TY - CHAP A1 - Gaigall, Daniel T1 - On Consistent Hypothesis Testing In General Hilbert Spaces N2 - Inference on the basis of high-dimensional and functional data are two topics which are discussed frequently in the current statistical literature. A possibility to include both topics in a single approach is working on a very general space for the underlying observations, such as a separable Hilbert space. We propose a general method for consistently hypothesis testing on the basis of random variables with values in separable Hilbert spaces. We avoid concerns with the curse of dimensionality due to a projection idea. We apply well-known test statistics from nonparametric inference to the projected data and integrate over all projections from a specific set and with respect to suitable probability measures. In contrast to classical methods, which are applicable for real-valued random variables or random vectors of dimensions lower than the sample size, the tests can be applied to random vectors of dimensions larger than the sample size or even to functional and high-dimensional data. In general, resampling procedures such as bootstrap or permutation are suitable to determine critical values. The idea can be extended to the case of incomplete observations. Moreover, we develop an efficient algorithm for implementing the method. Examples are given for testing goodness-of-fit in a one-sample situation in [1] or for testing marginal homogeneity on the basis of a paired sample in [2]. Here, the test statistics in use can be seen as generalizations of the well-known Cramérvon-Mises test statistics in the one-sample and two-samples case. The treatment of other testing problems is possible as well. By using the theory of U-statistics, for instance, asymptotic null distributions of the test statistics are obtained as the sample size tends to infinity. Standard continuity assumptions ensure the asymptotic exactness of the tests under the null hypothesis and that the tests detect any alternative in the limit. Simulation studies demonstrate size and power of the tests in the finite sample case, confirm the theoretical findings, and are used for the comparison with concurring procedures. A possible application of the general approach is inference for stock market returns, also in high data frequencies. In the field of empirical finance, statistical inference of stock market prices usually takes place on the basis of related log-returns as data. In the classical models for stock prices, i.e., the exponential Lévy model, Black-Scholes model, and Merton model, properties such as independence and stationarity of the increments ensure an independent and identically structure of the data. Specific trends during certain periods of the stock price processes can cause complications in this regard. In fact, our approach can compensate those effects by the treatment of the log-returns as random vectors or even as functional data. Y1 - 2022 U6 - http://dx.doi.org/10.11159/icsta22.157 N1 - Proceedings of the 4th International Conference on Statistics: Theory and Applications (ICSTA’22) Prague, Czech Republic – July 28- 30 SP - Paper No. 157 PB - Avestia Publishing CY - Orléans, Kanada ER - TY - JOUR A1 - Ditzhaus, Marc A1 - Gaigall, Daniel T1 - Testing marginal homogeneity in Hilbert spaces with applications to stock market returns JF - Test N2 - This paper considers a paired data framework and discusses the question of marginal homogeneity of bivariate high-dimensional or functional data. The related testing problem can be endowed into a more general setting for paired random variables taking values in a general Hilbert space. To address this problem, a Cramér–von-Mises type test statistic is applied and a bootstrap procedure is suggested to obtain critical values and finally a consistent test. The desired properties of a bootstrap test can be derived that are asymptotic exactness under the null hypothesis and consistency under alternatives. Simulations show the quality of the test in the finite sample case. A possible application is the comparison of two possibly dependent stock market returns based on functional data. The approach is demonstrated based on historical data for different stock market indices. Y1 - 2022 U6 - http://dx.doi.org/10.1007/s11749-022-00802-5 SN - 1863-8260 VL - 2022 IS - 31 SP - 749 EP - 770 PB - Springer ER - TY - JOUR A1 - Gaigall, Daniel A1 - Gerstenberg, Julian A1 - Trinh, Thi Thu Ha T1 - Empirical process of concomitants for partly categorial data and applications in statistics JF - Bernoulli N2 - On the basis of independent and identically distributed bivariate random vectors, where the components are categorial and continuous variables, respectively, the related concomitants, also called induced order statistic, are considered. The main theoretical result is a functional central limit theorem for the empirical process of the concomitants in a triangular array setting. A natural application is hypothesis testing. An independence test and a two-sample test are investigated in detail. The fairly general setting enables limit results under local alternatives and bootstrap samples. For the comparison with existing tests from the literature simulation studies are conducted. The empirical results obtained confirm the theoretical findings. KW - bootstrap KW - Categorial variable KW - Concomitant KW - Empirical process KW - Independence test Y1 - 2022 U6 - http://dx.doi.org/10.3150/21-BEJ1367 SN - 1573-9759 VL - 28 IS - 2 SP - 803 EP - 829 PB - International Statistical Institute CY - Den Haag, NL ER - TY - CHAP A1 - Staat, Manfred A1 - Tran, Ngoc Trinh T1 - Strain based brittle failure criteria for rocks T2 - Proceedings of (NACOME2022) The 11th National Conference on Mechanics, Vol. 1. Solid Mechanics, Rock Mechanics, Artificial Intelligence, Teaching and Training, Hanoi, December 2-3, 2022 N2 - When confining pressure is low or absent, extensional fractures are typical, with fractures occurring on unloaded planes in rock. These “paradox” fractures can be explained by a phenomenological extension strain failure criterion. In the past, a simple empirical criterion for fracture initiation in brittle rock has been developed. But this criterion makes unrealistic strength predictions in biaxial compression and tension. A new extension strain criterion overcomes this limitation by adding a weighted principal shear component. The weight is chosen, such that the enriched extension strain criterion represents the same failure surface as the Mohr–Coulomb (MC) criterion. Thus, the MC criterion has been derived as an extension strain criterion predicting failure modes, which are unexpected in the understanding of the failure of cohesive-frictional materials. In progressive damage of rock, the most likely fracture direction is orthogonal to the maximum extension strain. The enriched extension strain criterion is proposed as a threshold surface for crack initiation CI and crack damage CD and as a failure surface at peak P. Examples show that the enriched extension strain criterion predicts much lower volumes of damaged rock mass compared to the simple extension strain criterion. KW - Extension fracture KW - Extension strain criterion KW - Mohr–Coulomb criterion KW - Evolution of damage Y1 - 2023 SN - 978-604-357-084-7 SP - 500 EP - 509 PB - Nha xuat ban Khoa hoc tu nhien va Cong nghe (Verlag Naturwissenschaft und Technik) CY - Hanoi ER - TY - CHAP A1 - Chircu, Alina A1 - Czarnecki, Christian A1 - Friedmann, Daniel A1 - Pomaskow, Johanna A1 - Sultanow, Eldar T1 - Towards a Digital Twin of Society T2 - Proceedings of the 56th Hawaii International Conference on System Sciences 2023 N2 - This paper describes the potential for developing a digital twin of society- a dynamic model that can be used to observe, analyze, and predict the evolution of various societal aspects. Such a digital twin can help governmental agencies and policy makers in interpreting trends, understanding challenges, and making decisions regarding investments or policies necessary to support societal development and ensure future prosperity. The paper reviews related work regarding the digital twin paradigm and its applications. The paper presents a motivating case study- an analysis of opportunities and challenges faced by the German federal employment agency, Bundesagentur f¨ur Arbeit (BA), proposes solutions using digital twins, and describes initial proofs of concept for such solutions. KW - Digital twin KW - Digital transformation KW - Prototype KW - Society KW - Stress testing Y1 - 2023 SN - 978-0-9981331-6-4 SP - 6748 EP - 6757 PB - University of Hawai'i CY - Honolulu ER - TY - CHAP A1 - Butenweg, Christoph ED - Vacareanu, Radu ED - Ionescu, Constantin T1 - Seismic design and evaluation of industrial facilities T2 - Progresses in European Earthquake Engineering and Seismology. Third European Conference on Earthquake Engineering and Seismology – Bucharest, 2022 N2 - Industrial facilities must be thoroughly designed to withstand seismic actions as they exhibit an increased loss potential due to the possibly wideranging damage consequences and the valuable process engineering equipment. Past earthquakes showed the social and political consequences of seismic damage to industrial facilities and sensitized the population and politicians worldwide for the possible hazard emanating from industrial facilities. However, a holistic approach for the seismic design of industrial facilities can presently neither be found in national nor in international standards. The introduction of EN 1998-4 of the new generation of Eurocode 8 will improve the normative situation with specific seismic design rules for silos, tanks and pipelines and secondary process components. The article presents essential aspects of the seismic design of industrial facilities based on the new generation of Eurocode 8 using the example of tank structures and secondary process components. The interaction effects of the process components with the primary structure are illustrated by means of the experimental results of a shaking table test of a three story moment resisting steel frame with different process components. Finally, an integrated approach of digital plant models based on building information modelling (BIM) and structural health monitoring (SHM) is presented, which provides not only a reliable decision-making basis for operation, maintenance and repair but also an excellent tool for rapid assessment of seismic damage. KW - Industrial facilities KW - Seismic design KW - Tanks KW - EN 1998-4 KW - Structural health monitoring Y1 - 2022 SN - 978-3-031-15103-3 SN - 978-3-031-15106-4 SN - 978-3-031-15104-0 U6 - http://dx.doi.org/10.1007/978-3-031-15104-0 SN - 2524-342X SN - 2524-3438 N1 - Third European Conference on Earthquake Engineering and Seismology. 04-09.09 Bucharest, Romania. SP - 449 EP - 464 PB - Springer CY - Cham ER - TY - CHAP A1 - Gkatzogias, Konstantinos A1 - Veljkoviv, Ana A1 - Pohoryles, Daniel A. A1 - Tsionis, Georgios A1 - Bournas, Dionysios A. A1 - Crowley, Helen A1 - Norlén, Hedvig A1 - Butenweg, Christoph A1 - Gervasio, Helena A1 - Manfredi, Vincenzo A1 - Masi, Angelo A1 - Zaharieva, Roumiana ED - Gkatzogias, Konstantinos ED - Tsionis, Georgios T1 - Policy practice and regional impact assessment for building renovation T2 - REEBUILD Integrated Techniques for the Seismic Strengthening & Energy Efficiency of Existing Buildings N2 - The work presented in this report provides scientific support to building renovation policies in the EU by promoting a holistic point of view on the topic. Integrated renovation can be seen as a nexus between European policies on disaster resilience, energy efficiency and circularity in the building sector. An overview of policy measures for the seismic and energy upgrading of buildings across EU Member States identified only a few available measures for combined upgrading. Regulatory framework, financial instruments and digital tools similar to those for energy renovation, together with awareness and training may promote integrated renovation. A framework for regional prioritisation of building renovation was put forward, considering seismic risk, energy efficiency, and socioeconomic vulnerability independently and in an integrated way. Results indicate that prioritisation of building renovation is a multidimensional problem. Depending on priorities, different integrated indicators should be used to inform policies and accomplish the highest relative or most spread impact across different sectors. The framework was further extended to assess the impact of renovation scenarios across the EU with a focus on priority regions. Integrated renovation can provide a risk-proofed, sustainable, and inclusive built environment, presenting an economic benefit in the order of magnitude of the highest benefit among the separate interventions. Furthermore, it presents the unique capability of reducing fatalities and energy consumption at the same time and, depending on the scenario, to a greater extent. Y1 - 2022 SN - 978-92-76-60454-9 U6 - http://dx.doi.org/10.2760/883122 SN - 1831-9424 SP - 1 EP - 68 PB - Publications Office of the European Union CY - Luxembourg ER - TY - CHAP A1 - Evans, Benjamin A1 - Braun, Sebastian A1 - Ulmer, Jessica A1 - Wollert, Jörg T1 - AAS implementations - current problems and solutions T2 - 20th International Conference on Mechatronics - Mechatronika (ME) N2 - The fourth industrial revolution presents a multitude of challenges for industries, one of which being the increased flexibility required of manufacturing lines as a result of increased consumer demand for individualised products. One solution to tackle this challenge is the digital twin, more specifically the standardised model of a digital twin also known as the asset administration shell. The standardisation of an industry wide communications tool is a critical step in enabling inter-company operations. This paper discusses the current state of asset administration shells, the frameworks used to host them and their problems that need to be addressed. To tackle these issues, we propose an event-based server capable of drastically reducing response times between assets and asset administration shells and a multi-agent system used for the orchestration and deployment of the shells in the field. KW - Industry 4.0 KW - Multi-agent Systems KW - Digital Twin KW - Asset Administration Shell Y1 - 2022 SN - 978-1-6654-1040-3 U6 - http://dx.doi.org/10.1109/ME54704.2022.9982933 PB - IEEE ER - TY - JOUR A1 - Baringhaus, Ludwig A1 - Gaigall, Daniel T1 - A goodness-of-fit test for the compound Poisson exponential model JF - Journal of Multivariate Analysis N2 - On the basis of bivariate data, assumed to be observations of independent copies of a random vector (S,N), we consider testing the hypothesis that the distribution of (S,N) belongs to the parametric class of distributions that arise with the compound Poisson exponential model. Typically, this model is used in stochastic hydrology, with N as the number of raindays, and S as total rainfall amount during a certain time period, or in actuarial science, with N as the number of losses, and S as total loss expenditure during a certain time period. The compound Poisson exponential model is characterized in the way that a specific transform associated with the distribution of (S,N) satisfies a certain differential equation. Mimicking the function part of this equation by substituting the empirical counterparts of the transform we obtain an expression the weighted integral of the square of which is used as test statistic. We deal with two variants of the latter, one of which being invariant under scale transformations of the S-part by fixed positive constants. Critical values are obtained by using a parametric bootstrap procedure. The asymptotic behavior of the tests is discussed. A simulation study demonstrates the performance of the tests in the finite sample case. The procedure is applied to rainfall data and to an actuarial dataset. A multivariate extension is also discussed. KW - Bootstrapping KW - Collective risk model Y1 - 2022 U6 - http://dx.doi.org/10.1016/j.jmva.2022.105154 SN - 0047-259X SN - 1095-7243 VL - 195 IS - Article 105154 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Tran, Ngoc Trinh A1 - Trinh, Tu Luc A1 - Dao, Ngoc Tien A1 - Giap, Van Tan A1 - Truong, Manh Khuyen A1 - Dinh, Thuy Ha A1 - Staat, Manfred T1 - FEM shakedown analysis of structures under random strength with chance constrained programming JF - Vietnam Journal of Mechanics N2 - Direct methods, comprising limit and shakedown analysis, are a branch of computational mechanics. They play a significant role in mechanical and civil engineering design. The concept of direct methods aims to determine the ultimate load carrying capacity of structures beyond the elastic range. In practical problems, the direct methods lead to nonlinear convex optimization problems with a large number of variables and constraints. If strength and loading are random quantities, the shakedown analysis can be formulated as stochastic programming problem. In this paper, a method called chance constrained programming is presented, which is an effective method of stochastic programming to solve shakedown analysis problems under random conditions of strength. In this study, the loading is deterministic, and the strength is a normally or lognormally distributed variable. KW - limit analysis KW - shakedown analysis KW - chance constrained programming KW - stochastic programming KW - reliability of structures Y1 - 2022 U6 - http://dx.doi.org/10.15625/0866-7136/17943 SN - 0866-7136 SN - 2815-5882 VL - 44 IS - 4 SP - 459 EP - 473 PB - Vietnam Academy of Science and Technology (VAST) ER -