Imperfect Model Research Articles

Fair Competition and Inclusion in Sport: Avoiding the Marginalisation of Intersex and Trans Women Athletes

Despite the reality of intersex individuals whose biological markers do not necessarily all point towards a traditional binary understanding of either male or female, the vast majority of sports divide competition into categories based on a binary notion of biological sex and develop policies and regulations to police the divide. In so doing, sports governing bodies (SGBs) adopt an imperfect model of biological sex in order to serve their particular purposes, which, typically, will include protecting the fundamental sporting value of fair competition. Yet, one potential consequence of enforcing such an approach would seem to be the exclusion or marginalization of individuals whose biological development does not fit within the binary model, whether due to genetics or through a choice to undergo medical intervention to better represent a chosen gender identity. Any such exclusion or marginalization will inevitably tend to undermine another fundamental value of sport, that of inclusivity. In the context of those with differences of sex development, SGBs appear to be faced with a difficult problem: dealing with a conflict between two fundamental values of sport. Different approaches to this problem have been suggested, with some academics proposing that sports organisations, in general, ought to prioritise fairness above, while others suggest the need to ‘balance’ competing values or even to prioritise inclusion over fairness. However, it is argued that any of these approaches are, in principle, justifiable as any sport should be free to prioritise or balance its own values. What seems more important for any SGB is the need for a rational and transparent justification of regulations that pursue fair competition at the expense of inclusivity. Furthermore, where fair competition and inclusivity are fundamental values, any such justification would seem to demand adherence to some basic norms. First, the regulations should be built on (and articulate) a consistent and principled basis of what ‘fair competition’ means in a particular sport. Second, any regulations should only exclude or restrict participation to the minimum degree necessary to achieve the sense of fair competition so articulated. Third, SGBs should be transparent about what their values are and where their priorities lie so that participants and other stakeholders are able to make an informed choice as to whether they wish to participate in, support, or be associated with a particular sport. With reference to the adoption of the Eligibility Regulations for Athletes with Differences of Sex Development (the ‘DSD Regulations’) by the International Association of Athletic Federations (IAAF), this article seeks to evaluate whether the approach of the IAAF satisfied these basic requirements.

Geometric imperfections in CFS structural members: Part I: A review of the basics and some modeling strategies

Unavoidable geometric imperfections complicate the load–displacement response of thin-walled cold-formed steel (CFS) structural members. While the inclusion of geometric imperfections in shell finite element (FE) collapse simulations has long been the subject of research, no consensus exits on modeling their full three-dimensional spatial pattern. This paper is the first part in a two-part series and provides a review of the basics and a summary of some efforts geared towards modeling geometric imperfections. We discuss the necessary ingredients for systematic characterization of elastic buckling mode shapes, due to their frequent use in approximating geometric imperfections, and make a conscious effort to express some of the existing geometric imperfection models through three components: imperfection shape, magnitude, and combination coefficient. Different choices and selections of these components, pertaining to either the inherent buckling behavior of the members and/or physical measurements are critically examined. The details required to develop high fidelity nonlinear FE models of CFS members seeded with geometric imperfections are presented. We then perform a comparative study of collapse analysis results obtained from adopting different imperfection modeling strategies. The noticeable variability in the load carrying capacity and the stability behavior highlights an urgent need for reliable probabilistic frameworks for this class of problems. A stochastic framework to generate samples of imperfect shell FE models from limited available data and validate the prescribed or practice-oriented geometric imperfection models is presented in a companion paper (see Part II Farzanian et al., (2023)).

Geometric imperfections in CFS structural members, Part II: Data-driven modeling and probabilistic validation

This paper is the second part in a two-part series that examines the role of geometric imperfections in load–displacement response and collapse behavior of cold-formed steel (CFS) structural members. In part I (Farzanian et al., 2023) a review of the basics and a summary of efforts geared towards modeling geometric imperfections was provided. This included the ingredients needed for systematic identification of elastic buckling mode shapes, due to their frequent use in approximating geometric imperfections, and the development of high fidelity shell finite element (FE) nonlinear collapse analysis of CFS members seeded with different geometric imperfection models. Part II is the companion to the analysis in part I that revealed a noticeable variability in the collapse behavior and load carrying capacity of CFS members as a result of adopting different imperfection modeling strategies. In this part we provide the necessary steps to build a probabilistic framework that rests on machine learning, polynomial approximation, and parametric and non-parametric statistical inference and uses imperfection data to build a consistent stochastic field model of geometric imperfections. This data-driven model is then used to generate the much needed realizations of geometric imperfections that are faithful to the underlying statistics of measured data and therefore can be seeded, directly, in nonlinear collapse analysis of CFS members. Nonlinear shell FE analysis, within a stochastic simulation framework, is finally used to (statistically) quantify the impact of geometric imperfections and to enable probabilistic validation of geometric imperfection models.

Mathematical Modeling of COVID-19 with Vaccination Using Fractional Derivative: A Case Study

Vaccination against any infectious disease is considered to be an effective way of controlling it. This paper studies a fractional order model with vaccine efficacy and waning immunity. We present the model’s dynamics under vaccine efficacy, the impact of immunization, and the waning of the vaccine on coronavirus infection disease. We analyze the model under their equilibrium points. The model under the equilibrium points is discussed and proven that it is locally asymptotically stable if Rv is lesser than unity. We present the backward bifurcation hypothesis of the model and show that there is a parameter β2 that causes the backward bifurcation in the imperfect vaccine model. We show certain assumptions when ψ=1 for the imperfect vaccine case; the model is both stable globally asymptotically at the disease-free (R0≤1) and endemic cases (R0>1). By using infected cases from the recent wave throughout Pakistan, we shall estimate the model parameters and calculate the numerical value of the basic reproductive number R0≈1.2591. We present the comprehensive graphical results for the realistic parameter values and show many useful suggestions regarding the elimination of the infection from society. The vaccination efficacy that provides an important role in disease elimination is discussed in detail.

Analytical Study of Lateral Buckling of Pipelines with Initial Imperfection Based on Fixed-Fixed Beam Model

The beam analysis model and the initial imperfection are predominant factors in analyzing the lateral buckling behavior of submarine pipelines under high temperature. However, the existing beam models do not consider the inhibition provided by the virtual anchor point of the pipeline. In this study, a fixed-fixed beam model is introduced to simulate the lateral buckling response of a submarine pipeline. This model considers the suppression tension provided by the virtual anchor point during the pipeline feeding-in process, which better reduces the buckling response phenomenon of the pipeline. Based on the assumption of rigid-plastic pipe-soil interaction, the analytical solution of the buckling development of pipeline under full-contact repetitive cosine imperfection is derived. The effectiveness of the fixed-fixed model is verified by comparing with the analytical solutions in other literature. The influence of the imperfection model, the temperature difference, and the soil resistance on the pipeline buckling is investigated. Finally, the size effect of the pipeline on the effective axial force development is discussed. The results show that the pipeline undergoes stress vibration under tensile force, and the frequency and density of the pipeline stress vibration increase with the increase of the initial defect amplitude. Increasing the diameter–thick ratio will significantly increase the bending amplitude and bending stress of the pipeline. Attention should be paid to the fatigue damage caused by continuous stress mutations during pipeline buckling, which could further lead to the structural destruction of the pipeline.

Calibration of imperfect geophysical models by multiple satellite interferograms with measurement bias

Model calibration consists of using experimental or field data to estimate the unknown parameters of a mathematical model. The presence of model discrepancy and measurement bias in the data complicates this task. Satellite interferograms, for instance, are widely used for calibrating geophysical models in geological hazard quantification. In this work, we used satellite interferograms to relate ground deformation observations to the properties of the magma chamber at Kīlauea Volcano in Hawai‘i. We derived closed-form marginal likelihoods and implemented posterior sampling procedures that simultaneously estimate the model discrepancy of physical models, and the measurement bias from the atmospheric error in satellite interferograms. We found that model calibration by aggregating multiple interferograms and downsampling the pixels in the interferograms can reduce the computation complexity compared to calibration approaches based on multiple data sets. The conditions that lead to no loss of information from data aggregation and downsampling are studied. Simulation illustrates that both discrepancy and measurement bias can be estimated, and real applications demonstrate that modeling both effects helps obtain a reliable estimation of a physical model’s unobserved parameters and enhance its predictive accuracy. We implement the computational tools in the RobustCalibration package available on CRAN.

8-MW wind turbine tower computational shell buckling benchmark. Part 2: Detailed reference solution

An assessment of the elastic–plastic buckling limit state for multi-strake wind turbine support towers poses a particular challenge for the modern finite element analyst, who must competently navigate numerous modelling choices related to the tug-of-war between meshing and computational cost, the use of solvers that are robust to highly nonlinear behaviour, the potential for multiple near-simultaneously critical failure locations, the complex issue of imperfection sensitivity and finally the interpretation of the data into a safe and economic design.This paper presents a detailed reference solution to the computational buckling analysis of a standardised benchmark problem of an 8-MW multi-strake wind turbine support tower. Both linear and nonlinear analyses are performed, including advanced GMNIA with several different models of geometric imperfections. The crucial issue of interpreting the imperfection amplitude in a way that is compliant with the new prEN 1993-1-6 is discussed in detail. The solution presented herein is intended for use by analysts in both industry and academia for training, verification and calibration of finite element models and is intended to initiate a public repository of such computational solutions for metal civil engineering shell structures.This paper is the second of a pair. The first paper [37] presents a synthesis of 29 submissions to an international round-robin exercise performed on the same benchmark problem.

Characterizing spatial variability in the temperature field to support thermal model validation in a naturally ventilated building

ABSTRACT Night-time passive cooling is an energy-efficient cooling strategy, but the design of passive cooling systems relies on imperfect computational models, which require validation. This paper assesses the importance of spatial variability in the temperature field when performing model validation. Full-scale temperature measurements in a three story atrium building reveal spatial variability of up to on each floor during the natural ventilation process. Validation of a dynamic thermal model with uncertainty quantification reveals accurate volume-averaged air temperature predictions. Discrepancies are on the order of the sensor accuracy (), and are primarily due to slightly under-predicted cooling rates in the model. Importantly, this trend would be identified incorrectly when validating the model against the building's built-in sensors, which consistently record 0.05–1.63 higher temperatures than the volume-averaged air temperature. These findings highlight the importance of spatial variability and careful temperature sensor placement in naturally ventilated buildings.

Axisymmetric thermal postbuckling of functionally graded graphene nanocomposite annular plates with various geometric imperfections

This paper presents the axisymmetric thermal postbuckling analysis of functionally graded graphene platelets-reinforced composite (FG-GPLRC) annular plates with various geometric imperfections within the framework of first-order shear deformation theory and von Kármán geometric nonlinearity. An imperfection model composed of trigonometric and hyperbolic functions is used to simulate possible imperfections with different shapes, amplitudes and locations. The 3D Halpin–Tsai model is employed to estimate the effective modulus of graphene nanocomposites. Nonlinear governing equations are derived by the variational principle and are then solved by the generalized differential quadrature method combined with the modified Newton–Raphson iteration. Parametric studies are conducted to highlight the influences of imperfection amplitude, localization degree, location and half-wave number on the thermal postbuckling behaviour of FG-GPLRC annular plates. It is found that the thermal postbuckling resistance is reduced due to the existence of geometric imperfections, and this effect become more/less significant as the imperfection amplitude/half-wave number increases.

Guidelines for a Finite Element Based Design of Timber Structures and Their Exemplary Application on Modelling of Beech LVL

Design verifications of buildings are usually carried out supported by a finite element analysis (FEA), for which, however, there are only a few and almost exclusively non-binding application rules. Within the Cluster of Excellence Integrative Computational Design and Construction for Architecture (IntCDC) at the University of Stuttgart, Guidelines for a Finite Element-Based Design of Timber Structures have been developed. The scope of the guidelines is daily engineering practice, expert engineering applications and product development and certification. Essential parts of the guidelines are design procedures, modelling (including geometrical, material and imperfection modelling), analysis, model verification and validation and design. The content and application of the guidelines are described and illustrated in this paper using two benchmarks. These two benchmarks, which are based on experimental investigations, deal with the elastic material modelling of glulam made of beech laminated veneer lumber (beech LVL) and dowel-type connections for beech LVL members. The experimental basis of the benchmarks is described. With the experiments for the benchmarks, all Poisson’s ratios and the complete elastic material stiffness matrix of beech LVL are determined by means of an optical measuring system. The experimentally determined stiffnesses of the investigated dowel-type connections in beech LVL are compared with normative values. Based on the experiments, a numerical model is developed in RFEM (Dlubal).

Using many different voltage protocols to characterise discrepancy in mathematical ion channel models.

The Kv11.1 protein encoded by the hERG gene forms the primary subunit of a voltage-sensitive ion channel responsible for IKr in cardiomyocytes. Mathematical models of the macroscopic current are fitted to data from patch-clamp experiments - in which the whole-cell current is recorded in response to an applied voltage protocol. These models are a valuable tool for understanding the proarrhythmic effects of drugs and mutations, as they can provide accurate, quantitative predictions of the macroscopic current. In recent years, information rich protocols (that do not rely on the channels returning to steady state between voltage pulses) were designed to calibrate mathematical IKr models using short, dense time series. These protocols have been adapted for use on high-throughput automated patch clamp machines in CHO cells overexpressing hERG at either room or physiological temperatures. There are many choices of such protocols to apply during a patch-clamp experiment. We designed twelve protocols under various criteria, all of which should provide enough information to fit simple models of IKr uniquely. However, the parameters in imperfect models are forced to make different compromises to fit data from different protocols. The results highlight the impact of model discrepancy (the difference between models and reality) on parameter estimation and prediction. In particular, we show that the parameter estimates obtained depend on the chosen protocol, and how parameters fitted to protocols which highlight a significant amount of model discrepancy can lead to poor predictions. These results motivate the need for new experimental design methods that account for model discrepancy and aid in model selection. Furthermore, we suggest cross-validation as a tool to help evaluate the trustworthiness of model predictions, which may help identify good models of IKr as well as other macroscopic currents.

High-resolution X-ray spectra of RS Ophiuchi (2006 and 2021): Revealing the cause of SSS variability

Context. The ~ 10–20 yr recurrent symbiotic nova RS Oph exploded on 2021 August 9, the seventh confirmed recorded outburst since 1898. During the previous outburst in 2006, the current fleet of X-ray space observatories was already in operation, and thanks to the longevity of Swift, XMM-Newton, and Chandra, a direct comparison between these two outbursts is possible. The Swift monitoring campaign revealed similar behaviour during the early shock phase but very different behaviour during the super-soft source (SSS) phase. Two XMM-Newton observations were made during the 2021 SSS phase on days 37.1 and 55.6 after the 2021 optical peak. We focus in this work on the bright SSS observation on day 55.6 and compare to SSS Chandra and XMM-Newton grating observations made on days 39.7, 54, and 66.9 after the 2006 optical peak. Aims. By exploring the reasons for the differences between the 2006 and 2021 outbursts, we aim to obtain a better general understanding of the emission and absorption mechanisms. While the emission mechanisms hold the key to the physics of novae and nuclear burning, absorption processes may dominate what we observe, and we aim to explore the cause of the gross initial variability in the observed SSS emission. Methods. We present a novel approach to down-scaling the observed (brighter) 2006 SSS spectra to match the 2021 day 55.6 spectrum by parameter optimisation of: (1) a constant factor (representing fainter source emission, smaller radius, eclipses, etc.), (2) a multi-ionisation photoelectric absorption model (representing different line-of-sight absorption), and (3) scaling with a ratio of two blackbody models with different effective temperatures (representing different brightness and colours). This model approach does not depend on a source model assuming the intrinsic source to be the same. It is therefore more sensitive to incremental changes than modelling approaches where source and absorption are modelled simultaneously. Results. The 2021d55.6 spectrum can be reproduced remarkably well by multiplying the (brighter) 2006d39.7 and 2006d54 spectra with the absorption model, while the 2006d66.9 spectrum requires additional colour changes to match the 2021.d55.6 spectrum. The 2006d39.7 spectrum much more closely resembles the 2021d55.6 spectrum in shape and structure than the same-epoch 2006d54 spectrum: The spectra on days 2006d39.7 and 2021d55.6 are richer in absorption lines with a deeper O I absorption edge, and blueshifts are higher (~1200 km s−1) than on day 2006d54 (~700 km s−1). In the SSS light curves on days 2006d39.7, 2006d54, and 2021d55.6, brightness and hardness variations are correlated, indicating variations of the O I column density. Only on day 2006d39.7, a 1000 s lag is observed. The 35 s period was detected on day 2021d55.6 with lower significance compared to 2006d54. Conclusions. We conclude that the central radiation source is the same, while absorption is the principal reason for observing lower soft-X-ray emission in 2021 than in 2006. This is consistent with a similar 2006 and 2021 [Fe X] line-flux evolution. We explain the reduction in line blueshift, depth in O I edge, and number of absorption lines from day 2006d39.7 to 2006d54 by deceleration and heating of the ejecta within the stellar wind of the companion. In 2021, less such deceleration and heating was observed, which we interpret as due to viewing at different angles through an inhomogeneous density distribution of the stellar wind, allowing free expansion in some directions (probed in 2021) and a higher degree of deceleration in others (probed in 2006). The higher absorption in 2021 can then be explained by the lower-temperature absorbing plasma being more opaque to soft X-rays. Our approach of scaling observations against observations is free of ambiguities from imperfect source models and can be applied to other grating spectra with complex continuum sources.

Application of Recurrent Neural Networks to Model Bias Correction: Idealized Experiments With the Lorenz‐96 Model

AbstractSystematic biases in numerical weather prediction models cause forecast deviation from reality. While model biases also affect data assimilation and degrade the analysis accuracy, observation information incorporated through data assimilation can provide information for detecting and alleviating such biases. In this study, the application of machine learning to model bias correction is demonstrated, emphasizing the effectiveness of recurrent neural networks. Idealized experiments are performed using the two‐scale coupled Lorenz‐96 model as the true system and single Lorenz‐96 model as the imperfect forecast model, to compare the effectiveness of bias correction methods based on various architectures of neural networks and simple linear regression. The neural networks generally outperformed linear regression, and recurrent neural networks showed the best ability in finding the systematic bias component from the analysis increment data. Bias correction using the recurrent neural networks also gives the most significant improvement in reducing the error growth rate in extended range forecasts. The results suggest that including past time series of the forecast variables improve model bias correction when limited information of the observation is incorporated through data assimilation.

Predicting wind-driven spatial deposition through simulated color images using deep autoencoders

For centuries, scientists have observed nature to understand the laws that govern the physical world. The traditional process of turning observations into physical understanding is slow. Imperfect models are constructed and tested to explain relationships in data. Powerful new algorithms can enable computers to learn physics by observing images and videos. Inspired by this idea, instead of training machine learning models using physical quantities, we used images, that is, pixel information. For this work, and as a proof of concept, the physics of interest are wind-driven spatial patterns. These phenomena include features in Aeolian dunes and volcanic ash deposition, wildfire smoke, and air pollution plumes. We use computer model simulations of spatial deposition patterns to approximate images from a hypothetical imaging device whose outputs are red, green, and blue (RGB) color images with channel values ranging from 0 to 255. In this paper, we explore deep convolutional neural network-based autoencoders to exploit relationships in wind-driven spatial patterns, which commonly occur in geosciences, and reduce their dimensionality. Reducing the data dimension size with an encoder enables training deep, fully connected neural network models linking geographic and meteorological scalar input quantities to the encoded space. Once this is achieved, full spatial patterns are reconstructed using the decoder. We demonstrate this approach on images of spatial deposition from a pollution source, where the encoder compresses the dimensionality to 0.02% of the original size, and the full predictive model performance on test data achieves a normalized root mean squared error of 8%, a figure of merit in space of 94% and a precision-recall area under the curve of 0.93.

Research on Hydraulic Support Attitude Monitoring Method Merging FBG Sensing Technology and AdaBoost Algorithm

The hydraulic support is the key equipment of surrounding rock support in a stope, and thus monitoring the attitude of the hydraulic support has an important guiding role in the support selection, operation control and rock pressure analysis of the working face. At present, attitude monitoring technology for hydraulic support mainly includes inertial measurement, contact measurement and visual measurement. Aiming at the technical defects of imperfect attitude perception models, incomplete perception parameters and the low decision-making ability of such systems, the fiber Bragg grating (FBG) pressure sensor and the FBG tilt sensor are developed independently by combining with FBG sensing theory. The pressure sensitivity of the FBG pressure sensor is 35.6 pm/MPa, and the angular sensitivity of the FBG tilt sensor is 31.3 pm/(°). Additionally, an information platform for FBG sensing monitoring for hydraulic support attitude is constructed based on. NET technology and C/S architecture. The information platform realizes real-time monitoring, data management, report management, production information management and data querying of hydraulic support attitude monitoring data. An AdaBoost neural network hydraulic support working resistance prediction model is established using MATLAB. The AdaBoost neural network algorithm successfully predicts the periodic pressure of the coal mining face by training with the sample data of the working resistance of the hydraulic support. The predicting accuracy is more than 95%.

The ENBIS‐21 quality and reliability engineering international special issue

The ENBIS-21 Quality and Reliability Engineering International Special Issue is related to the contributions to the 21st Annual Conference of the European Network for Business and Industrial Statistics (ENBIS) held online from 13 to 15 September, 2021. The topics covered by the 12 papers included in this special issue fall within the scope of ENBIS, whose ultimate goal is to bridge the gap between methodology and application in the field of business and industrial statistics and foster networking between statisticians in academic and commercial settings. It becomes evident from the papers on this issue that classical methods of industrial statistics are still having a wide range of applications and expansions towards complex and big data structures as well as they are increasingly cross-fertilized by artificial intelligence and machine learning perspectives and approaches. The issue is opened by the contribution of Yang et al.1 in the Statistical Process Monitoring (SPM) of data in the form of tensors. The authors develop a hierarchical in-situ process monitoring approach for anomaly detection, which is applied to thermal video streams acquired during a metal additive manufacturing process for highly complex parts. A more traditional SPM approach based on generalized likelihood ratio (GLR) control charts is elaborated by Rizzo and Di Bucchianico2 to set up tailor-made monitoring for high-purity (high-quality) processes and deals with issues arising in GLR control charts for discrete processes. Along the line of developing statistical methods for complex data structures, Gril et al.3 set up a tensor-on-tensor regression model able to dynamically predict repetitive human motions helpful in avoiding unwanted collisions at the interface with robots in industrial assembly tasks. Chuquin et al.4 present a straightforward extension of the K-means clustering to spatially correlated functional data, with an application in the analysis of the normalized difference vegetation index in a large region of Ecuador. From a more general perspective, Vanacore et al.5 address the problem of assessing prediction performance in the multi-class classification of imbalanced data sets. In the optimal Design of Experiments (DoE) Pesce et al.6 offer new results that are oriented to bias reduction in large datasets and protection against confounders. Whereas, Kirchhoff et al.7 use DoE as the initial solution for the optimization of shift planning in high-bay warehouse operations based on Gaussian process models with low-rank correlation kernels. Risk assessment and management is the topic of the following three papers. Testik and Unlu8 compare traditional and fuzzy failure modes and effect analysis to rank risks in different areas of testing and calibration laboratories. Meynaoui et al.9 deal with an accidental scenario in a sodium-cooled fast nuclear reactor by means of a global sensitivity analysis of the input parameter distribution used in numerical simulator outputs to model physical phenomena. Lai and Zwetsloot10 offer a data-driven ensemble ranking system of product quality, which is validated in the identification of high-risk manufacturers in a solar industry case study. The final two papers are devoted to the Reliability and Maintenance of repairable systems. El-Aroui and Gaudoin11 propose a general goodness-of-fit test for imperfect repair models that has the favorable property of being asymptotically distribution-free for renewal and power law processes. Fouladirad et al.12 develop a new bounded transformed gamma process model to describe and predict degradation phenomena by relaxing the typical assumption that the degradation level can grow indefinitely, which is often unrealistic for technological units. The proposed model is also applied to a set of wear measures of cylinder liners that equip a diesel engine for marine propulsion. We are deeply grateful to the journal staff for their professional assistance in the editorial process, as well as to the anonymous referees for the time and effort spent to provide careful and constructive comments, and to all the authors, who made revisions on a very tight timescale.

Experimental and numerical study on flexural behaviour of cold-formed steel hat-shaped beams with geometrical imperfections

Experimental and numerical studies are conducted to investigate cold-formed hat-shaped members' flexural behaviour and determine the effects of different parameters on the behaviour. A total of ten specimens of cold-formed hat-shaped beams with different lengths are chosen for physical tests. The actual geometry and geometric imperfection distributions are acquired by processing 3D point clouds obtained by laser scanners. Four-point bending tests are performed to obtain benchmark results for numerical models. It is observed that numerical results are in accordance with the experimental results with high accuracy. Once the generated finite element models are calibrated based on the experiment results, a parametric study investigating the influence of the length, thickness, lip width, return length, radius, and lip angle on the beam behaviour is undertaken. In addition, the effect of geometric imperfection magnitude selection and imperfection modelling method on the member capacity is considered. The study's outcomes show that the initial geometric imperfections and input parameters selected for the generated numerical models significantly affect the flexural behaviour of CFS hat-shaped beams.

Deep learning-enhanced ensemble-based data assimilation for high-dimensional nonlinear dynamical systems

Data assimilation (DA) is a key component of many forecasting models in science and engineering. DA allows one to estimate better initial conditions using an imperfect dynamical model of the system and noisy/sparse observations available from the system. Ensemble Kalman filter (EnKF) is a DA algorithm that is widely used in applications involving high-dimensional nonlinear dynamical systems. However, EnKF requires evolving large ensembles of forecasts using the dynamical model of the system. This often becomes computationally intractable, especially when the number of states of the system is very large, e.g., for weather prediction. With small ensembles, the estimated background error covariance matrix in the EnKF algorithm suffers from sampling error, leading to an erroneous estimate of the analysis state (initial condition for the next forecast cycle). In this work, we propose hybrid ensemble Kalman filter (H-EnKF), which is applied to a two-layer quasi-geostrophic turbulent flow as a test case. This framework utilizes a pre-trained deep learning-based data-driven surrogate that inexpensively generates and evolves a large data-driven ensemble of the states to accurately compute the background error covariance matrix with smaller sampling errors. The H-EnKF framework outperforms EnKF with only dynamical model or only the data-driven surrogate, and estimates a better initial condition without the need for any ad-hoc localization strategies. H-EnKF can be extended to any ensemble-based DA algorithm, e.g., particle filters, which are currently too expensive to use for high-dimensional systems.

A Micromechanical Model for Damage Evolution in Thin Piezoelectric Films

Thin-film piezoelectric materials are advantageous in microelectromechanical systems (MEMS), due to large motion generation, high available energy and low power requirements. In this kind of application, thin piezoelectric films are subject to mechanical and electric cyclic loading, during which damage can accumulate and eventually lead to fracture. In the present study, continuum damage mechanics and asymptotic theory are adopted to model damage evolution in piezoelectric thin films. Our purpose is to develop a new interface model for thin piezoelectric films accounting for micro-cracking damage of the material. The methods used are matched asymptotic expansions, to develop an interface law, and the classic thermodynamic framework of continuum damage mechanics combined with Kachanov and Sevostianov’s theory of homogenization of micro-cracked media, to characterize the damaging behavior of the interface. The main finding of the paper is a soft imperfect interface model able to simulate the elastic and piezoelectric behavior of thin piezoelectric film in the presence of micro-cracking and damage evolution. The obtained interface model is expected to be a useful tool for damage evaluation in MEMS applications. As an example, an electromechanically active stack incorporating a damaging piezoelectric layer is studied. The numerical results indicate a non-linear evolution of the macroscopic response and a damage accumulation qualitatively consistent with experimental observations.

Long-term stability and generalization of observationally-constrained stochastic data-driven models for geophysical turbulence

Abstract Recent years have seen a surge in interest in building deep learning-based fully data-driven models for weather prediction. Such deep learning models, if trained on observations can mitigate certain biases in current state-of-the-art weather models, some of which stem from inaccurate representation of subgrid-scale processes. However, these data-driven models, being over-parameterized, require a lot of training data which may not be available from reanalysis (observational data) products. Moreover, an accurate, noise-free, initial condition to start forecasting with a data-driven weather model is not available in realistic scenarios. Finally, deterministic data-driven forecasting models suffer from issues with long-term stability and unphysical climate drift, which makes these data-driven models unsuitable for computing climate statistics. Given these challenges, previous studies have tried to pre-train deep learning-based weather forecasting models on a large amount of imperfect long-term climate model simulations and then re-train them on available observational data. In this article, we propose a convolutional variational autoencoder (VAE)-based stochastic data-driven model that is pre-trained on an imperfect climate model simulation from a two-layer quasi-geostrophic flow and re-trained, using transfer learning, on a small number of noisy observations from a perfect simulation. This re-trained model then performs stochastic forecasting with a noisy initial condition sampled from the perfect simulation. We show that our ensemble-based stochastic data-driven model outperforms a baseline deterministic encoder–decoder-based convolutional model in terms of short-term skills, while remaining stable for long-term climate simulations yielding accurate climatology.