Data-driven Extension Research Articles

Estimating cost function of expert players in differential games: A model-based method and its data-driven extension

In this paper, we introduce two algorithms for estimating the cost function of expert players engaged in optimal performance within linear continuous-time differential games. Initially, we propose a model-based algorithm, followed by its data-driven model-free extension. Both methods rely on optimal policy gains, obtained by observing Nash equilibrium trajectories of the expert players. The model-free method also utilizes the trajectories of the learner system. This method addresses the limitations found in existing model-free approaches, which may suffer from either high computational costs, limited applicability to specific systems, or both. The effectiveness of the proposed methods is demonstrated through numerical simulations.

Data-Driven Extension of “Measurement-Based Fast Coordinated Voltage Control for Transmission Grids”

In Tang et al. (2021) a measurement-based coordinated voltage controller for transmission systems was developed. As essential model information, the controller incorporates linear sensitivities between device set-points and voltages/power injections in the grid. This letter details how online sensitivity estimation using robust least squares can be used in place of model-based sensitivities, leading to a model-free voltage control approach.

OnsagerNet: Learning stable and interpretable dynamics using a generalized Onsager principle

Machine learning is becoming an increasingly popular method for building mathematical models from observations of natural processes. Here, the central challenge is to impart structure into the model parameterization to enforce physical relevance, yet retain a degree of generality so that a large variety of dynamics can be learned. We introduce a novel methodology, based on a data-driven extension of the classical Onsager principle, that strikes a balance between these competing aspects. We demonstrate its efficacy by learning quantitatively accurate and qualitatively faithful reduced order models of the Rayleigh-B\'enard convection equations.

Stochastic distribution tracking control for stochastic non-linear systems via probability density function vectorisation

This paper presents a new control strategy for stochastic distribution shape tracking regarding non-Gaussian stochastic non-linear systems. The objective can be summarised as adjusting the probability density function (PDF) of the system output to any given desired distribution. In order to achieve this objective, the system output PDF has first been formulated analytically, which is time-variant. Then, the PDF vectorisation has been implemented to simplify the model description. Using the vector-based representation, the system identification and control design have been performed to achieve the PDF tracking. In practice, the PDF evolution is difficult to implement in real-time, thus a data-driven extension has also been discussed in this paper, where the vector-based model can be obtained using kernel density estimation (KDE) with the real-time data. Furthermore, the stability of the presented control design has been analysed, which is validated by a numerical example. As an extension, the multi-output stochastic systems have also been discussed for joint PDF tracking using the proposed algorithm, and the perspectives of advanced controller have been discussed. The main contribution of this paper is to propose: (1) a new sampling-based PDF transformation to reduce the modelling complexity, (2) a data-driven approach for online implementation without model pre-training, and (3) a feasible framework to integrate the existing control methods.

Data-Driven quasi-LPV Model Predictive Control Using Koopman Operator Techniques

A fast data-driven extension of the velocity-based quasi-linear parameter-varying model predictive control (qLMPC) approach is proposed for scenarios where first principles models are not available or are computationally too expensive. We use tools from the recently proposed Koopman operator framework to identify a quasi-linear parameter-varying model (in input/output and state-space form) by choosing the observables from physical insight. An online update strategy to adapt to changes in the plant dynamics is also proposed. The approach is validated experimentally on a strongly nonlinear 3-degree-of-freedom Control Moment Gyroscope, showing remarkable tracking performance.

Inference of the bottom topography in anisothermal mildly-sheared shallow ice flows

This study proposes a new inverse method to estimate the bed topography elevation beneath glaciers flows from surface observations (altimetry elevations and InSAR velocities) and (very) sparse depth measurements (e.g. acquired during airborne campaigns). To do so an original form of depth-integrated flow equations (long-wave assumption) is derived. The latter are valid for highly to mildly-sheared regimes hence including moderately fast flows; varying internal thermal profiles are taken into account. The inverse problem is particularly challenging since the surface signatures integrate the bottom features (bed elevation and friction–slip amount) plus the internal deformation. The first key ingredient of the inverse method is the derivation of this non-isothermal Reduced Uncertainty (RU) version of the classical SIA equation (lubrication type model for generalised Newtonian fluids) by intrinsically integrating the surface measurements in the formulation. This resulting multi-physics RU-SIA equation contains a unique uncertain dimensionless parameter only (the parameter γ). The next key ingredient is an advanced Variational Data Assimilation (VDA) formulation combined with a purely data-driven extension of γ based on the trend observed in the (sparse) depth measurements (e.g. along the flight tracks). The resulting inverse method provides the first physical-based depth estimations in mildly-sheared mildly-slippery shallow flows. In poorly monitored ice-sheet areas (e.g. in Antarctica), the resulting estimations are noticeably less uncertain than the current ones (in particular compared to those obtained by gravimetry inversions). The present numerical experiments and experimental sensitivity analyses demonstrate the reliability of this new RU-SIA equation and the robustness of the inverse method. In other respect, the RU-SIA equation may provide a-posteriori estimations of the thermal boundary layer at bottom.

Simultaneous design of non-Newtonian lubricant and surface texture using surrogate-based multiobjective optimization

Surface textures decrease friction in lubricated sliding with Newtonian fluids. Viscoelastic non-Newtonian lubricants can enhance frictional performance, but the optimal rheological material properties and their coupling to the texture design are non-obvious. In this study, we present a simultaneous design of both surface texture shape and non-Newtonian properties, which can be achieved by fluid additives that introduce viscoelasticity, shear thinning, and normal stress differences. Two models with different fidelity and computational cost are used to model laminar non-Newtonian fluid flow between a rotating flat plate and a textured disk. At lower fidelity, we use the Criminale-Ericksen-Filbey (CEF) constitutive model and a thin-film approximation for conservation of momentum (Reynolds equation). At higher fidelity, we use a fully nonlinear constitutive model typically applicable to polymer solutions (multimode Giesekus model) and the full 3-D momentum equations. Fluid additive design is parameterized by two relaxation modes each having a timescale, added viscosity, and a nonlinear anisotropic drag parameter. To manage the computational complexity and constraints between design variables, we use our previously developed multiobjective adaptive surrogate modeling-based optimization (MO-ASMO) method. A new data-driven extension of MO-ASMO is introduced that constructs general boundaries to prevent attempts to evaluate designs that would lead to simulation failure. We demonstrate the efficiency of our MO-ASMO method and provide insights into co-designing the lubricant and textured surface. The Pareto-optimal solutions include fluid designs with both high and low viscoelastic additive loading. We rationalize this trade-off and discuss how the optimal design targets can be physically realized.

Ultrasound spatiotemporal despeckling via Kronecker wavelet-Fisz thresholding

We propose a novel framework for despeckling ultrasound image sequences while respecting the structural details. More precisely, we use thresholding in an adapted wavelet domain that jointly takes into account for the non-Gaussian statistics of the noise and the differences in spatial and temporal regularities. The spatiotemporal wavelet is obtained via the Kronecker product of two sparsifying wavelet bases acting, respectively, on the spatial and temporal domains. Besides enabling a structured sparse representation of the time–space plan, it also makes it possible to perform a variance stabilization routine on the spatial domain through a Fisz transformation. The proposed method enjoys adaptability, easy tuning and theoretical guaranties. We propose the corresponding algorithm together with results that demonstrate the benefits of the proposed spatiotemporal approach over the successive spatial treatment. Finally, we describe a data-driven extension of the proposed method that is based on temporal pre-filtering.

Towards virtual deformation dilatometry for the design of hot stamping process

Abstract Hot stamping is a well-established process for the production of structural automotive parts with an excellent strength-to-weight ratio. The complexity of the thermo-mechanical history in hot stamping requires a precise virtual design of hot stamping processes. The thermal and mechanical characteristics of the most common press hardening steel 22MnB5 were investigated comprehensively and are well represented by numerical models. For new steel compositions and parts involving tailored tempering, numerous experiments, e.g., on a deformation dilatometer or thermo-mechanical simulator are needed to characterise the microstructure evolution and the resulting properties. If appropriate material models were available, new steel compositions and thermo-mechanical histories could be partly explored virtually by simulated deformation dilatometer tests. This paper presents a comparison of experimental and virtual deformation dilatometer tests for the hot stamping steel 22MnB5. The virtual dilatometer is implemented as finite element model in the software LS-Dyna based on the material model *MAT248. With this model, virtual and real dilatometer curves correspond well only for conditions of full martensitic hardening, while pre-strains cause larger differences between model and experiments. When the most sensitive model parameters are formulated as a function of pre-strain, all experimental dilatometer curves can be reproduced by the model. Such a data-driven extension of the model seems to be effective for creating a virtual dilatometer model of high accuracy.

Kernel-based dimensionality reduction using Renyi's α-entropy measures of similarity

Dimensionality reduction (DR) aims to reveal salient properties of high-dimensional (HD) data in a low-dimensional (LD) representation space. Two elements stipulate success of a DR approach: definition of a notion of pairwise relations in the HD and LD spaces, and measuring the mismatch between these relationships in the HD and LD representations of data. This paper introduces a new DR method, termed Kernel-based entropy dimensionality reduction (KEDR), to measure the embedding quality that is based on stochastic neighborhood preservation, involving a Gram matrix estimation of Renyi's α-entropy. The proposed approach is a data-driven framework for information theoretic learning, based on infinitely divisible matrices. Instead of relying upon regular Renyi's entropies, KEDR also computes the embedding mismatch through a parameterized mixture of divergences, resulting in an improved the preservation of both the local and global data structures. Our approach is validated on both synthetic and real-world datasets and compared to several state-of-the-art algorithms, including the Stochastic Neighbor Embedding-like techniques for which DR approach is a data-driven extension (from the perspective of kernel-based Gram matrices). In terms of visual inspection and quantitative evaluation of neighborhood preservation, the obtained results show that KEDR is competitive and promising DR method.

Hyperbolic Wavelet-Fisz Denoising for a Model Arising in Ultrasound Imaging

We present an algorithm and its fully data-driven extension for noise reduction in ultrasound imaging. The proposed method computes the hyperbolic wavelet transform of the image, before applying a multiscale variance stabilization technique, via a Fisz transformation. This adapts the wavelet coefficients statistics to the wavelet thresholding paradigm. The use of hyperbolic wavelets makes it possible to recover the image while respecting the anisotropic nature of structural details. The data-driven extension obviates the need for any prior knowledge of the noise model parameters by estimating the noise variance using an isotonic Nadaraya–Watson estimator. Experiments on synthetic and real data demonstrate the potential of the proposed algorithm to recover ultrasound images while preserving tissue details. Furthermore, comparisons with other noise-reduction methods show that our technique is competitive with the state-of-the-art OBNLM filter. Finally, the variance estimation procedure is applied to real images emphasizing the noise model.