Curve Fitting Algorithm Research Articles

On the Distillation of Stories for Transferring Narrative Arcs in Collections of Independent Media.

The act of telling stories is a fundamental part of what it means to be human. This work introduces the concept of narrative information, which we define as the overlap in information space between a story and the items that compose the story. Using contrastive learning methods, we show how modern artificial neural networks can be leveraged to distill stories and extract a representation of the narrative information. We then demonstrate how evolutionary algorithms can leverage this to extract a set of narrative template curves and how these-in tandem with a novel curve-fitting algorithm we introduce-can reorder music albums to automatically induce stories in them. In doing so, we give statistically significant evidence that (1)these narrative information template curves are present in existing albums and that (2)people prefer an album ordered through one of these learned template curves over a random one. The premises of our work extend to any form of (largely) independent media, and as evidence, we also show that our method works with image data.

Inverse problem-solving method applied to the acoustic characterisation of a thin film via the Debye series method (DSM)

ABSTRACT The study of the ultrasonic acoustic response of materials is of increasing interest for the characterisation of high-frequency applications. In this work, some elastic properties (acoustic velocity and acoustic attenuation) and some physical properties (thickness and density), together with the phase shift of the transducer, are estimated via one method. Scanning acoustic microscopy was performed via an innovative and different method using a high-frequency (50 MHz) planar wave transducer. In addition, the Debye series model (DSM) was used to model the acoustic response of the bilayer structure of the glass substrate and the resin‒epoxy sample. The inverse problem of estimating the acoustic parameters that results in a DSM reflected echo that matches the experimental signal is solved by proposing an innovative step-by-step curve fitting algorithm. The algorithm for solving the inverse problem is then optimised via relative mean square error (RMSE) curves, resulting in a robust method for assessing the uniqueness of the multiparameter solution.

Optimal Curve Fitting for Serial Chain in Six-Crease Origami Unit

Abstract Origami-inspired structures have been widely used in aerospace and robotics for three-dimensional (3D) symmetrical configurations using crease-symmetrical origami basic patterns. These patterns offer advantages in repeatable and systematic modeling and mass production. However, few studies have focused on 3D non-symmetrical structures using symmetrical origami basic patterns due to their structure complexity, limiting their application. Therefore, we aim to analyze the folding behavior in 3D non-symmetrical structures using a 6-crease symmetry origami base pattern. To achieve this goal, we first focus on behavior in a two-dimensional (2D) plane. This paper presents a scheme for the behavior of origami units with an optimal curve-fitting algorithm. The curve can be any 2D space curve. The fitting curve, constructed by numerical analysis and an optimal approaching scheme, can satisfy error requirements and retain foldable origami unit features. The paper verifies the feasibility of the curve-fitting scheme by presenting two curve examples, including a quadratic curve and a sin wave function. The results show that the fitting error is reduced by 99% when no boundary conditions are applied. This research provides valuable insights into understanding origami unit kinematic optimization through forward and inverse kinematics. It offers potential applications in the engineering design of foldable structures and precision origami-inspired mechanism, thereby opening avenues for further exploration of complex origami structures and their applications in emerging technologies.

Multi-method piecewise low-frequency identification

Inter-area frequency modes of electromechanical oscillations are decisive factors that influence the performance of electrical power systems. However, the accurate estimation of these frequencies remains a challenge due to the non-linear behavior of the response system following a disturbance and the strong coupling among the frequencies. This work describes a curve fitting and electromechanical frequency estimation algorithm, called Multi-method Piecewise Identification (MPI), based on a combination of the Matrix Pencil Method (MPM), the Prony method, and Subspace Identification (SSI), choosing the best approximation of an interval basis according to the model accuracy index (MAI) and the mean square error (MSE). The advantages and limitations of MPI were analyzed by computational analyses that were carried out with Python-based code that estimates the low frequencies for several ringdown signals, including oscillating signals from Australian and Brazilian systems that arise after large disturbances. To ensure robustness to random and noisy conditions, the method was tested with a synthetic signal with Gaussian white noise and time-variant frequencies, and compared to the methods mentioned above, the Hilbert–Huang Transform (HHT), and Eigensystem Realization Algorithm (ERA). The MPI has shown robust results and is capable of obtaining a better fitting for the signal than the other methods.

A Novel Bézier LSTM Model: A Case Study in Corn Analysis

Accurate prediction of agricultural product prices is instrumental in providing rational guidance for agricultural production planning and the development of the agricultural industry. By constructing an end-to-end agricultural product price prediction model, incorporating a segmented Bézier curve fitting algorithm and Long Short-Term Memory (LSTM) network, this study selects corn futures prices listed on the Dalian Commodity Exchange as the research subject to predict and validate their price trends. Firstly, corn futures prices are fitted using segmented Bézier curves. Subsequently, the fitted price sequence is employed as a feature and input into an LSTM network for training to obtain a price prediction model. Finally, the prediction results of the Bézier curve-based LSTM model are compared and analyzed with traditional LSTM, ARIMA (Autoregressive Integrated Moving Average Model), VMD-LSTM, and SVR (Support Vector Regression) models. The research findings indicate that the proposed Bézier curve-based LSTM model demonstrates significant predictive advantages in corn futures price prediction. Through comparison with traditional models, the effectiveness of this model is affirmed. Consequently, the Bézier curve-based LSTM model proposed in this paper can serve as a crucial reference for agricultural product price prediction, providing effective guidance for agricultural production planning and industry development.

Digital twinning, prediction and multi-objective optimization of an azeotrope system separation process in pharmaceutical manufacturing process

Digital twin is to make full use of the physical model, sensor update, operation history and other data to integrate multidisciplinary, multi-physical quantity, multi-scale and multi-probability simulation process, and to complete the full life cycle process of the corresponding physical equipment in the virtual space. In this paper, digital twin technology was used to simulate the production process of a pharmaceutical workshop, thus realizing solvent recovery by an azeotrope system separation process. The separation was optimized by multi-objective genetic algorithm. separation process, wherein the polynomial curve fitting and entropy-weighted TOPSIS data evaluation algorithms were combined to optimize the operating parameters, then the solvent purity and yield reach 99.96 % and 77.9 %, respectively, which is much higher than the corporate requirements. In addition, the effectiveness of the digital twin in providing data-driven prediction capability was verified by a CNN-LSTM-based regression prediction model, and the CNN-LSTM model has an accuracy of more than 98.9 % for all prediction results. Finally, a 3D visualization model was built using the Unity engine, enabling researchers to visualize and explore changes in key metrics during the separation process. This study can provide some guidance for digital transformation and intelligent development in pharmaceutical industry.

Sensorless Capability Expansion for SPMSM Based on Inductance Parameter Identification

Pulsating high-frequency voltage injection can be used for the sensorless control of a surface-mounted permanent magnet synchronous motor (SPMSM) at zero- and low-speed ranges. However, the sensorless capability still faces challenges to the requirements of industrial application, especially at heavy load status. Aiming at this issue, this article proposes a sensorless capability expansion method for an SPMSM based on inductance parameter identification. Firstly, incremental inductances at the d-q-axis and cross-coupling inductance are identified offline by three steps combining the rotating high-frequency voltage injection and pulsating high-frequency voltage injection. Using a polynomial curve fitting algorithm, apparent inductances are calculated. Secondly, positive DC current injection at the d-axis is proposed to enhance the saliency ratio based on the analysis of parameter identification results. Compared with the conventional id = 0 or id < 0 method, the saliency ratio is enhanced obviously when a positive DC current is injected at the d-axis. Then, the convergence region of the sensorless control method at heavy load status is expanded and the accuracy of rotor position estimation is improved using the proposed method. Finally, the experimental results validate that the sensorless capability of the SPMSM is expanded.

Microvascular Autoregulation in Skeletal Muscle Using Near-Infrared Spectroscopy and Derivation of Optimal Mean Arterial Pressure in the ICU: Pilot Study and Comparison With Cerebral Near-Infrared Spectroscopy.

Microvascular autoregulation (MA) maintains adequate tissue perfusion over a range of arterial blood pressure (ABP) and is frequently impaired in critical illness. MA has been studied in the brain to derive personalized hemodynamic targets after brain injury. The ability to measure MA in other organs is not known, which may inform individualized management during shock. This study determines the feasibility of measuring MA in skeletal muscle using near-infrared spectroscopy (NIRS) as a marker of tissue perfusion, the derivation of optimal mean arterial pressure (MAPopt), and comparison with indices from the brain. Prospective observational study. Medical and surgical ICU in a tertiary academic hospital. Adult critically ill patients requiring vasoactive support on the first day of ICU admission. Fifteen critically ill patients were enrolled. NIRS was applied simultaneously to skeletal muscle (brachioradialis) and brain (frontal cortex) while ABP was measured continuously via invasive catheter. MA correlation indices were calculated between ABP and NIRS from skeletal muscle total hemoglobin (MVx), muscle tissue saturation index (MOx), brain total hemoglobin (THx), and brain tissue saturation index (COx). Curve fitting algorithms derive the MAP with the lowest correlation index value, which is the MAPopt. MAPopt values were successfully calculated for each correlation index for all patients and were frequently (77%) above 65 mm Hg. For all correlation indices, median time was substantially above impaired MA threshold (24.5-34.9%) and below target MAPopt (9.0-78.6%). Muscle and brain MAPopt show moderate correlation (MVx-THx r = 0.76, p < 0.001; MOx-COx r = 0.69, p = 0.005), with a median difference of -1.27 mm Hg (-9.85 to -0.18 mm Hg) and 0.05 mm Hg (-7.05 to 2.68 mm Hg). This study demonstrates, for the first time, the feasibility of calculating MA indices and MAPopt in skeletal muscle using NIRS. Future studies should explore the association between impaired skeletal muscle MA, ICU outcomes, and organ-specific differences in MA and MAPopt thresholds.

Contrast-Enhanced Magnetic Resonance Imaging Based T1 Mapping and Extracellular Volume Fractions Are Associated with Peripheral Artery Disease.

Extracellular volume fraction (ECV), measured with contrast-enhanced magnetic resonance imaging (CE-MRI), has been utilized to study myocardial fibrosis, but its role in peripheral artery disease (PAD) remains unknown. We hypothesized that T1 mapping and ECV differ between PAD patients and matched controls. A total of 37 individuals (18 PAD patients and 19 matched controls) underwent 3.0T CE-MRI. Skeletal calf muscle T1 mapping was performed before and after gadolinium contrast with a motion-corrected modified look-locker inversion recovery (MOLLI) pulse sequence. T1 values were calculated with a three-parameter Levenberg-Marquardt curve fitting algorithm. ECV and T1 maps were quantified in five calf muscle compartments (anterior [AM], lateral [LM], and deep posterior [DM] muscle groups; soleus [SM] and gastrocnemius [GM] muscles). Averaged peak blood pool T1 values were obtained from the posterior and anterior tibialis and peroneal arteries. T1 values and ECV are heterogeneous across calf muscle compartments. Native peak T1 values of the AM, LM, and DM were significantly higher in PAD patients compared to controls (all p < 0.028). ECVs of the AM and SM were significantly higher in PAD patients compared to controls (AM: 26.4% (21.2, 31.6) vs. 17.3% (10.2, 25.1), p = 0.046; SM: 22.7% (19.5, 27.8) vs. 13.8% (10.2, 19.1), p = 0.020). Native peak T1 values across all five calf muscle compartments, and ECV fractions of the anterior muscle group and the soleus muscle were significantly elevated in PAD patients compared with matched controls. Non-invasive T1 mapping and ECV quantification may be of interest for the study of PAD.

Exploring the Factors that Affect Creativity among Adolescents

Aims: Ideas are the key to innovation. In this competitive era the excellence of the mankind depends on their innovation. Innovative outcomes laid stress on how to think divergently. Creativity is varied in nature. Several factors are responsible to perform any creative task. Therefore, it is necessary to find out the most important factor which can help to expedite creativity among the person, more specifically to explore the scientific reason behind the specific factor and multivariate relationship between two or more factors. Study Design: In the present study the investigator used explanatory-case study method. Methodology: The present research included under non-probability sampling technique. For conducting the present research work systematically researcher used purposive sampling method for sample selection. It is basically selected for solving several purposes properly. Therefore the willing and accessible 31 subjects are chosen for this purpose. Out of 31 subjects, 20 students arefrom Bengali Medium School and remaining 11students are from English Medium School. These schools are affiliated to West Bengal Board of Secondary Education and CBSE Board. Results: A scatter analysis is used to compare two data sets for finding out the relationship between them. Simultaneously, curve fitting algorithm is used to examine the relationship between one or more predictors (independent variable) and a response variable (dependent variable) with the goal of defining a best fit model of the relationship. The major aim of this study is to find out the relationship between one or more predictors (independent variable) and a response variable (dependent variable) with the goal of defining a best fit model of the relationship. Conclusion: Exploring the effective factors of creativity is addressed on 14 years age of boys and girls.

Efficient Modeling of Distributed Energy Resources’ Impact on Electric Grid Technical Losses: A Dynamic Regression Approach

Technical losses in electrical grids are inherent inefficiencies induced by the transmission and distribution of electricity, resulting in energy losses that can reach up to 40% of the generated energy. These losses pose significant challenges to grid operators regarding energy sustainability, reliability, and economic viability. Distributed Energy Resources (DERs) offer promising solutions to lower technical losses by decentralizing energy generation and consumption, reducing the need for long-distance transmission and optimizing grid operation. Hence, estimating the impact of DERs on grid technical losses becomes paramount for grid operators and planners. In response, this article proposes the application of regression modeling and nonlinear curve fitting algorithms to provide a more nuanced understanding and better characterize the intricate interplay between DER deployment and technical losses. Through a comprehensive case study based on more than 1080 computer simulations, we demonstrate the effectiveness of our proposed dynamic polynomial varying coefficient regression model in estimating the impact of DERs on technical losses within electrical grids. The proposed model offers a simple and effective methodology that allows grid operators to gain insights into the nonlinear dynamics of DER integration and make quicker and more informed decisions regarding grid management strategies, infrastructure investments, and policy interventions. Also, this research contributes to advancing the field of grid optimization by offering a simple equation that enhances our ability and haste to assess and mitigate technical losses in the context of an evolving energy landscape characterized by increasing DER adoption.

High dynamic range 3D shape reconstruction: Combination of adaptive fringe intensity, iterative exposure time adjustment and least quadratic curve fitting

For three-dimensional (3D) reconstruction of specular surfaces based on fringe projection profilometry (FPP), a hybrid approach combining adaptive fringe projection, iterative exposure time adjustment and least quadratic curve fitting is proposed. First, we propose an adaptive projection fringe intensity generation method in the camera image. Second, we build a new pixel matching between the camera and projector, and correct the pixel matching on the specular surfaces based on linear interpolation. Third, we propose an iterative exposure time adjustment method based on saturated pixel statistics. Fourth, we fuse the multiple results to obtain the final 3D reconstructed surface. Finally, we adopt a least quadratic curve fitting algorithm to fit the residual phase errors. Experiments confirmed the validity of the proposed method.

Adaptive tempered reversible jump algorithm for Bayesian curve fitting

Bayesian curve fitting plays an important role in inverse problems, and is often addressed using the reversible jump Markov chain Monte Carlo (RJMCMC) algorithm. However, this algorithm can be computationally inefficient without appropriately tuned proposals. As a remedy, we present an adaptive RJMCMC algorithm for the curve fitting problems by extending the adaptive Metropolis sampler from a fixed-dimensional to a trans-dimensional case. In this presented algorithm, both the size and orientation of the proposal function can be automatically adjusted in the sampling process. Specifically, the curve fitting setting allows for the approximation of the posterior covariance of the a priori unknown function on a representative grid of points. This approximation facilitates the definition of efficient proposals. In addition, we introduce an auxiliary-tempered version of this algorithm via non-reversible parallel tempering. To evaluate the algorithms, we conduct numerical tests involving a series of controlled experiments. The results demonstrate that the adaptive algorithms exhibit significantly higher efficiency compared to the conventional ones. Even in cases where the posterior distribution is highly complex, leading to ineffective convergence in the auxiliary-tempered conventional RJMCMC, the proposed auxiliary-tempered adaptive RJMCMC performs satisfactorily. Furthermore, we present a realistic inverse example to test the algorithms. The successful application of the adaptive algorithm distinguishes it again from the conventional one that fails to converge effectively even after millions of iterations.

Comparison-Transfer Learning Based State-of-Health Estimation for Lithium-Ion Battery

Abstract Rapid and accurate estimation of the state of health of lithium-ion batteries is of great significance. This paper aims to address two issues faced when applying deep learning methods to estimate the health status of lithium-ion batteries: high data quality requirements and poor model generalizability. This paper proposes a comparison-transfer learning approach with cyclic synchronization to estimate the state of health of lithium-ion batteries. First, a cyclic synchronization method based on the Bezier curve fitting algorithm is introduced to synchronize the data obtained at different charge–discharge cycles of the lithium-ion battery, facilitating input to the model. Second, a comparison-transfer network using the Pearson correlation coefficient is proposed to transfer knowledge from the source dataset to predict the target dataset under different environmental temperatures. By training a pre-trained model on the source dataset and utilizing the correlation coefficient to analyze the similarity between the source and target datasets, the accumulated knowledge in the source dataset can be effectively utilized to enhance prediction performance on the target dataset. In the experiments, the proposed method is validated using the lithium-ion battery aging public datasets. The experimental results demonstrate that the proposed approach achieves superior prediction performance in the case of small-sample sizes, exhibiting higher accuracy and stability compared to traditional deep learning methods.

A behavioral model for the linear variable gain amplifier

AbstractIn this paper, a behavioral model for the variable gain amplifiers working in the liner region is proposed. An iterative least‐square algorithm for complex curve fitting is proposed to model the variable gain amplifiers as an infinite impulse response filter. The polynomial fittings are used to obtain the coefficient matrix for the gain response and phase response to the frequency at different control voltages. The relationship between gain and control voltage is fitted by a hyperbolic tangent function. The modeling flow is given in this paper. Comparing the frequency response of the behavioral model and circuit model, the simulation results are similar at the operating frequency. Finally, an application is given, which is used to compare the effect of the nonlinear phase system with two different band signals modulated by 4QAM. This application proves that the model can be used in the simulation of large‐scale systems.

Photon-Counting Detector CT Versus Energy-Integrating Detector CT of the Lumbar Spine: Comparison of Radiation Dose and Image Quality.

BACKGROUND. Photon-counting detector (PCD) CT could be useful to help address the typically high radiation doses of conventional energy-integrating detector (EID) CT of the lumbar spine. OBJECTIVE. The purpose of our study was to compare PCD CT and EID CT of the lumbar spine, both performed using tin filtration, in terms of radiation dose and image quality. METHODS. This study included a prospective sample of 39 patients (22 men, 17 women; mean age, 27.2 years) who underwent investigational PCD CT of the lumbar spine as part of a separate study and a retrospective sample of 39 patients (22 men, 17 women; mean age, 34.9 years) who underwent clinically indicated EID CT of the lumbar spine. In both groups, all examinations were performed using unenhanced technique with tin prefiltration between June 2022 and January 2023. Patients were matched between groups using age, sex, and BMI. A custom gaussian curve-fitting algorithm was used to automatically calculate image noise, SNR, and CNR for each examination, on the basis of all voxels within the image set. Three radiologists independently reviewed examinations to perform a subjective visual assessment of visualization of trabecular architecture, cortical bone, neuroforaminal content, paraspinal muscles, and intervertebral disk, as well as overall image quality, using a 4-point Likert scale (1 = poor, 4 = excellent). PCD CT and EID CT examinations were compared. RESULTS. Mean CTDIvol was 4.4 ± 1.0 (SD) mGy for PCD CT versus 11.1 ± 1.9 mGy for EID CT (p < .001). Mean size-specific dose estimate (SSDE) was 6.2 ± 1.0 (SD) mGy for PCD CT versus 14.2 ± 1.8 mGy for EID CT (p < .001). PCD CT and EID CT examinations were not significantly different in terms of image noise or SNR (both p > .05). PCD CT, in comparison with EID CT, showed significantly higher CNR (mean ± SD, 33.6 ± 3.3 vs 29.3 ± 4.1; p < .001). For all three readers, the median score for overall image quality was 4 (range, 3-4) for both PCD CT and EID CT. PCD CT and EID CT examinations showed no significant difference in terms of any qualitative measure for any reader (all p > .05). CONCLUSION. PCD CT, in comparison with EID CT, yielded significantly lower radiation dose with preserved image quality. CLINICAL IMPACT. The findings support expanded use of PCD CT for lumbar spine evaluation.

Generating lane-level road networks from high-precision trajectory data with lane-changing behavior analysis

– Recent advances in mobile mapping systems have facilitated the collection of high-precision trajectory data in centimeter positioning accuracy. It provides the potential to infer lane-level road networks, which are essential for autonomous driving navigation. This task is challenging due to the complicated lane merging and diverging structures as well as the lane-changing patterns in trajectory data. This paper presents a lane-level road network generation method from high-precision trajectory data with lane-changing behavior analysis. Trajectories are firstly partitioned by detecting road intersections and changes in lane structure. Subsequently, in regions with consistent lane structure, a principal curve fitting algorithm is developed to extract lane centerlines. Erroneous lanes generated by lane-changing behavior are pruned based on a constructed lane intersection graph. In regions with merging and diverging lanes, a lane-group fitting algorithm is designed. This algorithm estimates lane locations by incorporating a Gaussian mixture model with lane width prior knowledge and then infers lane-level topological structures using trajectory flow information. The proposed method is evaluated on a real-world high-precision trajectory dataset. Comprehensive experiments demonstrate that it outperforms state-of-the-art methods in four metrics. Under complex scenarios, the method is capable of generating lane-level road networks with higher completeness and fewer fragments.

Aero-engine pipe gap automatic detection based on 3D scanning point clouds

Complex pipe systems are an important part of aero-engines to ensure reliable operations. These pipes are typically distributed in a narrow space while retaining a safe distance from each other. Thus, the gap between pipes needs to be periodically measured. Due to the complex structure of aero-engine pipes, there is no current effective method to detect pipe gaps. This paper proposes an automatic detection method for aero-engine pipe gaps based on raw point clouds. First, an iterative random point method is presented to obtain the center point set by relying on the geometric characteristics of the pipe. However, due to the complex background, the center point set contains significant noise and outliers. The key observation shows that the point density along a center curve and the mass of this curve are higher. We propose a mass and density-aware curve fitting algorithm capable of extracting the aero-engine pipe center curves with topological relationships and geometric details. We formulate the aero-engine pipe gap as the optimization model based on the distances between the center curves. Various experiments demonstrate the effectiveness and efficiency of the proposed approach, which exhibits superiority over several state-of-the-art methods in terms of the robustness to clutter and occlusion.

Visual Communication Design Features Based on Traditional Animal and Plant Patterns

Abstract This paper contributes to the visual communication design of traditional animal and plant patterns by recreating the traditional pattern graphics based on the specific skeletal laws of traditional patterns. Based on the demand for vectorization of traditional animal and plant tattoos, a vectorization algorithm based on edge structure extraction is proposed to pre-process the tattoos using the gradient minimization model, and the tattoos are processed by image vectorization using the edge structure extraction algorithm of clustered segmentation and the Bézier curve fitting algorithm of the least squares method. Based on the image vectorization rendering of traditional animal and plant patterns, the visual communication design is carried out, and the color matching effect is analyzed in terms of single-factor color matching and comprehensive color matching. 10 extracted colors are analyzed in terms of the hue angle difference on the color ring, and the two comparative colors are the contrasting colors when the angle difference is 120~180°. The contrast height is highest when the difference value is 180°.

An Efficient and Robust Complex Weld Seam Feature Point Extraction Method for Seam Tracking and Posture Adjustment

To realize high-quality robotic welding, an efficient and robust complex weld seam feature point extraction method based on a deep neural network (Shuffle-YOLO) is proposed for seam tracking and posture adjustment. The Shuffle-YOLO model can accurately extract the feature points of butt joints, lap joints and irregular joints, and the model can also work well despite strong arc radiation and spatters. Based on the nearest neighbor algorithm and cubic B-spline curve fitting algorithm, the position and posture models of the complex spatially curved weld seams are established. The robot welding postures adjustment and high-precision seam tracking of complex spatially curved weld seams are realized. Experiments show that the method proposed in this paper can extract weld seam feature points quickly and robustly, which enables welding robots to accurately track the weld seams and adjust the welding torch postures simultaneously.