Optimal Perturbation Research Articles

On the laminar solutions and stability of accelerating and decelerating channel flows

We study the effect of acceleration and deceleration on the stability of channel flows. To do so, we derive an exact solution for laminar profiles of channel flows with an arbitrary, time-varying wall motion and pressure gradient. This solution then allows us to investigate the stability of any unsteady channel flow. In particular, we restrict our investigation to the non-normal growth of perturbations about time-varying base flows with exponentially decaying acceleration and deceleration, with comparisons to growth about a constant base flow (i.e. the time-invariant simple shear or parabolic profile). We apply this acceleration and deceleration through the velocity of the walls and through the flow rate. For accelerating base flows, perturbations never grow larger than perturbations about a constant base flow, while decelerating flows show massive amplification of perturbations – at a Reynolds number of $500$ , properly timed perturbations about the decelerating base flow grow $ {O}(10^5)$ times larger than perturbations grow about a constant base flow. This amplification increases as we raise the rate of deceleration and the Reynolds number. We find that this amplification arises due to a transition from spanwise perturbations leading to the largest amplification to streamwise perturbations leading to the largest amplification that only occurs in the decelerating base flow. By evolving the optimal perturbations through the linearized equations of motion, we reveal that the decelerating base flow achieves this massive amplification through the Orr mechanism, or the down-gradient Reynolds stress mechanism, which accelerating and constant base flows cannot maintain.

Observing Array Designed for Improving the Short‐Term Prediction of Kuroshio Extension State Transition Processes

AbstractGiven the essential implications of Kuroshio Extension (KE) bimodality on oceanic dynamical environment and climate, the present study investigates the targeted observation schemes, based on the conditional nonlinear optimal perturbation (CNOP) method and a reduced‐gravity shallow‐water model, to improve the forecast skills of transition processes of KE bimodal states. To obtain a suitable observing array, the observation schemes, with different numbers of observation sites and observation distances between two sites, are designed. Furthermore, to demonstrate the superiority of the observing networks in predicting KE transition processes, two existing observation schemes and six random observation schemes are compared with the CNOP‐determined observing array. Based on this, a relatively optimal observing array with three sites and observation distance of 90 km is established, which is mainly located between 31°N and 33°N in the south of Japan. This targeted observing network is universal for two KE transition processes. The removal of initial errors on this array results in the mean prediction improvements of about 9.2% and 22.5% for KE transition processes from the low‐ to the high‐energy state and from the high‐ to the low‐energy state, respectively.

Linear stability analysis of oblique Couette–Poiseuille flows

We perform a detailed numerical study of modal and non-modal stability in oblique Couette–Poiseuille profiles, which are among the simplest examples of three-dimensional boundary layers. Through a comparison with the Orr–Sommerfeld operator for the aligned case, we show how an effective wall speed succinctly characterizes modal stability. Large-scale parameter sweeps reveal that the misalignment between the pressure gradient and wall motion is, in general, destabilizing. For flows that are sufficiently oblique, the instability is found to depend exclusively on the direction of wall motion and not on its speed, a conclusion supported, in part, by the perturbation energy budget and the evolution of the critical layers. Closed forms for the critical parameters in this regime are derived using a simple analysis. From a non-modal perspective, pseudoresonance is examined through the resolvent and the $\epsilon$ -pseudospectra. An analysis of the unforced initial value problem shows that the maximum energy gain is highly dependent on both the magnitude and direction of the wall velocity. However, the strongest amplification is always achieved for configurations that are only weakly skewed. Finally, the optimal perturbations appear to develop via a lift-up effect enhanced by an Orr-like mechanism, the latter driven by cross-flow shear.

The first kind of predictability problem of El Niño predictions in a multivariate coupled data‐driven model

AbstractEl Niño‐Southern Oscillation (ENSO) is the dominant atmosphere–ocean coupled mode of year‐to‐year variations in the tropical Pacific. It shows diverse spatiotemporal characteristics and casts major influences on seasonal predictions of global weather–climate extrema. Despite numerous dynamical and statistical models for ENSO prediction and predictability studies, they are commonly subjected to one‐to‐three issues among less skillful simulation of El Niño diversity, huge requirements of computational resources and a low robustness in statistics. Here, an efficient deep‐learning model involving nonlinear coupling of multiple variables is independently developed to study the predictability of two types of El Niño events related to initial uncertainty, which is the first kind of predictability problem. The model can skillfully simulate statistically robust features of observed El Niño diversity in terms of periodicity, amplitude, and seasonal phase‐locking. Using this model, we have revealed mathematically several new types of fastest‐growing initial errors in two types of El Niño predictions based on a novel concept of conditional nonlinear optimal perturbation (CNOP), especially including one that can strengthen central Pacific types of events, which is rarely investigated before. Moreover, CNOPs are superimposed into a numerical model, GFDL CM2p1, for comprehensive validation and growth mechanism mining, which demonstrates the consistent dynamical evolution of initial errors in both numerical and AI models. Our study represents the first attempt to explore the first kind of ENSO predictability problem from perspectives of nonlinear error‐evolving dynamics using a data‐driven model. This is of great importance as it offers us sufficient confidence to perform ENSO‐related (such as the Madden–Julian Oscillation, etc.) mechanisms and predictability studies in the future without strongly relying on dynamical numerical models.

Precision game engineering through reshaping strategic payoffs

Nash equilibrium is a key concept in game theory fundamental for elucidating the equilibrium state of strategic interactions, with applications in diverse fields such as economics, political science, and biology. However, the Nash equilibrium may not always align with desired outcomes within the broader system. This article introduces a novel game engineering framework that tweaks strategic payoffs within a game to achieve a pre-defined desired Nash equilibrium while averting undesired ones. Leveraging mixed-integer linear programming, this framework identifies intricate combinations of players and strategies and optimal perturbations to their payoffs that enable the shift from undesirable Nash equilibria to more favorable ones. We demonstrate the effectiveness and scalability of our approach on games of varying complexity, ranging from simple prototype games such as the Prisoner’s Dilemma and Snowdrift games with two or more players to complex game configurations with up to 106\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${10}^{6}$$\\end{document} entries in the payoff matrix. These studies showcase the capability of this framework in efficiently identifying the alternative ways of reshaping strategic payoffs to secure desired Nash equilibria and preclude undesired equilibrium states. Our game engineering framework offers a versatile toolkit for precision strategic decision-making with far-reaching implications across diverse domains.

Optimal initial duty for improved MPPT under change in irradiances and partial shading conditions

Abstract Solar photovoltaic cells are widely used in renewable energy power generation. The efficient operation of these photovoltaic (PV) system is based on maximum power point tracking (MPPT). Various MPPT methods have been proposed to increase the output of a PV system. But confusion arises when choosing the optimal MPPT algorithm and its parameters such as perturbation time and initial duty. This paper examines the optimal initial duty and perturbation time to improve the performance of conventional MPPT techniques under uniform shading and partial shading. During the change in irradiances, at the initial irradiance the Modified P&O tracked MPPT faster because the modified P&O had less settling time during changes in irradiance for different initial duty ratios. During partial shading conditions, the TCT generates more power than the S and SP topologies and modified P&O tracked the MPPT in less time. However, at the high duty ratio, the P&O and INC gave similar results, which were better than the modified P&O. It was also observed that the initial duty ratio (Di) in the MPPT algorithm had a negligible effect on TCT configuration under partial shading conditions. These findings help in various applications for PV systems.

Impacts of the Thermocline Feedback Uncertainty on El Niño Simulations in the Tropical Pacific

AbstractAs a key dynamic element of the Bjerknes feedback mechanism, the thermocline effect (TE) is critically important to El Niño modeling. In this study, the potential influence of TE‐related parametric uncertainties on El Niño is investigated using the conditional nonlinear optimal parametric perturbation (CNOP) method based on an intermediate coupled model (ICM). The optimal perturbation of the TE‐related parameter (OTEP), which substantially affects El Niño simulations, is estimated through the CNOP approach. Results reveal that the El Niño simulation is highly sensitive to the TE uncertainty in the eastern equatorial Pacific, with OTEP‐induced simulation errors demonstrating an El Niño‐like growth trend. On one hand, as indicated by the simulated El Niño intensity, the uncertainty in the TE in the eastern region can easily affect the strength of the Bjerknes feedback‐related thermocline effect and atmospheric circulation. On the other hand, the enhanced TE is highly favored to accelerate the growth of the SST error due to the air–sea interaction, thus severely affecting the El Niño simulations. Therefore, adequately representing the TE in the equatorial eastern Pacific is emphasized for effectively improving El Niño simulations.

Optimal disturbances in round submerged jets

In this paper, optimal growth analysis of spatial disturbances in round submerged jets is performed. Optimal energy growth is studied for various Reynolds numbers Re and frequencies ω. Different velocity profiles proposed by Michalke [“Survey on jet instability theory,” Prog. Aerosp. Sci. 21, 159–199 (1984)] are investigated by varying the shear layer momentum thickness δ, while the jet radius R is considered fixed (as characteristic length). In the case of stationary disturbances, there are no amplified eigenmodes, so eventually the energy of such disturbances decays downstream. Such disturbances are characterized by optimal energy growth as a function of streamwise coordinate z. At certain location downstream zmax this value reaches its maximum Gmax and then decays, although not monotonically, unlike the result of the temporary setting [Jimenez-Gonzalez et al., “Modal and non-modal evolution of perturbations for parallel round jets,” Phys. Fluids 27, 044105 (2015); Jimenez-Gonzalez and Brancher, “Transient energy growth of optimal streaks in parallel round jets,” Phys. Fluids 29, 114101 (2017)]. The well-known scaling Gmax∝Re2 and zmax∝Re is confirmed for stationary disturbances. Conversely, for nonstationary disturbances there is a range of frequencies in which an amplified mode is present. In this case, optimal perturbations far downstream consist only of the amplified mode. The main effect of non-modality here is “the energy pumping” of the amplified mode, so the disturbances are characterized by the “energy ratio” G/Em, i.e., the ratio of the energy of an arbitrary perturbation to the energy of the amplified mode. The influence of the shear layer momentum thickness on optimal disturbances is studied; increasing the shear layer momentum thickness of the base flow “smears” the area occupied by the optimal disturbance, although it does not dramatically affect energy gain values, slightly decreasing maximum energy as shear layer momentum thickness increases. Spatial oscillations in the energy of stationary optimal disturbances in jet flows are discovered. The spectrum structure examination shows that the frequency of these oscillations corresponds to the frequencies of the two least damped discrete eigenmodes.

Identification Source Term of the Distributed Order Time-Space Fractional Diffusion Equation

Abstract The inverse source problem for time-distributed order spatial fractional diffusion equations is examined in this study. The forward problem is solved by combining finite difference methods with matrix transformation techniques. The Tikhonov regularization approach is then applied to convert the inverse problem into a variational problem. The optimal perturbation approach is used to find the minimizer of the variational problem, leading to an approximation solution that depends solely on the time-dependent source term. The algorithm’s effectiveness and stability are demonstrated using numerical examples in one-dimensional domains.

Ensemble forecasting of Indian Ocean Dipole events generated by conditional nonlinear optimal perturbation method

Ensemble forecasting of Indian Ocean Dipole events generated by conditional nonlinear optimal perturbation method

Entropy production-based nonlinear optimal perturbation for subsonic flows around an airfoil

The extraction and time evolution of optimal perturbation (OP) offers abundant physical insights in fluid dynamics. Nonlinear OP (NLOP) analysis provides an approach for obtaining the trajectory to induce the maximum changes in the flow field. In an extension into unsteady flow field, we tracked the changes of trajectory by an application of initial perturbation field in the compressible Navier–Stokes equation, and we focused on the entropy production (EP) to characterize the trajectory. We proposed entropy production-based NLOP (EP-NLOP) analysis for compressible flows and investigated the effect of evaluation function on the extracted Ops using the subsonic flow around an airfoil. Compared with the conventional disturbance energy (DE-) based NLOP (DE-NLOP) analysis, we demonstrated that the OPs with different spatial wavelength and concentration regions were successfully extracted due to the different spatial sensitivity of evaluation function. In the EP-NLOP analysis, the spatial distribution of OP extracted the larger energy dissipation upstream of the separation points for the short evaluation time. For the long evaluation time, EP-NLOP analysis extracted the transient-time evolution of interacting separation vortices, attributing the multiple wavelengths of OPs. These differences in the OPs offer promising insights into fluid dynamics.

An extension to ensemble forecast of conditional nonlinear optimal perturbation considering nonlinear interaction between initial and model parametric uncertainties

Initial and model uncertainties are the main sources of forecast errors, making the single and deterministic forecasts unreliable. To estimate these uncertainties, a growing consensus shifts towards ensemble forecasting, aiming to provide the probability density distribution of the atmosphere. However, current ensemble methods either focus on single-source uncertainties or employ a simple superposition of the two, neglecting the nonlinear interaction between them, and thus fail to reflect the real forecast uncertainty. Motivated by this, this study extends the CNOP approach, defined as the optimal growth considering nonlinear interaction between initial and model parameters, to the scenario of ensemble forecasts and proposes an orthogonal CNOPs method (O-CNOP-IPs). This method concerns the nonlinear effect of initial and model parametric uncertainties through a joint optimization strategy and enhances the estimation of this effect by providing diversity and independent CNOPs (via orthogonality). To evaluate the performance of O-CNOP-IPs, extensive experiments are conducted for North Atlantic Oscillation (NAO) ensemble forecasts in the realistically configured Community Earth System Model (CESM). Our findings reveal that the O-CNOP-IPs method outperforms existing methods in forecast skill and reliability, improving deterministic skill by 17.5 % and probabilistic skill by 52 %–63 %. Our dynamic analysis also unveils that this method undergoes rapid development in the early stage and effectively neutralizes errors in control forecasts, significantly enhancing the reliability of ensemble forecasts. It is expected that O-CNOP-IPs plays a significant role in accurately representing the forecast uncertainty of other high-impact weather and climate phenomena.

Nonlinear transient disturbance growth analysis for the compressible external flow and application to a flow around circular cylinder

The property of nonlinear optimal perturbation (NLOP) analysis for the flow around the circular cylinder was investigated with a comparison with the linear optimal perturbation analysis (LOP). Our analysis revealed that NLOP is highly dependent on the initial disturbance norm and highlighted the limitation of linear prediction in triggering instability in the flow field. This NLOP shows an asymmetric and deformed vortex structure on the cylinder wall, with the angle of the maximum wall vorticity shifting in relation to the initial disturbance norm. We also observed that the circulation and disturbance vorticity at the shear layer in boundary layer efficiently contributed to larger disturbance growth of the separation vortex behind the cylinder compared with the LOP.

Adversarial Attack and Defense in Deep Ranking.

Deep Neural Network classifiers are vulnerable to adversarial attacks, where an imperceptible perturbation could result in misclassification. However, the vulnerability of DNN-based image ranking systems remains under-explored. In this paper, we propose two attacks against deep ranking systems, i.e., Candidate Attack and Query Attack, that can raise or lower the rank of chosen candidates by adversarial perturbations. Specifically, the expected ranking order is first represented as a set of inequalities. Then a triplet-like objective function is designed to obtain the optimal perturbation. Conversely, an anti-collapse triplet defense is proposed to improve the ranking model robustness against all proposed attacks, where the model learns to prevent the adversarial attack from pulling the positive and negative samples close to each other. To comprehensively measure the empirical adversarial robustness of a ranking model with our defense, we propose an empirical robustness score, which involves a set of representative attacks against ranking models. Our adversarial ranking attacks and defenses are evaluated on MNIST, Fashion-MNIST, CUB200-2011, CARS196, and Stanford Online Products datasets. Experimental results demonstrate that our attacks can effectively compromise a typical deep ranking system. Nevertheless, our defense can significantly improve the ranking system's robustness and simultaneously mitigate a wide range of attacks.

Stability patterns in plane porous Poiseuille flow with uniform vertical cross-flow: A dual approach

In this study, we examine the effects of a porous parameter and a uniform vertical cross-flow on the onset of instability in a plane Poiseuille flow (PPF) subjected to infinitesimal disturbances. The linearized Navier-Stokes (N–S) equations, which govern the stability of the fluid flow system, are addressed using the Chebyshev collocation method (CCM). Our approach includes both modal and non-modal analyses, each providing distinct insights into the system's behavior. The modal analysis involves a linear stability assessment using both non-normalized and normalized basic velocity approaches. Assuming a constant pressure gradient, the first approach aligns with the traditional Poiseuille flow framework, where a uniform pressure difference drives the flow. This simplifies calculations and aids in predicting flow characteristics. The second approach, which varies the pressure gradient to maintain a constant maximum streamwise velocity, offers a different perspective by focusing on a specific flow velocity profile through the porous medium. This variation in the pressure gradient allows us to explore changes in flow behavior and the system's responses under these conditions. This analysis includes examining the eigenspectrum, neutral stability curves, and determining critical triplets. On the non-modal front, we explore the intricacies of the non-normal Orr-Sommerfeld (O–S) operator. This involves studying the pseudospectrum and transient energy growth rate (G(t)) plots for optimal perturbations. Identification of regions of stability, potential instability, and instability is achieved using contour plots of maximum transient energy growth (Gmax). Interestingly, our results reveal that the porous parameter acts as a stabilizing agent, mitigating instability. In contrast, the uniform vertical cross-flow plays a dual role, contributing to both stabilization and destabilization of the system. Additionally, our study highlights the impact of examining basic velocity through both normalized and non-normalized approaches, leading to different stability predictions.

Forecasting a Short-Term Photovoltaic Power Model Based on Improved Snake Optimization, Convolutional Neural Network, and Bidirectional Long Short-Term Memory Network.

The precision of short-term photovoltaic power forecasts is of utmost importance for the planning and operation of the electrical grid system. To enhance the precision of short-term output power prediction in photovoltaic systems, this paper proposes a method integrating K-means clustering: an improved snake optimization algorithm with a convolutional neural network-bidirectional long short-term memory network to predict short-term photovoltaic power. Firstly, K-means clustering is utilized to categorize weather scenarios into three categories: sunny, cloudy, and rainy. The Pearson correlation coefficient method is then utilized to determine the inputs of the model. Secondly, the snake optimization algorithm is improved by introducing Tent chaotic mapping, lens imaging backward learning, and an optimal individual adaptive perturbation strategy to enhance its optimization ability. Then, the multi-strategy improved snake optimization algorithm is employed to optimize the parameters of the convolutional neural network-bidirectional long short-term memory network model, thereby augmenting the predictive precision of the model. Finally, the model established in this paper is utilized to forecast photovoltaic power in diverse weather scenarios. The simulation findings indicate that the regression coefficients of this method can reach 0.99216, 0.95772, and 0.93163 on sunny, cloudy, and rainy days, which has better prediction precision and adaptability under various weather conditions.

Inversion of image-only intrinsic parameters for steel fibre concrete under combined rate-temperature conditions: An adaptively enhanced machine learning approach

Concrete not only bears quasi-static loads during the service of engineering structures, but also bears impact or explosion due to accidental accidents, so more and more attention has been paid to the study of concrete deformation characteristics and stress distribution. Obtaining the correct constitutive parameters is crucial for the study of the mechanical behavior of concrete, and the determination of constitutive parameters is essentially an inverse process, which is very challenging. In this paper, third-order Bessel curves are used to construct dynamic constitutive equations for steel-fibre concrete under rate-temperature union conditions, and to establish a database of the constitutive parameters corresponding to the factors influencing the mechanical behaviour of concrete. In order to select highly accurate and adaptive intelligent inversion models, Firstly, the black-winged kite optimisation algorithm (BKA) has been improved by improving the black-winged kite leader condition and integrating the optimal perturbation strategy of Morlet wavelet factor, which proves the superiority of the MBKA algorithm by comparing it with the BKA, Dung Beetle Optimisation Algorithm (DBO), Grey Wolf Optimisation Algorithm (GWO), and Harris Hawk Algorithm (HHO) in searching for the optimal results. Secondly, based on the database, the MBKA-LSSVR model, MBKA-LSSVR-Adaboost model, CNN-GRU model and CNN-LSTM model were built sequentially, respectively. The final results show that the MBKA-LSSVR-Adaboost model has the highest accuracy and the best performance for the parameter Pi (i = 0,1,2,3), and the inverted stress-strain curve proves that the proposed method is effective and accurate in determining the proposed constitutive parameters.

Co and Ni Ratio Modulation‐Derived Electron Deficient Pd Trimetallic Catalysts for Enhanced Formic Acid Electrooxidation

AbstractPdCoNi trimetallic catalysts attracted extensive interest in direct formic acid fuel cells due to high poisoning resistance and high activity for formic acid electro‐oxidation (FAO). Herein, a series of Pd0.75CoxNiy/C alloys with a modulated ratio of Co and Ni are synthesized to investigate the effect of Co and Ni content on the electronic structure of Pd for FAO. The physical analysis demonstrated that the introduction of Co and Ni induces the lattice strain effect compared to monometallic Pd catalysts. As a consequence of fixing the total amount of Co and Ni, the strain effect is restricted, and the electronic perturbation of Pd is successfully regulated by varying the ratio of Co and Ni in Pd0.75CoxNiy/C trimetallic alloys. Pd loses more electrons, the bond strength of Pd−H is weakened, and FAO activity is enhanced first and then decreased as the Co content increases. Among the trimetallic catalysts, Pd0.75Co0.125Ni0.125/C trimetallic catalyst exhibits the highest current density of 3.253 mA cm−2 owing to the optimum electronic perturbation and Pd−H bond strength. This work provides a valuable guideline for future studies of Pd‐based trimetallic alloys.

Dynamic channel selection based on vertical sensitivities for the assimilation of FY‐4A geostationary interferometric infrared sounder targeted observations

AbstractTarget observations have garnered significant attention owing to their successful applications in enhancing forecasting skills of extreme weather events, particularly tropical cyclone (TC) events. The key step of implementing target observation is to determine the sensitive area in advance. Previous studies often obtained the sensitive areas for TC forecasting by vertically integrating the energy of optimal perturbation and taking the horizontal area of large energy, in an attempt to use it to represent roughly the sensitivity of the whole atmospheric layer. The advent of the geostationary interferometric infrared sounder on the FY‐4A satellite and then corresponding satellite data assimilation have opened up a new possibility for identifying the vertical sensitivity for TC forecasting to improve the forecasting skill. This article proposes a targeting satellite channel (TSC) approach to accurately capture the sensitivity along vertical directions of the atmosphere that allows one to preferentially select the channels whose observations locate on the sensitive vertical atmospheric layers. Numerical experiments demonstrate that, when preferentially assimilating the channel observations obtained from the TSC approach, the TC tracks achieve a considerably smaller forecast error than the information entropy channel selection approach. The TSC approach, therefore, has the potential for the satellite data assimilation to improve TC track forecasting skill very effectively, which can also provide guidance to targeting observations in field campaigns for TC forecasting.

Origin of symmetry breaking in the grasshopper model

The planar grasshopper problem, originally introduced by Goulko and Kent [], is a striking example of a model with long-range isotropic interactions whose ground states break rotational symmetry. In this paper we analyze and explain the nature of this symmetry breaking with emphasis on the importance of dimensionality. Interestingly, rotational symmetry is recovered in three dimensions for small jumps, which correspond to the nonisotropic cogwheel regime of the two-dimensional problem. We discuss simplified models that reproduce the symmetry properties of the original system in N dimensions. For the full grasshopper model in two dimensions we obtain quantitative predictions for optimal perturbations of the disk. Our analytical results are confirmed by numerical simulations. Published by the American Physical Society 2024