SOLVING 2-D NONLINEAR COUPLED HEAT AND MOISTURE TRANSFER PROBLEMS VIA A SELF-ADAPTIVE PRECISE ALGORITHM IN TIME DOMAIN

A self-adaptive precise algorithm in the time domain was employed to solve 2-D nonlinear coupled heat and moisture transfer problems. By expanding variables at a discretized time interval, the variations of variables can be described more precisely,and a nonlinear coupled initial and boundary value problem was converted into a series of recurrent linear boundary value problems which are solved by FE technique. In the computation, no additional assumption and the nonlinear iteration are required, and a criterion for self-adaptive computation is proposed to maintain sufficient computing accuracy for the change sizes of time steps. In the numerical comparison, the variations of material properties with temperature, moisture content, and both temperature and moisture content are taken into account, respectively. Satisfactory results have been obtained, indicating that the proposed approach is capable of dealing with complex nonlinear problems.

Exact Time Domain Solutions of 1-D Transient Dynamic Piezoelectric Problems with Nonlinear Damper Boundary Conditions

Novel exact solutions of one-dimensional transient dynamic piezoelectric problems for thickness polarized layers and disks, or length polarized rods, are obtained. The solutions are derived using a time-domain Green’s function method that leads to an exact analytical recursive procedure which is applicable for a wide variety of boundary conditions including nonlinear cases. A nonlinear damper boundary condition is considered in more detail. The corresponding nonlinear relationship between stresses and velocities at a current time moment is used in the recursive procedure. In addition to the exact recursive procedure that is effective for calculations, some new practically important explicit exact solutions are presented. Several examples of the time behavior of the output electric potential difference are given to illustrate the effectiveness of the proposed exact approach.

Nonlinear Time History Analysis for the Different Column Orientations under Seismic Wave Synthetic Approach

The significant impact of earthquakes on human lives and the built environment underscores the extensive human and economic losses caused by structural collapses. Over the years, researchers have focused on improving seismic design to mitigate earthquake-induced damages and enhance structural performance. In this study, a specific reinforced concrete (RC) frame structure at Kyungpook National University, designed for educational purposes, is analyzed as a representative case. Utilizing SAP 2000, the research conducts a nonlinear time history analysis to assess the structural performance under seismic conditions. The primary objective is to evaluate the influence of different column section designs, while maintaining identical column section areas, on structural behavior. The study employs two distinct seismic waves from Abeno (ABN) and Takatori (TKT) for the analysis, comparing the structural performance under varying seismic conditions. Key aspects examined include displacement, base shear force, base moment, joint radians, and layer displacement angle. This research is anticipated to serve as a valuable reference for seismic restraint reinforcement work on RC buildings, enriching the methods used for evaluating structures through nonlinear time history analysis based on the synthetic seismic wave approach.

NONLINEAR DRIFT MOTION SIMULATION OF MULTI-CHAIN MOORING BUOY IN TIME DOMAIN

This paper deals with the nonlinear effect of the drift motion of multi-chain mooring buoys. The buoy's motion in time domain is determined for the case that the wave and mooring force are nonlinear. The Kotorayama's method of hydrodynamic effect in a single mooring chain is expanded to multi-mooring chains. The time history of drift motion of the mooring buoy in regular waves and wave groups is calculated. The relation between the drift motion and the wave height or difference frequency is discussed. It can be shown that the effect of the hydrodynamic force acting on the mooring chain has remarkable influence on the total drift motion of the mooring buoy. In a wave group, its amplitude is mainly controled by the wave height and has little relation with difference frequency.

Prescribed Performance Tracking Control of Time-Delay Nonlinear Systems With Output Constraints

The problem of prescribed performance tracking control for unknown time-delay nonlinear systems subject to output constraints is dealt with in this paper. In contrast with related works, only the most fundamental requirements, i.e., boundedness and the local Lipschitz condition, are assumed for the allowable time delays. Moreover, we focus on the case where the reference is unknown beforehand, which renders the standard prescribed performance control designs under output constraints infeasible. To conquer these challenges, a novel robust prescribed performance control approach is put forward in this paper.Herein, a reverse tuning function is skillfully constructed and automatically generates a performance envelop for the tracking error. In addition, a unified performance analysis framework based on proof by contradiction and the barrier function is established to reveal the inherent robustness of the control system against the time delays. It turns out that the system output tracks the reference with a preassigned settling time and good accuracy,without constraint violations. A comparative simulation on a two-stage chemical reactor is carried out to illustrate the above theoretical findings.

Linear and Nonlinear Time Domain Block Equalizers on MIMO Frequency Selective Channels

Single-Carrier (SC) transmission with the same bandwidth as Multi-Carrier (MC) transmission (such as OFDM) may have far shorter symbol duration and is considered to be more robust against time selective fading. In this paper, we proposed the novel equalization and signal separation schemes in time domain for short block length transmission, i.e., Block Linear Equalization (BLE) and Block Nonlinear Equalization (BNLE) on MIMO frequency selective fading channels. The proposed BLE uses the MMSE based inverse matrix in time domain and the BNLE utilizes the QRD-M (QR Decomposition with M algorithm) with appropriate receiver complexity. We compared the computational complexity among the conventional SC-FDE (Frequency Domain Equalization) scheme and the proposed equalizers. We also used the Low-Density Parity Check (LDPC) decoder concatenated to the proposed BLE and BNLE.

MINIMIZERS OF L^(2)-SUBCRITICAL VARIATIONAL PROBLEMS WITH SPATIALLY DECAYING NONLINEARITIES IN BOUNDED DOMAINS

This paper is concerned with the minimizers of L^(2)-subcritical constraint variar tional problems with spatially decaying nonlinearities in a bounded domain Ω of R~N(N≥1).We prove that the problem admits minimizers for any M> 0.Moreover,the limiting behavior of minimizers as M→∞ is also analyzed rigorously.

Quasi-anti-parity–time-symmetric single-resonator micro-optical gyroscope with Kerr nonlinearity

Parity–time(PT) and quasi-anti-parity–time(quasi-APT) symmetric optical gyroscopes have been proposed recently which enhance Sagnac frequency splitting. However, the operation of gyroscopes at the exceptional point(EP) is challenging due to strict fabrication requirements and experimental uncertainties. We propose a new quasi-APT-symmetric micro-optical gyroscope which can be operated at the EP by easily shifting the Kerr nonlinearity. A single resonator is used as the core sensitive component of the quasi-APT-symmetric optical gyroscope to reduce the size, overcome the strict structural requirements and detect small rotation rates. Moreover, the proposed scheme also has an easy readout method for the frequency splitting. As a result, the device achieves a frequency splitting 10~5 times higher than that of a classical resonant optical gyroscope with the Earth's rotation. This proposal paves the way for a new and valuable method for the engineering of micro-optical gyroscopes.

Highly Accurate Golden Section Search Algorithms and Fictitious Time Integration Method for Solving Nonlinear Eigenvalue Problems

This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solved from a nonhomogeneous linear system obtained by reducing the number of eigen-equation one less,where one of the nonzero components of the eigenvector is normalized to the unit and moves the column containing that component to the right-hand side as a nonzero input vector.1D and 2D golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues.Simultaneously,the real and complex eigenvectors can be computed very accurately.A simpler approach to the nonlinear eigenvalue problems is proposed,which implements a normalization condition for the uniqueness of the eigenvector into the eigenequation directly.The real eigenvalues can be computed by the fictitious time integration method(FTIM),which saves computational costs compared to the one-dimensional golden section search algorithm(1D GSSA).The simpler method is also combined with the Newton iterationmethod,which is convergent very fast.All the proposed methods are easily programmed to compute the eigenvalue and eigenvector with high accuracy and efficiency.

Research on the Damping Mechanism of Time-Delay Coupled Negative Stiffness Dynamic Absorber in Nonlinear Vibration Damping System

A study was conducted on the effect of time delay and structural parameters on the vibration reduction of a time delayed coupled negative stiffness dynamic absorber in nonlinear vibration reduction systems. Taking dynamic absorbers with different structural and control parameters as examples, the effects of third-order nonlinear coefficients, time-delay control parameters, and negative stiffness coefficients on reducing the replication of the main system were discussed. The nonlinear dynamic absorber has a very good vibration reduction effect at the resonance point of the main system and a nearby area, and when 1 increases to a certain level, the stable region of the system continues to increase. The amplitude curve of the main system of a nonlinear dynamic absorber will generate Hop bifurcation and saddle node bifurcation in the region far from the resonance point, resulting in almost periodic motion and jumping phenomena in the system. For nonlinear dynamic absorbers with determined structural parameters, time-delay feedback control can be adopted to control the amplitude of the main system. For different negative stiffness coefficients, there exists a minimum damping point for the amplitude of the main system under the determined system structural parameters and time-delay feedback control parameters.

Thermomechanical Dynamics (TMD) and Bifurcation-Integration Solutions in Nonlinear Differential Equations with Time-Dependent Coefficients

The new independent solutions of the nonlinear differential equation with time-dependent coefficients (NDE-TC) are discussed, for the first time, by employing experimental device called a drinking bird whose simple back-and-forth motion develops into water drinking motion. The solution to a drinking bird equation of motion manifests itself the transition from thermodynamic equilibrium to nonequilibrium irreversible states. The independent solution signifying a nonequilibrium thermal state seems to be constructed as if two independent bifurcation solutions are synthesized, and so, the solution is tentatively termed as the bifurcation-integration solution. The bifurcation-integration solution expresses the transition from mechanical and thermodynamic equilibrium to a nonequilibrium irreversible state, which is explicitly shown by the nonlinear differential equation with time-dependent coefficients (NDE-TC). The analysis established a new theoretical approach to nonequilibrium irreversible states, thermomechanical dynamics (TMD). The TMD method enables one to obtain thermodynamically consistent and time-dependent progresses of thermodynamic quantities, by employing the bifurcation-integration solutions of NDE-TC. We hope that the basic properties of bifurcation-integration solutions will be studied and investigated further in mathematics, physics, chemistry and nonlinear sciences in general.

Inversion of Seabed Geotechnical Properties in the Arctic Chukchi Deep Sea Basin Based on Time Domain Adaptive Search Matching Algorithm

The chirp sub-bottom profiler,for its high resolution,easy accessibility and cost-effectiveness,has been widely used in acoustic detection.In this paper,the acoustic impedance and grain size compositions were obtained based on the chirp sub-bottom profiler data collected in the Chukchi Plateau area during the 11th Arctic Expedition of China.The time-domain adaptive search matching algorithm was used and validated on our established theoretical model.The misfit between the inversion result and the theoretical model is less than 0.067%.The grain size was calculated according to the empirical relationship between the acoustic impedance and the grain size of the sediment.The average acoustic impedance of sub-seafloor strata is 2.5026×10^(6) kg(s m^(2))^(-1)and the average grain size(θvalue)of the seafloor surface sediment is 7.1498,indicating the predominant occurrence of very fine silt sediment in the study area.Comparison of the inversion results and the laboratory measurements of nearby borehole samples shows that they are in general agreement.

Remaining useful life prediction based on nonlinear random coefficient regression model with fusing failure time data

Remaining useful life(RUL) prediction is one of the most crucial elements in prognostics and health management(PHM). Aiming at the imperfect prior information, this paper proposes an RUL prediction method based on a nonlinear random coefficient regression(RCR) model with fusing failure time data.Firstly, some interesting natures of parameters estimation based on the nonlinear RCR model are given. Based on these natures,the failure time data can be fused as the prior information reasonably. Specifically, the fixed parameters are calculated by the field degradation data of the evaluated equipment and the prior information of random coefficient is estimated with fusing the failure time data of congeneric equipment. Then, the prior information of the random coefficient is updated online under the Bayesian framework, the probability density function(PDF) of the RUL with considering the limitation of the failure threshold is performed. Finally, two case studies are used for experimental verification. Compared with the traditional Bayesian method, the proposed method can effectively reduce the influence of imperfect prior information and improve the accuracy of RUL prediction.

Harmonic balance method with alternating frequency/time domain technique for nonlinear dynamical system with fractional exponential

Comparisons of the common methods for obtaining the periodic responses show that the harmonic balance method with alternating frequency/time （HB-AFT） do- main technique has some advantages in dealing with nonlinear problems of fractional exponential models. By the HB-AFT method, a rigid rotor supported by ball bearings with nonlinearity of Hertz contact and ball passage vibrations is considered. With the aid of the Floquet theory, the movement characteristics of interval stability are deeply studied. Besides, a simple strategy to determine the monodromy matrix is proposed for the stability analysis.

Finite Time Domain Dynamics of Dirac Fields

In the present paper we consider the case of a Dirac field in a finite time domain and coupled to an external field. We decompose the field and its Hamiltonian in terms of creation and annihilation operators and path integrate it via Grassmannian variables techniques. In that way we obtain its finite time domain Green function. We use it in the perturbative study of the interaction of Dirac particles with classical electromagnetic waves.

Evaluation of the seismic behavior of reinforced concrete structures with flat slab-column gravity frame and shear walls through nonlinear analysis methods

This paper presents an investigation of the seismic behavior of reinforced concrete(RC)structures in which shear walls are the main lateral load-resisting elements and the participation of flat slab floor systems is not considered in the seismic design procedure.In this regard,the behavior of six prototype structures(with different heights and plan layouts)is investigated through nonlinear static and time history analyses,implemented in the OpenSees platform.The results of the analyses are presented in terms of the behavior of the slab-column connections and their mode of failure at different loading stages.Moreover,the global response of the buildings is discussed in terms of some parameters,such as lateral overstrength due to the gravity flat slab-column frames.According to the nonlinear static analyses,in structures in which the slab-column connections were designed only for gravity loads,the slab-column connections exhibited a punching mode of failure even in the early stages of loading.However,the punching failure was eliminated in structures in which a minimum transverse reinforcement recommended in ACI 318(2019)was provided in the slabs at joint regions.Furthermore,despite neglecting the contribution of gravity flat slab-column frames in the lateral load resistance of the structures,a relatively significant overstrength was imposed on the structures by the gravity frames.

Noise-Tolerant ZNN-Based Data-Driven Iterative Learning Control for Discrete Nonaffine Nonlinear MIMO Repetitive Systems

Aiming at the tracking problem of a class of discrete nonaffine nonlinear multi-input multi-output(MIMO) repetitive systems subjected to separable and nonseparable disturbances, a novel data-driven iterative learning control(ILC) scheme based on the zeroing neural networks(ZNNs) is proposed. First, the equivalent dynamic linearization data model is obtained by means of dynamic linearization technology, which exists theoretically in the iteration domain. Then, the iterative extended state observer(IESO) is developed to estimate the disturbance and the coupling between systems, and the decoupled dynamic linearization model is obtained for the purpose of controller synthesis. To solve the zero-seeking tracking problem with inherent tolerance of noise,an ILC based on noise-tolerant modified ZNN is proposed. The strict assumptions imposed on the initialization conditions of each iteration in the existing ILC methods can be absolutely removed with our method. In addition, theoretical analysis indicates that the modified ZNN can converge to the exact solution of the zero-seeking tracking problem. Finally, a generalized example and an application-oriented example are presented to verify the effectiveness and superiority of the proposed process.

Event-Triggered Finite-Time H∞ Filtering for Discrete-Time Nonlinear Stochastic Systems

This paper addresses the problem of event-triggered finite-time H∞ filter design for a class of discrete-time nonlinear stochastic systems with exogenous disturbances. The stochastic Lyapunov-Krasoviskii functional method is adopted to design a filter such that the filtering error system is stochastic finite-time stable (SFTS) and preserves a prescribed performance level according to the pre-defined event-triggered criteria. Based on stochastic differential equations theory, some sufficient conditions for the existence of H∞ filter are obtained for the suggested system by employing linear matrix inequality technique. Finally, the desired H∞ filter gain matrices can be expressed in an explicit form.

Finite-Time H∞ Control of Switched Nonlinear Systems under State-Dependent Switching

This paper investigates the finite-time H∞ control problem of switched nonlinear systems via state-dependent switching and state feedback control. Unlike the existing approach based on time-dependent switching strategy, in which the switching instants must be given in advance, the state-dependent switching strategy is used to design switching signals. Based on multiple Lyapunov-like functions method, several criteria for switched nonlinear systems to be finite-time H∞ control are derived. Finally, a numerical example with simulation results is provided to show the validity of the conclusions.

Equilibrium Control Theory and Direct Method of Feedback Linearization for Nonlinear Time Varying Systems

Aim To present a simple and effective method for the design of nonlinear and time varying control system. Methods A new concept of dynamic equilibrium of a system and its stability were presented first. It was pointed out that what is controlled directly by the input of a control system is the system's dynamic equilibrium rather than the states. Based on it, a new feedback linearization method for nonlinear system based on the Lyapunov direct method was given. Simulation studies were also carried out. Results The example and simulation show that by use of the method, the controller design becomes very simple and the control effect is quite satisfying. Conclusion The new method unifies the stabilizing problem(regulating problem) with the tracking problem. It is a very simple and effective method for the design of nonlinear and time varying control system.