Probabilistic Design Research Articles

Shape investigation and probabilistic representation of coastal storms. Applications to Mykonos and Barcelona

The main objective of the present work is the probabilistic representation of coastal storms’ parameters through non-parametric probability distributions that can give satisfactory estimates in the whole range of the variables’ values. Their proper probabilistic representation can provide crucial information for many applications including the probabilistic design of marine and coastal structures. Different non-parametric univariate distributions in combination with different copula types or the conditional model are applied, to check the closeness of their fit to the available bivariate coastal storm data (e.g., the storms’ maximum wave height and the associated peak wave period). Moreover, except for the classical kernel distribution, a new, recently developed Box-Cox transformed kernel method is also examined and applied. The latter has been already evaluated so far to sea states data but not to storm data. Therefore, the adopted methodology is implemented to real coastal storms in two different locations, derived from wave recordings from Mykonos (Greece) and Barcelona (Spain). Furthermore, some of the significant statistical properties of the observed coastal storms, such as the calm period, the duration, and the shape (triangular or trapezoid) are also detected. From the present analysis, the derived methodology for representing accurately coastal storms is clarified, giving thus a useful tool to engineers and researchers to consider extreme events probability of occurrence, which is essential for the design of coastal structures and consequently for the protection of coastal communities.

Probabilistic defect-based modelling of fatigue strength for incomplete datasets assisted by literature data

Probabilistic defect-tolerant fatigue design protocols have become the leading paradigms in structural engineering. To effectively deal with this problem, El Haddad’s (EH) curves are generally employed for the evaluation of the fatigue endurance limit. Herein, the synergic exploitation of Logistic Regression (LR) and Maximum a Posteriori (MAP) allows for calibrating EH parameters using the sole data from fatigue characterisation and post-mortem fractography. An extensive literature research provided the ground to introduce, when necessary, prior information for some of the more commonly used metallic alloys. Eventually, EH curves are retrieved upon a Monte Carlo simulation to support probabilistic engineering practice.

Stochastic analysis of excavation-induced wall deflection and box culvert settlement considering spatial variability of soil stiffness

In this study, a three-dimensional (3D) finite element modelling (FEM) analysis is carried out to investigate the effects of soil spatial variability on the response of retaining walls and an adjacent box culvert due to a braced excavation. The spatial variability of soil stiffness is modelled using a variogram and calibrated by high-quality experimental data. Multiple random field samples (RFSs) of soil stiffness are generated using geostatistical analysis and mapped onto a finite element mesh for stochastic analysis of excavation-induced structural responses by Monte Carlo simulation. It is found that the spatial variability of soil stiffness can be described by an exponential variogram, and the associated vertical correlation length is varied from 1.3 m to 1.6 m. It also reveals that the spatial variability of soil stiffness has a significant effect on the variations of retaining wall deflections and box culvert settlements. The ignorance of spatial variability in 3D FEM can result in an underestimation of lateral wall deflections and culvert settlements. Thus, the stochastic structural responses obtained from the 3D analysis could serve as an effective aid for probabilistic design and analysis of excavations.

A probabilistic multi-objective optimization mechanical design

Optimization design of machinery is usually a multi-objective one inevitably. At present, the popular mechanical optimization design is limited by the intrinsic shortcomings of the previous multi-objective optimization methods, which leads to the difficulty of non-comprehensive and nonsystematic optimal solutions in the viewpoint of probability theory. In the linear weighting “additive” method, there is inherent problems of normalization and introduction of subjective factors, and the final results depend on the normalization method to a great extent; the Pareto solution set is a “set” instead of an exact solution. In this paper, the probability—based multi-objective optimization, discretization with uniform design and sequential optimization are combined to establish a new approach of multi-objective optimization mechanical design based on probability theory; the probabilistic multi-objective optimization is used to transform the multi-objective optimization problem into single-objective optimization one from the perspective of probability theory; the discretization by means of uniform design provides an effective sampling to simplify the mathematical processing, which is especially important for dealing with multi-objective optimization problems with continuous objective functions; the sequential optimization algorithm is used to conduct the successive deep optimization. Furthermore, the implementation steps are illustrated with two examples. The results show that the approach can not only give excellent optimization results, but also provide a relatively simple processing.

Probability of unsatisfactory performance of monopile foundations for offshore wind turbines considering variations in seabed properties

Safe design of monopiles for Offshore Wind Turbines (OWT) requires an accurate estimation of the foundation soil material properties. Uncertainty in soils is mainly due to their inherent variability which involves various spatial and temporal processes they have been exposed to over their natural geological process. The limited amount of information from geotechnical investigations in the seabed, considering the size of OWT farms, adds to the uncertainty. Commonly used deterministic design approaches idealize soil layers by assigning average values to the mechanical soil properties and make use of empirical correlations that can significantly differ from offshore conditions. Probabilistic design approaches have been suggested in the literature to account for the effect of uncertainties on the foundation’s performance by applying a coefficient of variation (COV) to soil properties. Such methods include theoretical investigations by applying selected COV values to predetermined mean CPT profiles for sands and undrained shear strength for clays. This study calculates the probability of unsatisfactory performance, Pfsys, of monopiles in sands by implementing variation in friction angle and unit weight using current API and DNV-GL design guidelines. Monte Carlo Simulation is employed to generate random fields using lognormal, normal, and uniform distributions. Pfsys is presented for a case study found in the literature and a design exercise for which local COV for the Belgian coast is also proposed.

Reliability Assessment of Reinforced Concrete Beams under Elevated Temperatures: A Probabilistic Approach Using Finite Element and Physical Models

A novel computational model is proposed in this paper considering reliability analysis in the modelling of reinforced concrete beams at elevated temperatures, by assuming that concrete and steel materials have random mechanical properties in which those properties are treated as random variables following a normal distribution. Accordingly, the reliability index is successfully used as a constraint to restrain the modelling process. A concrete damage plasticity constitutive model is utilized in this paper for the numerical models, and it was validated according to those data which were gained from laboratory tests. Detailed comparisons between the models according to different temperatures in the case of deterministic designs are proposed to show the effect of increasing the temperature on the models. Other comparisons are proposed in the case of probabilistic designs to distinguish the difference between deterministic and reliability-based designs. The procedure of introducing the reliability analysis of the nonlinear problems is proposed by a nonlinear code considering different reliability index values for each temperature case. The results of the proposed work have efficiently shown how considering uncertainties and their related parameters plays a critical role in the modelling of reinforced concrete beams at elevated temperatures, especially in the case of high temperatures.

Analytical Modeling of Electronic and Photonic Materials Reliability: Perspective and Extension

Abstract The objective of this review is twofold: to show materials scientists, mechanical engineers, and reliability physicists not involved in electronics, photonics, microelectronic-mechanical-systems (MEMS), or MOEMS (optical MEMS) engineering what kind of value they could bring to this important “high-tech” area, as well as to demonstrate to “high-tech” engineers how they could benefit from the application of what has been developed, for many years, in the general field of physical design for reliability of materials and structures employed in various fields of engineering and applied science and what could be effectively applied to their body of knowledge. Accordingly, in the perspective part of the review, some critical and even paradoxical, i.e., a priori nonobvious, problems encountered in microelectronics and photonics materials science, reliability physics, and structural analysis are addressed using what could be called analytical (“mathematical”) modeling. The extension part has to do with some specific, mostly aerospace, recent applications of the probabilistic design for reliability concept and analytical modeling effort.

A probabilistic framework of creep life assessment of structural components at elevated temperatures

Current creep life assessment methods of components at elevated temperatures are mainly based on deterministic analysis strategies, which could not achieve the goal of probabilistic evaluation on creep failure. Based on this, a probabilistic framework of creep life assessment for components at elevated temperatures was provided. A method of determining distribution characteristics of material parameters was provided by randomly selecting a group of results at each stress level. Monte Carlo simulation was combined with finite element analysis technology to capture the distribution characteristic of creep rupture life of one typical structural component. Effect of standard derivation of material parameters on creep reliability assessment was discussed. Comparisons between probabilistic and deterministic creep design methods were made. Results indicated that the probabilistic analysis strategy can calculate the specific value of failure probability at various loading conditions, not two values of failure probability (i.e. 100% and 0%) by deterministic analysis strategy. The effect of standard derivation on mean values of effective stress and creep rupture life of the component is dependent on distribution characteristics of material parameters and related variables. A small standard derivation reduces the data scatter of effective stress and creep rupture life of the component.

ENERGY ASPECTS OF RELAXATION AND AGING OF NONWOVEN FIBROUS MATERIALS

The article proposes a model of the structure of a nonwoven fibrous material as a complex proba-bilistic design of fiber elements and areas of interaction between fibers and a mechanism for the interaction of elastic properties of fibers with friction between them, taking into account the structure of the material. The proposed mechanism for the behavior of fibers in a material under external influences made it possible to qualitatively explain the complex behavior of a material: reversible elastic deformations, plastic deformations, aging, and the gradual loss of operational advantages of non-woven fibrous fabrics. Generalized energy ideas about the accumulation and consumption of the residual energy of fiber deformation are used.

Risk-Based Assessment of the Reliability Level for Extreme Limit States in IEC 61400-1

The annual target reliability level for structural components is given as β = 3.3 in the main design standard for wind turbines IEC 61400-1 ed. 4. However, since the same safety factors are used for a range of load cases and limit states, deviations in the obtained reliability level can be expected, and it should be considered how to handle this in relation to the development of the IEC TS 61400-9 on probabilistic design measures. In this paper, structural reliability analyses were performed for components designed using safety factors for a range of extreme load cases, and by using the correlation between limit states for different years, the development of the reliability level over time was calculated. A relative risk-based assessment was applied to assess the optimal target reliability level and safety factors. The risk-based assessment explicitly includes the uncertainties, benefits, and costs and can motivate differentiation of the annual reliability level between load cases. Annual reliability indices were found to be in the range of 2.9–3.4, and although this includes values below the target of 3.3, it was also found that the optimal reliability indices were in the same range. The variation in reliability level can be motivated since the optimal target reliability is found to be lower than the current target for load cases with high correlation, as this causes the lifetime reliability level to be comparable to that of other extreme load cases with less correlation.

Design and validation of microperforated panel absorbers using Occam's razor and causal inference

Microperforated panel absorbers in forms of micro-poles /-slits (MPP/MSP) can achieve high absorption. However, noise control practice usually requires broadband high absorption. Single- or double-layer MSP/MPP absorbers often cannot meet practical requirements. Multilayers become a natural option. Multiple layers of MSP/MPP absorbers inherently complicates the design process upon a given design scheme. This work applies a Bayesian framework using a potentially multilayered prediction model. The Bayesian design involves two-levels of probabilistic inference to design a parsimonious number of layers using the model-selection solution, a quantitative implementation of Occam's razor, while the parameter estimation is used to estimate MPP/MSP parameters given the selected number of multilayers. This probabilistic design process rapidly hones in on the MPP/MSP parameters of each individual layer so that the overall composite meets the design goal. When experimentally validating the designed prediction upon the design scheme, manufacture inaccuracies may lead to deviations. In analyzing reasons of the deviations, this work further applies causal inference to analyze the cause-effect relationship. To this end a causal model has also been established. Using both parametric prediction model for the absorption performance and the causal model for causal inference of the deviation causes, the Bayesian multilayer design can be satisfactorily validated.

Reliability based topology optimization of thermoelastic structures using bi-directional evolutionary structural optimization method

The aim of this paper is to propose a novel computational technique of applying reliability-based design to thermoelastic structural topology optimization. Therefore, the optimization of thermoelastic structures' topology based on reliability-based design is considered by utilizing geometrical nonlinearity analysis. For purposes of introducing reliability-based optimization, the volume fraction parameter is viewed as a random variable with a normal distribution having a mean value and standard deviation. The Monte Carlo simulation approach for probabilistic designs is used to calculate the reliability index, which is used as a constraint related to the volume fraction constraint of the deterministic problem. A new bi-directional evolutionary structural optimization scheme is developed, in which a geometrically nonlinear thermoelastic model is applied in the sensitivity analysis. The impact of changing the constraint of a defined volume of the required design in deterministic problems is examined. Additionally, the impact of altering the reliability index in probabilistic problems is investigated. The effectiveness of the suggested approach is shown using a benchmark problem. Additionally, this research takes into account probabilistic thermoelastic topology optimization for a 2D L-shaped beam problem.

Potential and limitations of crowdsourced data for high-resolution rice mapping in Madagascar: The importance of representation

Given the projected population growth and rice consumption in Madagascar, assessing its rice production potential is important. Existing spatial representations of rice are characterized by coarse resolutions and diverge widely. Mapping rice production based on remote sensing offers a potential solution to this problem but its application in Sub-Saharan Africa is hindered by scarce ground truth data and a complex array of cropping systems. While crowdsourcing initiatives provide data that could in principle be used to overcome this hurdle, their usefulness in rice mapping is hitherto underexplored. Here, we investigate the usefulness of crowdsourced data to enhance the mapping of rice production areas in the data-poor context of Madagascar. At present, dedicated crowdsourcing initiatives only limitedly cover rice but do provide sufficient information to build a dataset of data points characterizing a No-Rice class. On the other hand, geotagged pictures from social media, which do document rice production areas, predominantly represent 'scenic' fields appealing to social media contributors, i.e. irrigated, intensive rice production systems. The archetypal nature of these data leads to distinct feature signatures. Consequently, these data could be successfully used for rice mapping in the Lake Alaotra basin, which is characterized by the type of intensive rice cropping that is well-represented by the crowdsourced data. However, it was not possible to construct an accurate map of rice production in the greater Antananarivo region or at the national scale using crowdsourced data as they do not sufficiently represent the present variety in rice production systems. The value of crowdsourced data thus depends on the representativeness of the data, which in turn depends on the application and can be improved through applying a probabilistic sampling design. Our study also highlights the need for data representation checks prior to data augmentation or classification for future applications wanting to construct credible maps using crowdsourcing within their sampling design for which we present a multi-faceted evaluation framework.

Limited Optimal Plastic Behavior of RC Beams Strengthened by Carbon Fiber Polymers Using Reliability-Based Design.

The plastic behavior of strengthened haunched beams utilizing carbon fiber-reinforced polymers (CFRP) was investigated using a probabilistic design that took into account random concrete properties, CFRP properties, and complementary strain energy values, with the reliability index serving as a limiting index, as the proposed method considers a novel method that deals with probabilistic parameters for models with limited plastic behavior designed based on the reliability index. The data used in this research were gathered and evaluated in a recent study on simply supported haunched beams reinforced with carbon fiber-reinforced polymers. The purpose of this research was to use the reliability limitation index for simulated strengthened haunched beams by taking into account randomness in concrete and CFRP properties and the complementary strain energy value, which is considered a plastic behavior controller that provides an illustration of the damage amount within the reinforcement steel bars. The results indicate how randomness affects the behavior of the presented models, which are chosen to have different numbers of CFRP strips. The variable randomness affects load and deflection values where the reliability index value increases as the corresponding load value decrease, reflecting the increased probability of failure in models subjected to higher loading conditions, while tension concrete damage percentages are reflected in the damage pattern presented in the results, showing that as the produced load increases, so does the damage intensity. It is also obvious that the reliability index served as a limitation index while taking concrete characteristics and complementary strain energy as random variables.

A decoupled double-loop method with the adaptive allowable limits for probabilistic performance-based design optimization

In this study, inspired by the idea of the sequential optimization and reliability assessment (SORA) method, a new decoupled double-loop method for probabilistic performance-based design optimization (PPBDO) has been proposed. The highlight of the proposed method is the independence of this method from the type of problem and the limit state function; in such a way that it can be used in non-linear problems with multiple probabilistic constraints with the implicit form of the limit state function. However, it requires less computational effort than conventional double-loop methods. In each cycle of this method, deterministic performance-based design optimization was performed and then the reliability of the optimal design was evaluated. If the results of the reliability assessment are not desirable, the allowable limit of the constraints in the deterministic optimization problem will be changed based on the results of the reliability assessment. This process repeats until the results of the reliability assessment become desirable. The metaheuristic enhanced vibrating particle system algorithm and the Monte Carlo simulation method were used for optimization process and reliability analysis, respectively. To evaluate the efficiency of the proposed method, the optimization problem was defined so as to reduce the structural weight while meeting the acceptance criteria for performance-based design of steel moment frames according to ASCE 41-13. The PPBDO of three- and nine-story steel moment frames were investigated and the results showed that the proposed method was able to reduce the volume of calculations and direct the search path toward a reliable space.

Tracking Control for Output Probability Density Function of Stochastic Systems Using FPD Method

Output probability density function (PDF) tracking control of stochastic systems has always been a challenging problem in both theoretical development and engineering practice. Focused on this challenge, this work proposes a novel stochastic control framework so that the output PDF can track a given time-varying PDF. Firstly, the output PDF is characterised by the weight dynamics following the B-spline model approximation. As a result, the PDF tracking problem is transferred to a state tracking problem for weight dynamics. In addition, the model error of the weight dynamics is described by the multiplicative noises to more effectively establish its stochastic dynamics. Moreover, to better reflect the practical applications in the real world, the given tracking target is set to be time-varying rather than static. Thus, an extended fully probabilistic design (FPD) is developed based on the conventional FPD to handle multiplicative noises and to track the time-varying references in a superior way. Finally, the proposed control framework is verified by a numerical example, and a comparison simulation with the linear-quadratic regulator (LQR) method is also included to illustrate the superiority of our proposed framework.

Reliability modeling and contrastive learning for unsupervised person re-identification

Unsupervised person re-identification (ReID) aims to learn discriminative identity features in scenarios without a ground-truth. Fully unsupervised person ReID methods usually iterate between pseudo-labels prediction and representation learning and have achieved promising performance. However, these methods are usually hampered by noisy labels. To address this issue, we propose a reliability modeling and contrastive learning (RMCL) method, which aims to reduce the impact of noisy labels and enhance the robustness of the model to hard samples. On the basis of existing work, first, we define the concept of probabilistic stability and design a stability estimation scheme to improve pseudo-labels reliability modeling. Second, we explore the reliability–informativity function to redefine the weights of samples, which can be easily introduced to existing optimization methods. Finally, we expand the range of hard samples and design an identity hard contrastive loss, which is used to increase the robustness of the model to hard samples. Experiments on three large-scale person ReID datasets (Market-1501, DukeMTMC-reID and MSMT17) validate the effectiveness of RMCL, which surpasses state-of-the-art fully unsupervised methods and cross-domain methods. Furthermore, we explore the superiority of RMCL in a new “three2one” scenario.

Failure-oriented-accelerated-testing (FOAT) and its role in assuring electronics reliability: review

A highly focused and highly cost-effective failure-oriented-accelerated-testing (FOAT) suggested about a decade ago as an experimental basis of the novel probabilistic design for reliability (PDfR) concept is intended to be carried out at the design stage of a new electronic packaging technology and when high operational reliability (like the one required, e.g., for aerospace, military, or long-haul communication applications) is a must. On the other hand, burn-in-testing (BIT) that is routinely conducted at the manufacturing stage of almost every IC product is also of a FOAT type: it is aimed at eliminating the infant mortality portion (IMP) of the bathtub curve (BTC) by getting rid of the low reliability “freaks” prior to shipping the “healthy” products, i.e., those that survived BIT, to the customer(s). When FOAT is conducted, a physically meaningful constitutive equation, such as the multi-parametric Boltzmann-Arrhenius-Zhurkov (BAZ) model, should be employed to predict, from the FOAT data, the probability of failure and the corresponding useful lifetime of the product in the field, and, from the BIT data, as has been recently demonstrated, - the adequate level and duration of the applied stressors, as well as the (low, of course) activation energies of the “freaks”. Both types of FOAT are addressed in this review using analytical (“mathematical”) predictive modeling. The general concepts are illustrated by numerical examples. It is concluded that predictive modeling should always be conducted prior to and during the actual testing and that analytical modeling should always complement computer simulations. Future work should be focused on the experimental verification of the obtained findings and recommendations.

Probabilistic seismic design of pile-supported building structure incorporating inherent variability of subsoil and ground motion uncertainty

Probabilistic seismic design of pile-supported building structure incorporating inherent variability of subsoil and ground motion uncertainty

Will That Color Bring Me Good Luck? The Effect of Package Color Saturation of Probabilistic Goods on Consumers’ Purchase Intention

Probabilistic goods are unique products or services that consumers obtain from sellers at a discounted price for any one of different goods. They are also common in everyday life, such as blind boxes and lucky bags. However, there are still many consumers unwilling to pay for them, and the current research on probabilistic goods fails to reveal the mechanism behind it, and cannot solve the marketing problem well. In this regard, based on construal-level theory, three empirical studies were conducted to investigate the effect of package color saturation of probabilistic goods on consumers’ purchase intention. The study found that compared with low saturation, high saturation packaging can significantly increase consumers’ purchase intention, which is mediated by subjective probability and moderated by transaction utility. Specifically, in the context of low transaction utility, the higher the saturation, the stronger the consumers’ purchase intention; in the context of high transaction utility, the effect of saturation is not significant. The conclusion of this paper expands the research on the visual effect of probabilistic goods packaging, and provides theoretical basis and practical guidance for marketers to consider probabilistic goods packaging design.