Original Curve Research Articles

Advances in Gas Detection of Pattern Recognition Algorithms for Chemiresistive Gas Sensor

Gas detection and monitoring are critical to protect human health and safeguard the environment and ecosystems. Chemiresistive sensors are widely used in gas monitoring due to their ease of fabrication, high customizability, mechanical flexibility, and fast response time. However, with the rapid development of industrialization and technology, the main challenges faced by chemiresistive gas sensors are poor selectivity and insufficient anti-interference stability in complex application environments. In order to overcome these shortcomings of chemiresistive gas sensors, the pattern recognition method is emerging and is having a great impact in the field of sensing. In this review, we focus systematically on the advancements in the field of data processing methods for feature extraction, such as the methods of determining the characteristics of the original response curve, the curve fitting parameters, and the transform domain. Additionally, we emphasized the developments of traditional recognition algorithms and neural network algorithm in gas discrimination and analyzed the advantages through an extensive literature review. Lastly, we summarized the research on chemiresistive gas sensors and provided prospects for future development.

Multivariate stochastic generation of meteorological data for building simulation through interdependent meteorological processes

In recent years, the uncertainty of weather conditions and the impact of future climate change on building energy assessment has received increasing attention. As an important part of these studies, several types of methods for generating stochastic meteorological data have also been developed. Since solar radiation drops to zero at night, unlike the continuous 24-hour data for elements such as temperature and humidity, this has posed challenges for previous research to fully account for the simultaneity among multiple elements. Therefore, this study proposes a framework for meteorological data generation: First, perform multivariate time series modeling of meteorological data of air temperature, solar radiation and absolute humidity at 12:00 of each day of a typical year based on the S-vine copula method and simulating daily series data at 12:00 for 365 days. Then, based on the probability of change of each element evaluated from the historical meteorological observation data, the daily series data at 12:00 were expanded to 24 h, after which the yearly stochastic weather data were obtained. The analysis of 30 years of stochastic data generated by this method, compared with the original data, reveals that air temperature and solar radiation closely match the original distribution characteristics, except for a minor deviation in the absolute humidity’s kurtosis. Furthermore, the comparison of thermal load distributions for office buildings shows that the original data curve falls within the range of the generated data. This suggests that the generated data includes more information about uncertainty but still keeps the original data’s characteristics.

Topological recursion, symplectic duality, and generalized fully simple maps

For a given spectral curve, we construct a family of symplectic dual spectral curves for which we prove an explicit formula expressing the n-point functions produced by the topological recursion on these curves via the n-point functions on the original curve. As a corollary, we prove topological recursion for the generalized fully simple maps generating functions.

Estimating Cadmium Concentration in Agricultural Soils with ZY1-02D Hyperspectral Data: A Comparative Analysis of Spectral Transformations and Machine Learning Models

The accumulation of cadmium (Cd) in agricultural soils presents a significant threat to crop safety, emphasizing the critical necessity for effective monitoring and management of soil Cd levels. Despite technological advancements, accurately monitoring soil Cd concentrations using satellite hyperspectral technology remains challenging, particularly in efficiently extracting spectral information. In this study, a total of 304 soil samples were collected from agricultural soils surrounding a tungsten mine located in the Xiancha River basin, Jiangxi Province, Southern China. Leveraging hyperspectral data from the ZY1-02D satellite, this research developed a comprehensive framework that evaluates the predictive accuracy of nine spectral transformations across four modeling approaches to estimate soil Cd concentrations. The spectral transformation methods included four logarithmic and reciprocal transformations, two derivative transformations, and three baseline correction and normalization transformations. The four models utilized for predicting soil Cd were partial least squares regression (PLSR), support vector machine (SVM), bidirectional recurrent neural networks (BRNN), and random forest (RF). The results indicated that these spectral transformations markedly enhanced the absorption and reflection features of the spectral curves, accentuating key peaks and troughs. Compared to the original spectral curves, the correlation analysis between the transformed spectra and soil Cd content showed a notable improvement, particularly with derivative transformations. The combination of the first derivative (FD) transformation with the RF model yielded the highest accuracy (R2 = 0.61, RMSE = 0.37 mg/kg, MAE = 0.21 mg/kg). Furthermore, the RF model in multiple spectral transformations exhibited higher suitability for modeling soil Cd content compared to other models. Overall, this research highlights the substantial applicative potential of the ZY1-02D satellite hyperspectral data for detecting soil heavy metals and provides a framework that integrates optimal spectral transformations and modeling techniques to estimate soil Cd contents.

Control of Thermal Uniformity in Microwave Heating Process by BPNN and Adaptive Particle Swarm Optimization

As China advances its green economy, innovative methods are being employed to enhance energy optimization and conservation within energy-intensive industries. Among these methods, microwave heating stands out due to its superior heating efficiency and lack of pollution. Nonetheless, uniform heating remains a challenge because the microwave absorption capacity of the heated medium varies with changes in heating time and temperature. To address this issue, an Adaptive Particle Swarm Optimization (APSO) neural network microwave system based on the Back Propagation Neural Network (BPNN) is proposed. This system leverages the fundamental principles of Particle Swarm Optimization (PSO), categorizing particle swarms into three types and iterating them through distinct processes to achieve optimal results. An APSO controller is designed based on system identification, adjusting the controller parameters according to the error between the real-time system output and the identification model. The feedback error is used as the fitness function in the PSO algorithm, continuously adjusting the weights and thresholds of the neural network. This intelligent control approach optimizes the microwave oven's input power to minimize the error between the actual temperature output and the identified temperature. The APSO controller is designed based on system identification, with the intelligently controlled microwave heating system adjusting its input power to minimize the error between the identified and actual temperature outputs. Unlike traditional Proportional Integral Differential (PID) and BPNN controllers, this approach calculates the output of the identified model and the error of the actual model, feeding this information back to the controller. The feedback error serves as the fitness function in the PSO algorithm, enabling continuous adjustment of the network's weights and thresholds to regulate the microwave equipment's output power, thereby ensuring the output temperature closely follows the preset temperature curve. Experimental results demonstrate that the actual output value of the system closely aligns with the original preset temperature curve, with a root mean square error of only 0.74. This designed identification and control system effectively achieves the desired outcome.

Research on upper bound limit analysis of slope stability in open-pit mine based on least square principle

So as to extend the application of upper bound limit analysis for slope stability in open-pit mine, this paper analyzed failure mechanism of rock mass when shear failure occurred based on plastic mechanics principles, and combined with discrete mathematical theory and least square principle to propose a visualization method of logarithmic spiral. At the same time, the visualization method was applied to engineering practice for slope stability in open-pit mine, and cycle algorithm of stability analysis for open-pit mine slope was proposed through energy balance conditions, then stability analysis results were evaluated reasonably through uniting with limit equilibrium method. The results show that visualization method of logarithmic spiral proposed in this paper is highly consistent with original curve, and can ensure correlation coefficient square is greater than 0.9995. What is more, upper bound limit analysis method has a superhigh accuracy in slope engineering. At the same time, the most dangerous sliding surface obtained by this method can satisfy the requirements of velocity separation, which solved velocity problems during the process of slope evolution. Therefore, the method proposed in this paper has a stronger application in the field of open-pit mining.

Comparison and evaluation of different constitutive models for predicting the hot deformation behavior of Mg-Gd-Y-Zr alloy

The popular constitutive models used in the field of hot forming of magnesium alloys can be divided into phenomenological models, machine learning models, and internal state variables (ISV) models based on physical mechanisms. Currently, there is a lack of comparison and evaluation regarding the suitability of different types of models. In this study, Mg-Gd-Y-Zr alloy is taken as the research object. The hot deformation behavior of the alloy was studied systematically. Subsequently, Arrhenius model with strain compensation, artificial neural network (ANN) model, and ISV model involving dynamic recrystallization (DRX), dislocation density and grain size evolution were established. ANN model demonstrates a higher level of accuracy in fitting the original stress-strain curves compared to both ISV model and modified Arrhenius model, but ANN model is not suitable for predicting the experimental results outside of the initial database. ISV model considers the impact of microstructure evolution history on stress, making it highly effective in reflecting the mechanical responses under complex loading condition. The established ISV model is embedded in the ABAQUS software, which shows good ability in calculating the mechanical response, dimension, and microstructure evolution information of the component during hot forming.

Generation of input spectrum for electrolysis stack degradation test applied to wind power PEM hydrogen production

Hydrogen production by proton exchange membrane electrolysis has good fluctuation adaptability, making it suitable for hydrogen production by electrolysis in fluctuating power sources such as wind power. However, current research on the durability of proton exchange membrane electrolyzers is insufficient. Studying the typical operating conditions of wind power electrolysis for hydrogen production can provide boundary conditions for performance and degradation tests of electrolysis stacks. In this study, the operating condition spectrum of an electrolysis stack degradation test cycle was proposed. Based on the rate of change of the wind farm output power and the time-averaged peak-valley difference, a fluctuation output power sample set was formed. The characteristic quantities that played an important role in the degradation of the electrolysis stack were selected. Dimensionality reduction of the operating data was performed using principal component analysis. Clustering analysis of the data segments was completed using an improved Gaussian mixture clustering algorithm. Taking the annual output power data of wind farms in Northwest China with a sampling rate of 1 min as an example, the cyclic operating condition spectrum of the proton-exchange membrane electrolysis stack degradation test was constructed. After preliminary simulation analysis, the typical operating condition proposed in this paper effectively reflects the impact of the original curve on the performance degradation of the electrolysis stack. This study provides a method for evaluating the degradation characteristics and system efficiency of an electrolysis stack due to fluctuations in renewable energy.

An Optimized Strain-Compensated Arrhenius Constitutive Model of GH4169 Superalloy Based on Hot Compression.

A precise constitutive model is essential for capturing the deformation characteristics of the GH4169 superalloy in numerical simulations of thermal plastic forming processes. Hence, the aim of this study was to develop a precise modified constitutive model to describe the hot deformation behavior exhibited by the GH4169 superalloy. The isothermal cylindrical uniaxial compression tests of the GH4169 superalloy were carried out at temperatures of 950~1100 °C and strain rates of 0.01~10 s-1 using a Thermecmastor-200KN thermal-mechanical simulator. The original strain-stress curves were corrected by minimizing the effects of plastic heat and interfacial friction. Based on the true stress-strain curves, the original strain-compensated Arrhenius constitutive model was constructed using polynomial orders of 3, 5, and 10, respectively. The results showed that once the polynomial order exceeds the 5th, further increasing the order has little contribution to the accuracy of the model. To improve prediction ability, a higher precision Arrhenius constitutive model was established by extending a series of material parameters as functions that depend on temperature, strain, and strain rate, in which the error can be reduced from 4.767% to 0.901% compared with the classic strain-compensated Arrhenius constitutive model.

Research on Sea Trial Techniques for Motion Responses of HDPE Floating Rafts Used in Aquaculture

The innovative aquaculture equipment known as high-density polyethylene (HDPE) floating rafts has gained popularity among fishermen in the southeast coastal regions of China. Compared to deep-water anti-wave fish cages, the construction costs of HDPE floating rafts are 50% to 75% less. There is a dearth of comprehensive publicly available records of HDPE floating rafts sea trial data, despite substantial numerical studies on the motion response of aquaculture fish cages and scale model experiments under controlled-wave conditions. This study involves sea trial techniques under operational and extreme environmental conditions for motion responses of HDPE floating rafts, presents a comprehensive procedure for sea trials of HDPE floating rafts, summarizes the issues encountered during the trials, and suggests solutions. Using MATLAB for independent programming, motion videos and photos collected from the sea trials are processed for image capture, yielding the original time history curve of vertical displacement. Based on the sea trials’ data, including motion displacement, acceleration, mooring line force, overall deformation patterns, and current and wave data, recommendations are provided for the design and layout of HDPE floating rafts. Based on the Fast Fourier Transform (FFT) method for spectral analysis, the influence of interference items on the observational data is eliminated; the rationality of the observational data is verified in conjunction with the results of the Gabor Transform. This study offers a scientific analytical method for the structural design and safe operation of HDPE floating rafts and provides a reference for subsequent numerical simulations.

Structural behaviour and design of cold-formed austenitic stainless steel flat-oval hollow section beam-columns

This paper presents experimental and numerical investigations into the global buckling behaviour and resistances of cold-formed austenitic stainless steel flat-oval hollow section beam-columns under combined compression and bending. A testing programme, including initial geometric imperfection measurements and ten beam-column tests about the cross-section major and minor principal axes, was firstly conducted. The key obtained test results, including failure loads, load–deformation histories and failure modes, were reported. Following the testing programme, a numerical modelling programme was performed, with finite element models developed to simulate the beam-column test results and then used to conduct parametric studies for generating additional numerical data. Then, the applicability of relevant codified design interaction curves to cold-formed austenitic stainless steel flat-oval hollow section beam-columns was evaluated based on the test and numerical data. The evaluation results revealed that the design interaction curve of the American specification resulted in an overall good level of design accuracy and consistency, while the design interaction curve of the European code led to slightly conservative resistance predictions, mainly due to the conservative bending end point. To address this shortcoming, a revised Eurocode design interaction curve with an improved bending end point was proposed and shown to provide more accurate resistance predictions for cold-formed austenitic stainless steel flat-oval hollow section beam-columns than the original Eurocode design interaction curve.

A Nonlinear Hybrid Modeling Method for Pump Turbines by Integrating Delaunay Triangulation Interpolation and an Improved BP Neural Network

In order to solve the problem that the data processing accuracy of the characteristic curves is not high, which affects the accuracy of the simulation of variable-speed pumped storage units, this paper proposes a nonlinear hybrid modeling method for pump turbines by integrating Delaunay triangulation interpolation and an improved back-propagation neural network. Firstly, the improved Sutter transform is used to preprocess the original curve, and the convex hull of the transformed curve is calculated. With the unknown point inside the convex hull, Delaunay triangulation interpolation is used to model the transformed curve. With the unknown point outside the convex hull, the back-propagation neural network is first established based on the input and output, and then the initial weights and thresholds of the network are determined using the mind evolution algorithm to complete the modeling and simulation of the curve. Simulation results show that the proposed method fully integrates the high-precision features of interpolation and the powerful nonlinear fitting ability of the neural network, which greatly improves the efficiency and accuracy of pump turbine modeling.

Adaptive machining of damaged blades repaired by additive manufacturing: a novel double-constrained method for model reconstruction

This article introduces a novel model reconstruction method for machining turbine blades damaged in service and repaired via additive manufacturing (AM). Addressing the lack of a model for damaged parts crucial for precise adaptive machining, the method involves model registration and construction. Initially, the AM-repaired blade is aligned with a theoretical CAD model through rough registration using Principal Component Analysis (PCA), followed by precise alignment within the blade profile’s tolerance zone. The model construction employs the minimum curve energy principle to ensure seamless integration with undamaged areas and adherence to profile tolerance constraints. The interfacial profile curve between the undamaged and AM-repaired areas is used as the original curve to construct the curves in the AM-repaired area. The reconstructed curves are modified with a double constraint of being smooth and minimum occupation of the theoretical model tolerance zone. The efficacy of this method is validated through a case study. The repaired blade showed deviations from −0.101 mm to 0.115 mm, within profile tolerances, and a surface smoothness difference of less than 6.41 μm between the damaged and undamaged sections. This method significantly improves the precision and efficiency of turbine blade repair, offering substantial benefits for the turbomachinery manufacturing industry.

Functional Principal Component Regression Model Based on FIrst-order Boosting and Model Averaging

Functional regression model has always been an important research direction in the field of functional data analysis, in which functional principal component analysis as a common method of functional regression modeling, the determination of the number of truncations of the eigenfunctions has always been a problem to be solved. Based on this, this paper proposes a functional principal component regression model based on the idea of model averaging, which uses Bayesian model averaging instead of model selection, determines the number of truncations adaptively and balances the prediction error with the training error. In addition, the original function curves do not effectively capture the information of their functional characteristics. In this paper, the first-order derivative function is used as the supplementary information of the original function curve to jointly characterize the predictor variables. In the efficiency test, this paper averages the Bayesian model as the benchmark model and conducts real data analysis on several benchmark datasets. The results show that the proposed method has higher predictive accuracy and robustness than commonly used models.

A Workable Approach to Calculate the Rate of Silting in Small and Hillside Dams in the Rambiara watershed in Jammu and Kashmir

Abstract: In temperate regions, building small dams and hillside reservoirs is a popular solution to irregular and unevenly distributed rainfalls. Furthermore, it is advised that rural communities use these tiny hydraulic structures as a means of adapting to climate change. They are essential to the water resources' survival. These dams could, however, act as sinks for material from upstream. In order to better understand siltation and the proper operation of these essential structures, it would be helpful to monitor and measure the amount of sediments in minor dams. The bathymetry or topographical surveys needed for this control and these measurements are too costly for the people in charge of these minor dams. In this regard, the triangulation of the estimated silted level is a straightforward and inexpensive method that is proposed in this work. This technique is based on measuring the accessible silted level in the dam directly. This new approach is contrasted with an alternative that is based on the dam's original Elevation-Capacity curve and is typically employed when the bathymetry is unachievable. The bathymetry and electrical tomography findings from both of them were compared, confirming the proposal method's status as the most accurate. Consequently, this approach is suggested as a novel, straightforward, and easy way to assess the degree of silting in minor dams and hillside reservoirs

Visible Near-Infrared Hyperspectral Soil Organic Matter Prediction Based on Combinatorial Modeling

Non-destructive, fast, and accurate prediction of soil organic matter content in farmland is of great significance for soil fertility assessment and rational fertilization. In the process of soil organic matter prediction, it is important to give full play to the advantages of different prediction models and to integrate different prediction models to innovatively construct a combined prediction model of soil organic matter content so as to improve the prediction accuracy and generalization ability of the model. In this study, the soil organic matter content of agricultural soils was taken as the research object, and the visible near-infrared hyperspectral curves of soils were measured by the Starter Kit indoor mobile scanning platform (Headwall Photonics, Bolton, MA, USA), and the original spectral curves were firstly de-noised by Savitzky–Golay (S-G) smoothing. Secondly, the smoothed and denoised spectral data were subjected to a first-order differential transform, and the features were selected based on the first-order differential transformed spectral data using the L1-paradigm algorithm features. Then, secondly, eight algorithms based on the selected feature bands, such as LASSO Regression (LASSO) (Model 1), Multilayer Perceptron (MLP) (Model 2), Random Forest (RF) (Model 3), Gaussian Kernel Regression (GKR) (Model 4), Ridge Regression (Model 5), Long Short-Term Memory (LSTM) (Model 6), Convolutional Neural Networks (CNN) (Model 7), and Support Vector Regression (SVR) (Model 8), were applied to construct a single-prediction model of soil organic matter content. Finally, a superior linear combination-prediction model was proposed by the eight single-prediction models constructed, and the standard deviation-based prediction validity was added to test the model. The results showed the following: (1) the weights of the eight single-prediction models in the combined prediction model were ω1*=0.099, ω2*=0.202, ω3*=0.000, ω4*=0.357, ω5*=0.088, ω6*=0.089, ω7*=0.000, ω8*=0.165, respectively; (2) The average precision E of the predicted values of soil organic matter content constructed based on the eight single-prediction models was 0.856; the average standard deviation σ was 0.181, and the average prediction validity M was 0.702; (3) The accuracy E of the predicted value of soil organic matter content of the combined model was 0.893, which was 4.322% higher than the average accuracy of the single model; the standard deviation of the combined model was 0.129, which was 28.333% lower than the average standard deviation of the single model, and the prediction validity M of the combined model was 0.778, which was 10.826% higher than the average prediction validity of the single model. The combined model can be used for the effective estimation of soil organic matter content in farmland with visible near-infrared spectral data, which can provide a basis and reference for the rapid detection of soil organic matter content in farmland.

Exploring intertemporal decision-making dynamics through functional data analysis: investigating variations in different discount function's dimensions

AbstractIntertemporal preferences are closely related to essential aspects of an individual’s emotional and cognitive domains. Discount functions are used to quantify these preferences, which can help us understand conditions such as addiction, depression, and Attention Deficit Hyperactivity Disorder (ADHD). However, traditional parametric models are limited when dealing with intertemporal preferences, mainly when behavioural biases are involved. This study exploits Functional Data Analysis (FDA) to investigate the properties of discount functions in intertemporal choices comparing people suffering from the Hikikomori pathology (a condition that involves social withdrawal) and normal people. Notably, the goal of this research is to look for statistically significant differences in the dynamics of intertemporal decision-making according to different gravity of the Hikikomori condition through the magnified FDA lens on different functional dimensions; the distinctive curves of discount functions categorised by Hikikomori scores prompted a more profound investigation via the so-called augmented functional analysis of variance. The original curves and their derivatives, and the discount rates and their first derivatives provide the different functional dimensions explored. This original approach of analyzing differences between subgroups according to decision-making behaviours is exciting from a methodological and practical perspective.

Investigating the effects of reducing the number of temperatures and frequencies on the development of master curves for viscoelastic properties of bituminous composite

This study aimed to assess the feasibility of substituting temperature sweep tests for frequency sweep tests and explore the potential of utilizing fewer temperatures and frequencies in dynamic modulus tests to formulate viscoelastic properties master curves. The results indicated that master curves derived from temperature sweep tests mirrored the trends and values obtained from frequency sweep tests, presenting a viable alternative for constructing viscoelastic properties master curves of bitumen. Furthermore, models fitted to dynamic modulus test results at three temperatures and three frequencies exhibited comparable primary parameters, values, and trends to those derived from the complete dataset. The model fitted on reduced data demonstrated robust performance with correlation and R-squared values exceeding 0.95. Considering a marginal increase of about 5% in Residual Standard Error (RSE) values when using the reduced dataset, generating master curves with fewer test results underscored the feasibility and reliability of the original master curves.

Research on Coordinated Optimization of Source-Load-Storage Considering Renewable Energy and Load Similarity

Currently, the global energy revolution in the direction of green and low-carbon technologies is flourishing. The large-scale integration of renewable energy into the grid has led to significant fluctuations in the net load of the power system. To meet the energy balance requirements of the power system, the pressure on conventional power generation units to adjust and regulate has increased. The efficient utilization of the regulation capability of controllable industrial loads and energy storage can achieve the similarity between renewable energy curves and load curves, thereby reducing the peak-to-valley difference and volatility of the net load. This approach also decreases the adjustment pressure on conventional generating units. Therefore, this paper proposes a two-stage optimization scheduling strategy considering the similarity between renewable energy and load, including energy storage and industrial load participation. The combination of the Euclidean distance, which measures the similarity between the magnitude of renewable energy–load curves, and the load tracking coefficient, which measures the similarity in curve shape, is used to measure the similarity between renewable energy and load profiles. This measurement method is introduced into the source-load-storage optimal scheduling to establish a two-stage optimization model. In the first stage, the model is set up to maximize the similarity between renewable energy and the load profile and minimize the cost of energy storage and industrial load regulation to obtain the desired load curve and new energy output curve. In the second stage, the model is set up to minimize the overall operation cost by considering the costs associated with abandoning the new energy sources and shedding loads to optimize the output of conventional generator sets. Through a case analysis, it is verified that the proposed scheduling strategy can achieve the tracking of the load curve to the new energy curve, reducing the peak-to-valley difference of the net load curve by 48.52% and the fluctuation by 67.54% compared to the original curve. These improvements effectively enhance the net load curve and reduce the difficulty in regulating conventional power generation units. Furthermore, the strategy achieves the full discard of renewable energy and reduces the system operating costs by 4.19%, effectively promoting the discard of renewable energy and reducing the system operating costs.

Dispersion complexity-entropy curves: An effective method to characterize the structures of nonlinear time series.

The complexity-entropy curve (CEC) is a valuable tool for characterizing the structure of time series and finds broad application across various research fields. Despite its widespread usage, the original permutation complexity-entropy curve (PCEC), which is founded on permutation entropy (PE), exhibits a notable limitation: its inability to take the means and amplitudes of time series into considerations. This oversight can lead to inaccuracies in differentiating time series. In this paper, drawing inspiration from dispersion entropy (DE), we propose the dispersion complexity-entropy curve (DCEC) to enhance the capability of CEC in uncovering the concealed structures within nonlinear time series. Our approach initiates with simulated data including the logistic map, color noises, and various chaotic systems. The outcomes of our simulated experiments consistently showcase the effectiveness of DCEC in distinguishing nonlinear time series with diverse characteristics. Furthermore, we extend the application of DCEC to real-world data, thereby asserting its practical utility. A novel approach is proposed, wherein DCEC-based feature extraction is combined with multivariate support vector machine for the diagnosis of various types of bearing faults. This combination achieved a high accuracy rate in our experiments. Additionally, we employ DCEC to assess stock indices from different countries and periods, thereby facilitating an analysis of the complexity inherent in financial markets. Our findings reveal significant insights into the dynamic regularities and distinct structures of these indices, offering a novel perspective for analyzing financial time series. Collectively, these applications underscore the potential of DCEC as an effective tool for the nonlinear time series analysis.