Catastrophe Point Research Articles

Research on nonlinear instability of blended-wing-body aircraft based on experimental bifurcation analysis

Focusing on the nonlinear instability problem of the blended-wing-body aircraft, first, numerical bifurcation analysis is adopted to obtain catastrophe points and branches where the elevator is taken as a continuous parameter. Second, based on virtual flight tests and bifurcation theory, an experimental bifurcation analysis method is developed. Open-loop and closed-loop experiments are carried out, and the corresponding experimental bifurcation diagrams are obtained. The comparative analysis shows that the experimental bifurcation analysis enables the aircraft to make a response that is close to reality under the influence of nonlinear and unsteady aerodynamics and has a more intuitive embodiment of instability characteristics, providing an accurate prediction of departure. The open-loop experiment predicts a sudden longitudinal nose-up at an angle of attack of 7.4°. The closed-loop experiment can transform the open-loop unstable branch into a stable branch. However, roll instability still occurs at a critical angle of attack of 16.0°. These research results provide important dynamic information for the stable flight and the design of the controller.

Applying a thermodynamic-based method to reveal the failure laws of CFRP stiffened plates

The high specific strength and stiffness of carbon fiber-reinforced polymer (CFRP) stiffened plates make them popular in aerospace and other fields. Nevertheless, CFRP stiffened plates have unique characteristics and complicated and diversified failure patterns, so it is impossible to determine its failure law with a uniform failure criterion accurately. Its load-carrying capacity has always been calculated on the conservative side of empirical estimation. This work uses the stressing state theory to investigate the stressing state evolution of composite stiffened plates under axial loading. It conducts three CFRP stiffened plates of the same configuration from a thermodynamic perspective. By equating stiffened plates to thermodynamic systems, the measured strain data are modeled as state variables, and renormalization and clustering algorithms are applied to determine the phase transition loads of the structure, while the characteristic points before and after normalization are verified for their reasonableness and stability. Accordingly, this work reveals the failure laws of CFRP stiffened plates by applying a thermodynamic-based method. It characterizes the structural failure features by defining catastrophe points throughout the failure process, which provides a new reference for the failure analysis and strength design of CFRP stiffened plates.

Identification of the Catastrophic Phase Inversion Point of Water-in-Oil Emulsion Using Ultrasonic Measurements

Identification of the Catastrophic Phase Inversion Point of Water-in-Oil Emulsion Using Ultrasonic Measurements

Swirling electrolyte. Part 1. Hierarchy of catastrophic transitions in steady annular flows

This study extends our previous work (McCloughan & Suslov, J. Fluid Mech., vol. 887, 2020, A23), where the existence of a saddle-node bifurcation of steady axisymmetric electrolyte flows driven by the Lorentz force in a shallow annular domain was first reported. Here we perform further weakly nonlinear analysis over a wider range of the governing parameters to demonstrate that the previously reported saddle-node bifurcation is a local feature of a global fold catastrophe, which, in turn, is a part of cusp catastrophe occurring as the thickness of the fluid layer increases. The amplitude equation characterising multiple flow solutions in the finite vicinity of catastrophe points is derived. The sensitivity of its coefficients and solutions to the distance from the catastrophe points is assessed demonstrating the robustness of the used analytical procedure. The asymptotic flow solution past the catastrophe point is subsequently obtained and its topology is explored confirming the existence of the secondary circulation in the bulk of flow (two-tori background flow structure). The latter is argued to lead to the appearance of experimentally observable vortices on the fluid surface. The rigorous justification of this conjecture is to be given in Part 2 of the study.

Damage Process Criterion for the Concrete Dam in Geomechanical Model Test

The geomechanical model test (GMT), a means of intuitively exploring the model’s failure modes and revealing failure mechanisms, is considered an effective approach for studying the structural characteristics of dams under complex geological conditions. However, during the overloading process of the model, the catastrophe trends of monitoring data are unclear, and catastrophe points differ at different monitoring sites. These factors have led to large errors in the judgment of researchers regarding the model’s state and misperception of the structural properties during the damage process. In this study, a comprehensive evaluation method for the model’s state intervals in the damage process is proposed. The criterion employed an interval analysis hierarchy process that considered the differences, consistency, and credibility (CDC‐IAHP) among multiple decision‐makers (DMs), effectively reducing the subjectivity of their judgments. Additionally, this process was combined with cusp catastrophe theory (CCT) to determine whether the model underwent an abrupt change at various overload factors comprehensively. This is the first time that CDC‐IAHP and CCT have been combined as criterion for a comprehensive method on the damage process of concrete dams in GMTs, and was applied to the Wudu gravity dam, indicating its applicability is very good. Compared to the researcher’s judgment, this approach is used to analyze and judge the structural state more accurately and scientifically while reducing subjectivity, which can help to better understand the structural characteristics and bearing capacity of actual engineering projects.

Geopoetics

This article presents an alternative political history of recent planetary thought through an examination of geopoetics rooted in the colonial politics of Indonesia and Cold War geosciences. This history reveals how geopoetics has not been marginal or critical of dominant scientific narratives but has been central to the development of modern theories of the earth. The article traces the roots of that history in colonial Indonesia through debates between geologists, Theosophists, and orientalists, and in colonial endeavors to suppress Javanese Islam through new geological narratives. It considers the work of Johannes Umbgrove, his theory of geopoetry, and its influence on Harry Hess and the theory of plate tectonics. Acknowledging this history shows us just how deeply connected geopoetics is to much longer religious, cosmological, and political conversations about narrating the earth. The article examines how geopoetics has long been preoccupied with understanding the connectivity of nature and catastrophic histories and points to contemporary possibilities for rethinking the relationship between humans, the earth, and cosmos.

Bursting oscillations of a geometrical nonlinear system with a third-order catastrophe point

Bursting oscillations of a geometrical nonlinear system with a third-order catastrophe point are investigated. The third-order catastrophe point is a high order cusp point at which the geometrical nonlinear system can achieve the third-order quasi-zero stiffness for vibration isolation. The symmetry of triple-wells, double-wells and single-wells near the catastrophe point is broken due to the introduction of a slow-varying parameter, which results in the appearance of asymmetrical triple-wells, double-wells and single wells. Complex evolution dynamics of both the non-autonomous system and the generalized autonomous system are studied through a natural connection that treats the low frequency excitation as a slow-varying parameter. Bursting oscillations are found and the mechanisms are revealed through the analysis of asymmetrical global dynamics. The relations between the isolation performance and bursting oscillations are studied through the coordinates corresponding to the force transmissibility. Results showed that both the increase of geometrical parameters and the introduction of the nonlinear damping with multiple roots could result in the appearance of more quiescent states. A novel step-up curve of inter spike intervals for quiescent states is found which corresponds to the fish-scale curve of inter spike intervals for spiking states. A smaller excitation amplitude can be used to generate the inter spike intervals of spiking states which means that vibrations can be observed earlier with the increase of the small stiffness and small restoring force regions near the origin. Low transmissibility can be achieved when the system trajectory reaches its amplitude at the quiescent states for any situation near the third-order catastrophe point.

A catastrophe identification method for rainfall time series coupled sequential Mann-Kendall algorithm and Bernaola Galvan algorithm: a case study of the Qinglong River watershed, China

AbstractThe identification of rainfall catastrophe characteristics is important for rainfall consistency testing in hydrostatistical analysis. In this study, a new classification method (trend, mean and change-rate catastrophe) was proposed and applied to the Qinglong River watershed, Northern China. Two groups of algorithms were compared to obtain the optimal algorithm: the Cumulative-anomaly method and the Sequential Mann-Kendall (SQ-MK) algorithm, the Pettitt algorithm and the Bernaola-Galvan heuristic segmentation (B-G) algorithm. Its parameters were optimized and its robustness was tested. Results revealed that: (1) The SQ-MK algorithm was suitable for trend catastrophe and sensitive to the length of the time series. The most significant point of trend catastrophe in the Qinglong River watershed was in 2012. (2) The sensitivity of parameter P0 (Range value (R) = 4.333) in the B-G algorithm was greater than that of parameter l0 (R = 2.889). (3) The B-G algorithm was suitable for identifying mean catastrophes and insensitive to the length of the time series. In the Qinglong River watershed, mean catastrophe points were identified in 1997, 2002, 2004, 2006, 2009, 2012, and 2018. (4) There was no change-rate catastrophe point in the Qinglong River watershed. Trend catastrophe and mean catastrophe do not necessarily lead to change-rate catastrophe.

Characterization and Simulation of Nanoscale Catastrophic Failure of Metal/Ceramic Interfaces.

The catastrophic failure of metal/ceramic interfaces is a complex process involving the energy transfer between accumulated elastic strain energy and many types of energy dissipation. To quantify the contribution of bulk and interface cohesive energy to the interface cleavage fracture without global plastic deformation, we characterized the quasi-static fracture process of both coherent and semi-coherent fcc-metal/MgO(001) interface systems using a spring series model and molecular static simulations. Our results show that the theoretical catastrophe point and spring-back length by the spring series model are basically consistent with the simulation results of the coherent interface systems. For defect interfaces with misfit dislocations, atomistic simulations revealed an obvious interface weakening effect in terms of reduced tensile strength and work of adhesion. As the model thickness increases, the tensile failure behaviors show significant scale effects-thick models tend to catastrophic failure with abrupt stress drop and obvious spring-back phenomenon. This work provides insight into the origin of catastrophic failure at metal/ceramic interfaces, which highlights a pathway by combining the material and structure design to improve the reliability of layered metal-ceramic composites.

Effects of Heating and Liquid Nitrogen on Mechanical Characteristics and Rockburst Characteristics of Granite

Due to the depletion of shallow resources and the reduction of the space for human life and development, in recent years, human beings began to gradually expand to the deep underground. The increase of development depth will bring a series of safety problems, so it is particularly important to study and deal with rockburst. In this paper, based on laboratory tests, relevant literature, and research at home and abroad, the TAWD-2000 electrohydraulic servo rock mechanics testing machine and PIC-2 acoustic emission (AE) testing system are used. Uniaxial compression tests and AE monitoring tests were carried out on granite samples to analyze the property and AE characteristic parameters of granite under the action of liquid nitrogen (LN2) and to further study the fracture mode of granite. The following conclusions can be obtained: the LN2 cooling has a deterioration influence on the strength of rock, and the elastic modulus and peak stress of granite show a downward trend with the increasing number of cycles. With the cycle times of LN2 actions increasing, the AE ring count of granite and the frequency and amplitude of energy in each stage have an upward trend. When the rock reaches the failure stage, the energy at the catastrophe point increases, and the ring count also increases sharply. The RA-AF diagram of AE parameters can characterize two failure modes of rock, tensile failure and shear failure. In the process of fracture of granite samples, shear cracks dominate, leading to shear failure or compression failure of granite. Based on the method of elastic energy, the tendency index of rockburst of granite samples under different working conditions is calculated. The tendency of rockburst decreases with the decrease of elastic modulus. Under the repeated action of LN2, the tendency of rockburst of granite samples presents a downward trend, and the action of LN2 reduces the probability of rockburst to a certain extent.

Grounding electrode line fault location method based on simulation after test and deduction

• Fault characteristics of the grounding electrode line are weak. • Fault location by injecting signals into the line. • The initial pulse signal is eliminated after linear mode transformation. • Using simulation after test and deduction to obtain fault distance. • No need to calibrate the arrival time of the wave head. When a high-voltage direct current (HVDC) transmission system with the grounding electrode line (GEL) is in the balanced operation mode, the unbalanced current in the GEL and the neutral potential of the system are extremely small. In the GEL, after a fault incident, the additional fault component will be small, and fault characteristics will be weak. As the traditional passive fault location methods are challenging to apply, a GEL fault location method based on simulation after test and deduction (SATD) is proposed in this paper. Firstly, the pulse signal is injected into the GEL. Then, the mutation point of the pulse response signal is projected along the line to form a virtual fault point matrix. Based on the mentioned matrix, the fault location function is constructed, and the fault distance is obtained by the catastrophe point of the function. In this method, the bottleneck of precisely identifying the traveling wave (TW) arrival time in the time domain is broken, and the automated single-ended TW location of the GEL can easily be implemented. Many real time digital simulator (RTDS) tests validate the high accuracy and strong robustness of the method.

Baseline Correction Algorithm Based on Catastrophe Point Detection and Lipschitz Exponent’s Analysis

In order to quantitatively analyze the proportions of independent components in mixtures, it is necessary to extract line spectra corresponding to those components from the spectrum signal of some mixture and evaluate the amplitude of the spectral lines. Multiple factors cause the drift and tilt of a spectrum signal’s baseline, such as environment noises, instrument bias, and sample size, which affect the identification and quantitative analysis of the line spectra superimposed on the baseline. Therefore, the baseline of a spectrum signal should be removed before the line spectra are identified. A baseline correction algorithm based on Catastrophe Point detection and Lipschitz exponent’s analysis is proposed in this paper. With the algorithm, the strong spectral lines are identified and removed, and then the spectral baseline is evaluated without the interference of strong spectrum signals. First, catastrophe points are located based on the local modulus maxima theory of wavelet coefficients. Second, according to the Lipschitz exponent theory, the strong spectral peaks’ regions are identified and removed by a smoothing filter. Then the slowly varying spectrum is segmented adaptively and fitted by the least square fitting method. After the segments are attached and the boundaries are smoothed, the baseline of the spectrum is acquired and extracted finally. The algorithm is more accurate than classical ones because identifying the baseline is implemented after strong peaks are removed, so their influences to baseline extracting are eliminated. The results of experiments show that the algorithm is accurately performed for the spectrum signal of a gas mixture, [Formula: see text].

Forecasting short-term electricity load using hybrid support vector regression with grey catastrophe and random forest modeling

This paper develops a novel short-term load forecasting model that hybridizes several machine learning methods, such as support vector regression (SVR), grey catastrophe (GC (1,1)), and random forest (RF) modeling. The modeling process is based on the minimization of both SVR and risk. GC is used to process and extract catastrophe points in the long term to reduce randomness. RF is used to optimize forecasting performance by exploiting its superior optimization capability. The proposed SVR-GC-RF model has higher forecasting accuracy (MAPE values are 6.35% and 6.21%, respectively) using electric loads from Australian-Energy-Market-Operator; it can provide analytical support to forecast electricity consumption accurately.

Universality Near the Gradient Catastrophe Point in the Semiclassical Sine‐Gordon Equation

AbstractWe study the semiclassical limit of the sine‐Gordon (sG) equation with below threshold pure impulse initial data of Klaus‐Shaw type. The Whitham averaged approximation of this system exhibits a gradient catastrophe in finite time. In accordance with a conjecture of Dubrovin, Grava, and Klein, we found that in a neighborhood near the gradient catastrophe point, the asymptotics of the sG solution are universally described by the Painlevé I tritronquée solution. A linear map can be explicitly made from the tritronquée solution to this neighborhood. Under this map: away from the tritronquée poles, the first correction of sG is universally given by the real part of the Hamiltonian of the tritronquée solution; localized defects appear at locations mapped from the poles of the tritronquée solution; the defects are proved universally to be a two‐parameter family of special localized solutions on a periodic background for the sG equation. We are able to characterize the solution in detail. Our approach is the rigorous steepest descent method for matrix Riemann‐Hilbert problems, substantially generalizing [5] to establish universality beyond the context of solutions of a single equation. © 2021 Wiley Periodicals LLC.

DEEPER COMPREHENSION OF BASIC ENVIRONMENTAL ISSUES THROUGH SERIOUS GAME

AbstractDuring the last three decades we observe growing use of ecodesign, but we observe also misuse of ecodesign methods, leading often to time and financial loss. In coherence with several failure analysis and with our observation, we base our work on a hypothesis: Misuse of ecodesign is often caused by lack of basic comprehension of environmental issues: Non linearity of the processes, their inertia and their excessive costs.Building on this hypothesis, we decided to enhance our education program with an innovative serious game. The goal is to achieve comprehension of the basic environmental issues. Innovation of the game lies in revealing to students at the end of the game, that the fictive initial situation of the game corresponded to a starting point of a real catastrophe. Students can thus not only compare their decisions with those of real leaders, but also to understand how and why bad decisions were taken.Experiments indicate that students who played the game tend to evaluate environmental problems, while those who followed a lecture tend to describe them. This trend (going further than to a description) seems to be useful in decision making and in deployment of ecodesign methods.

Barnes Update Applied in the Gauss-Newton Method: An Improved Algorithm to Locate Bond Breaking Points.

A mechanochemical reaction is a reaction induced by mechanical energy. A general accepted model for this type of reaction consists of a first-order perturbation on the associated potential energy surface (PES) of the unperturbed molecular system due to mechanical stress or pulling force. Within this theoretical framework, the so-called optimal barrier breakdown points or optimal bond breaking points (BBPs) are critical points of the unperturbed PES where the Hessian matrix has a zero eigenvector that coincides with the gradient vector. Optimal BBPs are "catastrophe points" that are particularly important because their associated gradient indicates how to optimally harness tensile forces to induce reactions by transforming a chemical reaction into a barrierless process. Building on a previous method based on a nonlinear least-squares minimization to locate BBPs (Bofill et al., J. Chem. Phys. 2017, 147, 152710-10), we propose a new algorithm to locate BBPs of any molecular system based on the Gauss-Newton method combined with the Barnes update for a nonsymmetric Jacobian matrix, which is shown to be more appropriate than the Broyden update. The efficiency of the new method is demonstrated for a multidimensional model PES and two medium size molecular systems of interest in enzymatic catalysis and mechanochemistry.

Behavior of rockfill dam under complex terrain condition

The behavior of concrete face rockfill dam (CFRD) is more dependent on valley terrain than rockfill deformation. The objectives of this study are to research the influence of valley topography condition on the deformation and stress of a CFRD, especially with relevance to the behavior of face slab under complex terrain conditions. First, the research on the effect of valley shape factor on perimeter joint deformation used monitoring data with a combined total of 22 CFRDs from 8 countries. The results show that the perimeter joint deformation decreases nonlinearly with increasing valley shape factor A/H2. A/H2 = 2 ~ 4 or L/H = 2 ~ 5 can be considered an intervenient valley which contains both characteristics of the narrow and wide valley. Then, numerical analysis is applied to predict the behavior of Nam Ngum 2, a 182-m-high concrete face rockfill dam, during initial impoundment via a three-dimensional finite element analysis. A series of finite element analyses aimed at investigating the influence of the intervenient valley and complex topography condition which in turn depends on slope angle and angle mutant of the abutment on stress and deformation of concrete face slab on CFRD. All results indicate that the arch effect is crucial to deformation and stress of the CFRD in the intervenient scale of valley shape factor. Steeper slope and convex catastrophe point in abutment rapidly aggravate the tensile stress of the face slab and the deformation of the joints, which threaten the safety of the impervious system of CFRD. The hardening soil model is used in the nonlinear analysis for rockfill, and the results show that a good agreement between computed results and dam field monitoring data can be achieved.

SPATIOTEMPORAL VARIATION OF NDVI IN THE YELLOW RIVER SOURCE REGION FROM 1998 TO 2016

Abstract. Quantification of vegetation change and its coupling relationship with climate change has become the central topic in current global change researches. The Normalized Difference Vegetation Index (NDVI) time series data and meteorological data from 1998 to 2016 were collected to investigate the temporal and spatial variations of NDVI in growing season in the Yellow River source region and its response to climate change, based on the trend analysis, Mann-Kendall test and correlation analysis．The results indicated that: (1) In the past 19 years, the average NDVI in the region showed a slow increase, with a growth rate of 0.002/a and a catastrophe point in 2005, and the area with an upward trend accounted for 71.4% of the total area. (2) The climate of the area had been becoming warm and moist since the recent 19 years, both precipitation and temperature in growing season showed an upward trend. The partial correlation analysis showed that NDVI was positively correlated with precipitation and temperature, significantly relevant area accounting for 31.01% and 56.40% of the total area individually. The sensitivity of NDVI to temperature was higher than that of precipitation. According to residual analysis over the 19 years, human activities had negative effects on NDVI accounting 53.58% of the study area, and the implementation of a series of ecological protection engineering measures was the main cause leading to an increasing trend of NDVI after 2005.

Entropic uncertainty relation and quantum phase transition in spin-1/2 Heisenberg chain

Based on the quantum-memory-assisted entropic uncertainty relation (QMA-EUR), we study the quantum phase transition (QPT) of a spin-1/2 frustrated Heisenberg chain and show that QMA entropy can be a useful tool to detect QPT. For the six-site case, we choose the reduced two-site as the detecting system and obtain the analytical result of QMA entropy and its bound. We find that the QMA entropy of the ground state is discontinuous at the first-order QPT point. Meanwhile for the excited state, the catastrophe point of QMA entropy approaches the infinite-order QPT point, which is confirmed by the numerical results in the 8-, 10- and 12-site cases. Moreover, we study the behavior of QMA entropy undergoing the dephasing process. Interestingly, two-site QMA entropy can still indicate the QPT point when the state degenerates into a mixed state. In this sense, QMA entropy is more effective than quantum correlation in reflecting the quantum criticality.

A NEW IDENTIFICATION METHOD OF THE TRANSFORMER INRUSH CURRENT BASED ON IMPROVED HILBERT-HUANG TRANSFORM ALGORITHM

As the main form of protection for transformers, differential protection requires correct operation because it directly influences the safe operation of transformers. Meanwhile, transformer inrush current is an important factor in the tendency of transformers to malfunction. To accurately and reliably discriminate inrush current from internal fault current, this study proposed a novel method based on the Hilbert–Huang transform (HHT) algorithm. We integrated the empirical mode decomposition (EMD) algorithm with the permutation entropy (PE) algorithm and put forward a new algorithm named modified ensemble EMD. First, the original current signal was added to an opposite white noise signal with several repetitions for the EMD. Next, PE was employed to detect the decomposition results, where the noise, intermittent, and high-frequency signals with relatively large entropies were removed from the original signal. The remainder of the signal was decomposed by the second EMD to obtain a group of approximately stationary intrinsic mode munction (IMF) signals. Finally, the first IMF signal was extracted for HHT to obtain an instantaneous frequency, and the transformer inrush current and internal fault current were accurately identified by the time intervals between two adjacent catastrophe points in the instantaneous frequency. Results demonstrated that the time intervals between two adjacent catastrophe points in the instantaneous frequency of the transformer inrush current were less than 14 ms and that of various internal faults (i.e., turn-to-turn, single-phase, phase-to-phase, and three-phase faults) were approximately 20 ms. Results indicate that the inrush current and internal fault current are correctly, reliably, and quickly identified by the time intervals between two adjacent catastrophe points in the instantaneous frequency. The time intervals of the catastrophe points in the instantaneous frequency of the inrush current under different closing initial phase angles (0°, 30°, …, 330°) are less than 12.5 ms, indicating that the method is unaffected by the dead angle of the inrush current, closing initial phase angle, and non-periodic components. The proposed method provides references for identifying inrush current with regard to transformer differential protection. Keywords: Hilbert–Huang transform, Inrush current, Internal fault current, Instantaneous frequency