Uncertainties In Material Properties Research Articles

Six sigma robust multi-objective design optimization of flat plate collector system under uncertain design parameters

Flat plate collectors (FPCs) can be considered as an important alternative to reduce the high costs of electrical energy used in heating water. Therefore, the development of FPCs with optimal performance has been much focused upon in recent research initiatives. However, due to the existence of uncertainties in material properties, geometry and environmental conditions, it is imperative to incorporate uncertainty analysis into the design optimization to obtain reliable results. In this work, a six sigma robust multi-objective optimization (SSRMO) of the FPC is developed where uncertain design parameters (UDP) are considered. A combined multi-objective modified imperialist competitive algorithm (MOMICA) and Monte Carlo simulation method (MCSM) is developed and used for the SSRMO. The SSRMO considers simultaneously three objectives functions including the FPC efficiency, the FPC cost and their sensitivities to UDP. The obtained results showed that the FPC design obtained by determinist optimization presents 31% sensitivity in terms of efficiency and 27% sensitivity in terms of total cost. However, the SSRMO provides a robust FPC design with the same optimal performances comparable to those obtained by deterministic method but with much lower sensitivity to UDP. Moreover, the robust FPC performances sensitivities were reduced by 60% compared to literature results.

Implementation of a novel Six Sigma multi-objective robustness optimization method based on the improved response surface model for bumper system design

In the vehicle industry, a car’s weight and crashworthiness are two conflicting indicators. Owing to uncertainties in loads, geometries, material properties, and operational conditions, deterministic optimization could lead to unreliable or unstable designs and increase the risk of design failure. This study combined the non-dominated sorting genetic algorithm (NSGA-II), Monte Carlo simulation with descriptive sampling (MCSDS), Six Sigma robustness approach, and improved response surface model (IRSM) to develop a general Six Sigma multi-objective reliability-based design optimization method algorithm (6σ-MORO). The proposed method was applied to examine the crashworthiness of a bumper system. In comparison to the response surface model (RSM), the accuracy of the IRSM was improved by only 10 groups of sample points, proving that the IRSM could construct each response surface function efficiently and accurately. Finally, based on the IRSM, a Six Sigma multi-objective robustness optimization was conducted to explore optimal reliability solutions. The results revealed that the proposed method improved the crashworthiness of the bumper system and also ensured its reliability. Note that the optimal design could be fairly promising for engineering design problems with high dimensions.

Evaluation of seismic performance of rotational-friction slip dampers in near-field and far-filed earthquakes

In this study, the performance of rotational-friction slip dampers in steel structures with different heights is investigated by the use of fragility curves. The use of dampers is one of the methods for vibration control of structures by simultaneously increasing both the structural stiffness and damping. Rotational-friction slip dampers are among the passive control devices that dampen the earthquake energy through their stable cyclic behavior. To study the performance of these devices in steel structures, 3, 6 and 9-story steel moment frame structures are designed, and the mentioned dampers are attached to the structure by Chevron braces. To account for the earthquake uncertainty, with the aid of incremental dynamic analysis (IDA), the damper-equipped structure is subjected to both near-field and far-field ground motion records. The acceleration and drift engineering demand parameters are selected as the functions to quantify the damage states, and the design, modeling and material properties uncertainties are considered in accordance with FEMA P-695. Evaluation of statistical results and comparison of the fragility curves, shows that the probability of failure at different damage states decreases when the dampers are added to the structure. This decrease is more remarkable in low-rise structures and near-fault ground motions.

Bayesian optimization for robust design of steel frames with joint and individual probabilistic constraints

This work proposes a Bayesian optimization (BO) method for solving multi-objective robust design optimization (RDO) problems of steel frames under aleatory uncertainty in external loads and material properties. Joint and individual probabilistic constrained RDO problems are formulated to consider two different ways the frame reaches its collapse state. Each problem involves three conflicting objective functions, namely, the total mass of the frame, the mean and variance of the maximum inter-story drift. Since the uncertain objective and probabilistic constraint functions of both problems are implicit within a finite element analysis program and the computation of the probabilistic constraints is an NP-hard problem, BO is used to guide the optimization process toward better solutions after it completes an iteration and offers a set of near Pareto-optimal solutions when it terminates. Specifically, Bayesian regression models called Gaussian processes (GPs) serve as surrogates for the structural responses. Two acquisition functions are then developed for the two RDO problems and a maximization problem of these functions is formulated as a mixed-integer nonlinear programming (MINLP) problem. A new random search coupled with simulated annealing is devised to solve the MINLP problem, thereby locating the most promising point in the input variable space at which the current solutions maximize their chance to be improved and the GP models are refined before the BO starts a new iteration. A test problem and two design examples show that exact or good Pareto-optimal solutions to the RDO problems can be found by the proposed method with 20 iterations.

Influence of input data uncertainties on failure probability of TRISO-coated particle

TRISO coated particle fuel exhibits statistical variations and large uncertainties in physical configurations and material properties from particle to particle. Besides, the dependence of mechanical behavior and failure mechanism of the coating layer on multiple variables (such as density, porosity, anisotropy, fluence and temperature) further increase the complexity of TRISO fuel performance analysis. Consequently, the particle failure probability would change in a relatively wide range. In this paper, we evaluate the effect of input data uncertainties on particle failure probability. First, uncertainty ranges of input data are determined based on literature review and irradiation conditions. Second, a perturbation study on dimensional parameters and material properties is performed. Finally, variation ranges of failure probability upon different input parameters are determined. Results show that the failure rate is sensitive to kernel diameter, SiC thickness and irradiation-induced material properties.

Reliability-based topology optimization for heterogeneous composite structures under interval and convex mixed uncertainties

With the rapid development of intelligent manufacturing and smart design, the optimal design conception for composite laminates is arising more attentions in both academic and engineering fields. Note that most of the current researches focus on the deterministic laminate design whereas the uncertainty-oriented topological design scheme for heterogeneous composites are rarely considered. In view of this, this study will present a new layout optimization process which combines the hybrid uncertainty quantification analysis and non-probabilistic reliability-based topology optimization (NRBTO). Owing to the sample limitation of multi-source uncertainties in material properties and external loads, the non-statistical convex-theoretical set theory is first explored to determine displacement response bounds of multi-layer structures under anisotropic constitutive relationship. As the safety judgment, a novel reliability index corresponding to the local stiffness features is defined via interval and convex mixed uncertainties, and its explicit expression is further deduced by the set-interference principle. To ensure the robustness and convergence of the large-scale iteration in NRBTO framework, the adjoint equations are also analyzed for the design sensitivity updating and the gradient algorithm is involved as well. Several typical optimization cases are presented to demonstrate the validity and effectiveness of the developed methodology.

Statistical Analysis for Transmission Error of Gear System with Mechanical and Thermal Deformation Uncertainties

We establish a robust algorithm to analyze the influence of system uncertainties on the transmission error of a spur gear pair under 2D simplification. The algorithm provides a way of generating smooth cutter profiles with machining uncertainties and measuring the thermal deformation through the uncertainties in material properties. Then, it produces realizations of gear tooth profiles based on the analytical method for accuracy and computational efficiency. Numerical investigations show the statistical analysis on the tooth contact analysis by comparing steel and plastic gears. It is worthwhile remarking that the plastic gear is susceptible to the geometric error caused by thermal deformation. Moreover, although the impact of thermal deformation on steel gear may seem slim, it can have a noticeable influence when it exists with mechanical uncertainties together.

The stochastic aeroelastic response analysis of helicopter rotors using deep and shallow machine learning

This paper addresses the influence of manufacturing variability of a helicopter rotor blade on its aeroelastic responses. An aeroelastic analysis using finite elements in spatial and temporal domains is used to compute the helicopter rotor frequencies, vibratory hub loads, power required and stability in forward flight. The novelty of the work lies in the application of advanced data-driven machine learning (ML) techniques, such as convolution neural networks (CNN), multi-layer perceptron (MLP), random forests, support vector machines and adaptive Gaussian process (GP) for capturing the nonlinear responses of these complex spatio-temporal models to develop an efficient physics-informed ML framework for stochastic rotor analysis. Thus, the work is of practical significance as (i) it accounts for manufacturing uncertainties, (ii) accurately quantifies their effects on nonlinear response of rotor blade and (iii) makes the computationally expensive simulations viable by the use of ML. A rigorous performance assessment of the aforementioned approaches is presented by demonstrating validation on the training dataset and prediction on the test dataset. The contribution of the study lies in the following findings: (i) The uncertainty in composite material and geometric properties can lead to significant variations in the rotor aeroelastic responses and thereby highlighting that the consideration of manufacturing variability in analyzing helicopter rotors is crucial for assessing their behaviour in real-life scenarios. (ii) Precisely, the substantial effect of uncertainty has been observed on the six vibratory hub loads and the damping with the highest impact on the yawing hub moment. Therefore, sufficient factor of safety should be considered in the design to alleviate the effects of perturbation in the simulation results. (iii) Although advanced ML techniques are harder to train, the optimal model configuration is capable of approximating the nonlinear response trends accurately. GP and CNN followed by MLP achieved satisfactory performance. Excellent accuracy achieved by the above ML techniques demonstrates their potential for application in the optimization of rotors under uncertainty.

Influence of structural and material property uncertainties on biomechanics of intervertebral discs - Implications for disc tissue engineering

This study investigated how variations of structural and material properties of human intervertebral discs (IVDs) affect the biomechanical responses of the IVDs under simulated physiological loading conditions using a stochastic finite element (SFE) model. An SFE method, which combined an anatomic FE model of human lumbar L3-4 segment and probabilistic analysis of its structural and material properties, was used to generate a dataset of 500 random disc samples with varying structural and material properties. The sensitivity of the biomechanical responses, including intervertebral displacements/rotations, intradiscal pressures (IDP), fiber stresses and matrix strains of annulus fibrosus (AF), were systematically quantified under various physiological loading conditions, including a 500N compression and 7.5Nm moments in the 3 primary rotations. Significant variations of the IDPs, IVD displacements/rotations, and stress/strain distributions were found using the dataset of 500 ramdom disc samples. Under all the loading conditions, the IDPs were positively correlated with the Poisson's ratio of the NP (r=0.46 to 0.75, p=0.004-0.001) and negatively with the Young's modulus of the annulus matrix (r=-0.48 to -0.65, p=0.003-0.001). The primary intervertebral rotations were significantly affected by the Young's modulus of the annulus matrix (r=-0.44 to -0.71, p=0.001-0.032) and the orientations of the annular fibers (r=-0.45 to -0.69, p=0.001-0.029). The heterogeneity of structures and material properties of the IVD had distinct effects on the biomechanical performances of the IVD. These data could help improve our understanding of the intrinsic biomechanics of the IVD and provide references for optimal design of tissue engineered discs by controlling structural and material properties of the disc components.

GPR-inferred fracture aperture widening in response to a high-pressure tracer injection test at the Äspö Hard Rock Laboratory, Sweden

We assess the performance of the Ground Penetrating Radar (GPR) method in fractured rock formations of very low transmissivity (e.g. T ≈ 10−9–10−10 m2/s for sub-mm apertures) and, more specifically, to image fracture widening induced by high-pressure injections. A field-scale experiment was conducted at the Äspö Hard Rock Laboratory (Sweden) in a tunnel situated at 410 m depth. The tracer test was performed within the most transmissive sections of two boreholes separated by 4.2 m. The electrically resistive tracer solution composed of deionized water and Uranine was expected to lead to decreasing GPR reflections with respect to the saline in situ formation water. The injection pressure was 5000 kPa leading to an injection rate of 8.6 mL/min (at steady state) that was maintained during 25 h, which resulted in a total injected volume of 13 L. To evaluate the fracture pathways between the boreholes, we conducted 3-D surface-based GPR surveys before and at the end of the tracer tests, using 160 MHz and 450 MHz antennas. Difference GPR data between the two acquisitions highlight an increasing fracture reflectivity in-between the boreholes at depths corresponding to the injection interval. GPR-based modeling suggests that the observed increasing reflectivity is not due to the tracer solution, but rather to a 50% widening of the fracture. Considering prevailing uncertainties in material properties, a hydromechanical analysis suggests that such a degree of widening is feasible. This research demonstrates that field-scale in situ GPR experiments may provide constraints on fracture widening by high-pressure injection and could help to constrain field-scale elastic parameters in fractured rock.

Reliability-based Design Optimization of Laminated Composite Structures under Delamination and Material Property Uncertainties

Delamination is a major type of defects from manufacturing process in laminated composite structures, exhibiting uncertain characteristics which are represented by mixed random variables of continuous in-plane position and delamination size, as well as discrete through-the-thickness position, which should be considered in the design phase of composite structures. Thus, this paper presents a reliability-based design framework for optimal design of composite stacking sequence, for the first time to consider both delamination and material property uncertainties from manufacturing process. Mixed continuous-discrete random variables are involved, and a reliability analysis method is newly proposed to tackle this mixed-variable problem, maintaining high levels of both accuracy and efficiency. The formula of total probability is first employed to formulate the reliability constraint so that discrete and continuous random variables are decoupled; Monte Carlo simulation is then used for reliability analysis with respect to continuous random variables, and a surrogate modelling approach based on Gaussian process regression model is adopted to reduce computation costs. As design variables of ply angles are limited to a discrete set, a genetic algorithm with some proposed improvements is used to handle discrete design variables. Consequently, an optimization framework is devised for composite laminate design under uncertainties from manufacturing process, which is verified via case studies of a cantilever composite plate and can also be extended as a general solution for other composite laminates. With integrated consideration of manufacturing limitations and imperfections as well as structural performances, the presented framework provides a valuable tool in composite structure design.

Online condition monitoring of floating wind turbines drivetrain by means of digital twin

This paper presents a digital twin (DT) condition monitoring approach for drivetrains on floating offshore wind turbines. Digital twin in this context consists of torsional dynamic model, online measurements and fatigue damage estimation which is used for remaining useful life (RUL) estimation. At first, methods for system parameter estimation are presented. The digital twin model provides sufficient inputs for the load observers designed in specific points of the drivetrain to estimate the online load and subsequently stress in the different components. The estimated real-time stress values feed the degradation model of the components. The stochastic degradation model proposed for estimation of real-time fatigue damage in the components is based on a proven model-based approach which is tested under different drivetrain operations, namely normal, faulty and overload conditions. The uncertainties in model, measurements and material properties are addressed, and confidence interval for the estimations is provided by a detailed analysis on the signal behavior and using Monte Carlo simulations. A test case, using 10 MW drivetrain, has been demonstrated.

A probabilistic creep model incorporating test condition, initial damage, and material property uncertainty

Uncertainty is prevalent in the creep resistance of alloys, where at elevated temperature and low pressure, rupture can range across logarithmic decades. In this study, a probabilistic continuum-damage-mechanics (CDM)-based model is derived to capture the uncertainty of creep resistance. To meet this objective, creep data for alloy 304 Stainless Steel is gathered. A constitutive model, “Sinh”, is calibrated deterministically to determine the statistical variability of the material properties. Three sources of uncertainty are injected into the model: test condition (stress and temperature), initial damage, and material properties. Probabilistic simulations are carried out by (a) calibrating probability distribution functions (pdfs) for each source of uncertainty (b) randomly sampling the pdfs using Monte Carlo methods and (c) executing simulations to replicate the uncertain creep behavior. A sensitivity analysis is performed to evaluate the relative effect of each source of uncertainty. In full probabilistic simulations, the cumulative uncertainty of creep behavior is evaluated. The probabilistic model accurately predicts the creep deformation and rupture of the available experiments. The probabilistic model is validated for interpolation but lacks extrapolation ability. Several future works are proposed to further improve the model.

Biomechanical Effects of a Cross Connector in Sacral Fractures - A Finite Element Analysis.

Background: Spinopelvic fractures and approaches of operative stabilization have been a source of controversial discussion. Biomechanical data support the benefit of a spinopelvic stabilization and minimally invasive procedures help to reduce the dissatisfying complication rate. The role of a cross connector within spinopelvic devices remains inconclusive. We aimed to analyze the effect of a cross connector in a finite element model (FE model).Study Design: A FE model of the L1-L5 spine segment with pelvis and a spinopelvic stabilization was reconstructed from patient-specific CT images. The biomechanical relevance of a cross connector in a Denis zone I (AO: 61-B2) sacrum fracture was assessed in the FE model by applying bending and twisting forces with and without a cross connector. Biomechanical outcomes from the numerical model were investigated also considering uncertainties in material properties and levels of osseointegration.Results: The designed FE model showed comparable values in range-of-motion (ROM) and stresses with reference to the literature. The superiority of the spinopelvic stabilization (L5/Os ilium) ± cross connector compared to a non-operative procedure was confirmed in all analyzed loading conditions by reduced ROM and principal stresses in the disk L5/S1, vertebral body L5 and the fracture area. By considering the combination of all loading cases, the presence of a cross connector reduced the maximum stresses in the fracture area of around 10%. This difference has been statistically validated (p < 0.0001).Conclusion: The implementation of a spinopelvic stabilization (L5/Os ilium) in sacrum fractures sustained the fracture and led to enhanced biomechanical properties compared to a non-reductive procedure. While the additional cross connector did not alter the resulting ROM in L4/L5 or L5/sacrum, the reduction of the maximum stresses in the fracture area was significant.

Experimental study on the mechanical properties of high-strength stainless steel at room and elevated temperatures

Tensile tests at room and elevated temperatures were conducted on a novel high-strength stainless steel to study its mechanical properties at different temperatures. The failure modes, stress–strain curves and strain–temperature curves for all the coupons were obtained and investigated. The tests at room temperature show that the stress–strain curves at room temperature do not include an obvious yield plateau and agree well with the constitutive model proposed by Gardner. The test results at elevated temperatures show that when the temperature is less than or equal to 200 °C and greater than or equal to 400 °C, the strength and initial stiffness of this novel material decreased gradually with increasing temperature, Whereas its strength did not change significantly at temperatures of 200∼400 °C. Based on the test results, a constitutive model and corresponding hardening index for elevated temperatures were deducted, and the reduction factors of mechanical parameters at elevated temperatures were proposed. In addition, a reliability analysis of these mechanical parameters was conducted, and then the standard values of the material strength and the statistical parameters of the material properties uncertainties for this type of high-strength stainless steel were presented.

Wind vulnerability analysis of standing seam roof system with consideration of multistage performance levels

The vulnerability analysis of cladding usually reflects the performance levels of roof systems under wind uplift failure. But the damage area of roof system under wind uplift failure is often large, and this causes difficulty in post-disaster reconstruction. In this study, the vulnerability analysis of a roof system was conducted considering the multistage performance levels during the wind uplift failure process of the roof system. First, based on a study on the wind uplift failure mechanism of the roof system, the failure process was divided into four stages according to the deformation of the roof system components and the change in structural responses. Second, the classification criteria and restoration measures corresponding to three-stage performance levels (moderate damage, severe damage, and failure) of the roof system were proposed based on the results of 50 numerical cases. Third, the damage parameter β was defined as a unified index to quantify the three-stage performance levels. The quantitative results for the numerical cases were consistent, and the damage parameter β values were 0.4, 0.73, and 1.0 respectively. Finally, the uncertainty of material properties was considered, and the Latin hypercube sampling was performed to generate structural samples. On this basis, 7000 load–structure samples were analyzed using numerical methods, and the vulnerability curves of the roof system were obtained by fitting the numerical calculations result using the least-squares method. The vulnerability curves can be used as a reference for selecting roof system models and adopting restoration measures after a disaster based on the engineering requirements.

Effects of soil–structure interaction on seismic performance of a low-rise R/C moment frame considering material uncertainties

This study investigated the effects of soil–structure interaction (SSI) on the performance of low-rise reinforced concrete (R/C) structures subjected to earthquakes. The uncertainty of material properties, such as steel yield and concrete compressive strengths, was addressed using the Monte Carlo simulation with Latin hypercube sampling. A planar R/C moment frame of three bays and three stories was subjected to 20 selected ground motions for this purpose. In the flexible-base models, the soil was modeled with springs and dashpots, and the mass and moment of inertia of the footing were lumped at the bottom of the column. In contrast, for the fixed-base model, the bottoms of the columns were fixed in all translational and rotational directions. A parametric study was conducted for the shear wave velocity of soil, varying from 1000 to 50 m/s. The responses of the flexible-base and fixed-base models were compared in terms of the ductility, maximum interstory drift, and maximum total drift (ratio of top displacement to building height) for three performance levels in ASCE 41-17: intermediate occupancy (IO), life safety (LS), and collapse prevention (CP). The pushover analysis results indicate that a higher shear wave velocity leads to a higher ductility capacity. The uncertainty of the material properties produces an extensive range of ductility factors. The seismic drift responses of the flexible-base models are larger than those of the fixed-base model, particularly in the range of shear wave velocities less than 180 m/s (i.e., soft soil). From the failure probability analyses, the threshold shear wave velocity below which the effects of SSI should be considered is approximately 180 m/s for IO and 100 m/s for both LS and CP.

Warpage Simulation During Fan-Out Wafer-Level Packaging Process with Uncertainty of Material Properties.

Along with the reduction in semiconductor chip size and enhanced performance of electronic devices, high input/output density is a desired factor in the electronics industry. To satisfy the high input/output density, fan-out wafer-level packaging has attracted significant attention. While fan-out wafer-level packaging has several advantages, such as lower thickness and better thermal resistance, warpage is one of the major challenges of the fan-out wafer-level packaging process to be minimized. There have been many studies investigating the effects of material properties and package design on warpage using finite element analysis. Current warpage simulations using finite element analysis have been routinely conducted with deterministic input parameters, although the parameter values are uncertain from the manufacturing point of view. This assumption may lead to a gap between the simulation and the field results. This paper presents an uncertainty analysis of wafer warpage in fan-out wafer-level packaging by using finite element analysis. Coefficient of thermal expansion of silicon is considered as a parameter with uncertainty. The warpage and the von Mises stress are calculated and compared with and without uncertainty.

Sequential mixture of Gaussian processes and saddlepoint approximation for reliability-based design optimization of structures

This paper presents an efficient optimization procedure for solving the reliability-based design optimization (RBDO) problem of structures under aleatory uncertainty in material properties and external loads. To reduce the number of structural analysis calls during the optimization process, mixture models of Gaussian processes (MGPs) are constructed for prediction of structural responses. The MGP is used to expand the application of the Gaussian process model (GPM) to large training sets for well covering the input variable space, significantly reducing the training time, and improving the overall accuracy of the regression models. A large training set of the input variables and associated structural responses is first generated and split into independent subsets of similar training samples using the Gaussian mixture model clustering method. The GPM for each subset is then developed to produce a set of independent GPMs that together define the MGP as their weighted average. The weight vector computed for a specified input variable contains the probability that the input variable belongs to the projection of each subset onto the input variable space. To calculate the failure probabilities and their inverse values required during the process of solving the RBDO problem, a novel saddlepoint approximation is proposed based on the first three cumulants of random variables. The original RBDO problem is replaced by a sequential deterministic optimization (SDO) problem in which the MGPs serve as surrogates for the limit-state functions in probabilistic constraints of the RBDO problem. The SDO problem is strategically solved for exploring a promising region that may contain the optimal solution, improving the accuracy of the MGPs in that region, and producing a reliable solution. Two design examples of a truss and a steel frame demonstrate the efficiency of the proposed optimization procedure.

Reliability-based seismic performance of masonry arch bridges

Seismic structural assessment of masonry arch bridges is essential due to their cultural, economic and strategic importance and vulnerability. A realistic and rigorous structural assessment is necessary in order to protect the bridges and use resources carefully. At this time, there are no standardised or widely accepted assessment procedures, and the performance criteria for masonry arch bridges are not available. This study presents an overarching reliability-based seismic assessment methodology based on analytical modelling, laboratory testing and probabilistic assessment. It investigates the performance criteria concept and proposes performance limit states. The methodology is applied to a historical masonry arch bridge in Turkey. To consider rigorously the uncertainties in material properties and seismic input, probabilistic nonlinear analyses are conducted using a detailed 3D finite element model. The results are combined with the proposed limit state definitions to generate the capacity and demand distributions. Both distributions are used in Monte Carlo simulation and First-Order Reliability Method (FORM) to estimate the probability of exceedance and reliability indexes for each limit state. The proposed probabilistic assessment methodology will be a useful approach to obtaining more reliable information about masonry arch bridges' expected seismic performance and for better-informed decision-making, especially when designing intervention actions and post-earthquake scenarios.