Nonlinear Least-squares Method Research Articles

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

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

Rapid simultaneous estimation of relaxation rates using multi-echo, multi-contrast MRI

PurposeMulti-echo, multi-contrast methods are increasingly used in dynamic imaging studies to simultaneously quantify R2∗ and R2. To overcome the computational challenges associated with nonlinear least squares (NLSQ) fitting, we propose a generalized linear least squares (LLSQ) solution to rapidly fit R2∗ and R2. MethodsSpin- and gradient-echo (SAGE) data were simulated across T2∗ and T2 values at high (200) and low (20) SNR. Full (four-parameter) and reduced (three-parameter) parameter fits were implemented and compared with both LLSQ and NLSQ fitting. Fit data were compared to ground truth using concordance correlation coefficient (CCC) and coefficient of variation (CV). In vivo SAGE perfusion data were acquired in 20 subjects with relapsing-remitting multiple sclerosis. LLSQ R2∗ and R2, as well as cerebral blood volume (CBV), were compared with the standard NLSQ approach. ResultsAcross all fitting methods, T2∗ was well-fit at high (CCC = 1, CV = 0) and low (CCC ≥ 0.87, CV ≤ 0.08) SNR. Except for short T2∗ values (5–15 ms), T2 was well-fit at high (CCC = 1, CV = 0) and low (CCC ≥ 0.99, CV ≤ 0.03) SNR. In vivo, LLSQ R2∗ and R2 estimates were similar to NLSQ, and there were no differences in R2∗ across fitting methods at high SNR. However, there were some differences at low SNR and for R2 at high and low SNR. In vivo NLSQ and LLSQ three parameter fits performed similarly, as did NLSQ and LLSQ four-parameter fits. LLSQ CBV nearly matched the standard NLSQ method for R2∗- (0.97 ratio) and R2-CBV (0.98 ratio). Voxel-wise whole-brain fitting was faster for LLSQ (3–4 min) than NLSQ (16–18 h). ConclusionsLLSQ reliably fit for R2∗ and R2 in simulated and in vivo data. Use of LLSQ methods reduced the computational demand, enabling rapid estimation of R2∗ and R2.

The circadian pattern of atrial fibrillation onset

Abstract Background/Introduction Atrial fibrillation (AF) is the most common sustained cardiac arrhythmia affecting 2% of the population. Within the broad spectrum of AF symptomatology, there is a particular subset of patients that show a predominant or even exclusive nocturnal onset of paroxysmal AF. Purpose The aim of this study is to assess the timing of onset of AF in the 24-hour cycle and to assess whether a circadian rhythm is present in the onset of AF. Methods The MEDLINE, EMBASE, and CENTRAL databases, searched from inception to September 2023, provided 18 studies detailing the onset of AF in a 24-hour cycle. Patients had either paroxysmal or persistent AF. Studies performed in ICU populations (n=3) were omitted due to different triggers for AF. Time of AF onset was determined either by Cardiac Implantable Electronic Device (CIED) (n=5), Holter (n=7) or minute history taking (n=3). The presence and statistical significance of a 24-hour periodicity is tested using the cosinor analysis: Y(t)= A ⋅ sin(2πft + α) + β where the amplitude, frequency, phase and error (A, f, α and β, respectively) are computed by single harmonic regression using a nonlinear least-squares method. Goodness of fit is estimated using R2, the statistical significance of the model is tested using a zero-amplitude test. Results The 15 studies included 2.080 patients with 11.886 onsets of AF. The blue bars in Figure 1 represent the total of AF onsets from all studies per hour. The pattern of onset AF can be approximated well by a single sine function (Onset(t)= 95.7915 ⋅ sin((2π ⋅ 0.0417 ⋅ t) – 1.8386) + 510.5500, R2 0.77, P = 0.03) with a 24-hour period, clearly establishing the 24-hour rhythmicity in the onset of AF (Figure 1, red line). Hours with significantly more onset of AF compared to the mean, assessed by residual Chi2 testing, are exclusively nocturnal (22.00-7.00, indicated by a moon symbol in Figure 1) while hours with significantly less onset are exclusively during daytime (7.00-22.00, indicated by a sun symbol in Figure 1). Conclusion Despite the potential limitations due to the methods used, such as arrhythmia discrimination in CIED-studies and asymptomatic episodes in case of history taking, the overall picture of predominance of nocturnal AF onset is clearly established. Multiple pathophysiological mechanisms might underlie this circadian pattern and nocturnal predominance, like obstructive sleep apnea and increased vagal tone, which should be subject of further research.time of onset of AF over a 24h period

Quasi-2D inversion of surface large fixed-loop transient electromagnetic sounding data

Abstract In many cases, 1D inversion is still an important step in transient electromagnetic data processing. Potential issues may arise in the calculation of apparent resistivity using induced electromotive force (EMF) due to overshoot and the presence of multi-valued functions. Obtaining reliable and consistent inversion results using a uniform half-space as the initial model is challenging, especially when aiming for efficient inversion. Focusing on these problems, we use the land-based transient electromagnetic (TEM) sounding data, which was acquired by using a large fixed-loop transmitter, and adopt a quasi-2D inversion scheme to generate improved images of the subsurface resistivity structure. First, we have considered directly using magnetic field data or converting induced EMF into magnetic field, and then calculating the apparent resistivity over the whole zone. Next, a resistivity profile that varies with depth is obtained through fast smoke ring imaging. This profile serves as the initial model for the subsequent optimal inversion. The inversion scheme uses a nonlinear least-squares method, incorporating lateral and vertical constraints, to produce a quasi-2D subsurface image. The potentiality of the proposed methodology has been exemplified through the interpretation of synthetic data derived from a 3D intricate resistivity model, as well as field data obtained from a TEM survey conducted in a coalmine field. In both cases, the inversion process yields quasi-2D subsurface images that exhibit a reasonable level of accuracy. These images appear to be less moulded by 3D effects and demonstrate a satisfactory level of agreement with the known target area.

Toward Optimal Fitting Parameters for Multi-Exponential DWI Image Analysis of the Human Kidney: A Simulation Study Comparing Different Fitting Algorithms

In DWI, multi-exponential signal analysis can be used to determine signal underlying diffusion components. However, the approach is very complex due to the inherent low SNR, the limited number of signal decay data points, and the absence of appropriate acquisition parameters and standardized analysis methods. Within the scope of this work, different methods for multi-exponential analysis of the diffusion signal in the kidney were compared. To assess the impact of fitting parameters, a simulation was conducted comparing the free non-negative (NNLS) and rigid non-linear least square (NLLS) fitting methods. The simulation demonstrated improved accuracy for NNLS in combination with area-under-curve estimation. Furthermore, the accuracy and stability of the results were further enhanced utilizing optimized parameters, namely 350 logarithmically spaced diffusion coefficients within [0.7, 300] × 10−3 mm2/s and a minimal SNR of 100. The NNLS approach shows an improvement over the rigid NLLS method. This becomes apparent not only in terms of accuracy and omitting prior knowledge, but also in better representation of renal tissue physiology. By employing the determined fitting parameters, it is expected that more stable and reliable results for diffusion imaging in the kidney can be achieved. This might enable more accurate DWI results for clinical utilization.

Development of Deep Learning for Power Energy Optimization in the Industrial Robot System

This paper established power consumption modeling and motion estimation optimization of industrial robots. We also studied factors affecting the use of electrical energy, such as friction, torque, and electric current. The energy consumption parameters of each coupling can be quantified through the Deep Learning (DL) technique, Scaled Conjugate Gradient (SCG) estimation, or Simulation and experimentation based on the movement posture of a given robot dynamic model to control the robot operation. The robot dynamic model parameters can be identified and expressed in mathematical equations. Electrical energy consumption estimates were analyzed using the SCG technique to compare with the Nonlinear Least Squares (NLS) method using a large dataset of approximately 60,000 samples. The results showed accurate parameter prediction and electrical energy consumption estimation of the robot locomotion pose. The maximum errors in the SCG and NLS methods were 0.89% and 1.54%, respectively. It indicated that the electric energy consumption model using the SCG estimation method is more efficient than the NLS method.

A new tilted aerial robotic platform: Modeling and control

Aerial Manipulators are considered in modern applications due to their essential features that have the maneuverability of Unmanned Aerial Vehicles (UAVs) and abilities of robotics arms. One of the primary challenges encountered by aerial manipulators is their inability to maintain a consistent orientation though the duration of flight. This limits the application of aerial manipulators for movement of fragile and liquid objects that should not change their orientation during the flight. To solve this issue, this study introduced a new Aerial Robot Platform (AR-P) which can decouple all motions by configuring tilting rotors into the structure of the AR-P. The AR-P consists of a Tilted-Rotor Quadcopter (T-RQ) and three linked Aerial Robot Arm (AR-A) that have a gripper to grasp objects. The AR-P with this new mechanism of tilting parts overcomes the problem of manipulation limitations by adjusting the direction of the thrusted rotors according to the exerted forces of the grasped object. The new dynamics model of the AR-P is derived using the Lagrange-d'Alembert approach. A special Multi Input Multi Output (MIMO) Proportional Derivative (PD) controller based on Computed Torque Control (CTC) is designed for the developed AR-P. The method of nonlinear least squares is applied to obtain the optimal gains of the over-looped PD controller. The simulation results showed the ability of the developed CTC to track the required joint angle of each the T-RQ and each link of the AR-A with minimizing steady state errors and without overshooting. The implemented controller showed its robustness against external disturbances in form of wind conditions. On one hand, the controller is tested considering traditional aerial manipulator. On the other hand, the controller is tested by our new tilted aerial robot platform. The comparison results of the flight scenario between the new tilted aerial manipulator and the traditional one approved the advantage of the proposed new tilted AR-P to transport the grasped objects in fixed orientation.

Determination of optical constants for thin-walled glass cell based on Haidinger fringes

A validated method based on Haidinger fringes has been proposed to measure the optical constants for thin-walled glass cells. The method can significantly enhance measurement accuracy by utilizing the reflected spectrum to determine the optical constants of the sample. The reflected light off the inner and the outer surfaces of the cell combined together and formed the interferential pattern (Haidinger fringes) detected by the photodiodes. Taking into account that the sample in our experiment is a sealed cell, we deliberately set the incident angle to a non-zero value. First, the measurement principle has been analyzed, and subsequently, the relevant experimental platform has been established. To reduce random errors, we recalibrated the relationship between the frequency of the laser and the operating temperature. Furthermore, the incident angle has been accurately estimated using the method of non-linear least squares. Finally, the weighted average, considering correlated uncertainties for all measurements, is 1.873 ± 0.005 016 mm, which showcases clear advantages over conventional mechanical methods that risk potential damages.

Were public interventions relevant for containing the covid-19 pandemic in Brazil in 2020?

Flattening the curve was the most promoted public health strategy worldwide, during the pandemic, to slow down the spread of the SARS-CoV-2 virus, and, consequently, to avoid overloading the healthcare systems. In Brazil, a relative success of public policies was evidenced. However, the association between public policies and the "flatten the curve" objectives remain unclear, as well as the association of different policies to reach this aim. This study aims to verify if the adoption of different public policies was associated with the flattening of the infection and death curves by covid-19 first wave in 2020. Data from the Sistema de Informação da Vigilância Epidemiológica da Gripe (Influenza Epidemiological Surveillance Information System - SIVEP-Gripe) and the Instituto Brasileiro de Geografia e Estatística (Brazilian Institute of Geography and Statistics - IBGE) were used to compute standardized incidence and mortality rates. The Oxford Covid-19 Government Response Tracker (OxCGRT) was used to obtain information about governmental responses related to the mitigation of pandemic effects, and the Human Development Index (HDI) was used as a measure of socioeconomic status. A non-linear least-square method was used to estimate parameters of the five-parameter sigmoidal curve, obtaining the time to reach the peak and the incremental rate of the curves. Additionally, ordinary least-square linear models were used to assess the correlation between the curves and the public policies adopted. Out of 51 municipalities, 261,326 patients had SARS-CoV-2 infection. Stringency Index was associated with reducing covid-19 incremental incidence and death rates,in addition to delaying the time to reach the peak of both pandemic curves. Considering both parameters, economic support policies did not affect the incidence nor the mortality rate curves. The evidence highlighted the importance and effectiveness of social distancing policies during the first year of the pandemic in Brazil, flattening the curves of mortality and incidence rates. Other policies, such as those focused on economic support, were not effective in flattening the curves but met humanitarian and social outcomes.

Accelerating Bayesian Estimation of Solar Cell Equivalent Circuit Parameters Using JAX-Based Sampling

Equivalent circuit models that reproduce the current–voltage characteristics of solar cells are useful not only to gain physical insight into the power loss mechanisms that take place in solar cells but also for designing systems that use renewable solar energy as a power source. As mentioned in a previous paper, Bayesian estimation of equivalent circuit parameters avoids the drawbacks of nonlinear least-squares methods, such as the possibility of evaluating estimation errors. However, it requires a long computation time because the estimated values are obtained by sampling using a Markov chain Monte Carlo method. In this paper, a trial to accelerate the calculation by upgrading the Bayesian statistical package PyMC is presented. PyMC ver. 4, the next version of PyMC3 used in the previous paper, started to support the latest sampling libraries using a machine learning framework JAX, in addition to PyMC-specific methods. The acceleration effect of JAX is remarkable, achieving a calculation time of less than 1/20 times that of the case without JAX. Recommended calculation conditions were disclosed based on the results of a number of trials, and a demonstration with testable Python code on Google Colaboratory using the recommended conditions is published on GitHub.

Non-iterative pulse tail extrapolation algorithms for correcting nuclear pulse pile-up

Radiation detection systems working at high count rates suffer from the overlapping of their output electric pulses, known as pulse pile-up phenomenon, resulting in spectrum distortion and degradation of the energy resolution. Pulse tail extrapolation is a pile-up correction method which tries to restore the shifted baseline of a piled-up pulse by extrapolating the overlapped part of its preceding pulse. This needs a mathematical model which is almost always nonlinear, fitted usually by a nonlinear least squares (NLS) technique. NLS is an iterative, potentially time-consuming method.The main idea of the present study is to replace the NLS technique by an integration-based non-iterative method (NIM) for pulse tail extrapolation by an exponential model. The idea of linear extrapolation, as another non-iterative method, is also investigated. Analysis of experimental data of a NaI(Tl) radiation detector shows that the proposed non-iterative method is able to provide a corrected spectrum quite similar with the NLS method, with a dramatically reduced computation time and complexity of the algorithm. The linear extrapolation approach suffers from a poor energy resolution and throughput rate in comparison with NIM and NLS techniques, but provides the shortest computation time.

Modeling Based on a Two-Step Parameter Identification Strategy for Liquid Crystal Elastomer Actuator Considering Dynamic Phase Transition Process.

Liquid crystal elastomer (LCE) is a promising candidate for actuation in light-driven soft robot applications. Due to the fact that LCE has complex hysteretic nonlinearities, which are highly dependent on the environment, modeling of actuators made of LCE is a very challenging issue. In this article, a model is proposed to describe the deformation of the LCE actuator accurately and analytically by considering the dynamic phase transition process of LCE molecules. First, an overview of the physical process of LCE's deformation is presented, and the schematic of the LCE actuator, as well as the modeling scheme are then introduced. Next, a thermodynamic analysis of the system's free energy is performed to establish the model for the LCE actuator, which gives the relationship between the system's deformation and the temperature. Here, to describe the complex hysteretic nonlinearity in the model, the dynamic process of the phase transition of LCE molecules is exploited. To effectively identify the model parameters, a two-step parameter identification strategy based on the differential evolution algorithm and nonlinear least-squares method is utilized. Finally, experimental results verify the validity of the proposed model. This modeling provides an approach to describe LCE's deformation with high accuracy and can fully reflect the physical nature of LCE's deformation, especially hysteresis. It can be utilized as a basis for accurate control over LCE actuators in photoresponsive soft robot applications.

EPH262 Preventing COVID-19 Outbreaks Using Wastewater Surveillance at Long-Term Care Facilities: A Pilot Modelling Study

Site-specific wastewater surveillance could potentially control COVID-19 outbreaks more effectively at long-term care facilities (LTCF). It could identify the presence of pre-symptomatic and asymptomatic COVID-19 infections in the facility and therefore initiate timely outbreak control measures. Besides, compared to repetitive screenings of residents and staff using diagnostic tests, screenings based on positive wastewater test results incur fewer costs and less discomfort. We evaluated the effectiveness of LTCF-site-specific wastewater surveillance in preventing COVID-19 outbreaks, by comparing the scenario where more diagnostic tests were initiated due to positive wastewater test results and the base case of no action. We built a susceptible-infected-cases-recovered model to study COVID-19 transmission at LTCF under the base-case and wastewater surveillance scenario. We used data from an outbreak during the Omicron wave in one LTCF in Edmonton, Canada (December 2021 – March 2022), where wastewater data did not initiate actions. We fit base-case model parameters with daily cases and testing data using the nonlinear least-squares method. We hypothesized 10%-50% more diagnostic tests in the wastewater scenario. We compared the outbreak size, i.e., predicted numbers of infections, to measure the effectiveness. We used the Mann-Whitney U test to identify whether the outbreak size in the wastewater scenario was significantly smaller. Results reported are subject to minor changes as modelling work is ongoing. The number of infections peaked on day 25 in the base case, with 23.8% of individuals being infected. In the wastewater scenario, all hypothesized values resulted in a significantly smaller outbreak size; only 10% more diagnostic tests could lead to 5.4% fewer infections (p=0.03) at the peak. This pilot study demonstrates the potential effectiveness of LTCF-site-specific wastewater surveillance to prevent COVID-19 outbreaks. Future works include engaging policymakers in analyzing specific wastewater-based actions and estimating the costs of controlling COVID-19 to explore the cost-effectiveness of wastewater surveillance.

Diffusion-Weighted MRI of the Liver in Patients With Chronic Liver Disease: A Comparative Study Between Different Fitting Approaches and Diffusion Models.

Diffusion-weighted imaging (DWI) has been considered for chronic liver disease (CLD) characterization. Grading of liver fibrosis is important for disease management. To investigate the relationship between DWI's parameters and CLD-related features (particularly regarding fibrosis assessment). Retrospective. Eighty-five patients with CLD (age: 47.9 ± 15.5, 42.4% females). 3-T, spin echo-echo planar imaging (SE-EPI) with 12 b-values (0-800 s/mm2 ). Several models statistical models, stretched exponential model, and intravoxel incoherent motion were simulated. The corresponding parameters (Ds , σ, DDC, α, f, D, D*) were estimated on simulation and in vivo data using the nonlinear least squares (NLS), segmented NLS, and Bayesian methods. The fitting accuracy was analyzed on simulated Rician noised DWI. In vivo, the parameters were averaged from five central slices entire liver to compare correlations with histological features (inflammation, fibrosis, and steatosis). Then, the differences between mild (F0-F2) or severe (F3-F6) groups were compared respecting to statistics and classification. A total of 75.3% of patients used to build various classifiers (stratified split strategy and 10-folders cross-validation) and the remaining for testing. Mean squared error, mean average percentage error, spearman correlation, Mann-Whitney U-test, receiver operating characteristic (ROC) curve, area under ROC curve (AUC), sensitivity, specificity, accuracy, precision. A P-value <0.05 was considered statistically significant. In simulation, the Bayesian method provided the most accurate parameters. In vivo, the highest negative significant correlation (Ds , steatosis: r = -0.46, D*, fibrosis: r = -0.24) and significant differences (Ds , σ, D*, f) were observed for Bayesian fitted parameters. Fibrosis classification was performed with an AUC of 0.92 (0.91 sensitivity and 0.70 specificity) with the aforementioned diffusion parameters based on the decision tree method. These results indicate that Bayesian fitted parameters may provide a noninvasive evaluation of fibrosis with decision tree. 1 TECHNICAL EFFICACY: Stage 1.

On the Short-Term Creep and Recovery Behaviors of Injection Molded and Additive-Manufactured Tough Polylactic Acid Polymer

The creep and recovery behaviors of a tough polylactic acid polymer are investigated experimentally and theoretically. We studied the influence of manufacturing methods and parameters on the viscoelastic responses. Experimental comparisons were carried out on 13 different samples manufactured using fused deposition modeling (FDM) and injection molding methods. The sample variations in the FDM were based on four infill densities (70-100%) and 3 infill directions (0^circ ,45^circ ,90^circ ). Theoretically, the Burgers and Weibull’s models are used to predict the creep and recovery responses of the samples. Our experimental findings suggest that the injection-molded samples perform better in creep for most of the cases. However, at higher stress loadings, the 90 and 100% infill density samples showed excellent creep resistance behaviors at the 90^circ infill direction. On the other hand, the theoretical creep and recovery predictions were based on the nonlinear least-squares regression method. The Burgers model predicted the creep responses with reasonable accuracies. A maximum of 5.83% mean absolute percentage error (MAPE) was found for the 0° infill direction and 80% infill density sample. On the contrary, the model lacks accuracy in recovery strain predictions, showing an average of 173.15% MAPE for all studied samples. Introducing Weibull’s distribution improved the accuracies showing a 3.44% average MAPE for all samples.

Biochemical Changes during Fruit and Seed Development in Nanjing Linden (Tilia miqueiana M.)

In China, the wild population of Nanjing Linden (Tilia miqueliana M.) is experiencing a drastic decline, primarily due to high levels of empty seeds. This study aimed to measure the biochemical and physiological changes during fruit and seed development in T. miqueliana to determine the developmental mechanism. The weight method and photosynthetic respiration were used to determine the biological aspects of both fruits and embryos, while transmission electron microscopy and the anthrone colorimetric method were used to determine the endosperm content, including sugar, starch, protein, and fat. Enzyme-linked immunosorbent assays were conducted to determine the levels of endogenous plant hormones such as indole-3-acetic acid (IAA), gibberellic acid 3 (GA3), zeatin riboside (ZR), and abscisic acid (ABA). The nonlinear least-squares method was used to fit the model of nutrient and hormone levels, revealing that fruit size expanded from the 5th to the 65th day and that fruit moisture content exhibited a downward trend, along with a decrease in fruit respiration intensity. Embryos were found to be fully developed between 35 DAF and 65 DAF, while the nutrients in the endosperm, i.e., sugar, starch, protein, and fat, continuously accumulated after 50 DAF. Additionally, ABA, IAA, GA3, and ZR contents were found to synergistically regulate seed development and maturation.

Optimization of the stability constants of the ternary system of diclofenac/famotidine/β-cyclodextrin by nonlinear least-squares method using theoretical equations

This study aimed to establish a new method for determining the stability constants of drug/β-cyclodextrin (β-CD) complexes when multiple drugs interacting with each other coexist in the solution of complexation. The basic drug famotidine (FAM) and the acidic drug diclofenac (DIC) were used as model drugs, their solubility decreasing owing to their mutual interaction. The dissolution of both FAM and DIC was characterized by AL-type phase solubility diagrams in the presence of the other’s 1:1 complex with β-CD. When the stability constant was calculated from the slope of the phase solubility diagram using the conventional phase solubility diagram method, it was modified in the presence of the other drug. However, by performing optimization calculations that considered the interactions between the drug/β-CD complex and the drug, drug/β-CD complexes, and drugs, we were able to accurately calculate the stability constant of DIC/β-CD and FAM/β-CD complexes even in the presence of FAM and DIC, respectively. The results of the solubility profile indicated that various molecular species, which are attributed to drug-drug and drug/β-CD interactions, interfere with the values of the dissolution rate constants and saturated concentration in the solubility profiles.

A variable projection method for the general radial basis function neural network

The variable projection (VP) method is a classical and effective method for the separable nonlinear least squares (SNLLS) problem. Training a radial basis function neural network (RBFNN) with only one output neuron by minimizing the sum of the squared errors (SSE) is an SNLLS problem, so that the classical VP method has been applied to RBFNN. However, the one-output-RBFNN (ORBFNN) is just one type of RBFNN, so that the paper proposes a new VP method for the general radial basis function neural network (GRBFNN) which has no limit of the number of the output neurons. The new VP method translates the problem corresponding to minimizing the SSE of GRBFNN into a lower-dimensional optimization problem. We prove theoretically that the set of stationary points of the objective function of the lower-dimensional problem is equivalent to that of the original objective function. In addition, the lower dimension leads to less guesses about the initial point for the new problem. The numerical experiments indicate that, with the same algorithm, minimizing the new objective function converges in fewer iterations and makes both a smaller training error and a testing error than minimizing the original objective function.

Dynamic modelling of liquid crystal elastomer actuators based on a physics-phenomenon-combined approach

Liquid crystal elastomer-based actuators (LCEAs) exhibit large, reversible deformation, which demonstrates superior advantages in developing remote controlled, light-weighted soft robots. However, deformation of LCEAs undergoes complicated physical dynamics and exhibits highly nonlinear hysteretic characteristics, posing challenges in the realization of related applications. It is necessary to develop a dynamic model that captures the characteristics of LCEAs. With this purpose, this paper proposes a dynamic modelling approach for LCEAs to provide a hybrid model for LCEAs with reduced computational complexity and high precision. In the research, a modelling scheme based on a physics-phenomenon-combined approach for LCEAs is proposed, which considers the elastic free energy, the nematic free energy and dissipation of the LCEA. Physics-based models are then developed to describe these energies. Meanwhile, a phenomenon-based model is proposed to characterise the hysteresis as a component of the nematic free energy. The above models are combined together to provide the final hybrid model for the LCEA. To verify the proposed model, a photo-responsive LCEA experimental platform is established and experiments are conducted. Model parameters are identified based on the nonlinear least-squares method. The experimental results demonstrate the proposed model as an excellent representative to characterise LCEAs' dynamic behaviours.

Evaluating the impact of multiple factors on the control of COVID-19 epidemic: A modelling analysis using India as a case study.

The currently ongoing COVID-19 outbreak remains a global health concern. Understanding the transmission modes of COVID-19 can help develop more effective prevention and control strategies. In this study, we devise a two-strain nonlinear dynamical model with the purpose to shed light on the effect of multiple factors on the outbreak of the epidemic. Our targeted model incorporates the simultaneous transmission of the mutant strain and wild strain, environmental transmission and the implementation of vaccination, in the context of shortage of essential medical resources. By using the nonlinear least-square method, the model is validated based on the daily case data of the second COVID-19 wave in India, which has triggered a heavy load of confirmed cases. We present the formula for the effective reproduction number and give an estimate of it over the time. By conducting Latin Hyperbolic Sampling (LHS), evaluating the partial rank correlation coefficients (PRCCs) and other sensitivity analysis, we have found that increasing the transmission probability in contact with the mutant strain, the proportion of infecteds with mutant strain, the ratio of probability of the vaccinated individuals being infected, or the indirect transmission rate, all could aggravate the outbreak by raising the total number of deaths. We also found that increasing the recovery rate of those infecteds with mutant strain while decreasing their disease-induced death rate, or raising the vaccination rate, both could alleviate the outbreak by reducing the deaths. Our results demonstrate that reducing the prevalence of the mutant strain, improving the clearance of the virus in the environment, and strengthening the ability to treat infected individuals are critical to mitigate and control the spread of COVID-19, especially in the resource-constrained regions.