Nonlinear Part Research Articles

Asymmetry in sagging and hogging responses of a ship hull

In this paper asymmetry in sagging and hogging of a hull progressing in regular waves is investigated by applying a weakly nonlinear potential flow theory. At first instance ship motions in waves are evaluated using a linear strip-theory yielding transfer functions of ship motions and sectional loads. Then, by assuming time-histories of ship motions the nonlinear part of the Froude-Krylov and restoring forces and moments are evaluated using a panel representation. Linear and weakly nonlinear predictions are compared against available model tests for a roll-on/off (Ro-Pax) ship hull. The results confirm that importance of nonlinearities of restoring and Froude-Krylov part of wave loading on asymmetry of sagging and hogging.

Homogenisation of Nonlinear Heterogeneous Thin Plate When the Plate Thickness and In-Plane Heterogeneities are of the Same Order of Magnitude

Summary In this work, we propose a new two-scale finite-strain thin plate theory for highly heterogeneous plates described by a repetitive periodic microstructure. For this type of theory, two scales exist, the macroscopic one is linked to the entire plate and the microscopic one is linked to the size of the heterogeneity. We consider the case when the plate thickness is comparable to in-plane heterogeneities. We assume that the nonlinear macroscopic part of the model is of Kirchhoff–Love type. We obtain the nonlinear homogenised model by performing simultaneously both the homogenisation and the reduction of the initial three-dimensional plate problem to a two-dimensional one. Since nonlinear equations are difficult to solve, we linearise this homogenised Kirchhoff–Love plate theory. Finally, we discuss the treatment of edge effects in the vicinity of the lateral boundary of the plate.

Air-quality prediction based on the ARIMA-CNN-LSTM combination model optimized by dung beetle optimizer

Air pollution is a serious problem that affects economic development and people’s health, so an efficient and accurate air quality prediction model would help to manage the air pollution problem. In this paper, we build a combined model to accurately predict the AQI based on real AQI data from four cities. First, we use an ARIMA model to fit the linear part of the data and a CNN-LSTM model to fit the non-linear part of the data to avoid the problem of blinding in the CNN-LSTM hyperparameter setting. Then, to avoid the blinding dilemma in the CNN-LSTM hyperparameter setting, we use the Dung Beetle Optimizer algorithm to find the hyperparameters of the CNN-LSTM model, determine the optimal hyperparameters, and check the accuracy of the model. Finally, we compare the proposed model with nine other widely used models. The experimental results show that the model proposed in this paper outperforms the comparison models in terms of root mean square error (RMSE), mean absolute error (MAE) and coefficient of determination (R2). The RMSE values for the four cities were 7.594, 14.94, 7.841 and 5.496; the MAE values were 5.285, 10.839, 5.12 and 3.77; and the R2 values were 0.989, 0.962, 0.953 and 0.953 respectively.

A robust class of nonlinear autoregressive models with regression function and dependent innovations using semiparametric kernel estimation

In this study, researchers examine a nonlinear autoregressive (NLAR) time-series model with regression function and dependent innovations in which the errors of the model follow the two-piece scale mixtures of normal (TP-SMN) distributions. Robustness and atypical forms of the proposed class of two-piece distributions along with the flexibility of the nonlinear autoregressive model develop desirable properties which can be applied to several types of datasets. The nonlinear regression function part of the autoregressive time-series model is estimated via the semiparametric and nonparametric curve estimation based on the conditional least square method and nonparametric kernel approach. The maximum likelihood (ML) estimates of the model parameters, using a suitable hierarchical representation of the TP-SMN family on the model are obtained via an expectation maximization (EM)-type algorithm. Performances and usefulness of the proposed model and estimates are shown via simulation studies and a real dataset.

Uniformly valid inference for partially linear high-dimensional single-index models

Uniformly valid inference is obtained for the linear part of a partially linear single-index model with a high-dimensional variable in the single-index part of the model. The linear model part consists of a fixed and limited number of variables, while the control variables in the single-index might consist of a large number of variables that is allowed to grow with the sample size and potentially exceeds the sample size. The unknown function in the nonlinear model part is estimated via B-splines in combination with a ℓ1-regularization to take the high dimensionality into account. We establish uniformly valid inferential properties for the parameters in the linear model part under imperfect selection of the control variables. The numerical results showcase the method’s behavior in practice.

Stability of the 2D anisotropic micropolar Rayleigh–Bénard problem with one direction dissipation

In this paper, we investigate the initial value problem for the 2D anisotropic micropolar Rayleigh–Bénard problem with one direction dissipation. But there are only vertical kinematic viscosity, horizontal angular viscosity, and diffusivity; some nonlinear terms cannot be controlled. In addition to the classical energy functional, we introduce the energy functional to help us dominate the nonlinear parts and make the energy closed. Then based on the energy method and the bootstrapping argument, global smooth solutions are proved under the assumptions of small initial data.

A modified IHB method for nonlinear dynamic and thermal coupling analysis of rotor-bearing systems

This paper presents a modified incremental harmonic balance (IHB) method to analyze the nonlinear dynamic and thermal coupling characteristics of rotor-bearing systems after thermal balance. The IHB method is modified by tensor contraction and fast Fourier transform (FFT) to efficiently calculate the residual vector and Jacobian matrix. Nonlinear dynamic and thermal full coupling is implemented through the nonlinear part of the Jacobian matrix. The presented method achieves the simultaneous and efficient calculation of the motion and heat balance equations in the frequency domain according to the improvement measures. The effectiveness of the presented method is tested using the vibration response and temperature variation analysis for the coupled thermo-mechanical model of a rotor-ball bearing system. Furthermore, the performance comparisons show the good consistency of results between the presented method and the step-by-step (S-S) method, which is a partitioned iterative solution method for dealing with fully coupled problems in the time domain. The presented method has greater computational efficiency, more accurate temperature prediction, and better recognition of nonlinear phenomena in the system rather than the S-S method. Consequently, the presented method has a broad application prospect in solving fully coupled thermo-mechanical problems of more complex and higher dimensional rotor-bearing systems.

NIXO-Based identification of the dominant terms in a nonlinear equation of motion of structures with geometric nonlinearity

The objective of this publication is to propose a novel technique for black-box identification of structures with geometric nonlinearity. The technique is based on a recently introduced frequency-domain system identification method called Nonlinear Identification through eXtended Outputs (NIXO). The proposed algorithm first expresses the nonlinear part of modal equation of motion (EOM) as a general polynomial of high order, and then removes the terms which are determined to be irrelevant to the mechanical system’s response. This division into dominant and irrelevant nonlinear terms relies on the values of two novel indicators that are particular to NIXO. The heuristic presented here was observed to work well only when the tested structure is excited with various swept-sine input signals of different magnitudes (so that the system oscillates at sufficiently distinctive amplitudes in different experimental tests). The technique is first demonstrated on a noise-free numerical case study employing a reduced model of a curved beam. The results obtained are verified via comparing the true Nonlinear Normal Mode (NNM) to the one computed using the modal EOM pointed out by NIXO. Then the method is demonstrated on experimental measurements collected on a 3D-printed flat beam exhibiting significant natural frequency shifts, and the outcomes are verified by overlaying the identified NNMs on the swept-sine responses.

Distributed control of time-delay interconnected nonlinear systems

This paper addresses the distributed control of delayed interconnected nonlinear systems with time-varying delays in both the local subsystems’ dynamics and the physical interconnections among the subsystems. The Takagi–Sugeno fuzzy model with nonlinear consequent parts (N-TS), which is capable to provide less complex representations than standard T–S fuzzy models, is considered to efficiently deal with this class of complex systems. Then, based on Lyapunov–Krasovskii stability arguments, a synthesis condition is proposed to design a distributed control law such that the origin of the closed-loop interconnected system is locally asymptotically stable together with a guaranteed set of admissible initial conditions for which the validity of the N-TS fuzzy model is ensured. Moreover, a quasi-convex optimization procedure is formulated to enlarge the set of admissible initial conditions. The effectiveness of the proposed synthesis condition is validated in two numerical examples, including an interconnected power network with seven generators.

High-precision dynamic torque control of high stiffness actuator for humanoids

The high stiffness actuator (HSA), applied to each joint of an electrical driven humanoid robot, can directly affect the motion performance of the torque-controlled humanoid robots. For high control performance of HSA, a high-precision dynamic torque control (HDTC) is proposed. The HDTC consists of two phases: (1) A novel dynamic current control is used to linearize high stiffness actuator torque control system, which can estimate and compensate the nonlinear coupling parts; (2) An enhanced internal model control is designed to ensure high tracking accuracy in the system containing noisy torque signal and even numerical differentiation signals. Benefitting from dynamic current control and the enhanced internal model control, the proposed HDTC is accurate and adaptable. Finally, the superiority of the HDTC is verified with comparative experiments.

Brain fingerprint is based on the aperiodic, scale-free, neuronal activity

Subject differentiation bears the possibility to individualize brain analyses. However, the nature of the processes generating subject-specific features remains unknown. Most of the current literature uses techniques that assume stationarity (e.g., Pearson's correlation), which might fail to capture the non-linear nature of brain activity. We hypothesize that non-linear perturbations (defined as neuronal avalanches in the context of critical dynamics) spread across the brain and carry subject-specific information, contributing the most to differentiability. To test this hypothesis, we compute the avalanche transition matrix (ATM) from source-reconstructed magnetoencephalographic data, as to characterize subject-specific fast dynamics. We perform differentiability analysis based on the ATMs, and compare the performance to that obtained using Pearson's correlation (which assumes stationarity). We demonstrate that selecting the moments and places where neuronal avalanches spread improves differentiation (P < 0.0001, permutation testing), despite the fact that most of the data (i.e., the linear part) are discarded. Our results show that the non-linear part of the brain signals carries most of the subject-specific information, thereby clarifying the nature of the processes that underlie individual differentiation. Borrowing from statistical mechanics, we provide a principled way to link emergent large-scale personalized activations to non-observable, microscopic processes.

Measures of slope stability in bonded soils governed by linear failure criterion with tensile strength cut-off

The linear failure criterion with a tensile strength cut-off is increasingly applied to geotechnical stability problems in response to the uncertainty originating from the predicted tensile strength in soil. However, several attempts at slope stability analysis have employed classical failure mechanisms with geometrical and computational constraints. In the context of limit analysis, an advanced failure mechanism was utilized in this study for more accurate and comprehensive solutions of practical stability measures, including stability factors and factors of safety. This mechanism delivers lower stability factors and enables the estimation of the traditionally defined factor of safety, particularly in the tensile regime associated with the nonlinear part of the envelope. A technique that transforms the Hoek–Brown rock strength criterion into the equivalent linear failure criterion with a tensile strength cut-off is presented. The factors of safety based on the equivalent Mohr–Coulomb envelope subjected to the tension cut-off showed exceptional agreement with those based on the original Hoek–Brown equation, owing to the truncation of the overestimated strength in the low-stress regime.

Adaptive actor‐critic neural optimal control for constrained nonstrict feedback nonlinear systems via command filter

AbstractThe actor‐critic neural optimal control is investigated for the state‐constrained nonlinear systems in the nonstrict feedback form with unmodeled dynamics in this paper. The filtering errors in the traditional dynamic surface control (DSC) are countervailed by the introduced compensation signals. Two design phases together determine the input: the feedforward input design and the near optimal input design. In the feedforward input design, a mapping rule is established to keep all the states in the finite range, and a first‐order adjunctive signal is designed to treat the unmodeled dynamics. In the near optimal input design, the cost function relying on the reconstructed error system is minimized by the near optimal input via adaptive dynamic programming (ADP). In the whole design processing, the unknown nonlinear uncertain parts are fitted by the radial basis function neural networks (RBFNNs). The stability analysis illustrates all the signals are bounded in the controlled system. Two simulation examples are employed to verify the theoretical findings.

Globally asymptotic stability analysis for memristor‐based competitive systems of reaction–diffusion delayed neural networks

The main aim of this investigation is to present a mathematical criterion that guarantees the global asymptotic stability of special class of nonlinear neural systems. Indeed, a memristor‐based competitive nonlinear reaction–diffusion Cohen–Grossberg neural network system is chosen to be investigated. Chasing the accuracy and comprehensiveness, our model has to be improved with the following elements: neutrality of the nonlinear part and being effected under time delays in the both of straight and neutral parts of the nonlinearity. Since the proposed neural network is novel, so we need to make use of a novel Lyapunov functional correspondingly to globally asymptotic stabilization of the neural network under investigation. Prior to this process, it is necessary to present a uniqueness criterion for solutions of the proposed neural network. To this aim, the well‐known M‐matrix technique of the linear algebra is applied that guarantees existence of a unique equilibrium point of the considered Cohen–Grossberg neural network. Numerical perspective of this investigation leads us to some numerical prototypes that justify our stability criterion is applicable. This investigation will be finalized with interesting discussion on the nature of time delays that are characterized as fundamental elements in modeling of the neural networks.

Integrated Photonic Tensor Processing Unit for a Matrix Multiply: A Review

The explosion of artificial intelligence and machine-learning algorithms, connected to the exponential growth of the exchanged data, is driving a search for novel application-specific hardware accelerators. Among the many, the photonics field appears to be in the perfect spotlight for this global data explosion, thanks to its almost infinite bandwidth capacity associated with limited energy consumption. In this review, we will overview the major advantages that photonics has over electronics for hardware accelerators, followed by a comparison between the major architectures implemented on Photonics Integrated Circuits (PIC) for both the linear and nonlinear parts of Neural Networks. By the end, we will highlight the main driving forces for the next generation of photonic accelerators, as well as the main limits that must be overcome.

Unknown input observers for time-varying delay Takagi–Sugeno fuzzy systems with unmeasured nonlinear consequents

This paper investigates the problem of unknown input observer (UIO) design for Takagi–Sugeno (TS) fuzzy systems with time-varying delay. For observer design, all the unmeasured nonlinearities are isolated in the nonlinear consequent parts of TS fuzzy systems. This allows dealing with the well-known issue related to unmeasured premise variables for TS fuzzy observer design in a more effective fashion via the mean value theorem. Using the unknown input (UI) decoupling technique, no a priori information on the UI is needed for the proposed TS fuzzy observer design, which can guarantee the asymptotic estimations of both the system state and the unknown input. Employing a fuzzy Lyapunov–Krasovskii functional with a suitable augmented vector, the effect of time-varying delay on the estimation error dynamics is taken into account in the observer design. Numerical examples are presented to demonstrate the effectiveness of the proposed fuzzy UIO design method for nonlinear time-varying delay systems.

A high order accurate numerical algorithm for the space-fractional Swift-Hohenberg equation

This paper presents a high order time discretization method by combining the time splitting scheme with semi-implicit spectral deferred correction method for the space-fractional Swift-Hohenberg equation (SFSH). Based on the operator splitting method, the original problem is split into linear and nonlinear subproblems, respectively. The Fourier spectral method is adopted for the linear part, and a first-order accurate finite difference scheme in time together with the Fourier spectral method in space is used for the nonlinear part. The stability and convergence of the obtained numerical scheme are analyzed theoretically. Moreover, the spectral deferred correction (SDC) method is then employed to improve the temporal accuracy. Various two and three dimensional numerical experiments are performed to validate the theoretical results and efficiency of the proposed method.

Stock Price Prediction using ML algorithms

Abstract: Stock Price Prediction using ML( Machine Learning) helps to determine the unborn value of stocks of any fiscal means traded on an exchange. The entire generality of prognosticating stock prices is to gain significant gains by minimizing losses vaticinating the stock request price is always challenging for numerous business judges and experimenters. vaticination of the stock request plays a vital part in the stock business. The compass gradationally expanded. The time series model cannot contribute to the non-linear part of the stock data and is therefore hamstrung for the long term, and LSTM neural network makes better use of non-sequential data and has better use of sequence data. Useful information in the long term which makes the root mean square error of the vaticination result, the LSTM neural network needs lower than the time series model, showing LSTM is a better stock price soothsaying system. Machine Learning approach to predict or sense the behavior tracking of the stock market Sensex. Random Forest is the Machine Learning model implemented effectively in predicting the stock prices anddefining the activity between the exchanges the securities between the buyers and sellers.

Asymptotic analysis for a second-order curved thin film

We consider a second-order thin curved film whose behavior is governed by an energy made up of a first-order nonlinear part depending on the gradient of the deformation augmented by a quadratic second-order part depending on the tensor of second derivatives of the deformation. We carry out a 3D–2D analysis through an asymptotic expansion in powers of the thickness of the film as it tends to zero.

Current mode multi scroll chaotic oscillator based on CDTA

Compared to voltage mode circuits, current mode circuits have advantages such as large dynamic range, fast speed, wide frequency band, and good linearity. In recent years, the development of call flow modeling technology has been rapid and has become an important foundation for analog integrated circuits. In this paper, a current mode chaotic oscillation circuit based on current differential transconductance amplifier (CDTA) is proposed. This proposed circuit fully utilizes the advantages of current differential transconductance amplifier: a current input and output device with a large dynamic range, virtual ground at the input, extremely low input impedance, and high output impedance. The linear and non-linear parts of the proposed circuit operate in current mode, enabling a true current mode multi scroll chaotic circuit. Pspice simulation results show that the current mode chaotic circuit proposed can generate multi scroll chaotic attractors.