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    Near-optimal decentralized diagnosis via structural analysis
    (Institute of Electrical and Electronics Engineers Inc., 2022-12-01)
    Health monitoring of current complex systems significantly impacts the total cost of the system. Centralized fault diagnosis architectures are sometimes prohibitive for large-scale interconnected systems, such as distribution systems, telecommunication networks, water distribution networks, or fluid power systems. Confidentiality constraints are also an issue. This article presents a decentralized fault diagnosis method that only requires the knowledge of local models and limited knowledge of their neighboring subsystems. The method, implemented in the decentralized diagnoser design ($D^{3}$) algorithm, is based on structural analysis and can advantageously be applied to high-dimensional systems, linear or nonlinear. Using the concept of isolation on request, a hierarchy is built according to diagnostic objectives. The resulting diagnoser is based on analytical redundancy relations (ARRs) generated along the hierarchy. Their number is optimized via binary integer linear programming (BILP) while still guaranteeing maximal diagnosability at each level.$D^{3}$proves of lower time complexity than its centralized equivalent. It is successfully applied to a nonlinear combined cycle gas-turbine power plant.
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    Wave packet dynamics in rotating fluids within the Benjamin–Ono–Ostrovsky equation
    (Elsevier BV, 2026-03-01)
    We investigate the evolution of algebraic solitons of the Benjamin–Ono (BO) equation and wave packets within the framework of the Benjamin–Ono–Ostrovsky (BOO) equation by combining asymptotic analysis with direct numerical simulations. The BOO model incorporates a low-frequency dispersive term that accounts for the effects of background rotation in a fluid. Through asymptotic expansion, we derive a cubic nonlinear Schrödinger (NLS) equation that governs the evolution of modulated wave trains and compare its predictions with numerical simulations of the full BOO equation. Theoretical and numerical results show good agreement for small-amplitude wave packets. Furthermore, near the boundary separating the modulationally stable and unstable regimes, the wave packets display pronounced broadening accompanied by enhanced amplitude attenuation. Finally, the evolution of BO algebraic solitons within the BOO framework is analyzed, revealing their gradual transformation into modulated wave packets.
      2
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    Stability of periodic traveling waves for the hydroelastic Whitham equation
    (Elsevier BV, 2026-01-01)
    In this work, we investigate the stability of hydroelastic periodic traveling waves within a Whitham-type equation framework. The Whitham equation is well known in the literature as a relatively simple model that nevertheless captures rich nonlinear phenomena such as short waves and breaking. Periodic traveling waves are computed numerically, and their stability is analyzed by evaluating the spectrum via the Fourier–Floquet–Hill method. We show that for small values of the flexural rigidity coefficient, small-amplitude periodic traveling waves are unstable; however, as the amplitude increases beyond a critical threshold, we first observe stabilization (not complete); subsequently, the spectrum bifurcates, and the traveling waves become increasingly unstable. In contrast, when the flexural rigidity coefficient is large, periodic traveling waves remain stable for all amplitudes. For moderate elasticity, two scenarios may occur: either (i) the maximal instability growth rate exhibits a monotonic dependence on the wave height, or (ii) complete stabilization is achieved for sufficiently large heights within numerical tolerance.
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    Asymptotic and numerical study to the damped Schamel equation
    (National Research Ogarev Mordovia State University, 2025-01-01)
    Analytical and numerical solutions of the damped Schamel equation, describing the dynamics of ion-acoustic waves in magnetized plasma, are presented. A small parameter is introduced in the equation before the dissipative term, ensuring that in its absence the solution reduces to a solitary wave (soliton). The asymptotic method employed for solving the equation is a variant of the Krylov-Bogolyubov-Mitropolsky multiple-scale technique. In the first-order approximation, the solution is described by a traveling solitary wave with slowly varying parameters. The second-order approximation yields the evolution laws for the soliton's amplitude and phase as functions of «slow» time. Additionally, exact integral conservation laws (mass and energy of the wave field), derived directly from the original damped Schamel equation, are utilized. These integrals allow estimating the soliton's radiative losses, particularly the mass of the so-called tail formed behind the soliton due to dissipation. Direct numerical solutions of the original equation, obtained via a pseudospectral method, confirm the asymptotic laws governing the soliton's amplitude decay caused by dissipation. Another limiting case - strong dissipation (dominant over nonlinearity and dispersion), is also investigated, demonstrating that the soliton decays as a linear impulse, which is validated numerically.
      1
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    Regularized Joint Estimator of the Nonlinearity Parameter and Attenuation Coefficient Using a Nonlinear Least-Squares Algorithm
    (SAGE Publications, 2025)
    The acoustic nonlinearity parameter (B/A) could enhance the diagnostic capabilities of conventional ultrasonography and quantitative ultrasound in tissues and diseases. Nonlinear acoustic propagation theory of plane waves has been used to develop a dual-energy model of the depletion of the fundamental related to the Gol’dberg number and subsequently to the B/A of media (a reference phantom is used as a baseline). The depletion method, however, needs a priori information of the attenuation coefficient (AC) of the assessed media. For this reason, recently, a work introduced a simultaneous estimator of the B/A and AC based on fitting depletion method measurements to a nonlinear model using the iterative algorithm Gauss-Newton Levenberg-Marquardt (GNLM). However, the GNLM method presented high sensitivity to the initial guess values of the algorithm which limits the robustness of the approach. In the present work, the Gauss-Newton method is combined with a total variation regularization approach (GNTV), which is achievable by expanding the nonlinear model of the GNLM method for joint estimation of the B/A and AC of all pixels of the parametric images instead of a block-wise approach. In addition, the GNTV used compounding data from several tone-burst transmissions at different center frequencies rather than only one narrowband tone-burst. The results suggest that incorporating regularization and increasing the number of frequencies improves the robustness of the GNTV compared to the GNLM method by accurately estimating B/A values in uniform and nonuniform experimental phantoms (mean relative error less than 18%). The best performance of B/A reconstruction was observed when the sample medium exhibited a constant Gol’dberg number.
      1
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    Nonlinearity parameter estimation method from fundamental band signal depletion in pulse-echo using a dual-energy model
    (Acoustical Society of America, 2025)
    The estimation of the nonlinearity parameter (B/A) has the potential to be used in the clinical diagnosis of conditions such as liver steatosis. Recently, a pulse-echo method to estimate B/A based on the theory of the fundamental band amplitude depletion of weak waves, namely, the depletion method, was proposed. In the present work, the depletion method is presented with more technical detail. Then, the robustness of the depletion method is assessed by using simulations that diverge from the model requirements: (1) monochromatic plane wave propagation and (2) quadratic power-law frequency dependence attenuation. Regarding requirement (1), the results led to a critical finding that when using wideband pulses (37%–113% bandwidth), the bias of the B/A estimates is larger than the bias obtained using narrowband pulses (11%–28% bandwidth), even if requirement (2) holds. Regarding requirement (2), power-law frequency dependence closer to those of soft tissues, i.e., 1.1 or 1.2, using narrowband pulses presented bias of less than 10%. The use of narrowband pulses also was shown to be robust when the reference phantom and sample had attenuation mismatches of around 60%. Finally, the experimental feasibility of the depletion method was evaluated, showing results with good accuracy (bias <17%), which are consistent with the observations in the simulations.
      1
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    Nonlinear trajectory tracking with a 6DOF AUV using an MRAFC controller
    (IEEE Computer Society, 2025)
    New technologies such as AUVs are used for marine exploration, considered a widespread solution in ocean monitoring, whose conventional controllers such as PID or LQR present inaccuracy in the path traversal and instability when faced with disturbances. Such that, in order to achieve sufficient precision in the path traversal and to be able to measure seabed parameters, the design of a Reference Model Adaptive Fuzzy Controller (MRAFC) is proposed. Which is a control strategy based on a combination of fuzzy systems theories using the Takagy- Sugeno model and adaptive control laws, respecting Lyapunovs nonlinear control theories to generate a robust control against inherent disturbances of the environment. Thus, the results obtained when comparing the MRAFC controller versus LQR and MRAC test controllers show better performance in different scenarios. Where the first scenario is ideal conditions, whose result is similar when the AUV is close to the origin and unstable in the LQR controller when it moves away from the design convergence point. A second scenario is considered the disturbances, obtaining unstable behaviors from the moment of the disturbance in the LQR and MRAC controllers, observing overstresses in the control variable causing chattering effect. While the last scenario is dedicated to recreate an environment with noise affecting the reading of the vehicle variables where only the MRAFC control law is able to compensate and control in a hostile environment. Therefore, based on the results of this research it is possible to identify the MRAFC controller as suitable for AUV where precision and stability are necessary.
      2
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    Multi-Frequency Regularized Approach for Simultaneous Estimation of the Acoustic Nonlinearity Parameter and Attenuation Coefficient
    (IEEE Computer Society, 2025)
    The acoustic nonlinearity parameter (B/A) could enhance conventional ultrasound diagnostics in diseases associated with changes in fat tissue content. Recently, a simultaneous estimator of the B/A and the attenuation coefficient (AC) in pulse-echo was introduced, which was based on fitting measurements derived from backscattered data from a dual-energy model to a nonlinear model using the Gauss-Newton Levenberg-Marquardt algorithm (GNLM). However, the GNLM algorithm presented high sensitivity to the initial guess values. This paper improves the Gauss-Newton method by using data from several tone-burst transmissions at different center frequencies rather than only one narrowband tone-burst. In addition, it is combined with a total variation regularization approach (GNTV). The results in simulated and experimental phantoms suggest that incorporating regularization and increasing the number of transmission frequencies improves robustness compared to the GNLM method by accurately estimating B/A values (mean relative error less than 13% in the experiments).
      1