SAM
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The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Thu, 29 Feb 2024 09:50:01 GMT2024-02-29T09:50:01ZLearning data-driven reduced elastic and inelastic models of spot-welded patches
http://hdl.handle.net/10985/20416
Learning data-driven reduced elastic and inelastic models of spot-welded patches
REILLE, Agathe; CHAMPANEY, Victor; DAIM, Fatima; TOURBIER, Yves; HASCOET, Nicolas; GONZALEZ, David; CUETO, Elias; DUVAL, Jean Louis; CHINESTA, Francisco
Solving mechanical problems in large structures with rich localized behaviors remains a challenging issue despite the enormous advances in numerical procedures and computational performance. In particular, these localized behaviors need for extremely fine descriptions, and this has an associated impact in the number of degrees of freedom from one side, and the decrease of the time step employed in usual explicit time integrations, whose stability scales with the size of the smallest element involved in the mesh. In the present work we propose a data-driven technique for learning the rich behavior of a local patch and integrate it into a standard coarser description at the structure level. Thus, localized behaviors impact the global structural response without needing an explicit description of that fine scale behaviors.
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10985/204162021-01-01T00:00:00ZREILLE, AgatheCHAMPANEY, VictorDAIM, FatimaTOURBIER, YvesHASCOET, NicolasGONZALEZ, DavidCUETO, EliasDUVAL, Jean LouisCHINESTA, FranciscoSolving mechanical problems in large structures with rich localized behaviors remains a challenging issue despite the enormous advances in numerical procedures and computational performance. In particular, these localized behaviors need for extremely fine descriptions, and this has an associated impact in the number of degrees of freedom from one side, and the decrease of the time step employed in usual explicit time integrations, whose stability scales with the size of the smallest element involved in the mesh. In the present work we propose a data-driven technique for learning the rich behavior of a local patch and integrate it into a standard coarser description at the structure level. Thus, localized behaviors impact the global structural response without needing an explicit description of that fine scale behaviors.Parametric analysis and machine learning-based parametric modeling of wire laser metal deposition induced porosity
http://hdl.handle.net/10985/22196
Parametric analysis and machine learning-based parametric modeling of wire laser metal deposition induced porosity
LOREAU, Tanguy; CHAMPANEY, Victor; HASCOET, Nicolas; LAMBARRI, Jon; MADARIETA, Mikel; GARMENDIA, Iker; CHINESTA, Francisco
Additive manufacturing is an appealing solution to produce geometrically complex parts, difficult to manufacture using traditional technologies. The extreme process conditions, in particular the high temperature, complex interactions and couplings, rich metallurgical transformations and combinatorial deposition trajectories, induce numerous process defects and in particular porosity. Simulating numerically porosity appearance remains extremely complex because of the multiple physics induced by the laser-material interaction, the multiple space and time scales, with a strong impact on the simulation efficiency and performances. Moreover, when analyzing parts build-up by using the wire laser metal deposition —wLMD— technology it can be noticed a significant variability in the porosity size and distribution even when process parameters remain unchanged. For these reasons the present paper aims at proposing an alternative modeling approach based on the use of neural networks to express the porosity as a function of different process parameters that will be extracted from the process analysis.
Fri, 01 Apr 2022 00:00:00 GMThttp://hdl.handle.net/10985/221962022-04-01T00:00:00ZLOREAU, TanguyCHAMPANEY, VictorHASCOET, NicolasLAMBARRI, JonMADARIETA, MikelGARMENDIA, IkerCHINESTA, FranciscoAdditive manufacturing is an appealing solution to produce geometrically complex parts, difficult to manufacture using traditional technologies. The extreme process conditions, in particular the high temperature, complex interactions and couplings, rich metallurgical transformations and combinatorial deposition trajectories, induce numerous process defects and in particular porosity. Simulating numerically porosity appearance remains extremely complex because of the multiple physics induced by the laser-material interaction, the multiple space and time scales, with a strong impact on the simulation efficiency and performances. Moreover, when analyzing parts build-up by using the wire laser metal deposition —wLMD— technology it can be noticed a significant variability in the porosity size and distribution even when process parameters remain unchanged. For these reasons the present paper aims at proposing an alternative modeling approach based on the use of neural networks to express the porosity as a function of different process parameters that will be extracted from the process analysis.Engineering empowered by physics-based and data-driven hybrid models: A methodological overview
http://hdl.handle.net/10985/22207
Engineering empowered by physics-based and data-driven hybrid models: A methodological overview
CHAMPANEY, Victor; CHINESTA, Francisco; CUETO, Elias
Smart manufacturing implies creating virtual replicas of the processing operations, taking into account the material dimension and its multi-physics transformation when forming processes operate. Performing efficient, that is, online accurate predictions of the induced properties (including potential defects) of the formed part (to optimally control the process parameters) needs moving beyond usual offline simulation based on nominal models, and proceeds by assimilating data. This will serve, from one side, to keep the model calibrated, and from the other, to enrich the model and its associated predictions, to avoid bias, to improve accuracy or for performing online diagnosis, by advertising on preventive maintenance. For all these purposes, a new alliance between physics-based and data-driven modelling approaches seems a very valuable route for empowering engineering in general, and smart manufacturing in particular. The present paper revisits the main methodologies involved in the construction of the component or system Hybrid Twins.
Tue, 05 Apr 2022 00:00:00 GMThttp://hdl.handle.net/10985/222072022-04-05T00:00:00ZCHAMPANEY, VictorCHINESTA, FranciscoCUETO, EliasSmart manufacturing implies creating virtual replicas of the processing operations, taking into account the material dimension and its multi-physics transformation when forming processes operate. Performing efficient, that is, online accurate predictions of the induced properties (including potential defects) of the formed part (to optimally control the process parameters) needs moving beyond usual offline simulation based on nominal models, and proceeds by assimilating data. This will serve, from one side, to keep the model calibrated, and from the other, to enrich the model and its associated predictions, to avoid bias, to improve accuracy or for performing online diagnosis, by advertising on preventive maintenance. For all these purposes, a new alliance between physics-based and data-driven modelling approaches seems a very valuable route for empowering engineering in general, and smart manufacturing in particular. The present paper revisits the main methodologies involved in the construction of the component or system Hybrid Twins.Multiparametric modelling of composite materials based on non-intrusive PGD informed by multiscale analyses: Application for real-time stiffness prediction of woven composites
http://hdl.handle.net/10985/22637
Multiparametric modelling of composite materials based on non-intrusive PGD informed by multiscale analyses: Application for real-time stiffness prediction of woven composites
EL FALLAKI IDRISSI, Mohammed; PRAUD, Francis; CHAMPANEY, Victor; CHINESTA, Francisco; MERAGHNI, Fodil
In this paper, a multiparametric solution of the stiffness properties of woven composites involving several microstructure parameters is performed. For this purpose, non-intrusive PGD-based methods are employed. From offline pre-computed solutions generated through a full-field multiscale modeling, the proposed method approximates the multidimensional solution as a sum of products of one-dimensional functions each depending on a single variable. The present work aims at providing an accurate approximation of this multiparametric solution with lower computational cost for dataset generation. Thus, a comparative analysis of three non-intrusive PGD formulations (SSL, s-PGD and ANOVA-PGD) is carried out. The obtained results reveal and demonstrate that the ANOVA-PGD model works well for approximating the stiffness properties over the entire parameter space, i.e., along its boundary as well as inside it, by using only few pre-computed high-fidelity solutions. Finally, a GUI application is developed to exploit this multiparametric solution by incorporating other composite weave architectures. This application could be easily used by engineers and composite designers, to deduce, in real-time, the macroscopic properties of woven composite for a given set of microstructural parameters by simply varying the cursors and without any microstructure generation and meshing nor FE computations using periodic homogenization.
Thu, 01 Sep 2022 00:00:00 GMThttp://hdl.handle.net/10985/226372022-09-01T00:00:00ZEL FALLAKI IDRISSI, MohammedPRAUD, FrancisCHAMPANEY, VictorCHINESTA, FranciscoMERAGHNI, FodilIn this paper, a multiparametric solution of the stiffness properties of woven composites involving several microstructure parameters is performed. For this purpose, non-intrusive PGD-based methods are employed. From offline pre-computed solutions generated through a full-field multiscale modeling, the proposed method approximates the multidimensional solution as a sum of products of one-dimensional functions each depending on a single variable. The present work aims at providing an accurate approximation of this multiparametric solution with lower computational cost for dataset generation. Thus, a comparative analysis of three non-intrusive PGD formulations (SSL, s-PGD and ANOVA-PGD) is carried out. The obtained results reveal and demonstrate that the ANOVA-PGD model works well for approximating the stiffness properties over the entire parameter space, i.e., along its boundary as well as inside it, by using only few pre-computed high-fidelity solutions. Finally, a GUI application is developed to exploit this multiparametric solution by incorporating other composite weave architectures. This application could be easily used by engineers and composite designers, to deduce, in real-time, the macroscopic properties of woven composite for a given set of microstructural parameters by simply varying the cursors and without any microstructure generation and meshing nor FE computations using periodic homogenization.Data-Driven Modeling for Multiphysics Parametrized Problems-Application to Induction Hardening Process
http://hdl.handle.net/10985/20595
Data-Driven Modeling for Multiphysics Parametrized Problems-Application to Induction Hardening Process
DEROUICHE, Khouloud; GAROIS, Sevan; CHAMPANEY, Victor; DAOUD, Monzer; TRAIDI, Khalil; CHINESTA, Francisco
Data-driven modeling provides an efficient approach to compute approximate solutions for complex multiphysics parametrized problems such as induction hardening (IH) process. Basically, some physical quantities of interest (QoI) related to the IH process will be evaluated under real-time constraint, without any explicit knowledge of the physical behavior of the system. Hence, computationally expensive finite element models will be replaced by a parametric solution, called metamodel. Two data-driven models for temporal evolution of temperature and austenite phase transformation, during induction heating, were first developed by using the proper orthogonal decomposition based reduced-order model followed by a nonlinear regression method for temperature field and a classification combined with regression for austenite evolution. Then, data-driven and hybrid models were created to predict hardness, after quenching. It is shown that the results of artificial intelligence models are promising and provide good approximations in the low-data limit case.
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10985/205952021-01-01T00:00:00ZDEROUICHE, KhouloudGAROIS, SevanCHAMPANEY, VictorDAOUD, MonzerTRAIDI, KhalilCHINESTA, FranciscoData-driven modeling provides an efficient approach to compute approximate solutions for complex multiphysics parametrized problems such as induction hardening (IH) process. Basically, some physical quantities of interest (QoI) related to the IH process will be evaluated under real-time constraint, without any explicit knowledge of the physical behavior of the system. Hence, computationally expensive finite element models will be replaced by a parametric solution, called metamodel. Two data-driven models for temporal evolution of temperature and austenite phase transformation, during induction heating, were first developed by using the proper orthogonal decomposition based reduced-order model followed by a nonlinear regression method for temperature field and a classification combined with regression for austenite evolution. Then, data-driven and hybrid models were created to predict hardness, after quenching. It is shown that the results of artificial intelligence models are promising and provide good approximations in the low-data limit case.Surrogate parametric metamodel based on Optimal Transport
http://hdl.handle.net/10985/22204
Surrogate parametric metamodel based on Optimal Transport
TORREGROSA, Sergio; CHAMPANEY, Victor; AMMAR, Amine; HERBERT, Vincent; CHINESTA, Francisco
The description of a physical problem through a model necessarily involves the introduction of parameters. Hence, one
wishes to have a solution of the problem that is a function of all these parameters: a parametric solution. However, the
construction of such parametric solutions exhibiting localization in space is only ensured by costly and time-consuming tests,
which can be both numerical or experimental. Numerical methodologies used classically imply enormous computational efforts
for exploring the design space. Therefore, parametric solutions obtained using advanced nonlinear regressions are an essential tool to address this challenge. However, classical regression techniques, even the most advanced ones, can lead to non physical interpolation in some fields such as fluid dynamics, where the solution localizes in different regions depending on the problem parameters choice. In this context, Optimal Transport (OT) offers a mathematical approach to measure distances and interpolate between general objects in a, sometimes, more physical way than the classical interpolation approach. Thus, OT has become fundamental in some fields such as statistics or computer vision, and it is being increasingly used in fields such as computational mechanics. However, the OT problem is usually computationally costly to solve and not adapted to be accessed in an online manner. Therefore, the aim of this paper is combining advanced nonlinear regressions with Optimal Transport in order to implement a parametric real-time model based on OT. To this purpose, a parametric model is built offline relying on Model Order Reduction and OT, leading to a real-time interpolation tool following Optimal Transport theory. Such a tool is of major interest in design processes, but also within the digital twin rationale.
Tue, 30 Nov 2021 00:00:00 GMThttp://hdl.handle.net/10985/222042021-11-30T00:00:00ZTORREGROSA, SergioCHAMPANEY, VictorAMMAR, AmineHERBERT, VincentCHINESTA, FranciscoThe description of a physical problem through a model necessarily involves the introduction of parameters. Hence, one
wishes to have a solution of the problem that is a function of all these parameters: a parametric solution. However, the
construction of such parametric solutions exhibiting localization in space is only ensured by costly and time-consuming tests,
which can be both numerical or experimental. Numerical methodologies used classically imply enormous computational efforts
for exploring the design space. Therefore, parametric solutions obtained using advanced nonlinear regressions are an essential tool to address this challenge. However, classical regression techniques, even the most advanced ones, can lead to non physical interpolation in some fields such as fluid dynamics, where the solution localizes in different regions depending on the problem parameters choice. In this context, Optimal Transport (OT) offers a mathematical approach to measure distances and interpolate between general objects in a, sometimes, more physical way than the classical interpolation approach. Thus, OT has become fundamental in some fields such as statistics or computer vision, and it is being increasingly used in fields such as computational mechanics. However, the OT problem is usually computationally costly to solve and not adapted to be accessed in an online manner. Therefore, the aim of this paper is combining advanced nonlinear regressions with Optimal Transport in order to implement a parametric real-time model based on OT. To this purpose, a parametric model is built offline relying on Model Order Reduction and OT, leading to a real-time interpolation tool following Optimal Transport theory. Such a tool is of major interest in design processes, but also within the digital twin rationale.Parametric Curves Metamodelling Based on Data Clustering, Data Alignment, POD-Based Modes Extraction and PGD-Based Nonlinear Regressions
http://hdl.handle.net/10985/22377
Parametric Curves Metamodelling Based on Data Clustering, Data Alignment, POD-Based Modes Extraction and PGD-Based Nonlinear Regressions
CHAMPANEY, Victor; PASQUALE, Angelo; AMMAR, Amine; CHINESTA, Francisco
In the context of parametric surrogates, several nontrivial issues arise when a whole curve shall be predicted from given input features. For instance, different sampling or ending points lead to non-aligned curves. This also happens when the curves exhibit a common pattern characterized by critical points at shifted locations (e.g., in mechanics, the elasticplastic transition or the rupture point for a material). In such cases, classical interpolation methods fail in giving physics-consistent results and appropriate pre-processing steps are required. Moreover, when bifurcations occur into the parametric space, to enhance the accuracy of the surrogate, a coupling with clustering and classification algorithms is needed. In this work we present several methodologies to overcome these issues. We also exploit such surrogates to quantify and propagate uncertainty, furnishing parametric stastistical bounds for the predicted curves. The procedures are exemplified over two problems in Computational Mechanics.
Wed, 01 Jun 2022 00:00:00 GMThttp://hdl.handle.net/10985/223772022-06-01T00:00:00ZCHAMPANEY, VictorPASQUALE, AngeloAMMAR, AmineCHINESTA, FranciscoIn the context of parametric surrogates, several nontrivial issues arise when a whole curve shall be predicted from given input features. For instance, different sampling or ending points lead to non-aligned curves. This also happens when the curves exhibit a common pattern characterized by critical points at shifted locations (e.g., in mechanics, the elasticplastic transition or the rupture point for a material). In such cases, classical interpolation methods fail in giving physics-consistent results and appropriate pre-processing steps are required. Moreover, when bifurcations occur into the parametric space, to enhance the accuracy of the surrogate, a coupling with clustering and classification algorithms is needed. In this work we present several methodologies to overcome these issues. We also exploit such surrogates to quantify and propagate uncertainty, furnishing parametric stastistical bounds for the predicted curves. The procedures are exemplified over two problems in Computational Mechanics.Data Completion, Model Correction and Enrichment Based on Sparse Identification and Data Assimilation
http://hdl.handle.net/10985/23041
Data Completion, Model Correction and Enrichment Based on Sparse Identification and Data Assimilation
DI LORENZO, Daniele; CHAMPANEY, Victor; GERMOSO, Claudia; CUETO, Elias; CHINESTA, Francisco
Many models assumed to be able to predict the response of structural systems fail to efficiently accomplish that purpose because of two main reasons. First, some structures in operation undergo localized damage that degrades their mechanical performances. To reflect this local loss of performance, the stiffness matrix associated with the structure should be locally corrected. Second, the nominal model is sometimes too coarse grained for reflecting all structural details, and consequently, the predictions are expected to deviate from the measurements. In that case, there is no small region of the model that needs to be repaired, but the entire domain needs to be repaired; therefore, the entire structure-stiffness matrix should be corrected. In the present work, we propose a methodology for locally correcting or globally enriching the models from collected data, which is, upon its turn, completed beyond the sensor’s location. The proposed techniques consist in the first case of an L1-minimization procedure that, with the support of data, aims at the same time period to detect the damaged zone in the structure and to predict the correct solution. For the global enrichment, instead, the methodology consists of an L2-minimization procedure with the support of measurements. The results obtained showed, for the local problem, a correction up to 90% with respect to the initially incorrectly predicted displacement of the structure, and for the global one, a correction up to 60% was observed (this results concern the problems considered in the present study, but they depend on different factors, such as the number of data used, the geometry or the intensity of the damage). The benefits and potential of such techniques are illustrated on four different problems, showing the large generality and adaptability of the methodology.
Fri, 01 Jul 2022 00:00:00 GMThttp://hdl.handle.net/10985/230412022-07-01T00:00:00ZDI LORENZO, DanieleCHAMPANEY, VictorGERMOSO, ClaudiaCUETO, EliasCHINESTA, FranciscoMany models assumed to be able to predict the response of structural systems fail to efficiently accomplish that purpose because of two main reasons. First, some structures in operation undergo localized damage that degrades their mechanical performances. To reflect this local loss of performance, the stiffness matrix associated with the structure should be locally corrected. Second, the nominal model is sometimes too coarse grained for reflecting all structural details, and consequently, the predictions are expected to deviate from the measurements. In that case, there is no small region of the model that needs to be repaired, but the entire domain needs to be repaired; therefore, the entire structure-stiffness matrix should be corrected. In the present work, we propose a methodology for locally correcting or globally enriching the models from collected data, which is, upon its turn, completed beyond the sensor’s location. The proposed techniques consist in the first case of an L1-minimization procedure that, with the support of data, aims at the same time period to detect the damaged zone in the structure and to predict the correct solution. For the global enrichment, instead, the methodology consists of an L2-minimization procedure with the support of measurements. The results obtained showed, for the local problem, a correction up to 90% with respect to the initially incorrectly predicted displacement of the structure, and for the global one, a correction up to 60% was observed (this results concern the problems considered in the present study, but they depend on different factors, such as the number of data used, the geometry or the intensity of the damage). The benefits and potential of such techniques are illustrated on four different problems, showing the large generality and adaptability of the methodology.Parametric Electromagnetic Analysis of Radar-Based Advanced Driver Assistant Systems
http://hdl.handle.net/10985/19416
Parametric Electromagnetic Analysis of Radar-Based Advanced Driver Assistant Systems
VERMIGLIO, Simona; CHAMPANEY, Victor; SANCARLOS, Abel; DAIM, Fatima; KEDZIA, Jean Claude; DUVAL, Jean Louis; DIEZ, Pedro; CHINESTA, Francisco
Efficient and optimal design of radar-based Advanced Driver Assistant Systems (ADAS) needs the evaluation of many different electromagnetic solutions for evaluating the impact of the radome on the electromagnetic wave propagation. Because of the very high frequency at which these devices operate, with the associated extremely small wavelength, very fine meshes are needed to accurately discretize the electromagnetic equations. Thus, the computational cost of each numerical solution for a given choice of the design or operation parameters, is high (CPU time consuming and needing significant computational resources) compromising the efficiency of standard optimization algorithms. In order to alleviate the just referred difficulties the present paper proposes an approach based on the use of reduced order modeling, in particular the construction of a parametric solution by employing a non-intrusive formulation of the Proper Generalized Decomposition, combined with a powerful phase-angle unwrapping strategy for accurately addressing the electric and magnetic fields interpolation, contributing to improve the design, the calibration and the operational use of those systems.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10985/194162020-01-01T00:00:00ZVERMIGLIO, SimonaCHAMPANEY, VictorSANCARLOS, AbelDAIM, FatimaKEDZIA, Jean ClaudeDUVAL, Jean LouisDIEZ, PedroCHINESTA, FranciscoEfficient and optimal design of radar-based Advanced Driver Assistant Systems (ADAS) needs the evaluation of many different electromagnetic solutions for evaluating the impact of the radome on the electromagnetic wave propagation. Because of the very high frequency at which these devices operate, with the associated extremely small wavelength, very fine meshes are needed to accurately discretize the electromagnetic equations. Thus, the computational cost of each numerical solution for a given choice of the design or operation parameters, is high (CPU time consuming and needing significant computational resources) compromising the efficiency of standard optimization algorithms. In order to alleviate the just referred difficulties the present paper proposes an approach based on the use of reduced order modeling, in particular the construction of a parametric solution by employing a non-intrusive formulation of the Proper Generalized Decomposition, combined with a powerful phase-angle unwrapping strategy for accurately addressing the electric and magnetic fields interpolation, contributing to improve the design, the calibration and the operational use of those systems.Learning the Parametric Transfer Function of Unitary Operations for Real-Time Evaluation of Manufacturing Processes Involving Operations Sequencing
http://hdl.handle.net/10985/20468
Learning the Parametric Transfer Function of Unitary Operations for Real-Time Evaluation of Manufacturing Processes Involving Operations Sequencing
LOREAU, Tanguy; CHAMPANEY, Victor; HASCOËT, Nicolas; MOURGUE, Philippe; DUVAL, Jean-Louis; CHINESTA, Francisco
For better designing manufacturing processes, surrogate models were widely considered in the past, where the effect of different material and process parameters was considered from the use of a parametric solution. The last contains the solution of the model describing the system under study, for any choice of the selected parameters. These surrogate models, also known as meta-models, virtual charts or computational vademecum, in the context of model order reduction, were successfully employed in a variety of industrial applications. However, they remain confronted to a major difficulty when the number of parameters grows exponentially. Thus, processes involving trajectories or sequencing entail a combinatorial exposition (curse of dimensionality) not only due to the number of possible combinations, but due to the number of parameters needed to describe the process. The present paper proposes a promising route for circumventing, or at least alleviating that difficulty. The proposed technique consists of a parametric transfer function that, as soon as it is learned, allows for, from a given state, inferring the new state after the application of a unitary operation, defined as a step in the sequenced process. Thus, any sequencing can be evaluated almost in real time by chaining that unitary transfer function, whose output becomes the input of the next operation. The benefits and potential of such a technique are illustrated on a problem of industrial relevance, the one concerning the induced deformation on a structural part when printing on it a series of stiffeners.
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10985/204682021-01-01T00:00:00ZLOREAU, TanguyCHAMPANEY, VictorHASCOËT, NicolasMOURGUE, PhilippeDUVAL, Jean-LouisCHINESTA, FranciscoFor better designing manufacturing processes, surrogate models were widely considered in the past, where the effect of different material and process parameters was considered from the use of a parametric solution. The last contains the solution of the model describing the system under study, for any choice of the selected parameters. These surrogate models, also known as meta-models, virtual charts or computational vademecum, in the context of model order reduction, were successfully employed in a variety of industrial applications. However, they remain confronted to a major difficulty when the number of parameters grows exponentially. Thus, processes involving trajectories or sequencing entail a combinatorial exposition (curse of dimensionality) not only due to the number of possible combinations, but due to the number of parameters needed to describe the process. The present paper proposes a promising route for circumventing, or at least alleviating that difficulty. The proposed technique consists of a parametric transfer function that, as soon as it is learned, allows for, from a given state, inferring the new state after the application of a unitary operation, defined as a step in the sequenced process. Thus, any sequencing can be evaluated almost in real time by chaining that unitary transfer function, whose output becomes the input of the next operation. The benefits and potential of such a technique are illustrated on a problem of industrial relevance, the one concerning the induced deformation on a structural part when printing on it a series of stiffeners.