Proceedings of the 6th International Symposium on Uncertainty Quantification and Stochastic Modelling

The wind turbine foundations are subject to dynamic and static loadings. Some studies have shown that it is necessary to study the liquefaction of the soil under the foundations due to the impact of these loadings. However, in literature there are not many studies focusing on the comparison between the experimental results and numerical modeling of static liquefaction. In this study, NorSand model was used to simulate the static liquefaction behavior of soil. First, a series of experimental data were selected from the literature to study the experimental behavior leading to liquefaction of saturated Hostun sand RF. Then, these experimental data were compared to the results simulated by using NorSand model. This study focuses on the uncertainties of experimental results leading to the uncertainties of numerical modeling results. Furthermore, the numerical model integrates physical parameters related to the nature of the soil and also mathematical parameters. To modelize the static liquefaction of soil, some input parameters are needed to be determined based on the experimental tests. The corresponding uncertainties are evaluated to quantify the effect of the model parameters on the liquefaction potential soil of Hostun sand RF. An analysis of the uncertainties linked to the choice of these parameters makes it possible to reduce the difference between the experimental results and their simulation and as well the uncertainties.

Silt-based construction material is an ecological and economical alternative for typical cement-based concrete and has received lately the researchers’ attention more than before. Some researches were done on the raw earth material to enhance its characteristics as strength and ductility for being widely used for various materials. Yet, many other mechanical properties can be used to study the mechanical properties of raw earth materials such as strain modulus and toughness. Studies concerning the toughness of a material were rarely considered previously except for metals despite its significant role associated to the energy absorbed by the material under loading before fracturing. The purpose of this paper is to restate the normal toughness definition used in the literature for typical construction materials and presents the possibilities of the repetitions of our experimental tests showing the statistical error occurred between same tests performed comparing the stress-strain graphs for three replicates done for each formulation out of 25. This paper will focus on the uncertainties and the possibility to neglect the intruding samples to reach better results and better simulate and fit the experimental data in numerical analysis. Experimental tests has some statistical errors and the uncertainties must be minimal compared to the complications of the experiment.

Day after day, soil liquefaction took the attention of the researchers due to its huge and dangerous impact on its surroundings. Generally, soil liquefaction is related to saturated soils; however, recent studies showed that it is possible for unsaturated soils. Laboratory tests are done using dynamic triaxial test on unsaturated Hostun sand RF. As all experimental tests, uncertainties are unavoidable due to many factors affecting these tests from the sample preparation, the considered approximations (the stopping conditions of each phase of the test) and the heterogeneity of the material. Dynamic triaxial experiments were done on Hostun Sand RF samples with relative density of 50% in undrained conditions. This paper presents the possibilities of the repetitions of our experimental tests showing the statistical error (standard deviation and coefficient of variation) occurring between the same tests performed, focusing on the different parameters that might cause these uncertainties. The experimental tests carried out showed that it is impossible to be 100% repeatable and perfect, but the statistical errors and the uncertainties must be minimal compared to the complexity of the experimental test. To reduce these uncertainties, it is necessary to perform more replicated tests; however, in geotechnical field, it costs additional time and expenses.

For many years, starting in the 1960s and 1970s, concrete was known only as a utilitarian material providing mechanical strength and durability for new construction (civil works; bridges, tunnels, and administrative and residential buildings). Today, environmental considerations complement the design of structures. Aesthetics has been treated differently, it has been too often forgotten in the construction of large complexes for many years, to become the “unloved” grey material. Indeed, raw concrete surfaces tend to be porous and have a relatively uninteresting appearance. However, Auguste Perret, the French architect of reinforced concrete was the initiator of the use of concrete as a stone in the design of building facades. The present study concerns the uncertainties on the Unconfined Compressive Strength (UCS) of raw and textured concrete. For do this, the nine raw concrete samples and the nine texture concrete samples were prepared. Thereafter, the Unconfined Compressive Strength test was carried out to measure the Unconfined Compressive Strength values. The corresponding uncertainties are evaluated to quantify the uncertainties on the Unconfined Compressive Strength for raw and texture concrete samples. Finally, the compression of the Uncertainties on the Unconfined Compressive Strength of raw and textured concrete samples was done.

New challenges in shape optimization design under uncertainties lead to inspiration from nature. In this paper, we choose trees as the inspiration resource and apply the axiom of uniform strains, a governing principle of tree design, to avoid material overloading or under-utilizing. The hypothesis of the uniform strains is formulated as the mean and standard deviation of strains which are defined as the optimization objectives. Then we use the isogeometric analysis (IGA) method to establish the numerical models. To take the geometric uncertainties into account, the coordinates of control points are defined as design variables. In the optimization process, the non-dominated sorting genetic algorithm II (NSGA-II) is applied to update design variables to figure out the optimal geometry. The Pareto front is obtained after iterative computation. The results based on bio-inspired criteria show that structural resistance can be increased significantly. This research provides new criteria for structural robust design under uncertainties.

In order to reduce the energy impact of building materials and, more generally, the environmental impact, raw earth can be an alternative to the conventional building materials like cement and fired earth bricks. Since earliest times, earthen building materials are becoming one of the most known construction techniques in the world thanks to its important benefits. This material has the capacity to play a significant role in regulating moisture and heat in buildings. It is distinguished by its low thermal conductivity, which renders it an effective thermal insulator. Additionally, it exhibits a remarkable ability to facilitate the diffusion of water vapor.

In this study, we are interested in the hygric characterization of raw earth material. Generally, in the experiment studies, one test is not representative and is not sufficient to analyze the results and the observed phenomenas. For this reason, a repetitive hygric experimental tests were carried out in this study and the results showing the uncertainties of the measurements will be presented and analyzed to determine the parameters that could cause these uncertainties.

The present work aims to analyze the effectiveness of a passive vibration control device in a structure subjected to random vibrations. The structure is a ten-story building equipped with a Tuned Mass Damper (TMD) at the top and it is subjected to artificial seismic excitations generated by the Kanai-Tajimi spectrum. The uncertainties present in both the systems and excitation parameters are taken into account. Thus, mass, stiffness and damping of the structure and the TMD, as well as peak ground acceleration (PGA), ground frequency and ground damping ratio are assumed as random variables, and the problem is solved via Monte Carlo Simulation. The study uses Newmark's numerical integration method to obtain the results of displacement, velocity, acceleration and maximum interstory drift values of the structure. The results obtained during the study demonstrate that the variance decreased and the dynamic response of the structure in terms of interstory drift is considerably reduced by about 55% after installing the TMD at the top of the building.

In the design of structures, there are uncertainties of different origin often associated with the properties of materials, geometry and applied loads. With the Reliability-Based Design Optimization (RBDO) method, it is possible to consider design constraints in terms of failure probabilities or target reliability indices, for a structure subject to performance constraints as limit state functions (LSF), in a classical optimization problem. In this way, RBDO analysis takes design variables uncertainties and its effects directly. This work intents to present a RBDO application in a steel frame, with an usual double-loop approach, considering the first and second order structural analysis, with optimization by Genetic Algorithms (GA). Target reliability indices are defined and assessed by FORM (First Order Reliability Method), while GA searches the optimal solution between 18 W-shapes from AISC database (2017), which represents the mininum material mass required for satisfy the constraints. In some cases, it is shown that considering second-order effects can result in lighter frames, as the calculated reliability index can get higher.

In the real world, multiple dynamic biological phenomena present an intrinsic randomness due to their nature. One of the most common ways of modeling them is to use random differential or random difference equations, whose parameters are considered as random variables. However, since these are complex models, independence between these parameters is usually assumed just for simplicity, without even having tested this hypothesis in the phenomenon under study. On the other hand, the impossibility of solving the calibration of random models with classical deterministic optimization techniques has given rise to new stochastic calibration techniques, such as bio-inspired algorithms. In this paper, we present a calibration method based on the Multi-Objective Particle Swarm Optimization (MOPSO) algorithm of a random model with a set of random parameters without assuming independence between them. The calibration goal is to find the multivariate probability distribution of the random parameters vector that best captures the uncertainty of the data by minimizing two fitness functions. To show the value of the method, we will apply it to a simple first-order difference model for the evolution of the growth of breast cancer.

Additive manufacturing is making it possible to increase the complexity of designed mechanical structures. However, the variability inherent to this manufacturing process can influence significantly the performance of structural elements, specially in phononic crystals and metamaterials since their working principles relies on the repetition of identical cells with a dedicated designed geometry. In this work, first, a design of experiments approach is applied to a determine a sampling strategy in order to characterize an additive manufacturing machine. Then, mechanical properties of the samples are inferred using material properties measured with an ultrasound transducer. The material density was measured using the weight of the samples, both dry and immersed in water, using the buoyancy force expression. It is known that the elastic modulus measured via ultrasound is biased. Therefore, the distributions inferred using ultrasound measurements were updated using experimental forced responses of sample rods and dynamic models via the Spectral Element Model. Updated values are used in statistical regression modeling to infer the stochastic field over print are of the 3D printer. The presented work is a first step in the longer term research goal: to show how to model the overall variability of a given additive manufacturing process, which is usually obtained in the statistical process control, and explain how to use it in the design of robust phononic crystal and metamaterial designs. The printing direction presented a statistically significant relationship with the elastic modulus and with the mass density, while only the printing direction presented a statistically significant relationship for the shear modulus.

To present ideas, a model problem consisting of a moving mass-belt system with random friction showing the stick-slip phenomenon is treated. The dynamics is simulated. The objective of this work is to assess the behaviour of the computation cost in terms of the run-time, which is random, and its relationship with some of the output variables that define the dynamical behaviour of the mechanical system, such as the duration of the phases present in the simulation, sticks and slips, and the number of phases that occur in each realisation. All this is analysed from a stochastic perspective. However, the probabilistic model to analyse the distribution of a three-dimensional random vector, formed by the run-time, duration and number, belongs to \(R^4\), thus it is difficult to characterise and visualise. Hence, in this study, the use of random variable transformations to produce new independent variables is explored as an attempt to reduce the number of dimensions that need to be considered. Also, the change of variables is used to assess the link between the behaviour of the results and the chosen integration method. It is shown that the predictions obtained with the Monte Carlo method combined with a Multiple Scales analytical approximation are influenced by the number of transition phases rather than their durations.

In this paper, the spread of a general epidemic over time is modeled as a branching process. It is a stochastic process sorted as an individual-based model, which records population growth over generations with uncertainties to its size. The source of randomness is inherently related to the individual behavior of each member in a population. In this context, the transmissibility of the disease, i.e., the contagion from an infected person to susceptible ones is the root. Therefore, a discrete random variable models the number of infections per infector and rules the branching process. Given the probabilistic model of the contagion, the objective of the paper is to compare three methodologies to evaluate the mass functions of further generations of the branching process: probability generating functions (pgf), Markov chains (MC) and Monte Carlo simulations (MCS). The former gives analytical expressions, that can be symbolic computed, to evaluate the probability of an arbitrary number of infected members for a desired generation, whereas MC is a semi-numerical methodology and the latter is indeed a numerical one. The comparison between all of them relies on computational cost (runtime and storage) and limitation of applicability in relation to the mass function of the contagion. One of the characteristics of interest in the analysis is the determination of which methodologies allow the calculation of the mass function of a further generation without computing the mass functions of previous ones. This feature is referred in here as not time-dependent. Another characteristic of interest is the determination of which methodologies allow the computation of just some values of the mass function of a generation, i.e., probabilities related to the same generation can be achieved independently from the others. This is so-called a local property.

Data Assimilation is a procedure for fusion from the observational system and previous forecasting to calculate the initial condition – also called analysis – for the next prediction cycle. Several methods have been developed and applied for data assimilation (DA). We can cite the Kalman filter, particle filter, and variational approach as methods employed for DA. However, the mentioned methods are computer intensive. One alternative to reduce the computational effort for DA is to apply a neural network (NN) to emulate a computationally expensive technique. The NN approach has been also applied for ensemble prediction to address uncertainty quantification for each forecasting cycle. A self-configuring framework was applied to design the best NN architecture to emulate the Kalman filter for DA, using the metaheuristic: Multiple Particles Collision Algorithm (MPCA). The optimal artificial neural network is implemented on two types of co-processors: FPGA (Field-Programmable Gate Array), and TPU (tensor processing unit). Shallow water 2D system is designed to simulate ocean circulation dynamics, where the finite difference scheme is used for numerical integration of the model. The artificial neural network was effective, with reduction of processing time. The use of FPGA or TPU as co-processors for data assimilation have similar precision in comparison with analysis calculated by software. The better processing time performance among multi-core CPU, FPGA, and TPU was obtained by the TPU when the number of grid points (\(N \times N\)) is greater than 150. For \(N \le 150\), the CPU presented a smaller execution time.

Uncertainty propagation has gained increasing attention in the research community in recent years. A better understanding of the uncertainty translates into a more efficient final product. Composite materials are susceptible to the aforementioned uncertainties, for instance by means of variations in material properties, loadings and manufacturing process. In this study, a composite plate uncertainty propagation problem is addressed with three techniques: Anti-optimization Interval Analysis, Polynomial Chaos Expansion (PCE), and the traditional Monte Carlo method. The dynamic mechanical response of the composite plate is analysed in the time domain. The anti-optimization interval analysis approach resulted in wider envelopes in the time histories (lower and upper bounds) when compared to PCE and Monte Carlo, especially in the last and more challenging example. Despite being unable to generate envelopes as broad as the other two approaches, PCE showed to be very attractive due to the small number of function evaluations used, especially in simpler problems. The adopted PCE algorithm is based in a non-intrusive approach: The Multivariate Collocation Method.

In this work, we explore the use of Uncertainty Quantification (UQ) techniques of representation in Bayes estimation and representation. UQ representation is a Hilbertian approach which furnishes distributions from experimental data in limited number. It can be used to generate priors to be used by Bayesian procedures. In a first use, we consider De Finetti’s representation theorem with few data points and we show that the UQ methods can furnish interesting priors, able to reproduce the correct distributions when integrated in the De Finetti’s representation theorem. In a second use, we consider Bayes estimation of the parameters of a distribution. Analogously to the preceding situation, a limited sample is used to generate a UQ representation of the parameters. Then, we use it as prior for the Bayesian procedure. The results show that the approach improves the quality of the estimation, when compared to the standard Bayesian procedure. The results are also compared to Fisher’s procedure of estimation.

Rainfall monitoring is of paramount importance for many applications, such as meteorology, hydrology, and flood prevention. In order to circumvent the expensive deployment of weather radar networks, many articles propose rainfall estimation by using the received signal power of microwave links as they are sensitive to precipitation at certain frequencies. In this context, the International Telecommunication Union (ITU) provides a power-law relationship that allows the computation of the precipitation rate from the attenuation due to rainfall. This physics-based approach uses scattering calculation to derive the power-law coefficients, which depend only on the frequency. However, the practical use of this equation faces other important parameters, such as the link length and the distance from the bucket gauge to the microwave link. These factors may significantly affect the prediction. In this article, it is proposed a data-based alternative for the estimation of the power-law coefficients, where the Levenberg-Marquardt algorithm is used to adjust them using several data collected from different radio links in West Africa. The estimation quality is assessed in terms of its correlation with rain rate measurements from bucket gauges spread across the African testbed.

In this paper, we apply a stochastic Kriging-based optimization algorithm to solve a generic infrastructure planning problem using direct policy search (DPS) as a heuristic approach. Such algorithms are particularly effective at handling high computational cost optimization, especially the sequential Kriging optimization (SKO). SKO has been proving to be well-suited to deal with noise or uncertainty problems, whereas assumes heterogeneous simulation noise and explores both intrinsic uncertainty inherent in a stochastic simulation and extrinsic uncertainty about the unknown response surface. Additionally, this paper employs a recent stochastic Kriging method that incorporates smoothed variance estimations through a deterministic Kriging metamodel. The problem evaluated is the DPS as a heuristic approach, this is a sequential decision problem-solving method that will be applied to a generic infrastructure planning problem under uncertainty. Its performance depends on system and cost model parameters. Previous research has employed Cross Entropy (CE) as a global optimization method for DPS, while this paper utilizes SKO as a stochastic Kriging-based optimization method and compares the results with those obtained by CE. The proposed approach demonstrates promising results and has the potential to advance the field of Kriging-based algorithms to solve engineering problems under uncertainties.

Numerical weather and climate prediction have been addressed by numerical methods. This approach has been under permanent development. In order to estimate the degree of confidence on a prediction, an ensemble prediction has been adopted. Recently, machine learning algorithms have been employed for many applications. Here, the con- fidence interval for the precipitation climate prediction is addressed by a decision tree algorithm, by using the Light Gradient Boosting Machine (LightGBM) framework. The best hyperparameters for the LightGBM models were determined by the Optuna hyperparameter optimization framework, which uses a Bayesian approach to calculate an optimal hyperparameter set. Numerical experiments were carried out over South America. LightGBM is a supervised machine-learning technique. A period from January-1980 up to December-2017 was em- ployed for the learning phase, and the years 2018 and 2019 were used for testing, showing very good results.

Uncertainty quantification has become a major interest for researchers nowadays, particularly in the field of risk analysis and optimization under uncertainties. Uncertainty is an essential parameter to take into consideration in time series forecasting. In this field we aim to develop mathematical models based on uncertainty quantification tools for road accidents forecasting as a part of the pre-disaster management phase and also provide an anticipative visualization of the most sensitive zones to accidents in Morocco. To achieve this goal, we use the Interpolation-based approximation method for resolution in order to describe and analyze the road traffic accidents by defining the cumulative distribution functions (CDFs) of road accidental deaths and injuries. The obtained CDFs show that the distribution of road accidental deaths and injuries in Morocco varies according to seasons i.e., High season and Low season. These models can be used for making predictions of the future occurrence and human impact of road traffic accidents as a part of the pre-disaster management phase which complete and validate our disaster risk management approach as a decision-making tool dedicated to governments and humanitarian organizations. This work deals with humanitarian logistical field and aims to use the developed models for probabilistic calculation of the road traffic accidents behavior which helps in the preparation of the logistical fabric for the future events.

During a delivery process, and in the global transportation network chain, milk and dairy products are considered as sensible and so a higher requirement must be imposed. This paper addresses a vehicle routing problem and propose an optimization model that consider the temperature as a source of uncertainty that has an impact on dairy products. Temperature is maintained and controlled within specified interval and limits, using some sensors introduced inside the vehicles. The process capability indices are introduced to measure the capability of the process, especially thermal characteristics. Dynamic Vehicle Routing (DVR) is presented in this work, optimizing both of the distance traveled and product’s temperature. The objective is to deliver products to different BIM stores in El Jadida city, and find the optimal route while maintaining the dairy product Temperature in their optimal values. We propose then a developed algorithm using the meta-heuristic Simulated Annealing (SA) algorithm. Numerical results show the optimized route sequence and also the optimized product’s temperature along the route.

Artificial neural networks (NNs) have shown remarkable success in a wide range of machine learning tasks. The activation function is a crucial component of NNs, as it introduces non-linearity and enables the network to learn complex representations. In this paper, we propose a novel activation function based on Hilbert basis, a mathematical concept from algebraic geometry. We formulate the Hilbert basis activation function and investigate its properties. We also compare its performance with popular activation functions such as ReLU and sigmoid through experiments on MNIST dataset under LeNet architecture. Our results show that the Hilbert basis activation function can improve the performance of NNs, achieving competitive accuracy and robustness via probability analysis.