Pub Date : 2021-10-30DOI: 10.1186/s13362-021-00114-7
Launay, Hugo, Willot, François, Ryckelynck, David, Besson, Jacques
We develop a methodology for classifying defects based on their morphology and induced mechanical response. The proposed approach is fairly general and relies on morphological operators (Angulo and Meyer in 9th international symposium on mathematical morphology and its applications to signal and image processing, pp. 226-237, 2009) and spherical harmonic decomposition as a way to characterize the geometry of the pores, and on the Grassman distance evaluated on FFT-based computations (Willot in C. R., Méc. 343(3):232–245, 2015), for the predicted elastic response. We implement and detail our approach on a set of trapped gas pores observed in X-ray tomography of welded joints, that significantly alter the mechanical reliability of these materials (Lacourt et al. in Int. J. Numer. Methods Eng. 121(11):2581–2599, 2020). The space of morphological and mechanical responses is first partitioned into clusters using the “k-medoids” criterion and associated distance functions. Second, we use multiple-layer perceptron neural networks to associate a defect and corresponding morphological representation to its mechanical response. It is found that the method provides accurate mechanical predictions if the training data contains a sufficient number of defects representing each mechanical class. To do so, we supplement the original set of defects by data augmentation techniques. Artificially-generated pore shapes are obtained using the spherical harmonic decomposition and a singular value decomposition performed on the pores signed distance transform. We discuss possible applications of the present method, and how medoids and their associated mechanical response may be used to provide a natural basis for reduced-order models and hyper-reduction techniques, in which the mechanical effects of defects and structures are decorrelated (Ryckelynck et al. in C. R., Méc. 348(10–11):911–935, 2020).
我们开发了一种基于其形态和诱导机械响应的缺陷分类方法。所提出的方法是相当通用的，依赖于形态学算子(Angulo和Meyer在第9届国际数学形态学及其在信号和图像处理中的应用研讨会上，pp. 226-237, 2009)和球面谐波分解作为表征孔隙几何形状的方法，以及基于fft计算评估的Grassman距离(Willot in C. R.， msamac .)。(3):232 - 245,2015)，用于预测弹性响应。我们在焊接接头的x射线断层扫描中观察到一组被困的气孔，并对其进行了实施和详细说明，这些气孔显著改变了这些材料的机械可靠性(Lacourt et al. in Int)。j .号码。方法工程学报，121(11):2581-2599,2020)。首先利用“k-介质”准则和相关的距离函数将形态和力学响应空间划分为簇。其次，我们使用多层感知器神经网络将缺陷和相应的形态表征与其机械响应联系起来。如果训练数据包含足够数量的代表每个机械类的缺陷，则该方法可以提供准确的机械预测。为此，我们通过数据增强技术来补充原始的缺陷集。对孔隙符号距离变换进行球谐分解和奇异值分解，得到人工生成的孔隙形状。我们讨论了本方法的可能应用，以及如何使用介质及其相关的机械响应来为降阶模型和超约化技术提供自然基础，其中缺陷和结构的机械效应是去相关的(Ryckelynck et al. in C. R.， m。348(年级):911 - 935,2020)。
{"title":"Mechanical assessment of defects in welded joints: morphological classification and data augmentation","authors":"Launay, Hugo, Willot, François, Ryckelynck, David, Besson, Jacques","doi":"10.1186/s13362-021-00114-7","DOIUrl":"https://doi.org/10.1186/s13362-021-00114-7","url":null,"abstract":"We develop a methodology for classifying defects based on their morphology and induced mechanical response. The proposed approach is fairly general and relies on morphological operators (Angulo and Meyer in 9th international symposium on mathematical morphology and its applications to signal and image processing, pp. 226-237, 2009) and spherical harmonic decomposition as a way to characterize the geometry of the pores, and on the Grassman distance evaluated on FFT-based computations (Willot in C. R., Méc. 343(3):232–245, 2015), for the predicted elastic response. We implement and detail our approach on a set of trapped gas pores observed in X-ray tomography of welded joints, that significantly alter the mechanical reliability of these materials (Lacourt et al. in Int. J. Numer. Methods Eng. 121(11):2581–2599, 2020). The space of morphological and mechanical responses is first partitioned into clusters using the “k-medoids” criterion and associated distance functions. Second, we use multiple-layer perceptron neural networks to associate a defect and corresponding morphological representation to its mechanical response. It is found that the method provides accurate mechanical predictions if the training data contains a sufficient number of defects representing each mechanical class. To do so, we supplement the original set of defects by data augmentation techniques. Artificially-generated pore shapes are obtained using the spherical harmonic decomposition and a singular value decomposition performed on the pores signed distance transform. We discuss possible applications of the present method, and how medoids and their associated mechanical response may be used to provide a natural basis for reduced-order models and hyper-reduction techniques, in which the mechanical effects of defects and structures are decorrelated (Ryckelynck et al. in C. R., Méc. 348(10–11):911–935, 2020).","PeriodicalId":44012,"journal":{"name":"Journal of Mathematics in Industry","volume":"33 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2021-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138526225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-11DOI: 10.1186/s13362-021-00113-8
Bundschuh, Jonas, D’Angelo, Laura A. M., De Gersem, Herbert
The finite element method is widely used in simulations of various fields. However, when considering domains whose extent differs strongly in different spatial directions a finite element simulation becomes computationally very expensive due to the large number of degrees of freedom. An example of such a domain are the cables inside of the magnets of particle accelerators. For translationally invariant domains, this work proposes a quasi-3-D method. Thereby, a 2-D finite element method with a nodal basis in the cross-section is combined with a spectral method with a wavelet basis in the longitudinal direction. Furthermore, a spectral method with a wavelet basis and an adaptive and time-dependent resolution is presented. All methods are verified. As an example the hot-spot propagation due to a quench in Rutherford cables is simulated successfully.
{"title":"Quasi-3-D spectral wavelet method for a thermal quench simulation","authors":"Bundschuh, Jonas, D’Angelo, Laura A. M., De Gersem, Herbert","doi":"10.1186/s13362-021-00113-8","DOIUrl":"https://doi.org/10.1186/s13362-021-00113-8","url":null,"abstract":"The finite element method is widely used in simulations of various fields. However, when considering domains whose extent differs strongly in different spatial directions a finite element simulation becomes computationally very expensive due to the large number of degrees of freedom. An example of such a domain are the cables inside of the magnets of particle accelerators. For translationally invariant domains, this work proposes a quasi-3-D method. Thereby, a 2-D finite element method with a nodal basis in the cross-section is combined with a spectral method with a wavelet basis in the longitudinal direction. Furthermore, a spectral method with a wavelet basis and an adaptive and time-dependent resolution is presented. All methods are verified. As an example the hot-spot propagation due to a quench in Rutherford cables is simulated successfully.","PeriodicalId":44012,"journal":{"name":"Journal of Mathematics in Industry","volume":"28 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2021-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138526260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-26DOI: 10.1186/s13362-021-00112-9
Yoshioka, Hidekazu, Yaegashi, Yuta
A stochastic impulse control problem with imperfect controllability of interventions is formulated with an emphasis on applications to ecological and environmental management problems. The imperfectness comes from uncertainties with respect to the magnitude of interventions. Our model is based on a dynamic programming formalism to impulsively control a 1-D diffusion process of a geometric Brownian type. The imperfectness leads to a non-local operator different from the many conventional ones, and evokes a slightly different optimal intervention policy. We give viscosity characterizations of the Hamilton–Jacobi–Bellman Quasi-Variational Inequality (HJBQVI) governing the value function focusing on its numerical computation. Uniqueness and verification results of the HJBQVI are presented and a candidate exact solution is constructed. The HJBQVI is solved with the two different numerical methods, an ordinary differential equation (ODE) based method and a finite difference scheme, demonstrating their consistency. Furthermore, the resulting controlled dynamics are extensively analyzed focusing on a bird population management case from a statistical standpoint.
{"title":"Mathematical and numerical analyses of a stochastic impulse control model with imperfect interventions","authors":"Yoshioka, Hidekazu, Yaegashi, Yuta","doi":"10.1186/s13362-021-00112-9","DOIUrl":"https://doi.org/10.1186/s13362-021-00112-9","url":null,"abstract":"A stochastic impulse control problem with imperfect controllability of interventions is formulated with an emphasis on applications to ecological and environmental management problems. The imperfectness comes from uncertainties with respect to the magnitude of interventions. Our model is based on a dynamic programming formalism to impulsively control a 1-D diffusion process of a geometric Brownian type. The imperfectness leads to a non-local operator different from the many conventional ones, and evokes a slightly different optimal intervention policy. We give viscosity characterizations of the Hamilton–Jacobi–Bellman Quasi-Variational Inequality (HJBQVI) governing the value function focusing on its numerical computation. Uniqueness and verification results of the HJBQVI are presented and a candidate exact solution is constructed. The HJBQVI is solved with the two different numerical methods, an ordinary differential equation (ODE) based method and a finite difference scheme, demonstrating their consistency. Furthermore, the resulting controlled dynamics are extensively analyzed focusing on a bird population management case from a statistical standpoint.","PeriodicalId":44012,"journal":{"name":"Journal of Mathematics in Industry","volume":"82 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2021-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138542928","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-22DOI: 10.1186/s13362-023-00132-7
R. Herzog, D. Strelnikov
{"title":"An optimal control problem for single-spot pulsed laser welding","authors":"R. Herzog, D. Strelnikov","doi":"10.1186/s13362-023-00132-7","DOIUrl":"https://doi.org/10.1186/s13362-023-00132-7","url":null,"abstract":"","PeriodicalId":44012,"journal":{"name":"Journal of Mathematics in Industry","volume":"13 1","pages":"1-18"},"PeriodicalIF":2.6,"publicationDate":"2021-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48674178","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-20DOI: 10.1186/s13362-022-00128-9
Claudia Drygala, M. Rottmann, H. Gottschalk, Klaus Friedrichs, Thomas Kurbiel
{"title":"Background-foreground segmentation for interior sensing in automotive industry","authors":"Claudia Drygala, M. Rottmann, H. Gottschalk, Klaus Friedrichs, Thomas Kurbiel","doi":"10.1186/s13362-022-00128-9","DOIUrl":"https://doi.org/10.1186/s13362-022-00128-9","url":null,"abstract":"","PeriodicalId":44012,"journal":{"name":"Journal of Mathematics in Industry","volume":"12 1","pages":"1-32"},"PeriodicalIF":2.6,"publicationDate":"2021-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45277538","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-08-31DOI: 10.1007/978-3-031-11818-0_22
J. P. Burgard, S. Heyder, T. Hotz, T. Krueger
{"title":"Regional estimates of reproduction numbers with application to COVID-19","authors":"J. P. Burgard, S. Heyder, T. Hotz, T. Krueger","doi":"10.1007/978-3-031-11818-0_22","DOIUrl":"https://doi.org/10.1007/978-3-031-11818-0_22","url":null,"abstract":"","PeriodicalId":44012,"journal":{"name":"Journal of Mathematics in Industry","volume":"7 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2021-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85170030","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-18DOI: 10.1186/s13362-021-00109-4
Christian Himpe, Sara Grundel, Peter Benner
To counter the volatile nature of renewable energy sources, gas networks take a vital role. But, to ensure fulfillment of contracts under these circumstances, a vast number of possible scenarios, incorporating uncertain supply and demand, has to be simulated ahead of time. This many-query gas network simulation task can be accelerated by model reduction, yet, large-scale, nonlinear, parametric, hyperbolic partial differential(-algebraic) equation systems, modeling natural gas transport, are a challenging application for model order reduction algorithms. For this industrial application, we bring together the scientific computing topics of: mathematical modeling of gas transport networks, numerical simulation of hyperbolic partial differential equation, and parametric model reduction for nonlinear systems. This research resulted in the morgen (Model Order Reduction for Gas and Energy Networks) software platform, which enables modular testing of various combinations of models, solvers, and model reduction methods. In this work we present the theoretical background on systemic modeling and structured, data-driven, system-theoretic model reduction for gas networks, as well as the implementation of morgen and associated numerical experiments testing model reduction adapted to gas network models.
{"title":"Model order reduction for gas and energy networks","authors":"Christian Himpe, Sara Grundel, Peter Benner","doi":"10.1186/s13362-021-00109-4","DOIUrl":"https://doi.org/10.1186/s13362-021-00109-4","url":null,"abstract":"To counter the volatile nature of renewable energy sources, gas networks take a vital role. But, to ensure fulfillment of contracts under these circumstances, a vast number of possible scenarios, incorporating uncertain supply and demand, has to be simulated ahead of time. This many-query gas network simulation task can be accelerated by model reduction, yet, large-scale, nonlinear, parametric, hyperbolic partial differential(-algebraic) equation systems, modeling natural gas transport, are a challenging application for model order reduction algorithms. For this industrial application, we bring together the scientific computing topics of: mathematical modeling of gas transport networks, numerical simulation of hyperbolic partial differential equation, and parametric model reduction for nonlinear systems. This research resulted in the morgen (Model Order Reduction for Gas and Energy Networks) software platform, which enables modular testing of various combinations of models, solvers, and model reduction methods. In this work we present the theoretical background on systemic modeling and structured, data-driven, system-theoretic model reduction for gas networks, as well as the implementation of morgen and associated numerical experiments testing model reduction adapted to gas network models.","PeriodicalId":44012,"journal":{"name":"Journal of Mathematics in Industry","volume":"150 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2021-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138542976","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-30DOI: 10.1186/s13362-021-00108-5
A. Thune, X. Cai, A. Rustad
{"title":"On the impact of heterogeneity-aware mesh partitioning and non-contributing computation removal on parallel reservoir simulations","authors":"A. Thune, X. Cai, A. Rustad","doi":"10.1186/s13362-021-00108-5","DOIUrl":"https://doi.org/10.1186/s13362-021-00108-5","url":null,"abstract":"","PeriodicalId":44012,"journal":{"name":"Journal of Mathematics in Industry","volume":"11 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13362-021-00108-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"65846686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-12DOI: 10.1186/s13362-021-00106-7
Ulrich Wilbrandt, Najib Alia, Volker John
Gas stirring is an important process used in secondary metallurgy. It allows to homogenize the temperature and the chemical composition of the liquid steel and to remove inclusions which can be detrimental for the end-product quality. In this process, argon gas is injected from two nozzles at the bottom of the vessel and rises by buoyancy through the liquid steel thereby causing stirring, i.e., a mixing of the bath. The gas flow rates and the positions of the nozzles are two important control parameters in practice. A continuous optimization approach is pursued to find optimal values for these control variables. The effect of the gas appears as a volume force in the single-phase incompressible Navier–Stokes equations. Turbulence is modeled with the Smagorinsky Large Eddy Simulation (LES) model. An objective functional based on the vorticity is used to describe the mixing in the liquid bath. Optimized configurations are compared with a default one whose design is based on a setup from industrial practice.
{"title":"Optimal control of buoyancy-driven liquid steel stirring modeled with single-phase Navier–Stokes equations","authors":"Ulrich Wilbrandt, Najib Alia, Volker John","doi":"10.1186/s13362-021-00106-7","DOIUrl":"https://doi.org/10.1186/s13362-021-00106-7","url":null,"abstract":"Gas stirring is an important process used in secondary metallurgy. It allows to homogenize the temperature and the chemical composition of the liquid steel and to remove inclusions which can be detrimental for the end-product quality. In this process, argon gas is injected from two nozzles at the bottom of the vessel and rises by buoyancy through the liquid steel thereby causing stirring, i.e., a mixing of the bath. The gas flow rates and the positions of the nozzles are two important control parameters in practice. A continuous optimization approach is pursued to find optimal values for these control variables. The effect of the gas appears as a volume force in the single-phase incompressible Navier–Stokes equations. Turbulence is modeled with the Smagorinsky Large Eddy Simulation (LES) model. An objective functional based on the vorticity is used to describe the mixing in the liquid bath. Optimized configurations are compared with a default one whose design is based on a setup from industrial practice.","PeriodicalId":44012,"journal":{"name":"Journal of Mathematics in Industry","volume":"78 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2021-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138512861","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-05DOI: 10.1186/s13362-021-00104-9
Tulsi Sagar Sheth, F. Acharya
{"title":"Optimizing similarity factor of in vitro drug release profile for development of early stage formulation of drug using linear regression model","authors":"Tulsi Sagar Sheth, F. Acharya","doi":"10.1186/s13362-021-00104-9","DOIUrl":"https://doi.org/10.1186/s13362-021-00104-9","url":null,"abstract":"","PeriodicalId":44012,"journal":{"name":"Journal of Mathematics in Industry","volume":"11 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2021-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13362-021-00104-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"65846622","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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