Category Archives: Systems And Signals

Using multiple data with diverse fidelities to provide surrogate simulations through GPs

November 14, 2024 16:42 ,

Ben Yang, Boyi Chen, Yanbin Liu, Jinbao Chen, Gaussian process fusion method for multi-fidelity data with heterogeneity distribution in aerospace vehicle flight dynamics, Engineering Applications of Artificial Intelligence, Volume 138, Part A, 2024, DOI: 10.1016/j.engappai.2024.109228.

In the engineering design of aerospace vehicles, design data at different stages exhibit hierarchical and heterogeneous distribution characteristics. Specifically, high-fidelity design data (such as from computational fluid dynamics simulations and flight tests) are costly and time-consuming to obtain. Moreover, the limited high-precision samples that are acquired often fail to cover the entire design space, resulting in a distribution characterized by small sample sizes. A critical challenge in data-driven modeling is efficiently fusing low-fidelity data with limited heterogeneous high-fidelity data to improve model accuracy and predictive performance. In response to this challenge, this paper introduces a Gaussian process fusion method for multi-fidelity data, founded on distribution characteristics. Multi-fidelity data are represented as intermediate surrogates using Gaussian processes, identifying heteroscedastic noise properties and deriving posterior distributions. The fusion is then treated as an optimization problem for prediction variance, using K-nearest neighbors and spatial clustering to determine optimal weights, which are adaptively adjusted based on sample density. These weights are adaptively adjusted based on the sample density to strengthen the local modeling behavior. The paper concludes with a comparative analysis, evaluating the proposed method against other conventional approaches using numerical cases and an aerodynamic prediction scenario for aerospace vehicles. A comparative analysis shows that the proposed method improves global modeling accuracy by 45% and reduces the demand for high-fidelity samples by over 40% compared to traditional methods. Applied in aerospace design, the method effectively merges multi-source data, establishing a robust hypersonic aerodynamic database while controlling modeling costs and demonstrating robustness to sample distribution.

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Detection of qualitative behaviours in signals

January 18, 2019 11:44 ,

Ying Tang, Alessio Franci, Romain Postoyan, On-line detection of qualitative dynamical changes in nonlinear systems: The resting-oscillation case, Automatica, Volume 100, 2019, Pages 17-28, DOI: 10.1016/j.automatica.2018.10.058.

Motivated by neuroscience applications, we introduce the concept of qualitative detection, that is, the problem of determining on-line the current qualitative dynamical behavior (e.g., resting, oscillating, bursting, spiking etc.) of a nonlinear system. The approach is thought for systems characterized by i) large parameter variability and redundancy, ii) a small number of possible robust, qualitatively different dynamical behaviors and, iii) the presence of sharply different characteristic timescales. These properties are omnipresent in neurosciences and hamper quantitative modeling and fitting of experimental data. As a result, novel control theoretical strategies are needed to face neuroscience challenges like on-line epileptic seizure detection. The proposed approach aims at detecting the current dynamical behavior of the system and whether a qualitative change is likely to occur without quantitatively fitting any model nor asymptotically estimating any parameter. We talk of qualitative detection. We rely on the qualitative properties of the system dynamics, extracted via singularity and singular perturbation theories, to design low dimensional qualitative detectors. We introduce this concept on a general class of singularly perturbed systems and then solve the problem for an analytically tractable class of two-dimensional systems with a single unknown sigmoidal nonlinearity and two sharply separated timescales. Numerical results are provided to show the performance of the designed qualitative detector.

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SLAM as a sampling problem, with some references to the signal sampling state-of-the-art

October 11, 2018 08:51 ,

Golnoosh Elhami, et. al Sampling at Unknown Locations: Uniqueness and Reconstruction Under Constraints, IEEE Transactions on Signal Processing, Vol 66 no. 22, DOI: 10.1109/TSP.2018.2872019.

Traditional sampling results assume that the sample locations are known. Motivated by simultaneous localization and mapping (SLAM) and structure from motion (SfM), we investigate sampling at unknown locations. Without further constraints, the problem is often hopeless. For example, we recently showed that, for polynomial and bandlimited signals, it is possible to find two signals, arbitrarily far from each other, that fit the measurements. However, we also showed that this can be overcome by adding constraints to the sample positions. In this paper, we show that these constraints lead to a uniform sampling of a composite of functions. Furthermore, the formulation retains the key aspects of the SLAM and SfM problems, whilst providing uniqueness, in many cases. We demonstrate this by studying two simple examples of constrained sampling at unknown locations. In the first, we consider sampling a periodic bandlimited signal composite with an unknown linear function. We derive the sampling requirements for uniqueness and present an algorithm that recovers both the bandlimited signal and the linear warping. Furthermore, we prove that, when the requirements for uniqueness are not met, the cases of multiple solutions have measure zero. For our second example, we consider polynomials sampled such that the sampling positions are constrained by a rational function. We previously proved that, if a specific sampling requirement is met, uniqueness is achieved. In addition, we present an alternate minimization scheme for solving the resulting non-convex optimization problem. Finally, fully reproducible simulation results are provided to support our theoretical analysis.

Posted in: Mobile robot SLAM, Systems and Signals