helicopter landing gear design; the nose gear is designed to collapse in a controlled manner so that it does not penetrate the cabin and cause secondary hazards, and the main gear has to absorb energy as much as possible in crash case to decelerate the aircraft. To satisfy the requirements, the collapse mechanism triggered by shear-pin rupture and the shock absorber using blow-off valve are implemented in the nose and main gear, respectively. The crash performance of landing gear is demonstrated by drop tests. In the tests, performance data such as ground reaction loads and shock absorber stroke are measured and crash behaviors are recorded by high-speed camera. The test data shows a good agreement with the prediction by simulation model, which proves the validity of the design and analysis.
TOPICS: Design, Gears, Testing, Crashworthiness, Risk, Shock absorbers, Collapse, Military systems, Regulations, Rupture, Valves, Aircraft, Simulation models, Stress, Shear (Mechanics), Hazards
Jason C. York and Jeremy M. Gernand
ASME J. Risk Uncertainty Part B   doi: 10.1115/1.4036309
The potential benefits of a safety program, are generally only realized after an incident has occurred. Resource allocation in an organization's safety program has the imperative task of balancing costs and often unrealized benefits. Management can be wary to allocate additional resources to a safety program because it is difficult to estimate the return on investment, especially since the returns are a set of negative outcomes not manifested. One way that safety professionals can provide an estimate of potential return on investment is to forecast how the organizations incident rate can be affected by implementing different resource allocation strategies and what the expected incident rate would have been without intervention. This study evaluates forecasting methods used to predict incidents against one another against a common definition of performance accuracy to identify the method that would be the most applicable to use as part of a safety resource allocation model. By identifying the most accurate forecasting method, the uncertainty of which method a safety professional should utilize for incident rate prediction is reduced. Incident data from the Mine Safety and Health Administration (MSHA) was used to make short and long term forecasts. The performance of each of these methods was evaluated against one another to ascertain which method has the highest level of accuracy, lowest bias, and best complexity-adjusted goodness-of-fit metrics. The double exponential smoothing and ARMA statistical forecasting methods provided the most accurate incident rate predictions.
TOPICS: Mining, Safety, Mine safety, Goodness-of-fit tests, Performance, Resource allocation, Uncertainty, Risk
Zili Zhang, Biswajit Basu and Søren R.K. Nielsen
ASME J. Risk Uncertainty Part B   doi: 10.1115/1.4036310
Energy dynamics in buildings are inherently stochastic in nature due to random fluctuations from various factors such as the solar gain and the ambient temperature. This paper proposes a theoretical framework for stochastic modeling of the building thermal dynamics as well as its analytical solution strategies. Both the external temperature and internal gain are modeled as a stochastic process, composed of a periodic (daily) mean-value function and a zero-mean deviation process obtained as the output process of a unit Gaussian white noise passing through a rational filter. Based on the measured climate data, the indicated mean-value functions and rational filters have been identified for different months of a year. Stochastic differential equations in the state vector form driven by white noise processes have been established, and analytical solutions for the mean-value function and covariance matrix of the state vector are obtained. This framework would allow a simple and efficient way to carry out predictions and parametric studies on energy dynamics of buildings with random and uncertain climate effects. It would also provide a basis for the robust design of energy efficient buildings with predictive controllers.
TOPICS: Dynamics (Mechanics), Temperature, Risk, Structures, White noise, Climate, Filters, Stochastic processes, Control equipment, Fluctuations (Physics), Design, Differential equations, Modeling, Solar energy
Lida Naseh Moghanlou and Mohammad Pourgol-Mohammad
ASME J. Risk Uncertainty Part B   doi: 10.1115/1.4036064
Corrosion degradation is a common problem for boiler tubes in power plants, resulting in unscheduled plant shut down. In this research, degradation of the corrosion is investigated for a boiler tubes with the corrosion lifetime estimated. A special focus is made on the corrosion failures, the important failure modes and mechanisms for the metallic boiler tubes via Failure Modes and Effect Analysis (FMEA) method, evaluating the pitting corrosion as the most common failure mode in the tubes. Majority of the available approaches estimate lifetime of pitting corrosion by deterministic approaches, in which the results are valid only for limited conditions. In order to improve deficiencies of available models, a stochastic method is proposed here to study the corrosion life. The temporal behavior of metal degradation is analyzed in different conditions through the developed approach and a proper degradation model is selected. Uncertainty intervals/distributions are determined for some of the model parameters. The deterministic model is converted to a probabilistic model by taking to account the variability of the uncertain input parameters. The model is simulated using Monte Carlo method via simple sampling. The result of the life estimation is updated by the Bayesian framework using Monte Carlo Markov Chain. Finally, for the element that is subjected to the pitting corrosion degradation, the life distribution is obtained. Modeling results shows that pitting corrosion has stochastic behavior with lognormal distribution as proper fit for the pitting corrosion behavior. In order to validate the results, the estimations were compared with the power plant field failure data.
TOPICS: Corrosion, Boiler tubes, Risk, Failure mechanisms, Power stations, Failure, Failure data, Log normal distribution, Monte Carlo methods, Modeling, Metals, Failure mode and effects analysis, Chain, Uncertainty
Ricardo Cruz-Lozano, Fisseha M. Alemayehu, Stephen Ekwaro-Osire and Haileyesus B. Endeshaw
ASME J. Risk Uncertainty Part B   doi: 10.1115/1.4035867
Sketches can be categorized as personal, shared, persuasive, and handover sketches. Depending on each category, their level of ambiguity also varies. The applications of sketches includes conceptual design, eliciting user preferences, shape retrieval, and sketch-based modeling. There is a need for quantification of uncertainty in sketches in mapping of sketches to 3D models in sketch-based modeling, in eliciting user preferences, and in tuning the level of uncertainty in sketches at the conceptual design stage. This paper investigates the role of probability of importance in quantifying the level of uncertainty in sketches by raising the following three research questions: How are the features in a sketch ranked? What is the probability of importance of features in a sketch? What is the level of uncertainty in a sketch? This paper presents an improved framework for uncertainty quantification in sketches. The framework is capable of identifying and ranking the features in the sketch, determining their probability of importance, and finally quantifying the level of uncertainty in the sketch. Ranking the features of a sketch is performed by a hierarchical approach, whereas probability of importance is determined by assessing the probability of likeliness using a shape matching approach and a probability transformation. Quantification of uncertainty is accomplished by using the principle of normalization of entropy. A case study of a bicycle sketch is used to demonstrate that the framework eliminates the need of expert input in assessment of uncertainty in sketches, and, hence, can be used by design practitioners with limited experience.
TOPICS: Probability, Risk, Uncertainty, Conceptual design, Shapes, Modeling, Preferences, Uncertainty quantification, Ambiguity, Bicycles, Entropy, Design, Three-dimensional models
Bin Zhou and Kumar Bhimavarapu
ASME J. Risk Uncertainty Part B   doi: 10.1115/1.4035704
Industry has been implementing condition monitoring for turbines to minimize losses and to improve productivity. Deficient conditions can be identified before losses occur by monitoring the equipment parameters. For any loss scenario, the effectiveness of monitoring depends on the stage of the loss scenario when the deficient condition is detected. A scenario-based semi-empirical methodology was developed to assess various types of condition monitoring techniques, by considering their effect on the risk associated with mechanical breakdown of steam turbines in the forest products (FP) industry. A list of typical turbine loss scenarios was first generated by reviewing loss data and leveraging expert domain knowledge. Subsequently, condition monitoring techniques that can mitigate the risk associated with each loss scenario were identified. For each loss scenario, an event tree analysis was used to quantitatively assess the variations in the outcomes due to condition monitoring, and resultant changes in the risk associated with turbine mechanical breakdown. An application was developed following the methodology to evaluate the effect of condition monitoring on turbine risk mitigation.
TOPICS: Condition monitoring, Steam turbines, Risk, Risk mitigation, Turbines, Performance
Guozheng Song, Faisal Khan, Ming Yang and Hangzhou Wang
ASME J. Risk Uncertainty Part B   doi: 10.1115/1.4035438
The reliable prediction and diagnosis of abnormal events provides much needed guidance for risk management. Traditional Bayesian Network (traditional BN) has been used to dynamically predict and diagnose the abnormal events. However, its inherent limitation caused by discrete categorization of random variables degrades the assessment reliability. This paper proposes a continuous Bayesian Network (CBN) based model to reduce the above-mentioned limitation. To compute complex posterior distributions of CBN, Markov Chain Monte Carlo method (MCMC) was applied. A case study was conducted to demonstrate the application of CBN. A comparative analysis of the traditional BN and CBN was also presented. This work highlights that the use of CBN can overcome the drawbacks of traditional BN to make the dynamic prediction and diagnosis analysis more reliable.
TOPICS: Reliability, Chain, Monte Carlo methods, Risk management, Risk
Technical Brief  
Shruti Rapur Janani and Rajiv Tiwari
ASME J. Risk Uncertainty Part B   doi: 10.1115/1.4035440
When the hydraulic flow path is incompatible with the physical contours of the centrifugal pump (CP), flow instabilities occur. A prolonged operation in the flow-instability region may result in severe damages of the CP system. Hence, two of the major causes of flow instabilities such as the suction blockage (with five levels of increasing severity) and impeller defects are studied in the present work. Thereafter, an attempt is made to classify these faults and differentiate the physics behind the flow instabilities caused due to them. The tri-axial CP vibration data in time domain is employed for the fault classification. Multi-distinct and multi-coexisting fault classifications have been performed with different combinations of these faults using support vector machine (SVM) algorithm with radial basis function (RBF) kernel. Prediction results from the experiments and the developed methodology help to, segregate the faults into appropriate class, identify the severity of the suction blockage, and substantiate the practical applicability of this study.
TOPICS: Vibration, Centrifugal pumps, Fault diagnosis, Support vector machines, Risk, Flow instability, Suction, Impellers, Hydraulic flow, Algorithms, Damage, Physics
Jesus Luque, Rainer Hamann and Daniel Straub
ASME J. Risk Uncertainty Part B   doi: 10.1115/1.4035399
Corrosion in ship structures is influenced by a variety of factors that are varying in time and space. Existing corrosion models used in practice only partially address the spatial variability of the corrosion process. Typical estimations of corrosion model parameters are based on averaging measurements for one ship type over structural elements from different ships and operational conditions. Most models do not explicitly predict the variability and correlation of the corrosion process among multiple locations in the structure. This variability is of relevance when determining the necessary inspection coverage, and it can influence the reliability of the ship structure. In this paper, we develop a probabilistic spatio-temporal corrosion model based on a hierarchical approach, which represents the spatial variability of the corrosion process. The model includes as hierarchical levels vessel - compartment - frame - structural element - plate element. At all levels, variables representing common influencing factors (e.g. coating life) are introduced. Moreover, at the lowest level, which is the one of the plate element, the corrosion process can be modeled as a spatial random field. For illustrative purposes, the model is trained through Bayesian analysis with measurement data from a group of tankers. In this application it is found that there is significant spatial dependence among corrosion processes in different parts of the ships, which the proposed hierarchical model can capture. Finally, it is demonstrated how this spatial dependence can be exploited when making inference on the future condition of the ships.
TOPICS: Corrosion, Modeling, Ships, Risk, Structural elements (Construction), Vessels, Tankers, Coating processes, Coatings, Inspection, Reliability
Souvik Chakraborty, Tanmoy Chatterjee, Rajib Chowdhury and Sondipon Adhikari
ASME J. Risk Uncertainty Part B   doi: 10.1115/1.4035439
Optimization for crashworthiness is of vast importance in automobile industry. Recent advancement in computational prowess has enabled researchers and design engineers to address vehicle crashworthiness, resulting in reduction of cost and time for new product development. However, deterministic optimum design often resides at the boundary of failure domain, leaving little or no room for modelling imperfections, parameter uncertainties and/or human error. In this study, a operational model based robust design optimization (RDO) scheme has been developed for designing crashworthiness of vehicle against side impact. Within this framework, differential evolution algorithm (DEA) has been coupled with polynomial correlated function expansion (PCFE). It is argued that the coupled DEA-PCFE is more efficient and accurate, as compared to conventional techniques. For RDO of vehicle against side impact, minimization of the weight and lower rib deflection of the vehicle are considered to be the primary design objectives. Case studies by providing various emphasis on the two objectives have also been performed. For all the cases, DEA-PCFE is found to yield highly accurate results.
TOPICS: Optimization, Vehicles, Design, Crashworthiness, Risk, Uncertainty, Modeling, Weight (Mass), Engineers, Automotive industry, Deflection, Errors, Evolutionary algorithms, Failure, Polynomials, Product development

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