Linear Components Research Articles

NUMERICAL SOLUTIONS OF THIRD ORDER FREDHOLM INTEGRO DIFFERENTIAL EQUATION VIA LINEAR MULTISTEP-QUADRATURE FORMULAE

In this study, we present a 6-step linear multistep mehod in union with some newton-cote quadrature family for solving third order Linear Fredholm Integro-Differential Equation(LIDE). The schemes were derived using Vieta-Pell-Lucas Polynomial as the approximating function. The linear multi-step component is for the non integral part while the quadrature family is for the Integral part. The quaudrature methods Boole , Simpson 3/8 and Trapezoidal rule were separately combined with the linear multistep method. The qualititaive analysis of the scheme revealed that the method is consistence, stable and convergent. In order to further attest to the behavioural attribute of the methods, numerical experiments were carried out on some selected Initial Value Problems.The results from the tested problems and their absolute errors of deviation revealed that the new method is very suitbale for solution to the tested problems. The scheme when combined with Boole and Simpson 3/8 merhod, performed better with Tracendental function than when combined with Trapezoidal rule and vice –versa. The results further showed that the proposed method perform creditably well with lesser computional steps when compared with some existing methods when applied to the selected examples.

Variational principles for a double Rayleigh beam system undergoing vibrations and connected by a nonlinear Winkler–Pasternak elastic layer

Abstract Variational principles and variationally consistent boundary conditions are derived for a system of double Rayleigh beams undergoing vibrations and subject to axial loads. The elastic layer connecting the beams are modelled as a three-parameter nonlinear Winkler–Pasternak layer with the Winkler layer having linear and nonlinear components and Pasternak layer having only a linear component. Variational principles are derived for the forced and freely vibrating double beam system using a semi-inverse approach. Hamilton’s principle for the system is given and the Rayleigh quotients are derived for the vibration frequency of the freely vibrating system and for the buckling load. Natural and geometric variationally consistent boundary conditions are derived which leads to a set of coupled boundary conditions due to the presence of Pasternak layer connecting the beams.

LDER: a classification framework based on ERP enhancement in RSVP task

Objective. Rapid serial visual presentation (RSVP) based on electroencephalography (EEG) has been widely used in the target detection field, which distinguishes target and non-target by detecting event-related potential (ERP) components. However, the classification performance of the RSVP task is limited by the variability of ERP components, which is a great challenge in developing RSVP for real-life applications. Approach. To tackle this issue, a classification framework based on the ERP feature enhancement to offset the negative impact of the variability of ERP components for RSVP task classification named latency detection and EEG reconstruction was proposed in this paper. First, a spatial-temporal similarity measurement approach was proposed for latency detection. Subsequently, we constructed a single-trial EEG signal model containing ERP latency information. Then, according to the latency information detected in the first step, the model can be solved to obtain the corrected ERP signal and realize the enhancement of ERP features. Finally, the EEG signal after ERP enhancement can be processed by most of the existing feature extraction and classification methods of the RSVP task in this framework. Main results. Nine subjects were recruited to participate in the RSVP experiment on vehicle detection. Four popular algorithms (spatially weighted Fisher linear discrimination-principal component analysis (PCA), hierarchical discriminant PCA, hierarchical discriminant component analysis, and spatial-temporal hybrid common spatial pattern-PCA) in RSVP-based brain–computer interface for feature extraction were selected to verify the performance of our proposed framework. Experimental results showed that our proposed framework significantly outperforms the conventional classification framework in terms of area under curve, balanced accuracy, true positive rate, and false positive rate in four feature extraction methods. Additionally, statistical results showed that our proposed framework enables better performance with fewer training samples, channel numbers, and shorter temporal window sizes. Significance. As a result, the classification performance of the RSVP task was significantly improved by using our proposed framework. Our proposed classification framework will significantly promote the practical application of the RSVP task.

Improving Hybrid Models for Precipitation Forecasting by Combining Nonlinear Machine Learning Methods

AbstractPrecipitation forecast is key for water resources management in semi-arid climates. The traditional hybrid models simulate linear and nonlinear components of precipitation series separately. But they do not still provide accurate forecasts. This research aims to improve hybrid models by using an ensemble of linear and nonlinear models. Preprocessing configurations and each of the Gene Expression Programming (GEP), Support Vector Regression (SVR), and Group Method of Data Handling (GMDH) models were used as in the traditional hybrid models. They were compared against the proposed hybrid models with a combination of all these three models. The performance of the hybrid models was improved by different methods. Two weather stations of Tabriz and Rasht in Iran with respectively annual and monthly time steps were selected to test the improved models. The results showed that Theil’s coefficient, which measures the inequality degree to which forecasts differ from observations, improved by 9% and 15% for SVR and GMDH relative to GEP for the Tabriz station. The applied error criteria indicated that the proposed hybrid models have a better representation of observations than the traditional hybrid models. Mean square error decreased by 67% and Nash Sutcliffe increased by 5% in the Rasht station when we combined the three machine learning models using genetic algorithm instead of SVR. Generally, the representation of the nonlinear models within the improved hybrid models showed better performance than the traditional hybrid models. The improved models have implications for modeling highly nonlinear systems using the full advantages of machine learning methods.

Microring-based programmable coherent optical neural networks.

Coherent programmable integrated photonics circuits have shown great potential as specialized hardware accelerators for deep learning tasks, which usually involve the use of linear matrix multiplication and nonlinear activation components. We design, simulate and train an optical neural network fully based on microring resonators, which shows advantages in terms of device footprint and energy efficiency. We use tunable coupled double ring structures as the interferometer components for the linear multiplication layers and modulated microring resonators as the reconfigurable nonlinear activation components. We then develop optimization algorithms to train the direct tuning parameters such as applied voltages based on the transfer matrix method and using automatic differentiation for all optical components.

Wind power forecasting: A hybrid forecasting model and multi-task learning-based framework

Accurate forecasting of wind power is of significance for scheduling the grid system when wind power is integrated. However, the deficiency of the training data restricts the models’ forecasting performance and modeling efficiency. In this study, we propose a hybrid forecasting model that is composed of a dual dilated convolution-based self-attention sub-model and an autoregressive sub-model. The dual-branch sub-model utilizes a dual convolution architecture to extract both global and local temporal patterns before capturing attention-based dependencies between multivariate inputs to reflect non-linear correlations. The autoregressive sub-model learns linear correlations to provide supplementary information that compensates for the insensitivity of model response. Furthermore, a multi-task learning-based framework is designed to address insufficient training data of a new turbine cluster. The framework can be divided into one task-shared linear component and multiple task-specific non-linear components. By weighting multiple forecasting tasks, the proposed framework utilizes the collaborative relationships between tasks to improve accuracy on the target turbines. Experiment results show that the proposed forecasting model presents the better forecasting accuracy on actual datasets, and the framework has a significant improvement of 20.08% in accuracy while further reducing dependence on training data, especially for source domain data in transfer learning.

Simulation of non-Hermitian disordered systems in linear circuits

Non-Hermitian skin effect (NHSE) is a novel phenomenon appearing in non-Hermitian systems. Here, we report the experimental observation of NHSE. Different from the previous non-reciprocal circuit implementation scheme using logic components, we construct our one-dimensional (1D) circuits using linear components only. Besides, we achieve the non-reciprocity by proportionally varying the parameter value of the components. By measuring the voltage response of each site, the information of eigenstates can be mapped out. The results show that the voltage response is always larger on one end of the circuit no matter on which end voltage driving is applied, indicating clearly the presence of the NHSE. Furthermore, we also simulate the interplay of NHSE and Anderson localization (AL) when additional disorder is introduced. Upon increasing the disorder strength, we observe the transformation from the skin effect phase to the localized phase. In the regime of skin effect phase, the eigenstates are all localized at one edge while eigenstates are affected by the voltage supply input in localized phase. Our findings unveil a possible new route for simulation of topological phenomena in non-Hermitian systems.

Fractional Effective Quark-Antiquark Interaction in Symplectic Quantum Mechanics

Considering the formalism of symplectic quantum mechanics, we investigate a two-dimensional nonrelativistic strong interacting system, describing a bound heavy quark-antiquark state. The potential has a linear component that is analyzed in the context of generalized fractional derivatives. For this purpose, the Schrödinger equation in phase space is solved with the linear potential. The ground state solution is obtained and analyzed through the Wigner function for the meson c c ¯ . One basic and fundamental result is that the fractional quantum phase-space analysis gives rise to the confinement of quarks in the meson, consistent with experimental results.

Genome Mining in Glass Chemistry Using Linear Component Analysis of Ion Conductivity Data.

Understanding the multivariate origin of physical properties is particularly complex for polyionic glasses. As a concept, the term genome has been used to describe the entirety of structure-property relations in solid materials, based on functional genes acting as descriptors for a particular property, for example, for input in regression analysis or other machine-learning tools. Here, the genes of ionic conductivity in polyionic sodium-conducting glasses are presented as fictive chemical entities with a characteristic stoichiometry, derived from strong linear component analysis (SLCA) of a uniquely consistent dataset. SLCA is based on a twofold optimization problem that maximizes the quality of linear regression between a property (here: ionic conductivity) and champion candidates from all possible combinations of elements. Family trees and matrix rotation analysis are subsequently used to filter for essential elemental combinations, and from their characteristic mean composition, the essential genes. These genes reveal the intrinsic relationships within the multivariate input data. While they do not require a structural representation in real space, how possible structural interpretations agree with intuitive understanding of structural entities known from spectroscopic experiments is finally demonstrated.

Vibration Analysis of a Nonlinear Absorber Coupled to a Hand-Held Impact Machine

Abstract Exposure of human hands to harmful levels of vibration can lead to severe injuries. To attenuate these hand transmitted vibrations, a nonlinear vibration absorber inerter (NVAI) is proposed in this work. The proposed NVAI is attached to a coupled nonlinear system of a hand-held impact machine and a hand-arm system. The combined coupled nonlinear system is modeled as a lumped parameter model with a combination of cubic and linear stiffness components, linear viscous dampers, and lumped masses. The governing equations of motion are solved analytically using the method of harmonic balance and validated using numerical simulations. A numerical bifurcation diagram of the system reveals the existence of complex solutions such as quasi-periodic and chaotic attractors. The appearances of quasi-periodic and chaotic attractors are later confirmed by Lyapunov exponents. Further, we explore the ability of the proposed NVAI to decrease the area corresponding to unstable quasi-periodic and chaotic motion in the excitation amplitude–frequency space. This observation further implies the delay in the onset of quasi-periodic and chaotic motion for a range of forcing amplitude using Lyapunov exponents. Finally, parametric analyses are carried out to identify the critical design parameters of the NVAI. These analyses reveal that an increase in the damping, mass, and inertance of the absorber ameliorates the performance of the NVAI. Furthermore, the critical value of the external excitation, corresponding to a sudden change in the response of the system, can be controlled using an appropriate selection of absorber parameters.

Model order reduction via substructuring for a nonlinear, differential‐algebraic machine tool model with moving loads

AbstractMachine tools are permanently exposed to complex static, dynamic and thermic loads. This often results in an undesired displacement of the tool center point (TCP), causing errors in the production process and thus limiting the achievable workpiece quality. Recent research efforts try to counter these effects by process‐parallel solutions utilizing machine internal data. Therefore, fast simulation models are a fundamental requirement. Here, model order reduction (MOR) becomes crucial. The resulting low‐dimensional models are required for various applications, e.g., in digital twins, the correction of thermally induced errors at the TCP during the production process as well as for lifetime calculations in predictive maintenance. In this contribution, we present a strategy of MOR for a coupled thermo‐mechanical model with a nonlinear subsystem and moving loads, using the example of a feed axis with nonlinear machine components. Applying tailored substructuring techniques, we are able to separate the linear and nonlinear system components. This allows to apply classic linear MOR methods to the much larger linear part, whereas the small nonlinear part is kept, and thus enables drastically reduced computing times. The relative movement is considered by a switched system approach. Transient thermo‐mechanical interactions of the feed axis are calculated in a final investigation, comparing the performance of the resulting reduced‐order model and the original one.

A Hybrid Univariate Traffic Congestion Prediction Model for IoT-Enabled Smart City

IoT devices collect time-series traffic data, which is stochastic and complex in nature. Traffic flow prediction is a thorny task using this kind of data. A smart traffic congestion prediction system is a need of sustainable and economical smart cities. An intelligent traffic congestion prediction model using Seasonal Auto-Regressive Integrated Moving Average (SARIMA) and Bidirectional Long Short-Term Memory (Bi-LSTM) is presented in this study. The novelty of this model is that the proposed model is hybridized using a Back Propagation Neural Network (BPNN). Instead of traditionally presuming the relationship of forecasted results of the SARIMA and Bi-LSTM model as a linear relationship, this model uses BPNN to discover the unknown function to establish a relation between the forecasted values. This model uses SARIMA to handle linear components and Bi-LSTM to handle non-linear components of the Big IoT time-series dataset. The “CityPulse EU FP7 project” is a freely available dataset used in this study. This hybrid univariate model is compared with the single ARIMA, single LSTM, and existing traffic prediction models using MAE, MSE, RMSE, and MAPE as evaluation indicators. This model provides the lowest values of MAE, MSE, RMSE, and MAPE as 0.499, 0.337, 0.58, and 0.03, respectively. The proposed model can help to predict the vehicle count on the road, which in turn, can enhance the quality of life for citizens living in smart cities.

Satellite retrieval of the linear polarization components of the water-leaving radiance in open oceans.

Atmospheric correction (AC) of polarized radiances acquired by polarization satellite sensors, remains a challenge due to the complex radiative transfer processes of the coupled ocean-atmosphere system. In this study, we proposed an innovative polarized AC algorithm built on the near-infrared band (PACNIR) with an emphasis on the retrieval of the linear polarization components of the water-leaving radiance in clear open oceans. This algorithm was based on the black ocean assumption in the near-infrared band and fitted polarized radiance measurements along multiple observation directions with nonlinear optimized processing. Our retrieval algorithm notably inverted the linearly polarized components of the water-leaving radiance and aerosol parameters. Compared with that of the simulated linear polarization components of the water-leaving radiance via the vector radiative transfer model for the studied sea regions, the mean absolute error of the PACNIR-retrieved linearly polarized components (nQw and nUw) exhibited a magnitude of 10-4, while the magnitude of that of the simulated nQw and nUw data was 10-3. Moreover, the PACNIR-retrieved aerosol optical thicknesses at 865 nm exhibited a mean absolute percentage error of approximately 30% relative to in situ values obtained from Aerosol Robotic Network-Ocean Color (AERONET-OC) sites. The PACNIR algorithm could facilitate AC of the polarized data provided by the next generation of multiangle polarization satellite ocean color sensors.

Exploring neural heterogeneity in inattention and hyperactivity

Inattention and hyperactivity are cardinal symptoms of Attention Deficit Hyperactivity Disorder (ADHD). These characteristics have also been observed across a range of other neurodevelopmental conditions, such as autism and dyspraxia, suggesting that they might best be studied across diagnostic categories. Here, we evaluated the associations between inattention and hyperactivity behaviours and features of the structural brain network (connectome) in a large transdiagnostic sample of children (Centre for Attention, Learning, and Memory; n = 383). In our sample, we found that a single latent factor explains 77.6% of variance in scores across multiple questionnaires measuring inattention and hyperactivity. Partial Least-Squares (PLS) regression revealed that variability in this latent factor could not be explained by a linear component representing nodewise properties of connectomes. We then investigated the type and extent of neural heterogeneity in a subset of our sample with clinically-elevated levels of inattention and hyperactivity. Multidimensional scaling combined with k-means clustering revealed two neural subtypes in children with elevated levels of inattention and hyperactivity (n = 232), differentiated primarily by nodal communicability—a measure which demarcates the extent to which neural signals propagate through specific brain regions. These different clusters had similar behavioural profiles, which included high levels of inattention and hyperactivity. However, one of the clusters scored higher on multiple cognitive assessment measures of executive function. We conclude that inattention and hyperactivity are so common in children with neurodevelopmental difficulties because they emerge through multiple different trajectories of brain development. In our own data, we can identify two of these possible trajectories, which are reflected by measures of structural brain network topology and cognition.

Identification of Nonlinear Systems Using the Hammerstein-Wiener Model with Improved Orthogonal Functions

Hammerstein-Wiener systems present a structure consisting of three serial cascade blocks. Two are static nonlinearities, which can be described with nonlinear functions. The third block represents a linear dynamic component placed between the first two blocks. Some of the common linear model structures include a rational-type transfer function, orthogonal rational functions (ORF), finite impulse response (FIR), autoregressive with extra input (ARX), autoregressive moving average with exogenous inputs model (ARMAX), and output-error (O-E) model structure. This paper presents a new structure, and a new improvement is proposed, which is consisted of the basic structure of Hammerstein-Wiener models with an improved orthogonal function of Müntz-Legendre type. We present an extension of generalised Malmquist polynomials that represent Müntz polynomials. Also, a detailed mathematical background for performing improved almost orthogonal polynomials, in combination with Hammerstein-Wiener models, is proposed. The proposed approach is used to identify the strongly nonlinear hydraulic system via the transfer function. To compare the results obtained, well-known orthogonal functions of the Legendre, Chebyshev, and Laguerre types are exploited.

Partially Linear Component Support Vector Machine for Primary Energy Consumption Forecasting of the Electric Power Sector in the United States

Energy forecasting based on univariate time series has long been a challenge in energy engineering and has become one of the most popular tasks in data analytics. In order to take advantage of the characteristics of observed data, a partially linear model is proposed based on principal component analysis and support vector machine methods. The principal linear components of the input with lower dimensions are used as the linear part, while the nonlinear part is expressed by the kernel function. The primal-dual method is used to construct the convex optimization problem for the proposed model, and the sequential minimization optimization algorithm is used to train the model with global convergence. The univariate forecasting scheme is designed to forecast the primary energy consumption of the electric power sector of the United States using real-world data sets ranging from January 1973 to January 2020, and the model is compared with eight commonly used machine learning models as well as the linear auto-regressive model. Comprehensive comparisons with multiple evaluation criteria (including 19 metrics) show that the proposed model outperforms all other models in all scenarios of mid-/long-term forecasting, indicating its high potential in primary energy consumption forecasting.

An Improved Genetic-XGBoost Classifier for Customer Consumption Behavior Prediction

AbstractIn an increasingly competitive market, predicting the customer’s consumption behavior has a vital role in customer relationship management. In this study, a new classifier for customer consumption behavior prediction is proposed. The proposed methods are as follows: (i) A feature selection method based on least absolute shrinkage and selection operator (Lasso) and Principal Component Analysis (PCA), to achieve efficient feature selection and eliminate correlations between variables. (ii) An improved genetic-eXtreme Gradient Boosting (XGBoost) for customer consumption behavior prediction, to improve the accuracy of prediction. Furthermore, the global search ability and flexibility of the genetic mechanism are used to optimize the XGBoost parameters, which avoids inaccurate parameter settings by manual experience. The adaptive crossover and mutation probabilities are designed to prevent the population from falling into the local extremum. Moreover, the grape-customer consumption behavior dataset is employed to compare the six Lasso-based models from the original, normalized and standardized data sources with the Isometric Mapping, Locally Linear Embedding, Multidimensional Scaling, PCA and Kernel Principal Component Analysis methods. The improved genetic-XGBoost is compared with several well-known parameter optimization algorithms and state-of-the-art classification approaches. Furthermore, experiments are conducted on the University of California Irvine datasets to verify the improved genetic-XGBoost algorithm. All results show that the proposed methods outperform the existing ones. The prediction results provide the decision-making basis for enterprises to formulate better marketing strategies.

An Application of the Melnikov Method to a Piecewise Oscillator

In this paper we present a new application of the Melnikov method to a class of periodically perturbed Duffing equations where the nonlinearity is non-smooth as otherwise required in the classical applications. Extensions of the Melnikov method to these situations is a topic with growing interests from the researchers in the past decade. Our model, motivated by the study of mechanical vibrations for systems with ''stops'', considers a case of a nonlinear equation with piecewise linear components. This allows us to provide a precise analytical representation of the homoclinic orbit for the associated autonomous planar system and thus obtain simply computable conditions for the zeros of the associated Melnikov function.

Binary Coati Optimization Algorithm- Multi- Kernel Least Square Support Vector Machine-Extreme Learning Machine Model (BCOA-MKLSSVM-ELM): A New Hybrid Machine Learning Model for Predicting Reservoir Water Level

Predicting reservoir water levels helps manage droughts and floods. Predicting reservoir water level is complex because it depends on factors such as climate parameters and human intervention. Therefore, predicting water level needs robust models. Our study introduces a new model for predicting reservoir water levels. An extreme learning machine, the multi-kernel least square support vector machine model (MKLSSVM), is developed to predict the water level of a reservoir in Malaysia. The study also introduces a novel optimization algorithm for selecting inputs. While the LSSVM model may not capture nonlinear components of the time series data, the extreme learning machine (ELM) model—MKLSSVM model can capture nonlinear and linear components of the time series data. A coati optimization algorithm is introduced to select input scenarios. The MKLSSVM model takes advantage of multiple kernel functions. The extreme learning machine model—multi-kernel least square support vector machine model also takes the benefit of both the ELM model and MKLSSVM model models to predict water levels. This paper’s novelty includes introducing a new method for selecting inputs and developing a new model for predicting water levels. For water level prediction, lagged rainfall and water level are used. In this study, we used extreme learning machine (ELM)-multi-kernel least square support vector machine (ELM-MKLSSVM), extreme learning machine (ELM)-LSSVM-polynomial kernel function (PKF) (ELM-LSSVM-PKF), ELM-LSSVM-radial basis kernel function (RBF) (ELM-LSSVM-RBF), ELM-LSSVM-Linear Kernel function (LKF), ELM, and MKLSSVM models to predict water level. The testing means absolute of the same models was 0.710, 0.742, 0.832, 0.871, 0.912, and 0.919, respectively. The Nash–Sutcliff efficiency (NSE) testing of the same models was 0.97, 0.94, 0.90, 0.87, 0.83, and 0.18, respectively. The ELM-MKLSSVM model is a robust tool for predicting reservoir water levels.

Considerations on the modified Maxwell electrodynamics in the presence of an electric and magnetic background

The properties of the modified Maxwell electrodynamics (ModMax) are investigated in the presence of external and uniform electric and magnetic fields. We expand the nonlinear theory around an electromagnetic background up to second order in the propagating fields to obtain the permittivity and permeability tensors, dispersion relations, group velocity and refractive indices as functions of external fields. The case with perpendicular background fields is contemplated. The phenomenon of birefringence is discussed and the fundamental role of the ModMax parameter becomes clear. We calculate the difference of the refractive indices in terms of this parameter and the external fields. Finally, we set up a scenario where the axion is present and compute the interaction energy for the coupled axion-ModMax electrodynamics if a magnetic background field is considered. This calculation is carried out in the framework of the gauge-invariant, but path-dependent variables formalism. Our results show that the interaction energy contains a linear component, leading to the confinement of static probe charges where the interference between the ModMax parameter, the axion mass, and the axion-photon coupling constant is pointed out.