Strong Nonlinearity Research Articles

Quasilinear elliptic and parabolic systems with nondiagonal principal matrices and strong nonlinearities in the gradient. Solvability and regularity problems

We consider nondiagonal elliptic and parabolic systems of equations with strongly nonlinear terms in the gradient. We review and comment known solvability and regularity results and describe the last author’s results in this field.

An optimized nonlinear generalized predictive control for steam temperature in an ultra supercritical unit

The optimize control of the ultra supercritical (USC) unit has been a major concern in power industry. The intermediate point temperature process is a multi-variable system with strong nonlinearity, large scale and great delay, which greatly affects the safety and economy of the USC unit. Generally, it is difficult to realize effective control by using conventional methods. This paper presents a nonlinear generalized predictive control based on a composite weighted human learning optimization network (CWHLO-GPC) to improve the control performance of intermediate point temperature. Based on the characteristics of the onsite measurement data, the heuristic information is incorporated into the CWHLO network, and expressed by different local linear models. Then, global controller is elaborately constituted based on a scheduling program inferred from the network. Compared with classical generalized predictive control (GPC), the non-convex problem is effectively solved by introducing CWHLO models into the convex quadratic program (QP) routine of local linear GPC. Finally, detailed analysis on set point tracking and interference resisting via simulation is addressed to illustrate the efficiency of the proposed strategy.

Steady State and Dynamic Oscillatory Shear Properties of Carbon Black Filled Elastomers

A correlation between the steady shear viscosity and complex dynamic viscosity of carbon black (CB) filled rubbers was found by evaluating the Cox-Merz rule and an alternative approach originally proposed by Philippoff for dilute polymer solutions, but since applied to amorphous polymers and concentrated suspensions. This was done by measuring the rheological properties of 16 industrially important rubber mixes containing CB N660 at concentrations of 20 and 35% by volume. A capillary rheometer at various shear rates and a dynamic oscillatory shear rheometer at small and large amplitude oscillatory shear (SAOS and LAOS) were used. The apparent viscosity, storage and loss moduli, complex dynamic viscosity and Fourier transform harmonics were measured. Generally, the shear stress, storage and loss moduli increased with increasing CB loading. Also, the ratio of third and fifth stress harmonics to first harmonics increased with increasing strain amplitude and filler loading. Viscous Lissajous figures (shear stress versus shear rate) at a strain amplitude of 14% showed a nearly linear response for compounds containing CB at 20% by volume. All other shear stress responses demonstrated a strong nonlinearity. The stress waveforms at a strain amplitude of 140% for compounds containing 35% CB by volume displayed a backwards tilted shape expected for highly filled compounds. The stress waveforms at a strain amplitude of 1,000% tended toward a rectangular shape expected for pure polymer. Generally, the nonlinear response of the compounds appeared to be dominated by the filler at strain amplitudes of 14% and 140% and by the rubber matrix at a strain amplitude of 1,000%. The Cox-Merz rule was not applicable for any of the compounds with their complex dynamic viscosity being greater than the apparent viscosity. However, a modification of the approach proposed by Philippoff provided reasonable agreement between the apparent viscosity and complex dynamic viscosity.

Prediction of wave force on netting under strong nonlinear wave action

Under the strong nonlinear wave environment, accurate simulation of wave force for aquaculture netting is an effective guarantee for cage design and safety. In this paper, the horizontal wave forces of a nylon square-mesh netting panel were obtained through a series of strong nonlinear regular wave tests, and their nonlinearity was analyzed by amplitude spectrum. Moreover, the Morison equation based on fifth-order Stokes wave theory was used to reasonably predict the wave force on the netting. The results showed that both wave and wave force have strong nonlinearity, especially the latter. The frequency domain characteristics of the test wave and wave force are similar, while the higher frequency components of the test force are more apparent. The predicted wave forces are in good agreement with the test values in time and frequency domain, and zero or higher frequency components of predicted force are more prominent with the increase of wave steepness. When the range of the Keulegan-Carpenter number is 35-120, the average drag and inertia coefficient of the predicted force are 2.4 and 2.1, respectively. The results can provide a more accurate assessment of the nonlinear wave force on aquaculture facilities.

Airfoil-based convolutional autoencoder and long short-term memory neural network for predicting coherent structures evolution around an airfoil

Airfoil stall induced by unsteady flow separation is a major inhibitor that constrains the aircraft design. Hence, it is critical to have a better understanding of the flow dynamics around the airfoil near stall conditions. Recently, machine learning (ML) has been widely used to predict the spatiotemporal evolutions of coherent structures over the airfoil. Nonetheless, due to the existence of strong nonlinearity introduced by turbulence, most of the existing approaches focus on prediction of the flow fields in the laminar flow regime. In this work, we seek to examine the applicability of deep neural network (DNN) to prediction of turbulent flows around a NACA (National Advisory Committee for Aeronautics) 4412 airfoil. Large eddy simulations (LES) are performed to prepare the training dataset. Both proper orthogonal decomposition (POD) and DNN-based reduced-order models (ROM) are employed for reconstructing the flow fields. A convolutional autoencoder (CAE) is applied to map the high-dimensional flow dynamics into the low-dimensional nonlinear manifold. The geometric features are considered in the input matrix of the CAE network by setting physical quantities inside the airfoil to zero to reflect the physics. Then, the multi-head attention-strengthened long short-term memory (MH-LSTM) is utilized to predict the evolutions of latent vectors. Finally, the high-dimensional flow dynamics can be reconstructed by utilizing the decoder part of CAE. We believe that the MH-LSTM methodology provides a promising path towards predicting the unsteady flow field over the airfoil by capitalizing on the capability of multi-head attention allowing for attending to distinct parts of input sequence.

Phase-field viscoelastic fracture modeling of polymer composites using strain tensor spectral decomposition

The mechanical behaviors of polymer composites exhibit strong time-dependent nonlinearities, and the tensile and compressive strengths can be vastly different. Such a strength differential effect poses a great challenge in fracture modeling using existing phase-field models. To address this problem, this study develops a new viscoelastic fracture phase-field model, in which the strain tensor spectral decomposition is proposed to decompose the elastic energy of the equilibrium and non-equilibrium branches into tensile and compressive components. The non-negativity of elastic energy and the thermodynamic consistency are theoretically verified. Various case studies, spanning from material uniaxial tension–compression and compression under isostatic pressure to fracture processes of realistic structural components, are used to validate the proposed method. Results of the proposed method are compared with those of existing methods and the actual testing data of polymer composites to demonstrate the effectiveness of the method. It is shown that the proposed method can accurately model not only the strong strength differential effect but also the isostatic pressure dependence of viscoelastic materials. Furthermore, the proposed method offers a more precise prediction of the fracture path and can deal with the loading rate effect.

Dynamic modeling of multi-input and multi-output controlled object for municipal solid waste incineration process

Municipal solid waste incineration (MSWI) is an important part of energy recovery and sustainable development, constructing the model of controlled object is the basis of studying its optimal control. MSWI is a typical multi-input and multi-output industrial process, which has many uncertain characteristics such as strong nonlinearity and multivariable coupling. To solve this problem, a model of controlled object in MSWI process is proposed in this paper. Firstly, the MSWI process based on grate incinerator is analyzed to summarize its relevant variables and control requirements. Secondly, the solid phase and gas phase of MSWI process are divided to construct material balance equations of subsystems. Next, the energy transfer process in incinerator is deduced and calculated through thermodynamic laws. Finally, the validity of the model is verified by the process data of a MSWI plant in Beijing, China, which lays a model foundation for the study of the optimal control of MSWI process.

Entry trajectory optimization for hypersonic vehicles based on convex programming and neural network

Trajectory optimization is important in achieving long-range atmospheric entry hypersonic vehicles. However, the trajectory optimization problem for atmospheric entry of hypersonic vehicles is characterized by strong nonlinearity, parameter uncertainties and multiple constraints. This study proposes a novel online trajectory optimization method for hypersonic vehicles based on convex programming and a feedforward neural network. A sequential second-order cone programming (SOCP) method is obtained to describe the trajectory optimization problem after the Gauss pseudo-spectral discretization. Subsequently, multiple optimal trajectories under aerodynamic uncertainties are generated offline and classified as the training and validation datasets. Then, a multilayer feedforward neural network is trained using these datasets and to output the optimal control command online. This method yields approximately 95% shorter computation time compared with the offline SOCP method. Considering the existence of the aerodynamic uncertainties, three terminal states calculated by this method are all smaller than 4.1%. In conclusion, the proposed trajectory optimization method can provide a high-precision, robust entry trajectory for hypersonic vehicles efficiently.

Electromagnetic Characteristics and Capacity Analysis of a Radial–Axial Hybrid Magnetic Bearing with Two Different Radial Stators

Compared with the widely used four-pole magnetic bearings, three-pole magnetic bearings are driven by a three-phase power inverter and have advantages pertaining to their small volume, low costs, and low power losses. However, the asymmetric structure of the three-pole bearings presents disadvantages in terms of their strong nonlinearity and couplings among the suspension forces of the control currents and displacements. The radial–axial hybrid magnetic bearing (RAHMB) with six-pole bearings is proposed to solve this problem. Firstly, the structure and working principle of the RAHMB are introduced. Secondly, the mathematical models of the RAHMB are established, and in order to obtain the radial capacity, the maximum suspension forces of the three-pole and six-pole RAHMBs are theoretically analyzed. Thirdly, the nonlinearity and couplings of the suspension forces with the control currents and displacements are analyzed. The radial capacity of the three-pole and six-pole RAHMB is 74.6 N and 83.6 N, respectively, which is an increase of 12.0%. Finally, the experiment results prove that the nonlinearity and couplings of the six-pole RAHMB are smaller than the nonlinearity and couplings of the three-pole RAHMB, and the maximum radial capacity of the three-pole and six-pole RAHMB is 84.1 N and 94.8 N, respectively, which is an increase of 12.7%. The simulation results are basically consistent with the experimental results, indicating the correctness of the theoretical analysis.

Fatigue condition diagnosis of rolling bearing based on normalized balanced multiscale sample entropy

Rolling bearing is a key component of machinery, its fatigue failure will affect the reliability of machinery. The bearing vibration signal has strong nonlinearity, resulting in weak fault information. Multiscale sample entropy (MSE) is an effective technique for analyzing nonlinear time series. However, MSE has limitations, such as a large deviation and weak information mining abilities, and even the calculation results have no definition. To this end, a normalized balanced multiscale sample entropy (NBMSE) is proposed in this study. For NBMSE, the data are first normalized to zero mean and unit standard deviation by zero-mean normalization, which eliminates the influence of abnormal data. Secondly, the balanced multiscale approach is advanced to coarse-grain the time series, which takes into account the uniqueness of different amplitudes and the globality of the time series. The method not only avoids no-definition results, but also reduces the entropy calculation error, thus mining useful amplitude information. The comparison of synthetic signals shows that the proposed NBMSE is more robust than other methods. Furthermore, the results of two bearing cases show that NBMSE not only provides sensitive features for fatigue diagnosis but also has higher diagnostic accuracy.

Data-driven modeling on anisotropic mechanical behavior of brain tissue with internal pressure

Brain tissue is one of the softest parts of the human body, composed of white matter and grey matter. The mechanical behavior of the brain tissue plays an essential role in regulating brain morphology and brain function. Besides, traumatic brain injury (TBI) and various brain diseases are also greatly influenced by the brain's mechanical properties. Whether white matter or grey matter, brain tissue contains multiscale structures composed of neurons, glial cells, fibers, blood vessels, etc., each with different mechanical properties. As such, brain tissue exhibits complex mechanical behavior, usually with strong nonlinearity, heterogeneity, and directional dependence. Building a constitutive law for multiscale brain tissue using traditional function-based approaches can be very challenging. Instead, this paper proposes a data-driven approach to establish the desired mechanical model of brain tissue. We focus on blood vessels with internal pressure embedded in a white or grey matter matrix material to demonstrate our approach. The matrix is described by an isotropic or anisotropic nonlinear elastic model. A representative unit cell (RUC) with blood vessels is built, which is used to generate the stress-strain data under different internal blood pressure and various proportional displacement loading paths. The generated stress-strain data is then used to train a mechanical law using artificial neural networks to predict the macroscopic mechanical response of brain tissue under different internal pressures. Finally, the trained material model is implemented into finite element software to predict the mechanical behavior of a whole brain under intracranial pressure and distributed body forces. Compared with a direct numerical simulation that employs a reference material model, our proposed approach greatly reduces the computational cost and improves modeling efficiency. The predictions made by our trained model demonstrate sufficient accuracy. Specifically, we find that the level of internal blood pressure can greatly influence stress distribution and determine the possible related damage behaviors.

Emergent second-harmonic generation in van der Waals heterostructure of bilayer MoS2 and monolayer graphene.

Van der Waals (vdW) stacking of two-dimensional (2D) materials to create artificial structures has enabled remarkable discoveries and novel properties in fundamental physics. Here, we report that vdW stacking of centrosymmetric 2D materials, e.g., bilayer MoS2 (2LM) and monolayer graphene (1LG), could support remarkable second-harmonic generation (SHG). The required centrosymmetry breaking for second-order hyperpolarizability arises from the interlayer charge transfer between 2LM and 1LG and the imbalanced charge distribution in 2LM, which are verified by first-principles calculations, Raman spectroscopy, and polarization-resolved SHG. The strength of SHG from 2LM/1LG is of the same order of magnitude as that from the monolayer MoS2, which is well recognized with strong second-order nonlinearity. The emergent SHG reveals that the interlayer charge transfer can effectively modify the symmetry and nonlinear optical properties of 2D heterostructures. It also indicates the great opportunity of SHG spectroscopy for characterizing interlayer coupling in vdW heterostructures.

Fuel performance uncertainty quantification and sensitivity analysis in the presence of epistemic and aleatoric sources of uncertainties

Fuel performance modeling and simulation includes many uncertain parameters from models to boundary conditions, manufacturing parameters and material properties. These parameters exhibit large uncertainties and can have an epistemic or aleatoric nature, something that renders fuel performance code-to-code and code-to-measurements comparisons for complex phenomena such as the pellet cladding mechanical interaction (PCMI) very challenging. Additionally, PCMI and other complex phenomena found in fuel performance modeling and simulation induce strong discontinuities and non-linearities that can render difficult to extract meaningful conclusions form uncertainty quantification (UQ) and sensitivity analysis (SA) studies. In this work, we develop and apply a consistent treatment of epistemic and aleatoric uncertainties for both UQ and SA in fuel performance calculations and use historical benchmark-quality measurement data to demonstrate it. More specifically, the developed methodology is applied to the OECD/NEA Multi-physics Pellet Cladding Mechanical Interaction Validation benchmark. A cold ramp test leading to PCMI is modeled. Two measured quantities of interest are considered: the cladding axial elongation during the irradiations and the cladding outer diameter after the cold ramp. The fuel performance code used to perform the simulation is FAST. The developed methodology involves various steps including a Morris screening to decrease the number of uncertain inputs, a nested loop approach for propagating the epistemic and aleatoric sources of uncertainties, and a global SA using Sobol indices. The obtained results indicate that the fuel and cladding thermal conductivities as well as the cladding outer diameter uncertainties are the three inputs having the largest impact on the measured quantities. More importantly, it was found that the epistemic uncertainties can have a significant impact on the measured quantities and can affect the outcome of the global sensitivity analysis.

An Overview of Complex Instability Behaviors Induced by Nonlinearity of Power Electronic Systems with Memristive Load

The proposal of the memristor, considered as the fourth basic circuit element, suggests a new possibility for the design of high-performance power electronic systems. However, it also brings new challenges. At present, more and more electrical equipment and systems have demonstrated that their external characteristics can exhibit “8”-shaped hysteresis loops and can be regard as memristive equipment and systems. In order to satisfy the requirements of controllability, flexibility, efficiently, and so on, most memristive equipment and systems are not directly connected to the power grid but instead obtain their own required powering through various forms of power electronic converters. Note that memristive loads are distinctive and demonstrate unique nonlinear behaviors. Similarly, there can be nonlinearity from the resistor (R), inductor (L), or capacitor (C) load, but there is no combination of only R, L, and C that could produce memristive characteristics. In particular, the memristance of memristive devices changes continuously during the operation process; in addition, practical power electronic systems composed of memristive devices and power supplies have strong nonlinear characteristics, which are more likely to result in various complex behaviors and are not conducive to the stable operation of the systems. Therefore, exploring complex instability behaviors of power electronic systems with strong nonlinearity in depth is necessary for better protection and utilization of memristive devices. This paper provides an outline of the status of research on complex behaviors of power electronic systems with memristive load; it is expected to provide guidance for the study of complex behavior of strongly nonlinear systems.

Active Disturbance Rejection Optimization Control for SOFCs in Offshore Wind Power

With the development of offshore wind power (OWP)-based hydrogen production technology, hydrogen fuel cells play a critical role in buffering the mismatch between energy supply and demand in OWP systems. Benefitting from high efficiency, cleanliness, and nontoxicity, solid oxide fuel cells (SOFCs) have been extensively investigated. However, OWP-based SOFC systems are characterized by strong nonlinearity and uncertainty and are vulnerable to disturbance, which leads to appreciable fluctuations and even instability to the system output voltage. Since conventional PID control schemes cannot achieve favorable performance, a more advanced control method is imperative. In response, this paper proposes a linear active disturbance rejection control (LADRC) method to reduce the influence of disturbance and ensure the stability of SOFC systems. In addition, an improved firefly algorithm (IFA) was adopted to optimize LADRC parameters. A step inertia weight was introduced, and a random generation mechanism was adopted to replace 30% of individuals with low luminous degrees. Using optimized LADRC parameters, a series of Monte Carlo experiments were carried out to verify the system’s robustness. The experimental results show that the overshoot of the LADRC method optimized by the IFA can be reduced by 5.7% compared with the traditional PID controller, i.e., the influence of the voltage disturbance can be well suppressed.

Model updating of dynamic structures with strong nonlinearities using fixed frequency continuation tests

Model updating using multivalued responses is an important approach to construct strongly nonlinear models. During updating, swept frequency tests are usually used to measure the multivalued responses, but the measured responses only contain the stable branches. Accordingly, updating mainly uses these stable responses for the nonlinear model construction. Unstable responses are rarely tested or participate in the updating process, which may lead to errors in the constructed model with strong nonlinearities. Recently, fixed frequency tests using a continuation scheme have been used to measure fully multivalued responses, including both the stable and unstable branches, for structures with the strong nonlinearity. However, the measured responses were then transformed to equivalent swept frequency tests for the existing updating schemes, where this transformation may induce errors in the updating process. In this paper, a novel method for strong nonlinear model updating using the results of the fixed frequency test is proposed. Such updating is based on the directly measured data of the fixed frequency tests and can handle both the stable and unstable responses. Fixed frequency continuation using the Multi-Harmonic Balance Method (MHBM) is developed to predict the multivalued responses and their sensitivities. The multivalued responses of the prediction and measurement are directly matched in sensitivity-based updating. The proposed method is numerically verified on a 2 DOF nonlinear model. Using the proposed method, the nonlinear model is updated from linear to strongly nonlinear and the updated parameters all converge to the simulated values after 7 iterations. The proposed method is then experimentally validated on a 3 DOF nonlinear system with a non-smooth nonlinearity. A nonlinear model with a 7th order polynomial stiffness represents the equivalent system and is directly updated based on the fixed frequency test results. The updated responses are generally a good fit to the tested responses. Compared with updating using only the stable responses, the proposed updating method achieves higher precision and its updated responses are closer to the tested responses. These results show the validity and superiority of the proposed method.

Influence of Eu3+ dopant on the third order nonlinear optical properties of PbO/PMMA nanocomposites

ABSTRACT PbO/PMMA, 3 and 6 mol% ion-doped PbO/PMMA nanocomposites were synthesised using an easy chemical precipitation method. For all of the nanocomposites, the XRD pattern confirms the orthorhombic structure of PbO. The morphology of PbO nanoparticles in PMMA is revealed by the SEM graph. The formation of nanocomposites containing Eu3+ doped PbO nanoparticles in PMMA is confirmed by FTIR. When Eu3+ doped PbO nanoparticles in PMMA are compared to bulk PbO, UV–Vis optical absorption findings demonstrate a blue shift on the absorption band. The optical band gap energy decreases with increasing Eu3+ dopant concentration and is related to red-shifted phenomena. The PL spectra reveal an emission peak associated with blue emission caused by a synthesis defect. For 6 mol% Eu3+ ion doped PbO/PMMA nanocomposites, third-order nonlinear optical parameters such as nonlinear optical susceptibility (χ(3)), nonlinear optical refractive index (n2), and nonlinear optical absorption coefficient (β) are determined by Z-scan technique, and the values are found to be 4.468 × 10−6 esu, 1.257 × 10−7cm2/W, and 9.837 × 10−3 cm/W, respectively. The strong nonlinearity in the current Eu3+ ion-doped PbO/PMMA nanocomposites empowers its promising applications in third-order nonlinear optical devices.

Parallel co-simulation of heavy-haul train braking dynamics with strong nonlinearities

A new wave of research interests on train braking dynamics has been raised which requires more accurate and faster train braking dynamics simulations. Simulations with fully nonlinear fluid dynamic air brake models and nonlinear friction draft gear models are more accurate, however these are not yet available. This paper developed a model that has combined both of these aspects. Simulations were achieved by using a parallel co-simulation method which requires minimum working loads to merge legacy codes. A case study was carried out to simulate a heavy haul train braking commencing with a minimum service brake and then followed by a full-service brake before the minimum service brake was fully executed. Such transient simulations were not able to be accurately conducted by using empirical air brake models, but only by using fluid dynamic air brake models. Influences of co-simulation synchronization frequencies on computing time and results of the simulations were also investigated. Simulation results have recommended a synchronization frequency of 100 Hz. The corresponding simulation was 43% faster than real-time for a 152-vehicle train.

Seismic mitigation of a benchmark twenty-story steel structure based on intermodal targeted energy transfer (IMTET)

This study investigates a new intermodal targeted energy transfer (IMTET) concept for rapid, effective, and purely passive seismic mitigation of a benchmark large-scale model of a twenty-story steel structure. IMTET is based on extremely rapid nonlinear scattering of seismic input energy from low to high frequency modes of a building. This effect is achieved by introducing strategically placed, local strong vibro-impact nonlinearities that are generated by contacts of the building floors with a relatively light, yet stiff, auxiliary core structure. Accordingly, the performance of IMTET is studied here, with the benchmark structure realized through a set of previously established performance criteria. The seismic loads are simulated based on records from three historical earthquakes, namely the 1995 Kobe, 1994 Northridge, and 1940 El Centro. To assess the robustness of the proposed passive nonlinear mitigation mechanism, the clearance distributions as well as the core structure parameters, are optimized for a specific seismic excitation (Kobe). Subsequently, the optimized design is tested against the two other historical earthquake records to demonstrate the effectiveness of the IMTET for these cases as well. The numerical results show that the vibro-impacts rapidly, robustly, and almost irreversibly redistribute the seismic input energy from low to high frequency structural modes, thus realizing a highly effective passive earthquake protective system. In addition, when optimized, this new concept can be realized fully passively, without the need to add any mass to the building, and at the cost of only moderate increases in the resulting floor accelerations and local stresses. In addition, the nonlinear vibro-impacts between the floors and the core structure reduce the seismic input energy to the building compared to the no core case, adding an additional benefit to the seismic mitigation approach. Therefore, the IMTET methodology for seismic mitigation has the potential to significantly enhance the seismic performance of building structures.

Out-of-Band Digital Predistortion for Power Amplifiers With Strong Nonlinearity

Conventional full-band digital predistortion (DPD) suppresses the inband (IB) distortion to improve the error vector magnitude (EVM) performance and simultaneously suppresses the out-of-band (OOB) distortion to reduce the adjacent-channel interference. However, its performance is very limited when the nonlinearity is strong, especially in terms of suppressing the OOB distortion. This paper proposes an OOB DPD scheme for strong nonlinearity with a special focus on suppressing the OOB distortion to reduce the adjacent-channel interference. The proposed OOB DPD is featured by specifying an arbitrary OOB-distortion band for linearization and controlling the improvement level of EVM performance. Experiments demonstrate that the proposed OOB DPD can achieve superior performance in suppressing the OOB distortion when the nonlinearity is strong. We also present analyses to show that in strong nonlinearity cases with high compression, focusing on suppressing the OOB distortion at a specific band is an effective way to improve the suppression level of the target distortion. The proposed OOB DPD can further improve the transmission power under the assurance of low adjacent-channel interference. It can be applied in communications with urgent needs in high transmission power, high efficiency, and low adjacent-channel interference, such as military communications that usually adopt low-order modulations with low EVM requirements.