Nonlinear Method Research Articles

Determination of boundary conditions from the solution of the inverse heat conduction problem in the gas nitriding process

Two non-linear unsteady methods for solving the inverse heat conduction problem are discussed and compared in this paper. The first method is based on the finite element method, uses the variational calculus and the BFGS (Broyden-Fletcher–Goldfarb–Shanno) optimization algorithm. The second is an analytical and numerical method based on the approximation of the solution in the form of a linear combination of Chebyshev polynomials. In numerical tests, the stability of the temperature, heat flux density, and heat transfer coefficient obtained from both methods was analyzed. On the basis of experimental data, oscillations of the measured gas temperature and temperature in the component were analyzed. Oscillations of the gas temperature obtained from the experiment were taken into consideration during tests. The first method to solve the inverse problem was used to determine the boundary conditions for the entire gas nitriding process. As a result, stable values of temperature, heat flux density, and the heat transfer coefficient on the surface of the component under treatment in a real gas nitriding process, so far unpublished, were obtained.

KFDAE: CircRNA-Disease Associations Prediction Based on Kernel Fusion and Deep Auto-Encoder.

CircRNA has been proved to play an important role in the diseases diagnosis and treatment. Considering that the wet-lab is time-consuming and expensive, computational methods are viable alternative in these years. However, the number of circRNA-disease associations (CDAs) that can be verified is relatively few, and some methods do not take full advantage of dependencies between attributes. To solve these problems, this paper proposes a novel method based on Kernel Fusion and Deep Auto-encoder (KFDAE) to predict the potential associations between circRNAs and diseases. Firstly, KFDAE uses a non-linear method to fuse the circRNA similarity kernels and disease similarity kernels. Then the vectors are connected to make the positive and negative sample sets, and these data are send to deep auto-encoder to reduce dimension and extract features. Finally, three-layer deep feedforward neural network is used to learn features and gain the prediction score. The experimental results show that compared with existing methods, KFDAE achieves the best performance. In addition, the results of case studies prove the effectiveness and practical significance of KFDAE, which means KFDAE is able to capture more comprehensive information and generate credible candidate for subsequent wet-lab.

Prediction of Wells Performance and Producing Life Applying Production Decline Analysis

Analyzing the production data became a common method in modern reservoir engineering practice, which is used to dynamically indicate the reservoir's characteristics, predict long-term performance, and determine the reservoir's criteria through daily production analysis. Input data required to analyze production data is production rate and sometimes flow pressure (if any). The decline curve analysis method analyzes well production data to history matching and forecasts the future well performance. The decline curve analysis (DCA) method is a non-linear regression method for production history matching and prediction. In this study, we used the DCA method to analyze eight oil wells' production data produced from the Mishrif reservoir in an Iraqi oil field. This work dealt with the prediction of the reservoir’s performance and future production rate using the DCA method tool integrated with IPM- MBAL software. Production decline rate trend analysis was performed by generating standard curves utilizing exponential, hyperbolic, and harmonic decline model equations based on historical production data. Afterward, a production forecast model was built for production to 2025. The producing life for each well at the economic flow rate (300 bbl/Day) is estimated. Results from the production forecast showed that the exponential and hyperbolic decline models yielded 54.057 MMSTB and 80.73 MMSTB, respectively. The decline rates for hyperbolic and exponential models till 2025 were estimated as 4614.25 STB/Day and 1153.1STB/Day.

Systematic comparison of unsupervised feature extraction methods for enhancing discrimination accuracy of brown rice flour adulteration in LIBS

Laser-induced breakdown spectroscopy (LIBS) is widely applied in various critical fields due to its technical advantages. However, with the explosive growth in spectral data volume, the challenges of high-dimension and redundant information of spectra are becoming increasingly prominent. Therefore, dimensionality reduction of spectra is crucial for LIBS. In this study, to enhance the discrimination accuracy of brown rice flour and its adulterants, a systematic comparative analysis of eight unsupervised feature extraction methods was conducted, including principal component analysis (PCA), non-negative matrix factorization (NMF), independent component analysis (ICA), multidimensional scaling (MDS), kernel PCA (KPCA), locally linear embedding (LLE), Laplacian eigenmaps (LE), and isometric mapping (ISOMAP). The results indicate that linear feature extraction methods (PCA, NMF, ICA, and MDS) show a more obvious improvement in the analytical performance of the classification models, compared to nonlinear feature extraction methods (KPCA, LLE, LE, and ISOMAP). Among these methods, the commonly used PCA has the best improvement effect. The accuracy, macro precision, macro recall, and macro F1-score of the classification models improve from 92.73%, 94.13%, 92.92%, and 0.93 to 95.52%, 95.67%, 95.63%, and 0.96. Therefore, this study can provide experience and guidance for selecting appropriate unsupervised feature extraction methods in subsequent research, contributing to the further application and development of LIBS.

Effect of Corrosion-Induced Structural Degradation on the Ultimate Strength of a High-Tensile-Steel Ship Hull

Standard structural assessments of ship hulls include the evaluation of the elastic structural response. Elastic analysis neglects extreme and unpredicted loadings, which can produce catastrophic outcomes, such as the loss of the ship’s ultimate strength. Moreover, hull elements are considered unaffected by age-related degradation. Therefore, this study models and quantifies the effect of corrosion-induced structural degradation on the ultimate strength of a high-tensile-steel (HTS) cargo ship using progressive collapse and nonlinear finite element methods. Uniform and pitting corrosion are modeled through selected scenarios, which hull elements might encounter during exploitation, producing a total of 148 calculation models. The findings show that corrosion-induced degradation can significantly decrease the ultimate strength of the hull (up to 30% for the most severe scenarios assessed). Furthermore, ultimate strength decreases almost proportionally to the amount of wastage considered. It was found that stiffener corrosion has a significant effect on the total ultimate strength. This study’s aim is to emphasize the vast importance of including ultimate strength along with ageing effects in industry-standard structural assessments of large HTS ship structures, designed to last for several decades whilst exposed to excessive and unpredicted bending moments.

Comparison of nonlinear modeling methods for the composite rubber clamp

Comparison of nonlinear modeling methods for the composite rubber clamp

Characteristics analysis and nonlinear control of a digital hydraulic pressure tracking system for high-speed helicopter wet friction clutch

The reliability and control precision of the engagement and disengagement of wet friction clutch are crucial to the transmission of high-speed helicopters. In contrast to the traditional proportional hydraulic system, the digital hydraulic system provides a viable solution due to the use of several fast switching valves (FSVs). In this research, a digital hydraulic pressure tracking system using two fast switching valve arrays (DHPTS-FSVA) is proposed and its nonlinear model is established. Firstly, the static and dynamic characteristics of the DHPTS-FSVA are deeply analyzed by virtue of the half-bridge resistance theory. Moreover, a novel pressure control strategy is proposed, which consists of nonlinear adaptive control method, differential PWM with pressure compensation, and logic allocation strategy of PWM duty ratio. Finally, comparative simulation and experimental results indicate that the maximum, average, and standard deviation of the errors are reduced by at least 16.1%, 45.1%, and 39.5%, respectively, at the tracking frequencies of 1Hz and 2Hz, which proves that the proposed controller exhibits better tracking performance at low frequencies.

Dynamical behaviour of a new model for the UJT relaxation oscillator

We propose a new two dimensional model for the UJT (Unipolar Junction Transistor) relaxation oscillator whose parameters were chosen by fitting the experimental data. The dynamical properties of the model were studied by using nonlinear dynamics methods and it was proved that self-sustained oscillations may occur. Then, the system was forced to study the transition to chaos, reproducing the torus breakdown mechanism observed experimentally. Finally, two identical systems were diffusively coupled and the synchronization properties have been studied.

Do Increases and Decreases in Non-renewable Energy Consumption Have the Same Effect on Growth in Türkiye?

This study examines the relationship between fossil energy consumption (FEC) and economic growth by applying the non-linear ARDL method in the Türkiye sample. This relationship was addressed in 3 different models to eliminate the multicollinearity between the oil, natural gas, and coal variables that make up the FEC. According to the analysis results, all models have an asymmetric cointegration between the variables. In all models, the effect of decreases in energy consumption on economic growth is more dominant than increases in the long run. According to the causality results, the neutrality hypothesis is valid for coal consumption, the feedback hypothesis is valid for natural gas consumption, and the growth hypothesis is valid for oil consumption.

Experimental Research on Dynamic Characteristics of a Multi-Disc Rotor System Supported by Aerostatic Bearings

Gas bearings have the advantages of small friction loss, wide applicable speed range, no pollution, etc., and have important application prospects in micro and small high-speed rotating machinery. However, due to its compressibility and low viscosity, its dynamic stability in high-speed rotating machinery is the key to constraining its development. The experimental study of shaft system dynamics is the main means to explore the mechanism of rotor behavior. On the test platform of dynamic characteristics of multi-disc rotor system supported by aerostatic bearings, experimental research on the nonlinear dynamic characteristics of a rotor system was carried out, and nonlinear vibration test and analysis methods, such as axial orbits, bifurcation diagrams, and spectral characteristics, were adopted, and vibration phenomena, including the critical rotational speed accumulating energy and low-frequency accumulating energy, were presented and the vibration characteristics of bearing fracture faults were presented. The bearing supply pressure and rubber damping pad were introduced as a method to suppress the low-frequency vibration of the aerostatic bearing rotor system, and its vibration-reduction effect was verified by experiments. The above results can provide technical support for vibration control and fault diagnosis of rotor systems supported by aerostatic bearings.

Backstepping Control of an AC/DC/AC Converter in a Grid Connected Wind Power System

The contribution of this paper is to study a nonlinear control approach known as the backstepping control method to manage reactive and active power using new parametric values for the grid connected wind power generation system. Specifically, the research focuses on a system containing a wind turbine system, a permanent magnet synchronous generator (PMSG), and a grid connected via AC/DC/AC converter. A comprehensive mathematical model for both the wind turbine system, PMSG, and the grid connected via AC/DC/AC converter was developed for this purpose. The Simulation results of the grid-connected wind power generation system are presented and analyzed to show the performance of the nonlinear backstepping control method. The characteristics of the response to variations in generator speed and the power injected into the grid show the highlight of the performance of the backstepping method, under varying wind conditions.

Neural network prediction model for site response analysis based on the KiK-net database

Currently, the most widely used site response analysis methods include linear, equivalent linear and nonlinear approaches. However, the results of these analyses gradually deviate from the true values as the site softens or the earthquake intensity increases. To overcome this issue, this study employs a 1D Convolutional Neural Network model to simulate the relationships between the surface and downhole motions. To ensure comprehensive coverage of various sites and earthquake conditions, a careful selection of stations and seismic intensities resulted in 56 stations and 34,538 seismic records from KiK-net. Additionally, 30 seismic intensity measures and three site condition parameters were chosen. The convolutional operation was utilized to consider the correlations between the parameters, enabling the prediction of surface motion intensity measures. The performance of the neural network model was assessed based on residual analysis, and the model’s generalization ability was tested using samples that were not included in the training dataset. The results demonstrate that the neural network can effectively predict surface motion intensity measures. Furthermore, in comparison with the equivalent linear and nonlinear methods that do not rely on site-specific detailed soil data, the 1D Convolutional Neural Network exhibits superior performance and maintains high prediction accuracy even for soft soil and strong earthquake scenarios, confirming the enhanced predictive capability of the proposed model.

Role of nonlinear transmission term in stability of hand, foot and mouth disease dynamics

Aim: This study focuses on the nonlinear characteristics of two linearly stable equilibrium states within a theoretical hand, foot and mouth disease (HFMD) dynamics model. Methods: The conditional nonlinear optimal perturbation method, the Lyapunov method and the linear singular vector method are employed. Results: By utilizing the conditional nonlinear optimal perturbation method, it is determined that the two linearly stable equilibrium states (namely the free disease and disease HFMD states) also exhibit nonlinear stability. It is found that the stabilities of the free disease and disease HFMD equilibrium states differ in terms of returning to their original states. Conclusion: It is discovered that nonlinearity plays a crucial role in reinstating the original equilibrium states.

A Multistage Nonlinear Method for Aeroengine Health Parameter Estimation Based on Adjacent Operating Points

Abstract Health parameter estimation is the core of engine gas path analysis (GPA), which is widely adopted for engine safety improvement, as well as for operation and maintenance cost reduction. The major challenge of GPA lies in the contradiction between the high dimensions of parameters under estimation, e.g., health parameters, and the limited measurements obtainable from a small number of sensors. Existent GPA methods for health parameters commonly apply dimension reduction before estimation, leading to information loss and hence inaccurate estimation. To tackle the challenge of limited sensor measurements and to have more system outputs than parameters under estimation, we proposed to augment the output vector of the system model by combining the measurements from multiple adjacent operating points. But the engine model can face the problem of homogenization if using data from adjacent operating points. This can, in turn, lead to a low identifiability of parameters. We analyze the internal mechanism of such large deviation of the parameter estimation results based on linear models and argue for the need of nonlinear method. Hence, we propose a multistage nonlinear parameter estimation method for health parameters, combining biased and unbiased estimation. In our extensive simulations based on 10 output measurements of a JT9D engine, our method can estimate 130% more parameters than the widely used GPA method, while reducing the maximum estimation error of health parameters from 2.2% to 0.1%.

Experimental study on flexural behavior and bending capacity prediction of Q550E steel beams within corroded shear span

An experimental study is carried out to investigate the degradation behavior of Q550E HPS steel beams with corroded shear span. At first, tensile tests of 15 pieces of steel are undertaken to obtain the degradation law of mechanical property parameters. Four steel beams with different corrosion damage levels in shear span are designed by electrochemical accelerated corrosion. The flexural loading tests of corroded steel beams are conducted, and the mechanical response of local corrosion to steel beams behavior is discussed. The necessity of lateral bracing is discussed theoretically. Considering the constitutive model affected by corrosion and the role of stiffeners, a predictive model of bending bearing capacity is proposed. The results show that the increasing corrosion damage will cause the failure position to move from mid-span to shear span, and the failure mode will shift from mid-span compressive flange buckling to bending-shear buckling, and finally appear web buckling. Corrosion damage level higher than 10% will lead to insufficient strain development. The proposed model can predict the flexural capacity and deflection well. Compared with the test results, the bearing capacity and deflection of corroded HPS beams are predicted by the nonlinear iterative method with high accuracy.

E-waste circular economy decision-making: a comprehensive approach for sustainable operation management in the UK

AbstractE-waste generation has broadly increased worldwide and is called intense pressure on sustainable practice implementation firms by recycling and redesigning the products. Thus, e-waste operation management in developed countries like the UK has become the top priority and is subjected to multiple sustainable circular economies (CE) contributing factors, including social, technical, environmental, and governmental policies. The authorized decision-makers can benefit from a well-established systematic decision-making tool to assess and evaluate the e-waste operation management considering the potential CE contributing factors. An extensive literature overview is expanded to identify the most relevant and influential contributing factors to e-waste CE. The city of London Metropolitan has been selected as the case location. In this regard, it is necessary to utilize an advanced multi-criteria decision-making tool to explore the interdependency and causality of CE-relevant factors. The present study proposed an innovative decision-making approach to address the multiple contributing factors of causality, interdependency, data, and model uncertainty in practice. It uses the step-wise weighted influence nonlinear gauge system method integrated with Fermatean fuzzy linguistic sets. This study conducted a sensitivity analysis to evaluate the effectiveness of the proposed decision-making approach in e-waste operation management. The results are promising, clearly demonstrating the framework’s competence. The CE index, crucial in designing e-waste operation management strategies, was calculated to be 2.8036. Among the various factors analyzed, “Environmental Management Systems” emerged as the most significant driving factor. This underscores the critical need to improve environmental management systems within e-waste operations.

A novel method for studying the wind speed probability distribution and estimating the average wind energy density

Traditional distribution models generally have large fitting errors at low wind speeds and poor fitting effects at multi-peak wind speed distributions. In this paper, a novel approach is proposed to fit different wind speed distributions, introducing a Gumbel distribution into common hybrid distribution models. The model parameters are solved by a combination of snake optimizer and nonlinear least squares (SO-NLS), using the optimal values obtained by the nonlinear least squares method as a set of initial input vectors for the snake optimizer. Simulation experiments were conducted using multi-peak wind speed distribution datasets with varying characteristics, comparing the fitting performance of the improved hybrid models against the conventional Weibull, Normal, and Rayleigh hybrid models. The results show that the proposed approach improved the model fit effects, particularly at low wind speeds, in all five experimental datasets. In most cases, the overall fitting effects were also improved. Furthermore, the validity and superiority of the improved hybrid models were further verified by comparing the estimated average wind energy density. Meanwhile, the experimental results also verified that SO-NLS not only yielded better optimization results but also accelerated the convergence speed than the snake optimizer. The improvements presented in this study effectively address the problem of large fitting errors at the low wind speed sections of the distribution, providing a theoretical basis for wind farm planning and design.

Prediction of Aircraft Departure/Spin Characteristics by Improving Kalviste Decomposing and Weak Nonlinear Analysis Method

Prediction of Aircraft Departure/Spin Characteristics by Improving Kalviste Decomposing and Weak Nonlinear Analysis Method

Nonlinear optimization DIC method inspired by unsupervised learning for high order displacement measurement

Digital Image Correlation (DIC) is the most widely used non-contact full-field strain measurement method, but due to the influence of subset calculations in principle, measuring complex deformation with high strain gradients within the subset remains a challenge. DIC based on neural networks performs well in complex deformation measurement scenarios, but its measurement accuracy and generalization ability depend on extensive training sets. This paper proposes a nonlinear optimization DIC method inspired by unsupervised learning that requires only a single pair of images. Unlike traditional unsupervised algorithms of optical flow estimation or Particle Image Velocimetry (PIV), the shape function in traditional DIC is incorporated into the loss function. This allows the use of only the reference image and the deformed image as input dataset, and the correct displacement field can be output after parameter optimization through training. This method does not require additional training sets to measure high-order strain fields like traditional neural networks-based DIC. The proposed method has demonstrated promising results in simulation experiments for high-order strain measurement and does not require additional datasets of the same type. In the measurement of the star-shaped displacement fields, its accuracy is better than the traditional DIC based on the subset, and it maintains convergence even when the strain is large, a situation where traditional DIC fails to converge. In addition, compared with the network obtained by supervised training as a pre-trained model, the method proposed in this paper can achieve superior results. The methods of the article can theoretically be applied to the result optimization of other networks beyond those discussed in this paper.

Joint shear strength prediction for fiber reinforced concrete beam-to-column connections

Beam-to-column joints experience substantial shear forces and deformations, playing a pivotal role in maintaining the overall stability and integrity of moment-resisting frames under earthquake loading. If fiber reinforced concrete is used instead of reinforced concrete, beam flexural failure can be achieved, which leads to a ductile behavior and increased energy dissipation capacity, when compared to joint shear failure. To ensure a ductile failure mode, accurate prediction of the joint shear strength is essential. However, there are only a limited number of analytical studies on predicting the shear strength of fiber reinforced concrete joints, most of which are only applicable to steel fibers. In this study, a comprehensive database of prior experiments conducted on fiber reinforced concrete beam-to-column connection subassemblies is compiled. Based on Pearson Correlation Analyses, the factors influencing the seismic response are determined to be the composite tensile cracking strength, axial load on the column, aspect ratios of member dimensions, and specific fiber properties such as aspect ratio and volume fraction. A joint shear strength prediction equation is then developed utilizing statistical nonlinear regression method. Validation against experimental data confirms that the proposed equation provides conservative estimates of joint shear strength and can be utilized for composites with any fiber type, even hybrid fibers; in contrast to existing equations which often lead to overestimation of strength and restricted to a specific fiber type. Moreover, the proposed equation provides engineers a practical tool to assess the seismic behavior of such connections, which has not been addressed by current structural design codes yet. The improved accuracy of the proposed equation, demonstrated by the lowest mean absolute error and coefficient of variation and the highest coefficient of correlation, positions it as a promising candidate for integration into structural design codes.