1D Stochastic Inversion of Airborne Time-Domain Electromagnetic Data with Realistic Prior and Accounting for the Forward Modeling Error

Airborne electromagnetic surveys may consist of hundreds of thousands of soundings. In most cases, this makes 3D inversions unfeasible even when the subsurface is characterized by a high level of heterogeneity. Instead, approaches based on 1D forwards are routinely used because of their computational efficiency. However, it is relatively easy to fit 3D responses with 1D forward modelling and retrieve apparently well-resolved conductivity models. However, those detailed features may simply be caused by fitting the modelling error connected to the approximate forward. In addition, it is, in practice, difficult to identify this kind of artifacts as the modeling error is correlated. The present study demonstrates how to assess the modelling error introduced by the 1D approximation and how to include this additional piece of information into a probabilistic inversion. Not surprisingly, it turns out that this simple modification provides not only much better reconstructions of the targets but, maybe, more importantly, guarantees a correct estimation of the corresponding reliability.

Electromagnetic Devices with Moving Parts—Simulation with FEM/BEM Coupling

The numerical analysis of electromagnetic devices by means of finite element methods (FEM) is often hindered by the need to incorporate the surrounding domain. The discretisation of the air may become complex and has to be truncated by artificial boundaries incurring a modelling error. Even more problematic are moving parts that require tedious re-meshing and mapping techniques. In this work, we tackle these problems by using the boundary element method (BEM) in conjunction with FEM. Whereas the solid parts of the electrical device are discretised by FEM, which can easily account for material non-linearities, the surrounding domain is represented by BEM, which requires only a surface discretisation. This approach completely avoids an air mesh and its re-meshing during the simulation with moving or deforming parts. Our approach is robust, shows optimal complexity, and provides an accurate calculation of electromagnetic forces that are required to study the mechanical behaviour of the device.

A Novel Stochastic Approach for Static Damage Identification of Beam Structures Using Homotopy Analysis Algorithm

This paper proposes a new damage identification approach for beam structures with stochastic parameters based on uncertain static measurement data. This new approach considers not only the static measurement errors, but also the modelling error of the initial beam structures as random quantities, and can also address static damage identification problems with relatively large uncertainties. First, the stochastic damage identification equations with respect to the damage indexes were established. On this basis, a new homotopy analysis algorithm was used to solve the stochastic damage identification equations. During the process of solution, a static condensation technique and a L1 regularization method were employed to address the limited measurement data and ill-posed problems, respectively. Furthermore, the definition of damage probability index is presented to evaluate the possibility of existing damages. The results of two numerical examples show that the accuracy and efficiency of the proposed damage identification approach are good. In comparison to the first-order perturbation method, the proposed method can ensure better accuracy in damage identification with relatively large measurement errors and modelling error. Finally, according to the static tests of a simply supported concrete beam, the proposed method successfully identified the damage of the beam.

Modelling Error Dependence in Categorical Longitudinal Data

Hidden Markov models (HMMs) offer an attractive way of accounting and correcting for measurement error in longitudinal data as they do not require the use of a ‘gold standard’ data source as a benchmark. However, while the standard HMM assumes the errors to be independent or random, some common situations in survey and register data cause measurement error to be systematic. HMMs can correct for systematic error as well if the local independence assumption is relaxed. In this chapter, we present several (mixed) HMMs that relax this assumption with the use of two independent indicators for the variable of interest. Finally, we illustrate the results of some of these HMMs with the use of an example of employment mobility. For this purpose, we use linked survey-register data from the Netherlands.

Insight into centrifuge modelling errors in predicting embedment depths of dynamically installed anchors

In centrifuge modelling of dynamic events, a common practice is to preserve the inertial effect. This will lead to a loss of similitude in the strain rate between model and prototype. For centrifuge tests of dynamic installation of anchors, such strain rate dissimilarity may give rise to significant discrepancy in the anchor embedment depth between the model and the prototype, i.e., modelling error. Large-deformation finite element analyses that simulate both the model and the prototype were undertaken in this study to provide insight into this phenomenon. The calculation results revealed that the centrifuge model tends to underpredict the anchor embedment depth of the prototype. A parametric study of the influence of anchor geometry and weight, soil strength and stiffness, strain softening and rate parameters, and centrifuge acceleration level was subsequently conducted. It was found that such underprediction depends heavily upon the strain rate parameter. Based on analyses results, practical advices were given for centrifuge modellers to minimize the modelling error. The results presented and advices given in this study may facilitate the design of centrifuge model tests especially when the anchor embedment depth is an essential detail to be replicated in these tests.

Observer-Based Control for Uncertain Nonlinear Systems Applied to Continuous Biochemical Reactors

The purpose of this paper is to present an observer-based control design with application to continuous bioreactors. For this purpose, phenomenological bioreactor models were represented by identified linear models plus unknown modelling error terms. Therefore, an uncertainty-based observer with a polynomial structure capable of estimating the unknown modelling error of the reactor representation is coupled to a linear input-output controller. The proposed methodology was evaluated in a sulphate reduction bioprocess and an acetone-butanol-ethanol (ABE) fermentation process for butanol (biofuel) production, under continuous regimes. Experimentally validated mathematical models were considered for this purpose. A theoretical framework is presented to demonstrate the corresponding closed-loop stability of the systems, and numerical simulations were carried out to corroborate the satisfactory performance of the proposed methodology.

Determination of Modelling Error Statistics for Cold-Formed Steel Columns

In this article, an attempt has been made to estimate the Modelling Error (ME) associated with compression capacity models available in international standards for different failure modes of compression members fabricated from Cold-Formed Steel (CFS) lipped channel sections. For the first time, a database has been created using test results available in the literature for compression capacities of CFS lipped-channel sections. The database contains details of 273 numbers of compression member tests which have failed in different failure modes, namely, (i) flexural, torsional, flexural-torsional, local, and distortion buckling and (ii) failure by yielding. Only those sources, which report all the details, required to compute the capacities using different standards are included in the database. The results of experimental investigations carried out at CSIR-Structural Engineering Research Centre, Chennai, are also included in this test database. The international codes of practice used in calculation of compression capacities of the database columns considered in this paper are ASCE 10-15 (2015), AISI S100-16 (2016), AS/NZS 4600: 2018 (2018), and EN 1993-1-3:2006 (2006). The ASCE, AISI, AS/NZS, and EN design standards have different design guidelines with respect to the failure modes, e.g., ASCE 10-15 (2015) standard provides stringent criteria for maximum width to thickness ratio for stiffened and unstiffened elements. Hence, guidelines for the distortional buckling mode are not provided, whereas the AISI S100-16 (2016) and AS/NZS 4600: 2018 (2018) standards consider separate guidelines for distortional buckling mode and EN 1993-1-3:2006 (2006) standard considers combined local and distortional buckling mode. Further, the sample size for each design standard is varying depending on the design criteria and failure mode. Studies on statistical analysis of ME suggest that the compression capacity predicting models for flexural-torsional buckling mode are associated with large variation irrespective of the design standard. Similar observations are made for the flexural buckling model as per EN 1993-1-3:2006 (2018) standard and distortional buckling models as per AISI S100-16 (2016) and AS/NZS 4600: 2018 (2018) standards. The compression capacities for test database sections are evaluated by neglecting the partial safety factors available in design standards. The probabilistic analysis to determine statistical characteristics of compression capacity indicates the importance of consideration of ME as a random variable. Hence, the ME results will be useful in code calibration studies and may have potential reference to design practice.