Publications
65 results found
Mélot A, Denimal E, Renson L, 2024, Multi-parametric optimization for controlling bifurcation structures, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol: 480, ISSN: 1364-5021
Bifurcations organize the dynamics of many natural and engineered systems. They induce qualitative and quantitative changes to a system's dynamics, which can have catastrophic consequences if ignored during design. In this paper, we propose a general computational method to control the local bifurcations of dynamical systems by optimizing design parameters. We define an objective functional that enforces the appearance of local bifurcation points at targeted locations or even encourages their disappearance. The methodology is an efficient alternative to bifurcation tracking techniques capable of handling many design parameters (>102). The method is demonstrated on a Duffing oscillator featuring a hardening cubic nonlinearity and an autonomous van der Pol-Duffing oscillator coupled to a nonlinear tuned vibration absorber. The finite-element model of a clamped-free Euler-Bernoulli beam, coupled with a reduced-order modelling technique, is also used to show the extension to the shape optimization of more complicated structures. Results demonstrate that several local bifurcations of various types can be handled simultaneously by the bifurcation control framework, with both parameter and state target values.
Bagheri AK, Sonneville V, Renson L, 2024, Nonlinear normal modes of highly flexible beam structures modelled under the SE(3) Lie group framework, Nonlinear Dynamics, Vol: 112, Pages: 1641-1659, ISSN: 0924-090X
This work presents a shooting algorithm to compute the periodic responses of geometrically nonlinear structures modelled under the special Euclidean (SE) Lie group formulation. The formulation is combined with a pseudo-arclength continuation method, while special adaptations are made to ensure compatibility with the SE framework. Nonlinear normal modes (NNMs) of various two-dimensional structures including a doubly clamped beam, a shallow arch, and a cantilever beam are computed. Results are compared with a reference displacement-based FE model with von Kármán strains. Significant difference is observed in the dynamic response of the two models in test cases involving large degrees of beam displacements and rotation. Differences in the contribution of higher-order modes substantially affect the frequency-energy dependence and the nonlinear modal interactions observed between the models. It is shown that the SE model, owing to its exact representation of the beam kinematics, is better suited at adequately capturing complex nonlinear dynamics compared to the von Kármán model.
Brake MRW, Renson L, Kuether RJ, et al., 2024, Preface, Conference Proceedings of the Society for Experimental Mechanics Series, Pages: v-vii, ISSN: 2191-5644
Tüfekci M, El Haddad F, Salles L, et al., 2023, Effects of the seal wire on the nonlinear dynamics of the aircraft engine turbine blades, Journal of Engineering for Gas Turbines and Power: Transactions of the ASME, Vol: 145, ISSN: 0742-4795
Complicated systems made of multiple components are known to be difficult to model, considering their solutions can change dramatically even with the slightest variations in conditions. Aircraft engines contain such complicated systems, and some components in aircraft engines' turbines can cause significant changes in the system's overall response. Hence, this study is focused on investigating the behavior of a turbine blade of an aircraft engine and the effects of the contact between the blade and the seal wire on the dynamics of the blade-disk system. The investigation is performed via various numerical simulations in time and frequency domains. One sector of the bladed disk is modeled using the finite element method with the lock plate and the seal wire imposing cyclic symmetry boundary conditions in the static, modal, and frequency domain forced response analyses. In time domain analyses, the cyclic symmetry is replaced with simplified displacement restricting boundary conditions. The time domain analysis contains steady-state forced responses of the system. The results show that contact with the seal wire is not a major source of nonlinearity and damping. The contacts with the lock plate contribute more to the vibration damping than the seal wire. However, compared to the contacts at the root of the blade, both components remain less significant with regard to frictional damping and nonlinearity.
Szydlowski MJ, Schwingshackl C, Renson L, 2023, Modeling nonlinear structures using physics-guided, machine-learnt models, 41st IMAC, A Conference and Exposition on Structural Dynamics 2023, Publisher: Springer Nature Switzerland, Pages: 71-74, ISSN: 2191-5644
The constant drive to improve the performance of aeronautic structures is leading to new designs where nonlinearity is ubiquitous. Accurately predicting the dynamic behavior of nonlinear systems is very challenging because they can exhibit a wide range of behaviors that have no linear equivalent and are very sensitive to parameter changes. In this work, we consider a physics-based model to capture the underlying linear behavior of the system. This linear model is then augmented with a data-driven, machine-learnt model that captures the nonlinearities present in the system. Standard ML models have, however, several important shortcomings from an engineering point of view. They often require large training datasets, do not generalize well to unseen conditions, and can even be physically inconsistent. To overcome these limitations, we investigate the use of Lagrangian Neural Networks (LNNs) where a neural network is used to directly model the Lagrangian function of the system. To enforce physical consistency, the Euler-Lagrange equations of motion of the system are obtained by differentiating this neural network using automatic differentiation techniques. The potential of this modeling approach is numerically and experimentally shown on a range of systems with stiffness and damping nonlinearities.
Lee KH, Barton DAW, Renson L, 2023, Modelling of physical systems with a Hopf bifurcation using mechanistic models and machine learning, MECHANICAL SYSTEMS AND SIGNAL PROCESSING, Vol: 191, ISSN: 0888-3270
Blyth M, Tsaneva-Atanasova K, Marucci L, et al., 2023, Numerical methods for control-based continuation of relaxation oscillations, NONLINEAR DYNAMICS, Vol: 111, Pages: 7975-7992, ISSN: 0924-090X
Tüfekci M, El Haddad F, Salles L, et al., 2023, EFFECTS OF THE SEAL WIRE ON THE NONLINEAR DYNAMICS OF THE AIRCRAFT ENGINE TURBINE BLADES
Complicated systems made of multiple components are known to be difficult to model, considering their solutions can change dramatically even with the slightest variations in conditions. Aircraft engines contain such complicated systems, and some components in aircraft engines’ turbines can cause significant changes in the system’s overall response. Hence, this study is focused on investigating the behaviour of a turbine blade of an aircraft engine and the effects of the contact between the blade and the seal wire on the dynamics of the blade-disc system. The investigation is performed via various numerical simulations in time and frequency-domains. One sector of the bladed disc is modelled using the finite element method with the lock plate and the seal wire imposing cyclic symmetry boundary conditions in the static, modal, and frequency-domain forced response analyses. In time-domain analyses, the cyclic symmetry is replaced with simplified displacement restricting boundary conditions. The time-domain analysis contains steady-state forced responses of the system. The results show that contact with the seal wire is not a major source of nonlinearity and damping. The contacts with the lock plate contribute more to the vibration damping than the seal wire. However, compared to the contacts at the root of the blade, both components remain less significant with regard to frictional damping and nonlinearity.
Lee KH, Barton D, Renson L, 2023, Mathematical Model Identification of Self-Excited Systems Using Experimental Bifurcation Analysis Data, 40th IMAC, A Conference and Exposition on Structural Dynamics, Publisher: Springer International Publishing, Pages: 61-63, ISSN: 2191-5644
Self-excited vibrations can be found in many engineering applications such as flutter of aerofoils, stick-slip vibrations in drill strings, and wheel shimmy. These self-excited vibrations are generally unwanted since they can cause serious damage to the system. To avoid such phenomena, an accurate mathematical model of the system is crucial. Self-excited systems are typically modelled as dynamical systems with Hopf bifurcations. The identification of such non-linear dynamical system from data is much more challenging compared to linear systems.In this research, we propose two different mathematical model identification methods for self-excited systems that use experimental bifurcation analysis data. The first method considers an empirical mathematical model whose coefficients are identified to fit the measured bifurcation diagram. The second approach considers a fundamental Hopf normal form model and learns a data-driven coordinate transformation mapping the normal form state-space to physical coordinates. The approaches developed are applied to bifurcation data collected on a two degree-of-freedom flutter rig and the two methods show promising results. The advantages and disadvantages of the methods are discussed.
Denimal E, Chevalier R, Renson L, et al., 2022, Shape optimisation for friction dampers with stress constraint, 40th Conference and Exposition on Structural Dynamics, Publisher: Springer International Publishing, Pages: 65-73, ISSN: 2191-5644
Friction dampers are classically used in turbomachinery for bladed discs to control the levels of vibrations at resonance and limit the risk of fatigue failure. It consists of small metal components located under the platforms of the blades, which dissipate the vibratory energy through friction when a relative displacement between the blades and the damper appears. It is well known that the shape of such component has a strong influence on the damping properties and should be designed with a particular attention. With the arrival of additive manufacturing, new dedicated shapes for these dampers can be considered, determined with specific numerical methods as topological optimisation (TO). However, the presence of the contact nonlinearity challenges the use of traditional TO methods to minimise the vibration levels at resonance. In this work, the topology of the damper is parametrised with the moving morphable components (MMC) framework and optimised based on meta-modelling techniques: here kriging coupled with the efficient global optimisation (EGO) algorithm. The level of vibration at resonance is computed based on the harmonic balance method augmented with a constraint to aim directly for the resonant solution. It corresponds to the objective function to be minimised. Additionally, a mechanical constraint based on static stress analysis is also considered to propose reliable damper designs. Results demonstrate the efficiency of the method and show that damper geometries that meet the engineers’ requirements can be identified.
de Cesare I, Salzano D, di Bernardo M, et al., 2022, Control-based continuation: a new approach to prototype synthetic gene networks., ACS Synthetic Biology, Vol: 11, Pages: 2300-2313, ISSN: 2161-5063
Control-Based Continuation (CBC) is a general and systematic method to carry out the bifurcation analysis of physical experiments. CBC does not rely on a mathematical model and thus overcomes the uncertainty introduced when identifying bifurcation curves indirectly through modeling and parameter estimation. We demonstrate, in silico, CBC applicability to biochemical processes by tracking the equilibrium curve of a toggle switch, which includes additive process noise and exhibits bistability. We compare the results obtained when CBC uses a model-free and model-based control strategy and show that both can track stable and unstable solutions, revealing bistability. We then demonstrate CBC in conditions more representative of an in vivo experiment using an agent-based simulator describing cell growth and division, cell-to-cell variability, spatial distribution, and diffusion of chemicals. We further show how the identified curves can be used for parameter estimation and discuss how CBC can significantly accelerate the prototyping of synthetic gene regulatory networks.
Abeloos G, Mueller F, Ferhatoglu E, et al., 2022, A consistency analysis of phase-locked-loop testing and control-based continuation for a geometrically nonlinear frictional system, MECHANICAL SYSTEMS AND SIGNAL PROCESSING, Vol: 170, ISSN: 0888-3270
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- Citations: 5
Song M, Renson L, Moaveni B, et al., 2022, Bayesian model updating and class selection of a wing-engine structure with nonlinear connections using nonlinear normal modes, Mechanical Systems and Signal Processing, Vol: 165, Pages: 1-15, ISSN: 0888-3270
This paper presents a Bayesian model updating and model class selection approach based on nonlinear normal modes (NNMs). The performance of the proposed approach is demonstrated on a conceptually simple wing-engine structure. Control-based continuation is exploited to measure experimentally the NNMs of the structure by tracking the phase quadrature condition between the structural response and single input excitation. A two-phase Bayesian model updating framework is implemented to estimate the joint posterior distribution of unknown model parameters: (1) at phase I, the effective Young’s modulus of a detailed linear finite element model and its estimation uncertainty are inferred from the data; (2) at phase II, a reduced-order model is obtained from the updated linear model using Craig-Bampton method, and coefficient parameters of structural nonlinearities are updated using the measured NNMs. Five different model classes representing different nonlinear functions are investigated, and their Bayesian evidence are compared to reveal the most plausible model. The obtained model is used to predict NNMs by propagating uncertainties of parameters and error function. Good agreement is observed between model-predicted and experimentally identified NNMs, which verifies the effectiveness of the proposed approach for nonlinear model updating and model class selection.
Denimal E, Renson L, Wong C, et al., 2022, Topology optimisation of friction under-platform dampers using moving morphable components and the efficient global optimization algorithm, Structural and Multidisciplinary Optimization: computer-aided optimal design of stressed solids and multidisciplinary systems, Vol: 65, Pages: 1-19, ISSN: 1615-147X
Under-platform dampers (UPDs) are traditionally used in aircraft engines to reduce the risk of high cycle fatigue. By introducing friction in the system, vibrations at resonance are damped. However, UDPs are also the source of nonlinear behaviours making the analysis and the design of such components complex. The shape of such friction dampers has a substantial impact on the damping performances, and topology optimisation is seldomly utilised—particularly for nonlinear structures. In the present work, we present a numerical approach to optimise the topology of friction dampers in order to minimise the vibration amplitude at a resonance peak. The proposed approach is based on the moving morphable components framework to parametrise the damper topology, and the efficient global optimisation algorithm is employed for the optimisation. The results demonstrate the relevance of such an approach for the optimisation of nonlinear vibrations in the presence of friction. New efficient damper geometries are identified in a few iterations of the algorithm, illustrating the efficiency of the approach. Results show that the most efficient geometry divides the vibration amplitude at resonance by 3, corresponds to a lower mass (80%) and a smaller frequency shift compared to the non-optimised case. More generally, the different geometries are analysed and tools for clustering are proposed. Different clusters are identified and compared. Thus, more general conclusions can be obtained. More specifically, the most efficient geometries correspond to geometries that reduce the mass of the damper and increase the length of the contact surface. Physically, it corresponds to a reduction of the initial normal contact pressure, which implies that the contact points enter stick/slip earlier, bringing more damping. The results show how topology optimisation can be employed for nonlinear vibrations to identify efficient layouts for components.
De Cherisey M, Salles L, Renson L, et al., 2022, OPTIMIZATION OF A TURBOMACHINERY BLADE WITH REGARDS TO TIP-RUB EVENTS
Tip-rub events, also called blade-casing interactions, are problematic structural phenomena that can lead to complete engine failure. They mainly occur in compressors when a blade tip touches the casing and starts vibrating. If one of the blade natural modes is excited by an engine order, this can lead to an uncontrolled resonance. Therefore, the understanding and the consideration of these interactions is crucial to the development of safe aircraft engines. Various numerical models and dynamic simulators have been developed, including the in-house one, jm62. It implements a stick-slip model and considers a potential liner and casing wear. Even if it gives precise results, it is computationally expensive and needs a significant amount of post-processing. It is therefore not really adapted to early design stages or quick automated processes (parametric study or optimization). An automated workflow using SALOME-MECA and its submodules had been developed and permits to perform simple and fast parametric studies and shape optimizations. The proposed tool has been used to study the influence of the twist, lean, sweep and tip thickness-to-chord ratio on a modified version of a NASA Rotor 37 blade. The risk of high-level vibration of a blade due to tip-rub events is assessed using the concept of clearance consumption. The clearance consumption is defined as the component of the linear or nonlinear mode shape that defines the distance between the tip of the blade and the casing. From the reference blade and the parametric study results, an optimized candidate was generated using the clearance consumption as the objective function to minimize This process resulted in a geometry with a lower twist angle and a significant forward sweep. Two scenario of tip rub events have been performed on the optimised blades. The testing relies on the in-house time integration software jm62. The candidate has showed a 85% reduction in the amplitude of the vibratory response for the first sce
de Cesare I, Salzano D, di Bernardo M, et al., 2021, Control-based continuation: a new approach to prototype synthetic gene networks
<jats:title>Abstract</jats:title><jats:p>Control-Based Continuation (CBC) is a general and systematic method to carry out the bifurcation analysis of physical experiments. CBC does not rely on a mathematical model and thus overcomes the uncertainty introduced when identifying bifurcation curves indirectly through modelling and parameter estimation. We demonstrate, <jats:italic>in silico</jats:italic>, CBC applicability to biochemical processes by tracking the equilibrium curve of a toggle switch which includes additive process noise and exhibits bistability. We compare results obtained when CBC uses a model-free and model-based control strategy and show that both can track stable and unstable solutions, revealing bistability. We then demonstrate CBC in conditions more representative of a real experiment using an agent-based simulator describing cells growth and division, cell-to-cell variability, spatial distribution, and diffusion of chemicals. We further show how the identified curves can be used for parameter estimation and discuss how CBC can significantly accelerate the prototyping of synthetic gene regulatory networks.</jats:p>
Abeloos G, Renson L, Collette C, et al., 2021, Stepped and swept control-based continuation using adaptive filtering, Nonlinear Dynamics, Vol: 104, Pages: 3793-3808, ISSN: 0924-090X
This paper introduces a new online method for performing control-based continuation (CBC), speeding up the model-less identification of stable and unstable periodic orbits of nonlinear mechanical systems. The main building block of the algorithm is adaptive filtering which can ensure the non-invasiveness of the controller without the need for offline corrective iterations. Two different strategies, termed stepped and swept CBC, are then developed for performing the continuation steps. A beam featuring different artificial stiffness and damping nonlinearities is considered for the experimental demonstration of the proposed developments. The performance of the CBC strategies are compared in terms of running time and identification accuracy.
Sadati H, Naghib E, Shiva A, et al., 2021, TMTDyn: A Matlab package for modeling and control of hybrid rigid–continuum robots based on discretized lumped system and reduced-order models, International Journal of Robotics Research, Vol: 40, Pages: 296-347, ISSN: 0278-3649
A reliable, accurate, and yet simple dynamic model is important to analyzing, designing, and controlling hybrid rigid–continuum robots. Such models should be fast, as simple as possible, and user-friendly to be widely accepted by the ever-growing robotics research community. In this study, we introduce two new modeling methods for continuum manipulators: a general reduced-order model (ROM) and a discretized model with absolute states and Euler–Bernoulli beam segments (EBA). In addition, a new formulation is presented for a recently introduced discretized model based on Euler–Bernoulli beam segments and relative states (EBR). We implement these models in a Matlab software package, named TMTDyn, to develop a modeling tool for hybrid rigid–continuum systems. The package features a new high-level language (HLL) text-based interface, a CAD-file import module, automatic formation of the system equation of motion (EOM) for different modeling and control tasks, implementing Matlab C-mex functionality for improved performance, and modules for static and linear modal analysis of a hybrid system. The underlying theory and software package are validated for modeling experimental results for (i) dynamics of a continuum appendage, and (ii) general deformation of a fabric sleeve worn by a rigid link pendulum. A comparison shows higher simulation accuracy (8–14% normalized error) and numerical robustness of the ROM model for a system with a small number of states, and computational efficiency of the EBA model with near real-time performances that makes it suitable for large systems. The challenges and necessary modules to further automate the design and analysis of hybrid systems with a large number of states are briefly discussed.
Müller F, Abeloos G, Ferhatoglu E, et al., 2021, Comparison between control-based continuation and phase-locked loop methods for the identification of backbone curves and nonlinear frequency responses, 38th IMAC, A Conference and Exposition on Structural Dynamics 2020, Publisher: Springer International Publishing, Pages: 75-78, ISSN: 2191-5644
Control-based continuation (CBC) and phase-locked loops (PLL) are two experimental testing methods that have demonstrated great potential for the non-parametric identification of key nonlinear dynamic features such as nonlinear frequency responses and backbone curves. Both CBC and PLL exploit stabilizing feedback control to steer the dynamics of the tested system towards the responses of interest and overcome important difficulties experienced when applying conventional testing methods such as sine sweeps to nonlinear systems. For instance, if properly designed, the feedback controller can prevent the system from exhibiting untimely transitions between coexisting responses or even losing stability due to bifurcations. This contribution aims to highlight the similarities that exist between CBC and PLL and present the first thorough comparison of their capabilities. Comparisons are supported by numerical simulations as well as experimental data collected on a conceptually simple nonlinear structure primarily composed of a thin curved beam. The beam is doubly clamped and exhibits nonlinear geometric effects for moderate excitation amplitudes.
Abeloos G, Renson L, Collette C, et al., 2021, Control-based continuation of nonlinear structures using adaptive filtering, 38th IMAC, A Conference and Exposition on Structural Dynamics, Publisher: Springer International Publishing, Pages: 109-112, ISSN: 2191-5644
Control-Based Continuation uses feedback control to follow stable and unstable branches of periodic orbits of a nonlinear system without the need for advanced post-processing of experimental data. CBC relies on an iterative scheme to modify the harmonic content of the control reference and obtain a non-invasive control signal. This scheme currently requires to wait for the experiment to settle down to steady-state and hence runs offline (i.e. at a much lower frequency than the feedback controller). This paper proposes to replace this conventional iterative scheme by adaptive filters. Adaptive filters can directly synthesize either the excitation or the control reference adequately and can operate online (i.e. at the same frequency as the feedback controller). This novel approach is found to significantly accelerate convergence to non-invasive steady-state responses to the extend that the structure response can be characterized in a nearly-continuous amplitude sweep. Furthermore, the stability of the controller does not appear to be affected.
Renson L, 2020, Identification of backbone curves and nonlinear frequency responses using control-based continuation and local gaussian process regression, 38th IMAC, A Conference and Exposition on Structural Dynamics 2020, Publisher: Springer International Publishing, Pages: 83-85, ISSN: 2191-5644
Control-based continuation (CBC) is a general and systematic method to probe the dynamics of nonlinear experiments. In this paper, CBC is combined with a novel continuation algorithm that is robust to experimental noise and enables the tracking of important nonlinear dynamic features such as backbone and nonlinear frequency response curves. The method uses Gaussian process regression to create a local model of the response surface on which standard numerical continuation algorithms can be applied. The local model evolves as continuation explores the experimental parameter space, exploiting previously captured data to actively select the next data points to collect such that they maximise the potential information gain about the feature of interest. The method is demonstrated experimentally on a nonlinear structure featuring harmonically-coupled modes. The regression model is also exploited to estimate the uncertainty of the identified features.
Lee KH, Barton DAW, Renson L, 2020, Model identification of a fluttering aerofoil using control-based continuation and normal form analysis, International Conference on Noise and Vibration Engineering (ISMA) / International Conference on Uncertainty in Structural Dynamics (USD), Publisher: KATHOLIEKE UNIV LEUVEN, DEPT WERKTUIGKUNDE, Pages: 261-268
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- Citations: 1
Renson L, Sieber J, Barton DAW, et al., 2019, Numerical continuation in nonlinear experiments using local Gaussian process regression, NONLINEAR DYNAMICS, Vol: 98, Pages: 2811-2826, ISSN: 0924-090X
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- Citations: 19
Renson L, Shaw AD, Barton DAW, et al., 2019, Application of control-based continuation to a nonlinear structure with harmonically coupled modes, MECHANICAL SYSTEMS AND SIGNAL PROCESSING, Vol: 120, Pages: 449-464, ISSN: 0888-3270
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- Citations: 31
Song M, Renson L, Noel J-P, et al., 2019, Model Updating of a Wing-Engine Structure with Nonlinear Connections, 36th International Modal Analysis Conference and Exposition (IMAC) on Structural Dynamics, Publisher: SPRINGER INTERNATIONAL PUBLISHING AG, Pages: 373-374, ISSN: 2191-5644
Renson L, Barton DAW, Neild SA, 2019, Application of Control-Based Continuation to a Nonlinear System with Harmonically Coupled Modes, 36th International Modal Analysis Conference and Exposition (IMAC) on Structural Dynamics, Publisher: SPRINGER INTERNATIONAL PUBLISHING AG, Pages: 315-316, ISSN: 2191-5644
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- Citations: 1
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