Research ArticleARTIFICIAL INTELLIGENCE

A robotic Intelligent Towing Tank for learning complex fluid-structure dynamics

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Science Robotics  27 Nov 2019:
Vol. 4, Issue 36, eaay5063
DOI: 10.1126/scirobotics.aay5063
  • Fig. 1 Schematic image of the ITT with the key steps for sequential learning of complex fluid-structure dynamics.

    The image of the ITT (A) shows the experimental model consisting of a cylinder and sensors mounted on the main carriage, which can be driven to perform combined in-line, cross-flow, and rotational motions. The graphic user interface (GUI) of the ITT controller, recording motion, and force signals is shown at bottom right. The process of the ITT commences once a hypothesis is proposed (such a hypothesis is human-generated or, in the future, may be synthesized in coordination by robots, computers, and humans). Then, the ITT performs the adaptive sequential experiment to learn target QoIs, interrupted only by pause periods between experiments to avoid cross-contamination of the results between successive experiments. Upon convergence, the results of learned QoIs are further post-processed to examine the validity of the hypothesis. During sequential experimental testing, there is no human in the loop. (B) Overview of the ITT with main components of a 10-m tank, a carriage of three-axis robotic linear stage, a computer, and motor controllers.

  • Fig. 2 A demonstration of GPR learning sequence for Clv of a rigid cylinder forced vibration in uniform flow at Re = 12,000.

    (A.1 to A.5) Contours of the mean of the predicted Clv versus reduced frequency fr (x axis) and nondimensional vibration amplitude Ay/d (y axis) along with the SD plot (inset). Black dots in each contour denote the existing data used for GPR learning at the current iteration. Black squares denote the new experiment performed for the current iteration, and the red stars represent the next experiment guided by the σmax in the SD. (B) Plot of the maximum SD σmax versus experiment number. The horizontal dashed line corresponds to 3σr, where σr is the SD for a reference case as described in the text (see also table S1 and fig. S1).

  • Fig. 3 Investigation of the GPR learning convergence for different types of kernels.

    The plots show σmax of each iteration with different kernel functions and a fixed basis function for (A) Cd, (B) Clv, and (C) Cmy. The horizontal dashed line corresponds to 3σr, where σr is the SD for a reference level as described in the text (see also table S1 and fig. S1).

  • Fig. 4 GPR versus uniform sampling.

    Comparison of adaptive (A.1, B.1, and C.1) GPR learning (multi-output) versus uniform (lattice) sampling (A.2, B.2, and C.2). Contours of Cd (A.1, 75 experiments; A.2, 2268 experiments). Contours of Clv (B.1, 77 experiments; B.2, 2268 experiments). Contours of Cmy (C.1, 90 experiments; C.2, 2268 experiments). (A.3 to C.3) Plots of the comparison of the average value of 30 randomly selected points (blue dots in A.2) between uniform sampling (red dashed line) and GPR learning (black dashed line) as a function of the experiment number. The blue shaded region denotes the 2-SD margin (averaged over the 30 selected points) as a function of the experiment number.

  • Fig. 5 Re effect in three-dimensional parametric space.

    Converged hydrodynamic coefficients in the three-dimensional parametric space (fr, Ay/d, and Re) using GPR learning (multi-output) strategy. Isosurfaces of the hydrodynamic coefficients: (A) Cd of 207 experiments (blue surface, Cd = 1.3; black surface, Cd = 2; red surface, Cd = 3; green surface, Cd = 4). (B) Clv of 1036 experiments (green surface, Clv = −3; blue surface: Clv = −1; black surface, Clv = 0; red surface, Clv = 0.3). (C) Cmy of 1288 experiments (black surface, Cmy = 0; red surface, Cmy = 2).

  • Fig. 6 Exploration of large parametric space (in this example: eight parameters).

    Comparison of Clv for a rigid cylinder undergoing combined in-line and cross-flow forced vibrations in uniform flow at Re = 5715 obtained in single-frequency (involving four parameters, total of 755 experiments) and two-frequency (involving eight parameters, total of 3944 experiments) experiments. (A) Contours of Clv versus Vr and θ/π for experiments of single frequency at fixed Ax/d = 0.15 and Ay/d = 0.75. (B.1) Contours of Clv versus Vr and θ/π for experiments of double frequency at Ax/d = 0.15 and Ay/d = 0.75, same as in (A), and fixed second frequency component of Ay2/d = 0.34, Ax2/d = 0.14, Vr2 = 11.75, and θ2/π = 1.5. (B.2 to B.5) Contours of Clv versus fr and θ/π with only one fixed input changed; compare with (B.1): (B.2), Ay2/d = 0.93; (B.2), Ax2/d = 0.25; (B.3), Vr2 = 5.25; (B.4), θ2/π = 0.5. (C) Results of the sensitivity analysis on χ. The sensitivity measures (∣μχ∣,∣σχ∣) for each parameter have been normalized by the value of the highest sensitivity measure (∣μχmax,∣σχmax) of the most sensitive parameter Vr2.

  • Table 1 Selected basis and kernel functions for different QoIs.

    CdClvCmy
    BasisPure quadraticLinearPure quadratic
    KernelARD Matern 3/2ARD Matern 5/2ARD Matern 5/2

Supplementary Materials

  • robotics.sciencemag.org/cgi/content/full/4/36/eaay5063/DC1

    Table S1. Statistics of hydrodynamic coefficients of a stationary rigid cylinder in uniform flow at Re = 12,000.

    Fig. S1. Histogram of Cd of a stationary rigid cylinder in uniform flow at Re = 12,000.

    Fig. S2. Evolution of GPR learning sequence for Clv of a rigid cylinder forced vibration in uniform flow at Re = 12,000.

    Fig. S3. Clv of a rigid cylinder forced vibration from GPR learning at various Re number values.

    Fig. S4. Cd of a rigid cylinder forced vibration from GPR learning at various Re number values.

    Fig. S5. Cmy of a rigid cylinder forced vibration from GPR learning at various Re number values.

    Data file S1. Sequential experimental data for hydrodynamic coefficients of a cross-flow only vibrating rigid cylinder at Re = 12,000.

    Data file S2. Sequential experimental data for hydrodynamic coefficients of a cross-flow only vibrating rigid cylinder at various Re from 1200 to 19,000.

    Data file S3. Sequential experimental data for hydrodynamic coefficients of a cross-flow and in-line combined single-frequency vibrating rigid cylinder at Re = 5715.

    Data file S4. Sequential experimental data for hydrodynamic coefficients of a cross-flow and in-line combined double-frequency vibrating rigid cylinder at Re = 5715.

    Movie S1. Experimental process of ITT sequential learning on Clv of a cross-flow only vibrating rigid cylinder at Re = 12,000.

    Movie S2. ITT sequential experiment of Re effect on a cross-flow only vibrating rigid cylinder.

  • Supplementary Materials

    The PDF file includes:

    • Table S1. Statistics of hydrodynamic coefficients of a stationary rigid cylinder in uniform flow at Re = 12,000.
    • Fig. S1. Histogram of Cd of a stationary rigid cylinder in uniform flow at Re = 12,000.
    • Fig. S2. Evolution of GPR learning sequence for Clv of a rigid cylinder forced vibration in uniform flow at Re = 12,000.
    • Fig. S3. Clv of a rigid cylinder forced vibration from GPR learning at various Re number values.
    • Fig. S4. Cd of a rigid cylinder forced vibration from GPR learning at various Re number values.
    • Fig. S5. Cmy of a rigid cylinder forced vibration from GPR learning at various Re number values.
    • Legends for data files S1 to S4
    • Legends for movies S1 and S2

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    Other Supplementary Material for this manuscript includes the following:

    • Data file S1 (.mat format). Sequential experimental data for hydrodynamic coefficients of a cross-flow only vibrating rigid cylinder at Re = 12,000.
    • Data file S2 (.mat format). Sequential experimental data for hydrodynamic coefficients of a cross-flow only vibrating rigid cylinder at various Re from 1200 to 19,000.
    • Data file S3 (.mat format). Sequential experimental data for hydrodynamic coefficients of a cross-flow and in-line combined single-frequency vibrating rigid cylinder at Re = 5715.
    • Data file S4 (.mat format). Sequential experimental data for hydrodynamic coefficients of a cross-flow and in-line combined double-frequency vibrating rigid cylinder at Re = 5715.
    • Movie S1 (.mp4 format). Experimental process of ITT sequential learning on Clv of a cross-flow only vibrating rigid cylinder at Re = 12,000.
    • Movie S2 (.mp4 format). ITT sequential experiment of Re effect on a cross-flow only vibrating rigid cylinder.

    Files in this Data Supplement:

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