Nonlinear Method Research Articles

A nonlinear interval finite element method for elastic–plastic problems with spatially uncertain parameters

This paper proposes a nonlinear interval finite element method for elastic–plastic analysis of structures with spatially uncertain parameters. The spatially uncertain parameters are described by the interval field, and the variation bounds of the elastic–plastic structural responses can be calculated effectively. Quantified by the interval field, the spatially uncertain parameters are represented by the interval Karhunen–Loève (K-L) expansion, based on which the nonlinear interval finite element equilibrium equation is formulated. An interval iterative method is then presented to solve the equilibrium equation and obtain an outer solution of the variation bounds of structural responses such as displacement. In this method, the Newton-Raphson iterative method is used to transform the nonlinear problem into a linear one, and then the interval iterative method is introduced to solve the interval linear equations. Three numerical examples are employed to illustrate the feasibility and accuracy of the proposed method.

Dynamic Viscosity Prediction for MWCNT-MgO (10%-90%) -SAE40 Oil Hybrid Nano-lubricant Using Artificial Neural Network and Multi-Dimensional Nonlinear Least Square Curve Fitting

In this study, the dynamic viscosity of MWCNT-MgO (10%-90%)/SAE40 Oil Hybrid Nanofluid (HNF) is investigated. To this end, two methods are used including artificial neural network (ANN) and least square curve fitting. This nonlinear method uses a multi-dimensional least square strategy to determine coefficients of various parameters in the viscosity function. The viscosity of MWCNT-MgO (10%-90%)/SAE40 Oil HNF is predicted using three input parameters including solid volume fraction (SVF), temperature, and shear rate (SR). According to the obtained data, the optimum ANN to predict the viscosity of HNF as a function of inputs has 14 neurons with a nonlinear activation function resulting in mean square error or MSE=7.74e-4 and R2=0.999226 for all data. Moreover, temperature is the most influential parameter, and the rest of the parameters, have much fewer effects on the viscosity of MWCNT-MgO (10%-90%)/SAE40 Oil HNF. Furthermore, this can be seen in the obtained nonlinear fitted function through coefficients of input parameters. To be more precise, T coefficient is -91.2407 much higher than the solid volume fraction and shear rate with coefficients of 34.0366 and -0.166 respectively. The obtained ANN structure and nonlinear fitted function can be used for optimization purposes in future research. It is worth mentioning that although the fitted function by least square curve fitting is a very handy and symbolic equation, the ANN showed higher accuracy.

Identification, uncertainty quantification and validation of orthotropic material properties for additively manufactured polymers

The mechanical behavior of polymeric parts manufactured by fused filament fabrication is often characterized as orthotropic because of the layer-wise extrusion of the material. To perform reliable simulations of the mechanical response of these parts subjected to certain loads, the material parameters have to be known. This leads to the task of material parameter identification from suitable experimental data. In this work, the identification of the material parameters for orthotropic material behavior is studied in detail with a focus on the specific characteristics of additively manufactured parts. This comprises working out the differences that arise compared to the parameter identification for classical orthotropic composite materials. Moreover, the material parameters are identified from tensile and shear test information together with full-field displacement data from digital image correlation measurements. Then, the obtained parameters are compared for analytical and numerical approaches, where a non-linear least-squares method with finite elements is drawn on. The parameters are not only identified, but also an uncertainty analysis is carried out and, subsequently, the different methods are validated. Further, a clear derivation of commonly applied analytical equations is provided with a special focus on the underlying assumptions. It turns out that the analytical parameter identification procedures can not be easily transferred to numerical procedures, especially when using full-field data, because of correlations between the parameters. Moreover, the identified parameters are employed to prove the reasonability of orthotropic material behavior for specimens manufactured by fused filament fabrication. Finally, during validation it turns out that all parameter identification methods provide a good agreement with experimental data, showing only small differences between the results of the different calibration strategies.

Gaussian Bistable Cascade Double Feedback Stochastic Resonance Weak Signal Enhancement Detection

Stochastic resonance (SR), as a nonlinear weak signal enhancement detection method, has found extensive applications in fields like fault diagnosis and biological information processing. However, further research has revealed that single stochastic resonance systems often fail to meet the requirements of practical engineering applications, leading to a growing interest in multi-system collaborative stochastic resonance. This article first constructs a cascaded SR system based on the Gaussian bistable model, and introduces the idea of feedback into the cascaded system. A Gaussian bistable cascaded dual feedback SR system is proposed to improve the output signal enhancement performance of the system. This system effectively utilizes the memory characteristics inherent in the output feedback and enables multi-level particle transitions and energy transfers in noisy input signals, thereby reducing noise and enhancing the extraction of weak signal features. Furthermore, the BSO optimization algorithm was utilized to optimize the system parameters of the model, resulting in an adaptive Gaussian bistable cascaded double feedback stochastic resonance (GBCDFSR) system. This system is applied to the processing of noisy periodic signals across various noise types. Simulation experiments and engineering applications show that the proposed model has stronger signal detection capabilities.

Predicting Structural Temperature of Ancient City Walls: A Case Study Using Ambient Temperature and Deep Learning

ABSTRACT Accurate prediction of the structural temperature field is required for the performance assessment of engineering structures and for maintaining structural safety. However, there are complex time-lag effects between ambient temperature and structural temperature. It is difficult to accurately describe and predict the structural temperature using traditional linear and nonlinear fitting methods. Hence, this study uses the advantages of gated recurrent unit (GRU) neural networks in dealing with complex nonlinear mapping issues, further considering solar radiation and developing a structural temperature prediction framework using ambient temperature and the deep learning model. The framework is applied in structural temperature prediction for an ancient city wall in China. The solar altitude angle at the location of the city wall is calculated, and the input and output structures of the deep learning neural network model are optimized. In the long-term prediction of the structural temperature of the city wall, the root mean square error (RMSE) of the GRU model is less than 0.6°C, which solves the problem of low accuracy caused by time-lag effects.

The urban desirability paradox: U.K. urban-rural differences in well-being, social satisfaction, and economic satisfaction.

As the majority of the global population resides in cities, it is imperative to understand urban well-being. While cities offer concentrated social and economic opportunities, the question arises whether these benefits translate to equitable levels of satisfaction in these domains. Using a robust and objective measure of urbanicity on a sample of 156,000 U.K. residents aged 40 and up, we find that urban living is associated with lower scores across seven dimensions of well-being, social satisfaction, and economic satisfaction. In addition, these scores exhibit greater variability within urban areas, revealing increased inequality. Last, we identify optimal distances in the hinterlands of cities with the highest satisfaction and the least variation. Our findings raise concern for the psychological well-being of urban residents and show the importance of nonlinear methods in urban research.

Frailty Modeling using Machine Learning Methodologies: A Systematic Review with Discussions on Outstanding Questions.

Studying frailty is crucial for enhancing the health and quality of life among older adults, refining healthcare delivery methods, and tackling the obstacles linked to an aging demographic. Approaches to frailty modeling often utilise simple analytic techniques rather than available advanced machine learning methods, which may be sub-optimal. There is no large-scale systematic review on applications of machine learning methods on frailty modeling. In this study we explore the use of machine learning methods to predict or classify frailty in older persons in routinely collected data. We reviewed 181 research articles, and categorised analytic methods into three categories: generalised linear models, survival models, and non-linear models. These methods have a moderate agreement with existing frailty scores and predictive validity for adverse outcomes. Limited evidence suggests that non-linear methods outperform generalised linear methods. The top-three predictor/input variables are specific diagnosis or groups of diagnoses, functional performance (e.g., ADLs), and impaired cognition. Mortality, hospital admissions and prolonged hospital stay are the mainly predicted outcomes. Most studies utilise classical machine learning methods with cross-sectional data. Longitudinal data collected by wearable sensors have been used for frailty modeling. We also discuss the opportunities to use more advanced machine learning methods with high dimensional longitudinal data for more personalised and accessible frailty tools.

Full waveform inversion of cross-hole radio frequency electromagnetic data

Summary We consider application of full waveform inversion (FWI) to radio-frequency electromagnetic (EM) data. Radio-frequency imaging (RIM) is a cross-borehole technique to image electromagnetic subsurface properties from measurements of transmitted radio-frequency waves. It is used in coal seam imaging, ore exploration and various engineering and civil engineering applications. RIM operates at frequencies from 50 kHz to several tens of MHz. It differs from other geophysical EM methods, because the frequency band includes the transition between the wave propagation and diffusion regimes. RIM data are acquired in two-dimensional cross-hole sections in a reciprocal manner. Traditionally, radio-frequency data are inverted by straight ray tomography because it is inexpensive and easy to implement. It is argued that due to attenuation, the sensitivity of the transmitted electric field is the strongest within the first Fresnel zone of the ray connecting the transmitter and receiver. While straight ray tomography is a simple to implement and fast method, the non-linearity in the relationship between model parameters and data is often strong enough to warrant non-linear inversion techniques. FWI is an iterative high resolution technique, in which the physical properties are updated to minimize the misfit between the measured and modelled wavefields. Full waveform techniques have been used and extensively studied for the inversion of seismic data, and more recently, they have been applied to the inversion of GPR data. Non-linear inversion methods for RIM data are less advanced. Their use has been hindered by the high cost of full wave modelling and the high conductivity contrasts of many RIM targets, and, to some extent, by the limitations of the measuring instruments. We present the first application of this methodology to simultaneous conductivity and permittivity inversion of RIM data. We implement the inversion in the frequency domain in two dimensions using L-BFGS optimization. We analyze the sensitivity of the data to the model parameters and the parameter trade-off and validate the proposed methodology on a synthetic example with moderate conductivity variations and localized highly conductive targets. We then apply the FWI methodology to a field data set from Sudbury, Canada. For the field data set, we determine the most appropriate preprocessing steps that take into account specific peculiarities of RIM: the insufficient prior information about the subsurface and the limitations of the measuring equipment. We show that FWI is applicable under the conditions of RIM and is robust to imperfect prior knowledge: we obtain satisfactory model recoveries starting from homogeneous initial models in all of our examples. Just as other methods, FWI underestimates large conductivity contrasts due to the loss of sensitivity of the transmitted electric field to the conductivity variations as the conductivity increases above a certain level. The permittivity inside high conductors can not be recovered, however, recovering permittivity variations in the resistive zones helps obtain better focused conductivity images with fewer artifacts. Overall, FWI produces cleaner, less noisy and higher resolution reconstructions than the methods currently used in practice.

Enhancement of DDST-MFAC for tracking performance by using dynamic data reconciliation

Abstract Model-free adaptive control (MFAC) stands out as an effective data-driven method for addressing nonlinear problems in industrial processes. To maintain good control performance, a data-driven set-point tuning (DDST) method is used to update the virtual set-point of the MFAC system. The DDST-based MFAC (i.e. DDST-MFAC) constantly approaches the target of the process through the nonlinear set-point tuning method. However, due to equipment errors and external interference, industrial sensors often suffer from measurement noise, which can have adverse effects on the control performance. In this article, an available dynamic data reconciliation (DDR) technique is adopted to improve the tracking performance of the DDST-MFAC, which suppresses the impact of process noise by using predicted information and measured data to achieve high-precision requirements for controlling nonlinear processes. Finally, considering both Gaussian and non-Gaussian distribution of measurement noise, the effectiveness of the proposed method was verified through the simulation of a nonlinear nonaffine plant. It is also applied to the steam-water heat exchange process, the control result is improved ultimately.

Operational stability study of lactate biosensors: modeling, parameter identification, and stability analysis

IntroductionThis paper investigates the operational stability of lactate biosensors, crucial devices in various biomedical and biotechnological applications. We detail the construction of an amperometric transducer tailored for lactate measurement and outline the experimental setup used for empirical validation.MethodsThe modeling framework incorporates Brown and Michaelis–Menten kinetics, integrating both distributed and discrete delays to capture the intricate dynamics of lactate sensing. To ascertain model parameters, we propose a nonlinear optimization method, leveraging initial approximations from the Brown model’s delay values for the subsequent model with discrete delays.ResultsStability analysis forms a cornerstone of our investigation, centering on linearization around equilibrium states and scrutinizing the real parts of quasi-polynomials. Notably, our findings reveal that the discrete delay model manifests marginal stability, occupying a delicate balance between asymptotic stability and instability. We introduce criteria for verifying marginal stability based on characteristic quasi-polynomial roots, offering practical insights into system behavior.DiscussionQalitative examination of the model elucidates the influence of delay on dynamic behavior. We observe a transition from stable focus to limit cycle and period-doubling phenomena with increasing delay values, as evidenced by phase plots and bifurcation diagrams employing Poincaré sections. Additionally, we identify limitations in model applicability, notably the loss of solution positivity with growing delays, underscoring the necessity for cautious interpretation when employing delayed exponential function formulations. This comprehensive study provides valuable insights into the design and operational characteristics of lactate biosensors, offering a robust framework for understanding and optimizing their performance in diverse settings.

Research on an Active Adjustment Mechanism Based on Non-Singular Terminal Sliding Mode and Finite-Time Disturbance Observer

With the continuous development of synchrotron radiation light sources, higher requirements have been put forward for the stability of double-crystal monochromators in synchrotron radiation facilities. This paper designs an active adjustment mechanism for a double-crystal monochromator to improve its stability. Firstly, three spatial degrees of freedom are designed based on the active adjustment mechanism of flexible leaf spring parallel coupling, and the prototype of the mechanism is fabricated. Secondly, system identification experiments are carried out and the system transfer function curve is fitted by the nonlinear least squares method. Thirdly, the controller based on non-singular terminal sliding modes and a finite-time disturbance observer was designed for stability control and disturbance compensation. Finally, the effectiveness of the controller is verified by a model-in-the-loop approach based on the performance of the real-time target machine. The results show that the non-singular terminal sliding mode + finite-time disturbance observer control strategy can reduce the RMS value of the vibration displacement of Axis-1/Axis-2/Axis-3 by 81.25%, 78.53%, and 71.82%.

The use of nonlinear guided-wave features for detection and assessment of intermetallic compounds within dissimilar joints – an experimental investigation

Abstract Welding dissimilar materials is widely employed in industrial construction and manufacturing to enhance cost-effectiveness and performance, often utilizing non-fusion methods like solid-state and high-energy beam welding. However, a significant challenge is the formation of intermetallic compounds (IMCs) at the joint interface, which can weaken the bond and increase brittleness, leading to hidden internal cracks. Nonlinear ultrasound detection methods are employed as advanced, non-destructive testing techniques for early damage inspection in various materials. This research investigates the assessment of the thickness of the intermetallic layer within dissimilar joints using non-linear ultrasound-wave features. Numerical and experimental investigations were performed using four friction stir welding (FSW) lap joints, between AA5052-H32 aluminum and ASTM 516-70 steel, with various intermetallic thicknesses. The methodology involved examining the generation of second-order harmonic frequency by exciting Lamb waves (LW) at specific frequencies. To determine the necessary LWs' excitation frequency, synchronism, and non-zero power flux conditions were employed. The collected signals were measured and analyzed in the time and frequency domains to understand the behavior of the non-linear parameter β′ with the thickness of the intermetallic layer. The results show that β′ changes in a linear manner with the thickness of the intermetallic compound layer (several micrometers in thickness). This provides strong evidence that nonlinear LW features are sensitive to microstructural variations in the FSW joints, which enables them to effectively evaluate their strength.

Research on Collapse Testing of Nuclear Icebreaker Reactor Hull Structure Based on Distortion Similarity Theory

In this study, the finite element method combined with the model test method are used to investigate the ultimate strength of a target ship reactor hull structure under a pure bending load. Based on the distortion similarity theory and nonlinear similarity method, a scale model of the actual ship reactor hull structure is designed and the model collapse test is conducted. The ultimate bending moment obtained by the model test is transformed to the actual ship through the similarity transformation relationship and compared with the nonlinear finite element analysis result of the actual structure. The results are consistent with each other, which indicates that the collapse characteristics of the actual ship reactor hull structure can be better forecasted using the model test results when the test model is designed based on the nonlinear similarity method and distortion similarity theory.

Nonlinear mirrored-stiffness design method for quasi-zero stiffness vibration isolators

Nonlinear mirrored-stiffness design method for quasi-zero stiffness vibration isolators

Parallel Implementation of K-Best Quadrature Amplitude Modulation Detection for Massive Multiple Input Multiple Output Systems

Massive MIMO (Multiple Input Multiple Output) systems impose significant processing burdens along with strict latency requirements. The combination of large-scale antenna arrays and wide bandwidth requirements for next-generation wireless systems creates an exponential increase in frontend to backend data. Balancing the processing latency and reliability is critical for baseband processing tasks such as QAM detection. While linear detection algorithms have low computational complexity, their use in Massive MIMO scenario has heavy degradation in error performance. Nonlinear detection methods such as Maximum Likelihood and Sphere Decoding have good error performance, but they suffer from high, variable, and uncontrollable computational complexity. For such cases, the K-best QAM detection algorithm can provide required control over the system performance while maintaining near-ML error performance. In this paper, hard-output, as well as soft-output K-best QAM detection, is implemented in a CPU by utilizing the multiple cores combined with vector processing. Similarly, hard-output detection in a GPU is implemented by leveraging the SIMD (Single Instruction, Multiple Data) architecture and Warp-based execution model. The processing time per bit and the energy consumption per bit are compared for CPU and GPU implementations for QAM constellation density and MIMO array size. The GPU implementation shows up to 5× processing latency per bit improvement and up to 120× energy consumption per bit improvement over the CPU implementation for typical QAM constellations such as 4, 16, and 64 QAM. GPU implementation also shows up to 125× improvement over CPU implementation in energy consumption per bit for larger MIMO configurations such as 24 × 24 and 32 × 32. Finally, the soft-output detector is combined with a LDPC (Low-Density Parity Check) decoder to obtain the FER (Frame Error Rate) performance for CPU implementation. The FER is then combined with frame processing latency to form a Goodput metric to demonstrate the latency and reliability tradeoff.

Compressible and anelastic governing-equation solution methods for thermospheric gravity waves with realistic background parameters

Abstract abstract A previously developed numerical-multilayer modeling approach for systems of governing equations is extended so that unwanted terms, resulting from vertical variations in certain background parameters, can be removed from the dispersion-relation polynomial associated with the system. The new approach is applied to linearized anelastic and compressible systems of governing equations for gravity waves including molecular viscosity and thermal diffusion. The ability to remove unwanted terms from the dispersion-relation polynomial is crucial for solving the governing equations when realistic background parameters, such as horizontal velocity and temperature, with strong vertical gradients, are included. With the unwanted terms removed, previously studied dispersion-relation polynomials, for which methods for defining upgoing and downgoing vertical wavenumber roots already exist, are obtained. The new methods are applied to a comprehensive set of medium-scale time-wavepacket examples, with realistic background parameters, lower boundary conditions at 30 km altitude, and modeled wavefields extending up to 500 km altitude. Results from the compressible and anelastic model versions are compared, with compressible governing-equation solutions understood as the more physically accurate of the two. The new methods provide significantly less computationally expensive alternatives to nonlinear time-step methods, which makes them useful for comprehensive studies of the behavior of viscous/diffusive gravity waves and also for large studies of cases based on observational data. Additionally, they generalize previously existing Fourier methods that have been applied to inviscid problems while providing a theoretical framework for the study of viscous/diffusive gravity waves. Graphic abstract

Global Optimization and Quantitative Assessment of Large-Scale Renewables-Based Hydrogen System Considering Various Transportation Modes and Multi-Field Hydrogen Loads

In the past, hydrogen was mostly produced from fossil fuels, causing a certain degree of energy and environmental problems. With the development of low-carbon energy systems, renewable energy hydrogen production technology has developed rapidly and become one of the focuses of research in recent years. However, the existing work is still limited by small-scale hydrogen production systems, and there is a lack of comprehensive research on the whole production-storage-transportation-utilization hydrogen system (PSTUH2S), especially on the modeling of different hydrogen transportation modes and various hydrogen loads in different fields. To make up for these deficiencies, the specific physical and mathematical models of the PSTUH2S are firstly described in this paper, with a full account of large-scale water-electrolytic hydrogen production from renewable power curtailment and grid power, various hydrogen storage and transportation modes, and multi-field hydrogen consumption paths. Furthermore, to achieve the maximum economic, energy, and environmental benefits from the PSTUH2S, a multi-objective nonlinear optimization model is also presented herein and then solved by the hybrid method combining the nonlinear processing method, the CPLEX solver and the piecewise time series production simulation method. Lastly, case studies are conducted against the background of a region in northwest China, where hydrogen consumption capacity in various years is accurately assessed and the potential advantages of the PSTUH2S are demonstrated. As the simulation results show, the power curtailment of renewable energy generation can be reduced by 3.61/11.87/14.72 billion kW·h in 2025/2030/2035, respectively, thus contributing to a 4.98%~10.09% increase in the renewable energy consumption rate and millions of tons of carbon emission reduction in these years. In terms of the total equivalent economic benefits, the proposed method is able to bring about a cost saving of USD 190.44 million, USD 634.66 million, and USD 865.87 million for 2025, 2030, and 2035, respectively.

Feasibility study of nonlinear ultrasonic imaging using a contact pulse-echo method for fatigue damage evaluation

ABSTRACT A contact pulse-echo nonlinear imaging method is proposed for the detection and localisation of fatigue damage in solid materials. A dual element transducer is designed based on nonlinear wave simulations and manufactured to improve the signal-to-noise ratio of harmonic waves. The transducer is clamped on a fixture device for scanning. The proposed method is introduced for scanning and imaging stainless steel specimens with different fatigue damage states. Experimental results for the specimen in the initial state show that both the fundamental and second harmonic waves are well measured and the imaging of nonlinear parameters is very stable over the scanning area. The imaging results for the specimen with an initial fatigue crack show that the fundamental waves remain the same but the second harmonic waves vary significantly in the potential growth area of the fatigue crack. Furthermore, the imaging results for the seriously fatigued specimen show that the amplitudes of fundamental waves decrease near the fatigue crack, while the amplitudes of second harmonic waves increase. These results indicate that the proposed pulse-echo method is effective for nonlinear ultrasonic imaging and early damage evaluation. The factors affecting the nonlinear waves in the lab experiments and possible problems with practical applications are also discussed for the proposed method.

Acceleration of a wave-structure interaction solver by the Parareal method

Potential flow theory-based solvers are commonly used in ocean engineering to investigate the interactions between ocean waves and floating bodies. Depending on assumptions, several methods have been proposed. Among them, the Weak-Scatterer method is an interesting trade-off in the sense that this approach is not limited in theory by the small wave amplitudes and small body motions assumptions of linear methods. Moreover, this approach is in practice more stable than the fully non-linear methods. An implementation of the Weak-Scatterer method is the WS-CN code (Letournel, 2015; Chauvigné, 2016; Wuillaume, 2019).The computational time of the WS-CN code which is considered in the present study is relatively long for engineering purposes. In order to reduce it, the present paper presents an implementation of the Parareal method in the WS-CN code. The Parareal method is an algorithm for parallelizing a simulation in time that can accelerate the complete simulation (Lions, 2001) . This is a key difference in comparison to other acceleration techniques which have been studied in the literature (e.g. the Fast Multipole Method (FMM), the precorrected Fast Fourier Transform (pFFT) method, … ). To the authors’ knowledge, the present study is the first to couple the Parareal method to a potential flow theory-based wave-structure interaction solver. It is shown that the method can significantly reduce the computational time for small wave steepness, but that the performance decreases rapidly with increasing steepness.

A New Modified Secant Condition for Non-linear Conjugate Gradient Methods with Global Convergence

A New Modified Secant Condition for Non-linear Conjugate Gradient Methods with Global Convergence