Nonlinear Algorithm Research Articles

Two-dimensional imaging of elastic properties of rock core samples from measurements of angle-dependent ultrasonic reflection coefficients

Laboratory and field measurements often fail to identify small-scale variations in rock elastic properties. Due to limited spatial resolution, conventional laboratory methods cannot properly describe rock formations exhibiting a high degree of heterogeneity, thereby masking differences between stiff and compliant layers. Continuous sample measurements can mitigate this problem but are not widely used by the industry. We build upon our previous work and apply laboratory angle-dependent ultrasonic reflection coefficient (ADURC) measurements to achieve detailed two-dimensional descriptions of the elastic properties of complex rock samples. This method successfully yields high-resolution information on P- and S-wave velocities, as well as bulk density, across the surface of rock samples. Elastic properties are estimated using a nonlinear inversion algorithm that matches laboratory measurements with numerical simulations. ADURC data acquired at various sample locations enable detailed rock descriptions, where the effective measurement area is determined by the size of the receiver, measurement frequency, and incidence angle. Consequently, the sampling area is smaller compared with triaxial loading and acoustic transmission tests, for which the resolution is controlled by sample size. Measurements conducted on samples exhibiting different levels of spatial complexity validate the capability of the ADURC method to identify small-scale heterogeneities. For the reported experiments, variations in angle-dependent reflectivity give rise to corresponding variations in the estimated P- and S-wave velocities and density, which can exceed 60%. These small-scale variations across heterogeneous rock samples often are overlooked by conventional laboratory methods.

Energy-Saving Data Acquisition Model of Wireless Sensor Network Based on Nonlinear Algorithm

Wireless sensor network significant data acquisition has a high cost, long completion time, and low accuracy. This paper adopts a sensor network data acquisition method based on a nonlinear algorithm to solve the above problems. In this paper, a distributed data acquisition method based on nonlinear regression is established by combining the time series relationship of data. First, this paper uses nonlinear regression analysis technology to establish the sensing data model and retain the characteristics of the sensing data. This makes the node pass only the parametric data of the regression model. This paper uses this method to replace the transmission of actual monitoring sensory data information. Experiments show that this method can effectively reduce data redundancy and network traffic under any conditions. The method has been verified in practical WSN applications.

Research on Dynamic Optimization Algorithm of Warehousing Location Layout Based on Nonlinear Optimization

The paper aims to improve the turnover rate and operation efficiency of goods that are shipped out and replenished in the warehouses of electric power enterprises through big data analysis and optimization algorithms.The data is distributed in diverse locations and data nonlinear optimization algorithms certainly helps to understand the patterns for effective management of warehouses.This article focuses on reducing the delay in the operational processes.A multi-objective optimization (MOO) has been proposed which is aiming at improving the efficiency of transition process of commodities, storage, and overall warehouse operations.The study helps in the optimization of the allocation of cargo spaces with the aid of big data analysis optimization technology which collects and manages data in a distributed environment. A multi-objective cargo space optimization algorithm is proposed along with consideration of dynamic constraints.The algorithm is based on the coefficient of variation adaptive differential evolution algorithm.Individual decoding is performed according to the real-time cargo space availability.The simulation results show that the convergence speed of the algorithm is greatly improved.Meanwhile, the efficiency of warehouse transition process, shelf stability and the classification of commodities are remarkably improved.In nutshell, the multi-objective decision-making with the integration of big data analysis optimization technology assists in the effective organization of warehouse allocation system by considering multiple factors and constraints.

Simulation of a synchronized methodology for MR-based electromechanical property imaging during transcranial electrical stimulation

Introduction: Recent investigations into the biomechanics of the brain have unveiled alteration in tissue stiffness triggered by external stimuli. For instance, visual stimulation effects can be measured in elasticity images of the cortex generated by functional magnetic resonance elastography (MRE). Such a mechanical characterization method combined with non-invasive brain stimulation (NIBS), a technique that seeks to selectively modulate particular parts of the brain using weak electrical currents, has the potential to influence research on various neurological disorders. In this in silico study, we aimed to elucidate individual and interdependent aspects related to a synchronized biomechanical imaging and non-invasive brain stimulation methodology. Magnetic resonance electrical impedance tomography (MREIT) was incorporated to the pipeline, providing a promising way of evaluating NIBS-induced electrical current patterns in the brain while leveraging MRE and transcranial alternating current stimulation (tACS) experimental settings.Methods: A mouse head model was assembled using open-access atlases to include five anatomical structures: skin/subcutaneous tissue, skull, cerebrospinal fluid (CSF), brain white and grey matters. MRE, tACS, and MREIT experiments were simulated using Comsol Multiphysics with Matlab Livelink. Synthetic MRE and MREIT data were processed using the subzone non-linear inversion and harmonic Bz algorithm, respectively, to reconstruct images of the distributed complex shear modulus and electrical conductivity.Results and Discussion: Lorentz body forces arising from simultaneous MRE and tACS elicited elastic waves of negligible amplitude compared with the extrinsic actuation levels reported in the literature, which allowed accurate reconstructions of the complex shear modulus. Qualitative electrical conductivity maps retrieved by MREIT accurately delineated anatomical regions of the brain model and could be used to recover reasonably accurate distributions of tACS-induced currents. This multi-physics approach has potential for translation to human brain imaging, and may provide more possibilities for the characterization of brain function together than in isolation.

Large deformation assessment of three-tower suspension bridges: An enhanced analytical model and solution algorithm

An enhanced nonlinear approach is proposed in this study to address the limitations of traditional deflection theory in analyzing large deformations of three-tower suspension bridges. In this approach, the three-tower suspension bridge is simplified as two quasi-independent bridges for analysis, and detailed considerations are given to the vertical and longitudinal deformations of the main cable, which produce the expression for the relationship between the cable's internal force and deformations. By employing the complementary energy principle and variational calculus, the nonlinear differential equations describing bridge deformations are then established. To ensure the displacement continuity at the middle tower, this paper proposes the use of Chebyshev polynomials to approximate the solutions of the differential equations, and the weighted residual method is then used to transform these differential equations into algebraic equations. On this basis, the developed nonlinear adjustment optimization algorithm enables efficient solving of the nonlinear equation and thus determination of bridge deformation under various load conditions. The accuracy and effectiveness of the proposed scheme are validated through the analysis of two suspension bridges with equal and unequal spans. Finally, the extended applications of the proposed scheme on the other type of multi-span suspension bridges are introduced for further applications.

A novel approach for generalized Green-Naghdi-type electro-magneto-thermo-hyperelasticity wave propagation and reflection investigations in near-incompressible layers under shock loads

A novel nonlinear coupled finite-strain electro-magneto-thermo-hyperelasticity (EMTHE) model is developed for the first- and second-sound wave propagation and reflection investigations in media that are exposed to electromagnetic fields and mechanical shocks. In contrast to the previous studies which studied behaviors of the finite-strain elastic or incompressible materials with small deformations, the current research proposes a much more complicated but much more accurate novel practical model for wave propagation and reflection analyses in near-incompressible finite-strain materials. Furthermore, to evaluate the effects of the electro-magneto-thermomechanical coupling, the strain energy density function of the hyperelastic material is expanded in a new way. The governing equations are obtained according to a nonlinear version of the Helmholtz free energy. The energy equations comprise the first- and second-order time rates of the temperature to enable the modeling of the finite-speed heat transfer; i.e., the establishment of a second-sound model. A nonlinear iterative finite element solution algorithm is proposed and implemented for the resulting coupled time-dependent generalized electro-magneto-thermo-hyperelasticity equations. The results show significant differences between the predicted wave propagation and reflection characteristics and behaviors of the near-incompressible and incompressible finite-strain models.

Sex determination based on craniometric parameters: a comparative approach between linear and non-linear machine learning algorithms

Introduction: Determining sex based on cranial characteristics is of great relevance in forensic anthropology. Most studies have employed linear methods (such as logistic regression) for this estimation with accuracies around 70%, rarely exceeding 90% accuracy. Several authors have tested non-linear models such as neural networks, support vector machines, and decision trees with good results, surpassing linear models. Objective: To compare linear models (logistic regression, linear regression, and linear discriminant analysis) with non-linear models (neural networks, extreme gradient boosting, support vector machine, naive Bayes, random forest, decision tree, k-nearest neighbors, and adaptive multivariate spline regression). Materials and Methods: 241 skulls used in this study were obtained from the collection of Center for Study and Research in Anatomy and Forensic Anthropology at Tiradentes University, Farolândia campus in Aracaju, Sergipe. Each skull in the collection has secure detailed records. Eighty-nine skulls with signs of craniotomy (n=58) or damage (n=30) and one unidentified were excluded. The 152 eligible skulls underwent cranial measurements. Using the Anaconda platform and Jupyter editor, the data were divided into a training group (80% of the sample) and then were tested (20% of the sample). Eleven machine learning algorithms, including both linear and non-linear models, were applied. Results: The best machine learning algorithm was a neural network with average accuracy of 93%, after 50 runs. The difference to logistic regression, which had an accuracy of 68%, was significantly (p-value of 0.01016). Conclusion: This study demonstrated the potential of the neural network for solving the sex classification problem. The study has a limitation in that neural networks perform better with a large volume of data, and this study used data from a single center. Nevertheless, in the future, more studies should be conducted testing neural networks with larger samples and skulls from other continents.

The tracing algorithm of re-entry vehicle based on SMO

The tracing problem of a re-entry vehicle includes the characters of lacking prior information on the target and disturbances. Thus, the classic nonlinear filtering algorithms are not suitable for high-accuracy tracing fields. In order to solve the problem, the tracing algorithm of a re-entry vehicle based on SMO is presented in this paper. SMO stems from the depth research of sliding mode control, which has nice robustness to disturbances and model error. The results of the simulation show that the tracing algorithm based on SMO has high accuracy and nice robustness.

Pixelwise high-temperature calibration for in-situ temperature measuring in powder bed fusion of metal with laser beam

High-temperature calibration methods in additive manufacturing involve the use of advanced techniques to accurately measure and control the temperature of the build material during the additive manufacturing process. Infrared cameras, blackbody radiation sources and non-linear optimization algorithms are used to correlate the temperature of the material with its emitted thermal radiation. This is essential for ensuring the quality and repeatability of the final product. This paper presents the calibration procedure of an imaging system for in-situ measurement of absolute temperatures and temperature gradients during powder bed fusion of metal with laser beam (PBF-LB/M) in the temperature range of 500 K–1500 K. It describes the design of the optical setup to meet specific requirements in this application area as well as the procedure for accounting the various factors influencing the temperature measurement. These include camera-specific effects such as varying spectral sensitivities of the individual pixels of the sensor as well as influences of the exposure time and the exposed sensor area. Furthermore, influences caused by the complex optical path, such as inhomogeneous transmission properties of the galvanometer scanner as well as angle-dependent transmission properties of the f-theta lens were considered. A two-step fitting algorithm based on Planck's law of radiation was applied to best represent the correlation. With the presented procedure the calibrated thermography system provides the ability to measure absolute temperatures under real process conditions with high accuracy.

The non-linear dynamics of South Australian regional housing markets: A machine learning approach

Traditional linear models often struggle to capture regional housing markets' complex, non-linear dynamics. This study addresses this gap by developing and applying advanced machine learning algorithms to unlock unique insights into South Australian housing price behavior. Leveraging a comprehensive dataset of over 10,000 regional house sales from 2010 to 2021, we explore the non-linear relationships between housing prices and microeconomic factors (e.g., house size, land area, building quality) and socioeconomic characteristics (e.g., proximity to amenities and income levels). Our analysis employs a multi-step approach, including feature engineering, spatial data integration, correlation tests, multilevel modeling, and non-linear machine learning algorithms including Decision Tree, Random Forest, Gradient-Boosted Tree, and Artificial Neural Network. The key finding is that machine learning models outperform traditional econometric models in predicting regional housing prices, with higher accuracy and greater goodness of fit. Furthermore, we identify specific non-linear relationships, such as the increasing marginal impact of proximity to the sea on house prices as distance decreases. These findings offer valuable insights for policymakers, real estate professionals, and stakeholders, informing regional planning, infrastructure provision, and economic development strategies. This study sheds light on the complex dynamics of South Australian housing markets and lays the foundation for further research.

Positioning algorithm based on space constraint of the PD array in VLP system

Due to factors such as indoor multipath effects and noise, the positioning signal becomes unstable, posing a challenge for visible light positioning systems relying on a single photodetector (PD) to achieve accurate position estimation. To enhance localization precision and ranging accuracy, a positioning algorithm based on spatial constraints of the PD array is introduced in this paper. By leveraging spatial information from the PD array and the channel state information (CSI) from multiple PDs, cross-matching among multiple PDs is performed to alleviate the limitation of unstable positioning information of a single PD during the positioning process. Moreover, the distances obtained through cross-matching are fused with those based on CSI, and the measured distance is iteratively updated to reduce the interference of reflection paths on ranging. This algorithm utilizes the spatial arrangement of the PD array to constrain positioning information received by multiple PDs, rather than relying on a single PD for positioning. This method can achieve joint optimization of positioning accuracy and ranging accuracy without requiring additional equipment or modifying the transceiver structure. Simulation results within a 4 m × 4 m × 3 m indoor space showcase the proposed method's effectiveness. The average positioning error has been reduced to 1.28 cm, and the root mean square error has been reduced to 1.51 cm. In comparison to the least squares (LS) algorithm based on CSI and the nonlinear LS algorithm based on CSI, the new approach reduces average localization errors by approximately 50.4% and 41.3%, respectively. Additionally, the algorithm attains a ranging accuracy of 3.86 cm, outperforming CSI-based distance estimation accuracy by 41.9%.

Autonomous flight performance optimization of fixed-wing unmanned aerial vehicle with morphing wingtip

PurposeThe purpose of this paper is to improve autonomous flight performance of a fixed-wing unmanned aerial vehicle (UAV) via simultaneous morphing wingtip and control system design conducted with optimization, computational fluid dynamics (CFD) and machine learning approaches.Design/methodology/approachThe main wing of the UAV is redesigned with morphing wingtips capable of dihedral angle alteration by means of folding. Aircraft dynamic model is derived as equations depending only on wingtip dihedral angle via Nonlinear Least Squares regression machine learning algorithm. Data for the regression analyses are obtained by numerical (i.e. CFD) and analytical approaches. Simultaneous perturbation stochastic approximation (SPSA) is incorporated into the design process to determine the optimal wingtip dihedral angle and proportional-integral-derivative (PID) coefficients of the control system that maximizes autonomous flight performance. The performance is defined in terms of trajectory tracking quality parameters of rise time, settling time and overshoot. Obtained optimal design parameters are applied in flight simulations to test both longitudinal and lateral reference trajectory tracking.FindingsLongitudinal and lateral autonomous flight performances of the UAV are improved by redesigning the main wing with morphing wingtips and simultaneous estimation of PID coefficients and wingtip dihedral angle with SPSA optimization.Originality/valueThis paper originally discusses the simultaneous design of innovative morphing wingtip and UAV flight control system for autonomous flight performance improvement. The proposed simultaneous design idea is conducted with the SPSA optimization and a machine learning algorithm as a novel approach.

Exploring super-resolution spatial downscaling of several meteorological variables and potential applications for photovoltaic power

We applied a perfect prognosis approach to downscale four meteorological variables that affect photovoltaic (PV) power output using four machine learning (ML) algorithms. In addition to commonly investigated variables, such as air temperature and precipitation, we also focused on wind speed and surface solar radiation, which are not frequently examined. The downscaling performance of the four variables followed the order of: temperature > surface solar radiation > wind speed > precipitation. Having assessed the dependence of the downscaling accuracy on the scaling factor, we focused on a super-resolution downscaling. We found that the convolutional neural network (CNN) generally outperformed the other linear and non-linear algorithms. The CNN was further able to reproduce extremes. With the rapid transition from coal to renewables, the need to evaluate low solar output conditions at a regional scale is expected to benefit from CNNs. Because weather affects PV power output in multiple ways, and future climate change will modify meteorological conditions, we focused on obtaining exemplary super-resolution application by evaluating future changes in PV power outputs using climate simulations. Our results confirmed the reliability of the CNN method for producing super-resolution climate scenarios and will enable energy planners to anticipate the effects of future weather variability.

Comprehensive evaluation measures of nonlinear estimation algorithm performance

Although many scholars say that their algorithms are better than others in the state estimation problem, only a fewer convincing algorithms were applied to engineering practices. The reason is that their algorithms outperform others only in some aspects such as the estimation accuracy or the computation load. To solve the problem of performance evaluation of state estimation algorithms, in this paper, the comprehensive evaluation measures (CEM) for evaluating the nonlinear estimation algorithm (NEA) is proposed, which can comprehensively reflect the performance of the NEAs. First, we introduce three types of the NEAs. Second, the CEM combining the flatness, estimation accuracy and computation time of the NEAs, is designed to evaluate the above NEAs. Finally, the superiority of the CEM is verified by a numerical example, which helps decision makers of nonlinear estimation algorithms theoretically and technically.

Surrogate optimisation strategies for intraocular lens formula constant optimisation.

To investigate surrogate optimisation (SO) as a modern, purely data-driven, nonlinear adaptive iterative strategy for lens formula constant optimisation in intraocular lens power calculation. A SO algorithm was implemented for optimising the root mean squared formula prediction error (rmsPE, defined as predicted refraction minus achieved refraction) for the SRKT, Hoffer Q, Holladay, Haigis and Castrop formulae in a dataset of N = 888 cataractous eyes with implantation of the Hoya Vivinex hydrophobic acrylic aspheric lens. A Gaussian Process estimator was used as the model, and the SO was initialised with equidistant datapoints within box constraints, and the number of iterations restricted to either 200 (SRKT, Hoffer Q, Holladay) or 700 (Haigis, Castrop). The performance of the algorithm was compared to the classical gradient-based Levenberg-Marquardt algorithm. The SO algorithm showed stable convergence after fewer than 50/150 iterations (SRKT, HofferQ, Holladay, Haigis, Castrop). The rmsPE was reduced systematically to 0.4407/0.4288/0.4265/0.3711/0.3449 dioptres. The final constants were A = 119.2709, pACD = 5.7359, SF = 1.9688, -a0 = 0.5914/a1 = 0.3570/a2 = 0.1970, C = 0.3171/H = 0.2053/R = 0.0947 for the SRKT, Hoffer Q, Holladay, Haigis and Castrop formula and matched the respective constants optimised in previous studies. The SO proves to be a powerful adaptive nonlinear iteration algorithm for formula constant optimisation, even in formulae with one or more constants. It acts independently of a gradient and is in general able to search within a (box) constrained parameter space for the best solution, even where there are multiple local minima of the target function.

High spatial resolution diffuse optical tomography based on cross-correlation of chaotic light.

A diffuse optical tomography system with chaotic laser is proposed for the three-dimensional optical phantom. The high signal-to-noise ratio is beneficial to improve the spatial resolution of diffuse optical tomography. It is essential to drive the chaotic laser as the incident light into the optical phantom. The transmitted light emitted from phantom as the detection light and a part of the incident light as the reference light to carry out cross-correlation analysis. The high-density source-detector configuration in parallel plate structure is designed for detecting targets in the phantom. The propagation of chaotic laser in the phantom is studied theoretically and experimentally based on the diffusion equation. Image reconstruction is achieved by the cross-correlation analysis of chaotic laser and the Newton-Raphson nonlinear algorithm. The performance of the proposed system has been assessed by reconstruction localization accuracy and contrast-noise-ratio. The results show that the spatial resolution of the proposed system can reach 1.5 mm and the localization error is less than 1 mm.

Reducing Water Conveyance Footprint through an Advanced Optimization Framework

This study investigates the optimal and safe operation of pumping stations in water distribution systems (WDSs) with the aim of reducing the environmental footprint of water conveyance processes. We introduced the nonlinear chaotic honey badger algorithm (NCHBA), a novel and robust optimization method. The proposed method utilizes chaotic maps to enhance exploration and convergence speed, incorporating a nonlinear control parameter to effectively balance local and global search dynamics. Single-objective optimization results on a WDS show that NCHBA outperforms other algorithms in solution accuracy and convergence speed. The application of the proposed approach on a water network with two variable-speed pumps demonstrated a significant 27% reduction in energy consumption. Expanding our focus to the multi-objective optimization of pump scheduling programs in large-scale water distribution systems (WDSs), we employ the non-dominated sorting nonlinear chaotic honey badger algorithm (MONCHBA). The findings reveal that the use of variable-speed pumps not only enhances energy efficiency but also bolsters WDS reliability compared to the use of single-speed pumps. The results showcase the potential and robustness of the proposed multi-objective NCHBA in achieving an optimal Pareto front that effectively balances energy consumption, pressure levels, and water quality risk, facilitating carbon footprint reduction and sustainable management of WDSs.

Forecasting Stock Market Realized Volatility using Random Forest and Artificial Neural Network in South Africa

Volatility is often used as a key input into several financial models, yet there is still no consensus on the best-performing model in forecasting stock market returns volatility. Conventional time series models such as GARCH are the preferred models in the literature. However, this project aims to first adopt two novel non-linear machine learning algorithms, namely the Random Forest and Artificial Neural Network (ANN). The project then compares the performance of these two models in predicting stock market realized volatility for the JSE Basic Material Index (JBIND) and the JSE Financials Index (JFIN) over a period of five years. Based on the results of the project, the Random Forest model outperformed the ANN model for both the JFIN and JBIND index. Lastly, the COVID effect on the model’s performance was also considered and the results show that the negative impact of COVID on the model’s performance is ambiguous.

Improving the performance of cryogenic calorimeters with nonlinear multivariate noise cancellation algorithms

State-of-the-art physics experiments require high-resolution, low-noise, and low-threshold detectors to achieve competitive scientific results. However, experimental environments invariably introduce sources of noise, such as electrical interference or microphonics. The sources of this environmental noise can often be monitored by adding specially designed “auxiliary devices” (e.g. microphones, accelerometers, seismometers, magnetometers, and antennae). A model can then be constructed to predict the detector noise based on the auxiliary device information, which can then be subtracted from the true detector signal. Here, we present a multivariate noise cancellation algorithm which can be used in a variety of settings to improve the performance of detectors using multiple auxiliary devices. To validate this approach, we apply it to simulated data to remove noise due to electromagnetic interference and microphonic vibrations. We then employ the algorithm to a cryogenic light detector in the laboratory and show an improvement in the detector performance. Finally, we motivate the use of nonlinear terms to better model vibrational contributions to the noise in thermal detectors. We show a further improvement in the performance of a particular channel of the CUORE detector when using the nonlinear algorithm in combination with optimal filtering techniques.

Prediction of Corrosion Inhibition Efficiency Based on Machine Learning for Pyrimidine Compounds: A Comparative Study of Linear and Non-linear Algorithms

The corrosion of materials poses a significant challenge in various industries, leading to substantial economic impacts. In this context, pyrimidine compounds emerge as promising, non-toxic, cost-effective, and versatile corrosion inhibitors. However, conventional methods for identifying such inhibitors are typically time-consuming, expensive, and labor-intensive. Addressing this challenge, our study leverages machine learning (ML) to predict pyrimidine compounds corrosion inhibition efficiency (CIE). Using a quantitative structure-property relationship (QSPR) model, we compared 14 linear and 12 non-linear ML algorithms to identify the most accurate predictor of CIE. The bagging regressor model demonstrated superior performance, achieving a root mean square error (RMSE) of 5.38, a mean square error (MSE) of 28.93, a mean absolute error (MAE) of 4.23, and a mean absolute percentage error (MAPE) of 0.05 in predicting the CIE values for pyrimidine compounds. This research marks a significant advancement in corrosion science, offering a novel and efficient ML-based approach as an alternative to traditional experimental methods. It shows that machine learning can quickly and accurately determine how well organic chemical inhibitors like pyrimidine stop material corrosion. This method gives the industry a new perspective and a workable solution to a problem that has existed for a long time.
 Keywords: machine learning, corrosion inhibition, pyrimidine, QSPR model, predictive analysis