Nonlinear Structure Research Articles

Disentangling and interpreting nonlinear molecular and isotopic variations in petroleum using machine learning

Nonlinear variations in the molecular and isotopic compositions of phases in complex geosystems greatly hinder the application of geochemical proxies. This study aims to disentangle the implicit nonlinear mathematical structures embedded in geochemical datasets, effectively disaggregating overlapping geological influences that drive the intricate variations in the geochemical signatures of phases. Employing a typical hybrid petroleum system as a case study, we utilize an unsupervised machine learning algorithm to visualize the effects of source disparities and distinct evolutionary processes, such as mixing, thermal maturation, biodegradation, and evaporative fractionation, on the molecular compositions among crude oils. We further investigate the regression relationship between molecular composition and bulk δ13C signal in petroleum. Our findings reveal that by decomposing the regression model to solely reflect a specific dominant influence, the model could provide a precise geological interpretation. Accordingly, we unravel the subtle variations and underlying mechanisms of carbon isotopic fractionation in petroleum substances from different origins under the impact of maturation. Our results underscore the substantial potential of strategically applied machine learning techniques in reconstructing the geochemical evolution of complex geosystems, advocating for their broader application.

MADE: Multicurvature Adaptive Embedding for Temporal Knowledge Graph Completion.

Temporal knowledge graphs (TKGs) are receiving increased attention due to their time-dependent properties and the evolving nature of knowledge over time. TKGs typically contain complex geometric structures, such as hierarchical, ring, and chain structures, which can often be mixed together. However, embedding TKGs into Euclidean space, as is typically done with TKG completion (TKGC) models, presents a challenge when dealing with high-dimensional nonlinear data and complex geometric structures. To address this issue, we propose a novel TKGC model called multicurvature adaptive embedding (MADE). MADE models TKGs in multicurvature spaces, including flat Euclidean space (zero curvature), hyperbolic space (negative curvature), and hyperspherical space (positive curvature), to handle multiple geometric structures. We assign different weights to different curvature spaces in a data-driven manner to strengthen the ideal curvature spaces for modeling and weaken the inappropriate ones. Additionally, we introduce the quadruplet distributor (QD) to assist the information interaction in each geometric space. Ultimately, we develop an innovative temporal regularization to enhance the smoothness of timestamp embeddings by strengthening the correlation of neighboring timestamps. Experimental results show that MADE outperforms the existing state-of-the-art TKGC models.

Analysis of the influence of nonlinear energy sink parameters applicable to helicopter main reduction systems

Abstract In response to the vibration problem of helicopter fuselage caused by continuous rotor periodic excitation force, a nonlinear energy sink is considered to be installed on the main reduction transmission channel to reduce the vibration level of the fuselage. This article conducts an analysis of the influence of nonlinear energy sink structure parameters under harmonic excitation force, establishes a coupled dynamic model of helicopter main reduction/absorber/fuselage, and uses harmonic balance method and stability analysis theory to analyze the periodic solution and stability of the system. Using the vibration amplitude of the system as the evaluation criterion, the influence of damping, stiffness, and mass ratio on the vibration suppression effect of the nonlinear energy sink was explored. The results showed that as the damping of the nonlinear energy sink increased, the resonance frequency of the coupled system shifted to the left, and the vibration amplitude of the main reduction system increased; As the stiffness of the nonlinear energy sink increases, the vibration amplitude of the coupled system will first decrease and then increase, gradually approaching the vibration amplitude of the system without coupled dampers; The influence of mass ratio on system amplitude follows the same trend as the influence of stiffness. By optimizing, the structural parameters of the nonlinear absorber with good vibration suppression effect are ultimately obtained.

Formation and decay of oscillons after inflation in the presence of an external coupling. Part I. Lattice simulations

We investigate the formation and decay of oscillons during the post-inflationary reheating epoch from inflaton oscillations around asymptotically flat potentials V(φ) in the presence of an external coupling of the form 1/2 g 2 φ 2 χ 2. It is well-known that in the absence of such an external coupling, the attractive self-interaction term in the potential leads to the formation of copious amounts of long-lived oscillons both for symmetric and asymmetric plateau potentials. We perform a detailed numerical analysis to study the formation of oscillons in the α-attractor E- and T-model potentials using the publicly available lattice simulation codeCosmoLattice. We observe the formation of nonlinear oscillon-like structures with the average equation of state ⟨wφ ⟩ ≃ 0 for a range of values of the inflaton self-coupling λ and the external coupling g 2. Our results demonstrate that oscillons form even in the presence of an external coupling and we determine the upper bound on g 2 which facilitates oscillon formation. We also find that eventually, these oscillons decay into the scalar inflaton radiation as well as into the quanta of the offspring field χ. Thus, we establish the possibility that reheating could have proceeded through the channel of oscillon decay, along with the usual decay of the oscillating inflaton condensate into χ particles. For a given value of the self-coupling λ, we notice that the lifetime of a population of oscillons decreases with an increase in the strength of the external coupling, following an (approximately) inverse power-law dependence on g 2.

Deep‐Learning Based Causal Inference: A Feasibility Study Based on Three Years of Tectonic‐Climate Data From Moxa Geodynamic Observatory

AbstractHighly sensitive laser strainmeters at Moxa Geodynamic Observatory (MGO) measure motions of the upper Earth's crust. Since the mountain overburden of the laser strainmeters installed in the gallery of the observatory is relatively low, the recorded time series are strongly influenced by local meteorological phenomena. To estimate the nonlinear effect of the meteorological variables on strain measurements in a non‐stationary environment, advanced methods capable of learning the nonlinearity and discovering causal relationships in the non‐stationary multivariate tectonic‐climate time series are needed. Methods for causal inference generally perform well in identifying linear causal relationships but often struggle to retrieve complex nonlinear causal structures prevalent in real‐world systems. This work presents a novel model invariance‐based causal discovery (CDMI) method that utilizes deep networks to model nonlinearity in a multivariate time series system. We propose to use the theoretically well‐established Knockoffs framework to generate in‐distribution, uncorrelated copies of the original data as interventional variables and test the model invariance for causal discovery. To deal with the non‐stationary behavior of the tectonic‐climate time series recorded at the MGO, we propose a regime identification approach that we apply before causal analysis to generate segments of time series that possess locally consistent statistical properties. First, we evaluate our method on synthetically generated time series by comparing it to other causal analysis methods. We then investigate the hypothesized effect of meteorological variables on strain measurements. Our approach outperforms other causality methods and provides meaningful insights into tectonic‐climate causal interactions.

Random Fourier features based nonlinear recurrent kernel normalized LMS algorithm with multiple feedbacks

The performance of kernel adaptive filtering algorithms (KAFs) with nonlinear recurrent structures surpasses traditional KAFs, attributed to the nonlinear contribution of feedback. Nevertheless, the existing nonlinear recurrent KAFs primarily focus on a single feedback output, potentially limiting their latent filtering capabilities. In this paper, we introduce a novel alternative, named nonlinear recurrent kernel normalized least-mean-square with multiple feedbacks (NR-KNLMS-MF), which leverages the information from multiple feedback outputs. Additionally, to tackle the computational complexity challenges associated with KAFs, we integrate random Fourier features (RFF) into NR-KNLMS-MF, resulting in an efficient variant called as RFF-NR-KNLMS-MF. Furthermore, we conduct a theoretical analysis of the mean-square convergence for RFF-NR-KNLMS-MF. Simulation results on time-series predictions demonstrate the superiority of our proposed algorithms over other competing alternatives, validating their effectiveness.

Axion-induced patchy screening of the Cosmic Microwave Background

Cosmic Microwave Background (CMB) photons can undergo resonant conversion into axions in the presence of magnetized plasma distributed inside non-linear large-scale structure (LSS). This process leads to axion-induced patchy screening: secondary temperature and polarization ani­sotropies with a characteristic non-blackbody frequency dependence that are strongly correlated with the distribution of LSS along our past light cone. We compute the axion-induced patchy screening contribution to two- and three- point correlation functions that include CMB anisotropies and tracers of LSS within the halo model. We use these results to forecast the sensitivity of existing and future surveys to photon-axion couplings for axion masses between 2 × 10-13 eV and 3 × 10-12 eV, using a combination of empirical estimates from Planck data of the contribution from instrumental noise and foregrounds as well as modeled contributions on angular scales only accessible with future datasets. We demonstrate that an analysis using Planck and the unWISE galaxy catalogue would be complementary to the most sensitive existing astrophysical axion searches, probing couplings as small as 3 × 10-12 GeV-1, while observations from a future survey such as CMB-S4 could extend this reach by almost an additional order of magnitude.

Discriminative Deep Canonical Correlation Analysis for Multi-View Data.

Over the past few years, multimodal data analysis has emerged as an inevitable method for identifying sample categories. In the multi-view data classification problem, it is expected that the joint representation should include the supervised information of sample categories so that the similarity in the latent space implies the similarity in the corresponding concepts. Since each view has different statistical properties, the joint representation should be able to encapsulate the underlying nonlinear data distribution of the given observations. Another important aspect is the coherent knowledge of the multiple views. It is required that the learning objective of the multi-view model efficiently captures the nonlinear correlated structures across different modalities. In this context, this article introduces a novel architecture, termed discriminative deep canonical correlation analysis (D2CCA), for classifying given observations into multiple categories. The learning objective of the proposed architecture includes the merits of generative models to identify the underlying probability distribution of the given observations. In order to improve the discriminative ability of the proposed architecture, the supervised information is incorporated into the learning objective of the proposed model. It also enables the architecture to serve as both a feature extractor as well as a classifier. The theory of CCA is integrated with the objective function so that the joint representation of the multi-view data is learned from maximally correlated subspaces. The proposed framework is consolidated with corresponding convergence analysis. The efficacy of the proposed architecture is studied on different domains of applications, namely, object recognition, document classification, multilingual categorization, face recognition, and cancer subtype identification with reference to several state-of-the-art methods.

Stochastic design optimization of nonlinear structures under random seismic excitations using incremental dynamic analysis

Stochastic design optimization of nonlinear structures under random seismic excitations using incremental dynamic analysis

Exploiting reprogrammable nonlinear structural springs for enhancing the manoeuvrability of a vibro-impact capsule robot

Vibro-impact capsule robots, propelled by rhythmic collisions of an internal mass triggered by an external magnetic field, are emerging as promising tools for minimally invasive surgery. This innovative actuation mechanism allows for delicate interaction with tissues, making them ideal candidates for navigating confined surgical spaces. However, their limited manoeuvrability and controllability remain significant hurdles, restricting their ability to navigate complex anatomies and perform precise interventions, ultimately hindering their broader clinical applications. This paper investigates the integration of reprogrammable structural springs in capsule robots, demonstrating how dynamic tuning can tailor the interaction between the inner mass and the capsule, thereby unlocking enhanced manoeuvrability and precise control of the capsule robot. A mathematical model describing the dynamic response of a vibro-impact capsule robot integrated with von Mises trusses (VMT), which are used to tailor the interaction between the inner mass and the capsule, is developed and verified using finite element modelling. Using the verified mathematical model, we explore how the transition between mono-stability and bi-stability of VMTs affects the capsule robot’s propelling performance. Our findings demonstrate that this state switch enables four distinct propulsion modes of the capsule robot. This work paves the way for a new paradigm in small-scale robot design by incorporating reprogrammable nonlinear structures. These structures empower the robots with unprecedented manoeuvrability and controllability within a compact, deployable form factor.

Experimental study on impact coupling characteristics of high-pressure accumulator for unconstant-pressurized chamber rock drills

In order to improve the efficiency of unconstant-pressurized chamber rock drills in large-hole and hard-rock conditions, the coupling characteristics of high-pressure accumulator and the impact system were analyzed. The multi-parameter mechanism experiment was designed. Piston displacement, oil return flow, main input-oil, and internal chamber pressure were obtained. Combining the structural characteristics and working principles of rock drills, the experiment-based accumulator volume calculation methods was proposed. According to the phase plane analysis of the accumulator diaphragm and the time series analysis of impact performance parameters, which indicate that the high-pressure accumulator and impact system have typical non-contact nonlinear structures. The dynamic performances also present complex nonlinear characteristics. With the increase of gas pre-charge pressure, the bifurcation points were developed from period-one motions to period-two motions, the coupling degree of flow coupling between the accumulator and the impact piston was gradually enhanced, and the impact performance was gradually improved. With the formation of the period-one motions and the increase of bifurcation strength, the diaphragm became more susceptible to fatigue damage. The optimum choice of high-pressure accumulator gas pre-charge pressure is 80–90 bar, which provides a reference for the application and parameter setting of high-pressure accumulators in unconstant-pressurized chamber rock drills.

A practical multiscale analysis for nonlinear RC structures using a smart substructure replacement strategy

This paper presents a novel practical multiscale analysis (MSA) method for simulating local damages in large reinforced concrete (RC) structures during seismic events. Traditional techniques like the finite element (FE) method often struggle to balance computational costs with detailed simulation. The proposed method facilitates sequential local refinement from macroscopic to mesoscopic scales of RC structures, focusing strategically on critical areas prone to damage and cracking. Key features include: (1) 'Correction forces' enable integration and collaboration among models of different refinement levels, keeping models unchanged (i.e., without additions, deletions, or further refinement of elements), streamlining analysis and independent implementation across methods, scales, and platforms. (2) A smart replacement strategy ensures smooth transitions and prevents abrupt force changes between models at different refinement levels. (3) A ‘training process’ before performing the replacement and a semi-explicit method guarantee the accuracy and efficiency of the MSA method. (4) Parallel and distributed computing is seamlessly applied, significantly accelerating the analysis at each level. Implemented in the open-source software OpenSees, this method is illustrated through three examples that efficiently capture both the macroscopic mechanical responses and detailed local damage behaviors. This approach provides a valuable tool for the refined analysis of large-scale RC structures.

A Spring Model for Pullout Behavior of Curved, Flexible Structures Embedded in Soil

ABSTRACTThe shape and flexibility of embedded structures, such as tree roots, piles, and anchors, have important impacts on the pullout behavior. However, the rate and manner of mobilization of soil resistances along such structures has not been rigorously explored across a wide range of shapes and structural properties. A spring model for computing compatible displacements of the structure and soil for curved, flexible structures is defined, validated against commonly used methods for computing pile pullout behavior, and then parametrically explored to demonstrate how resistances are mobilized along the length of such structures. The present model allows description of combined axial and transverse loading of these nonlinear structures. The simulation results for the case of normally consolidated clay show that the curvature of a structure causes the distribution of bearing resistance to extend further along the structure than for linear cases. The requirement of equilibrium of the structure produces a coupling between the mobilized bearing and tensile resistance in terms of rate of development and magnitude. Thus, the choices of structure shape impact the magnitude and distribution of mobilized resistance of embedded flexible structures. Implications for anchorage of tree root structures and principles of bioinspired design of anchorage systems are discussed.

Newly formed solitary wave solutions and other solitons to the (3+1)-dimensional mKdV–ZK equation utilizing a new modified Sardar sub-equation approach

In this paper, we are going to investigate the (3+1)-dimensional nonlinear modified Korteweg–de Vries-Zakharov–Kuznetsov (mKdV–ZK) equation, which governs the behavior of weakly nonlinear ion acoustic waves in magnetized electron–positron plasma. By taking advantage of the newly proposed modified Sardar sub-equation method, we derive a comprehensive set of exact soliton solutions to the mKdV–ZK equation. Additionally, we provide graphical representations of the solutions, including 2D, 3D, and contour plots, to visualize the characteristics and features of these nonlinear wave structures. These solutions encompass a diverse range of wave patterns, including traveling waves, bright solitons, periodic waves, dark–bright solitons, lump-type solitons, and multi-soliton solutions. The obtained solutions provide valuable insights into the nonlinear behaviors and dynamics exhibited by the mKdV–ZK equation. The success of the new modified Sardar sub-equation method in obtaining a diverse range of solutions for the [Formula: see text]-dimensional mKdV–ZK equation highlights its potential for applications in the analysis of various nonlinear systems in plasma physics and beyond. Also, the study reviewed the superiority of the modified method compared to the Sardar sub-equation method.

Research on random dynamic cylinder deactivation control strategy of engine based on nonlinear model prediction

In the process of cycle cylinder deactivation, the different proportion of cylinder deactivation between adjacent working cycles will cause the problem of uneven operation of each cylinder. In this paper, a random dynamic cylinder deactivation (RD-CDA) control method based on nonlinear model prediction is proposed. The RBF neural network model of the RD-CDA system is built. The K-means algorithm is applied to the offline training of the center position c of the hidden layer node. The P-nearest algorithm is used to train the hidden layer node width σ offline. The recursive least squares (RLS) algorithm is applied to train the output layer weight vector w online. The online adaptive change of the model is realized, and the model verification is carried out. Then, the nonlinear model predictive control system structures with the minimum torque fluctuation and brake specific fuel consumption rate (BSFC) are built respectively. Under different working conditions, the average torque fluctuation per cycle is improved by about 9% to 18.75%, and the average BSFC is improved by about 2 % -3.9 %, which verifies the effectiveness of this strategy in reducing the dynamic fluctuation of random dynamic cylinder deactivation torque and improving fuel economy.

A joint time–space extrapolation approach within the Wiener path integral technique for efficient stochastic response determination of nonlinear systems

A joint time–space extrapolation approach within the Wiener path integral (WPI) technique is developed for determining, efficiently and accurately, the non-stationary stochastic response of diverse nonlinear dynamical systems. The approach can be construed as an extension of a recently developed space-domain extrapolation scheme to account also for the temporal dimension. Specifically, based on a variational principle, the WPI technique yields a boundary value problem (BVP) to be solved for determining a most probable path corresponding to specific final boundary conditions. Further, the most probable path is used for evaluating, approximately, a point of the system response joint probability density function (PDF) corresponding to a specific time instant. Remarkably, the BVP exhibits two unique features that are exploited in this paper for developing an efficient joint time–space extrapolation approach. First, the BVPs corresponding to two neighboring grid points in the spatial domain of the response PDF not only share the same equations, but also the boundary conditions differ only slightly. Second, information inherent in the time-history of an already determined most probable path can be used for evaluating points of the response PDF corresponding to arbitrary time instants, without the need for solving additional BVPs. In a nutshell, relying on the aforementioned unique and advantageous features of the WPI-based BVP, the complete non-stationary response joint PDF is determined, first, by calculating numerically a relatively small number of PDF points, and second, by extrapolating in the joint time–space domain at practically zero additional computational cost. Compared to a standard brute-force implementation of the WPI technique, the developed extrapolation approach reduces the associated computational cost by several orders of magnitude. Two numerical examples relating to an oscillator with asymmetric nonlinearities and fractional derivative elements, and to a nonlinear structure under combined stochastic and deterministic periodic loading are considered for demonstrating the reliability of the extrapolation approach. Juxtapositions with pertinent Monte Carlo simulation data are included as well.

Elastic deep multi-view autoencoder with diversity embedding

Current research on multi-view clustering (MVC) is pushing the boundaries of knowledge, allowing the extraction of valuable insights from various points of view. Recently, many researchers in this field have turned to deep learning techniques, particularly autoencoders (AE). These methods are highly effective at recognizing nonlinear and complex structures, making them a popular choice in this area. However, while they effectively handle Gaussian noise through the use of the Frobenius norm, they exhibit sensitivity to outlier data and Laplacian noise. Additionally, existing multi-view methodologies tend to usually rely on shared information across multi-view data, this means they often miss out on the diverse and complementary information each view can provide, leading in an inadequate utilization of the information available. In this paper, we present an innovative solution to address these challenges. Our novel Elastic Deep Multi-view Autoencoder with Diversity Embedding (EDMVAE-DE) method incorporates an Elastic Deep AE to enhance its robustness. Furthermore, we integrate an exclusivity constraint term to enhance the diversity of specific representations across distinct views, increasing both modeling consistency and diversity within a unified framework. To address problems arising from incorrectly classified neighbors, we also incorporate a graph constraint term. Our experiments, performed on various multi-view datasets, clearly show that EDMVAE-DE achieves the best performance in its class1.

Formation of Conjugated Polymer Monolayer Networks on Water Surface and Nonlinear Charge Transport

AbstractMaterial‐networked conduction paths provide nonlinear electronic properties, which are essential components of computing and physically mimic the brain. In this study, the formation of conjugated polymer monolayer networks and their nonlinear charge transport is demonstrated. Poly(3‐hexylthiophene) (P3HT) monolayer networks doped with 2,3,5,6‐tetrafluoro‐7,7,8,8‐tetracyanoquinodimethane (F4TCNQ) is fabricated using the co‐spread method with an amphiphilic liquid crystal molecule at the air–water interface. Atomic force microscopy and Ultraviolet–visible–near‐infrared absorption spectroscopy measurements reveal the network surface morphologies and doped electronic states. The correlation between the nonlinear electronic characteristics and network structures of the P3HT/F4TCNQ monolayer networks is further systematically investigated through current–voltage and voltage–time measurements for various doping levels, network densities, and numbers of transferred layers. The current–voltage characteristics of the P3HT/F4TCNQ monolayer network device with a simple two‐terminal structure exhibit nonlinear and ohmic conduction behavior, which depend strongly on the network density and geometric dimension (number of transferred layers). It is concluded that the nonlinear properties arise from the limited and unique network of 2D conduction passes. This study highlights the unique features of conducting polymer monolayer networks, paving the way for neuromorphic device applications including conjugated semiconducting polymer‐based material reservoirs with controllable nanostructures.

An improve nonlinear robust control approach for robotic manipulators with PSO-based global optimization strategy

During the trajectory tracking of robotic manipulators, many factors including dead zones, saturation, and uncertain dynamics, greatly increase the modeling and control difficulty. Aiming for this issue, a nonlinear active disturbance rejection control (NADRC)-based control strategy is proposed for robotic manipulators. In this controller, an extended state observer is introduced on basis of the dynamic model, to observe the extend state of model uncertainties and external disturbances. Then, in combination with the nonlinear feedback control structure, the robust trajectory tracking of robotic manipulators is achieved. Furthermore, to optimize the key parameters of the controller, an improved particle swarm optimization algorithm (IPSO) is designed using chaos theory, which improves the tracking accuracy of the proposed NDRC strategy effectively. Finally, using comparative studies, the effectiveness of the proposed control strategy is demonstrated by comparing with several commonly used controllers.

Forecasting of Turkey's Hazelnut Export Amounts According to Seasons with Dendritic Neuron Model Artificial Neural Network

It is seen that artificial neural networks have begun to be used extensively in the literature in solving the time series forecasting problem. In addition to artificial neural networks, classical forecasting methods can often be used to solve this problem. It is seen that classical forecasting methods give successful results for linear time series analysis. However, there is no linear relationship in many time series. Therefore, it can be thought that deep artificial neural networks, which contain more parameters but create more flexible non-linear model structures compared to classical time series forecasting methods, may enable the production of more successful forecasting methods. In this study, the problem of forecasting hazelnut export amounts according to seasons in Turkey with a dendritic neuron model artificial neural network is discussed. In this study, a training algorithm based on the particle swarm optimization algorithm is given for training the dendritic neuron model artificial neural network. The motivation of the study is to investigate Turkey's hazelnut export amounts according to seasons, using a dendritic neuron model artificial neural network. The performance of the proposed method has been compared with artificial neural networks used in the literature.