Levenberg-Marquardt Research Articles

Fabrication of molecular-scale logic devices and implication of artificial neural networks for analysis of anion-responsive behaviors of luminescent ruthenium-terpyridine complex

Anion responsive spectral characteristics of a homoleptic luminescent Ru(II)-terpyridine complex derived from 4′-(p-triphenylphosphoniummethylphenyl)-2,2′:6′,2″-terpyridine bromide (tpy-PhCH2PPh3Br) ligand has been utilized here to mimic the operation of several advanced logic functions. The complex displays remarkable change in absorption and emission spectral profiles in presence of selected anions due to concerted hydrogen bonding followed by anion-induced proton abstraction. Importantly, deprotonation by specific anions followed by restoration to the initial form of the complex is feasible in presence of acid and the process could be recycled. The spectral responsiveness of the complex is employed to mimic various advanced Boolean logic functions, such as IMPLICATION, INHIBIT and combinational logic gates. Execution of exhaustive sensing investigations is often labor-intensive and time-consuming. To address the gap, we employed herein artificial neural network (ANN) models employing three different training algorithms, viz. Bayesian Regularization (BR), Scaled Conjugate Gradient (SCG), and Levenberg-Marquardt (LM) for comprehensive analysis and prediction of the experimental observations. We also compared the outcomes of these models with one another as well as with the experimental data to enable an accurate modeling of the complex’s anion-sensing behavior.

Artificial neural network for predicting the performance of waste polypropylene plastic-derived carbon nanotubes

AbstractIn this study, an artificial neural network model using function fitting neural networks was developed to describe the yield and quality of multi-walled carbon nanotubes deposited over NiMo/CaTiO3 catalyst using waste polypropylene plastics as cheap hydrocarbon feedstock using a single-stage chemical vapour deposition technique. The experimental dataset was developed using a user-specific design with four numeric factors (input variable): synthesis temperature, furnace heating rate, residence time, and carrier gas (nitrogen) flow rate to control the performance (yield and quality) of produced carbon nanotubes. Levenberg–Marquardt algorithm was utilized in training, validating, and testing the experimental dataset. The predicted model gave a considerable correlation coefficient (R) value close to 1. The presented model would be of remarkable benefit to successfully describe and predict the performance of polypropylene-derived carbon nanotubes and show how the predictive variables could affect the response variables (quality and yield) of carbon nanotubes.

Intelligent computing for the electro-osmotically modulated peristaltic pumping of blood-based nanofluid

The study delves into a novel application of artificial neural networks within the biomedical realm, specifically focusing on the peristaltic pumping of ionized blood-infused nanofluid using the Casson model. The investigation takes into account the impacts of electrokinetic forces, chemical reaction, thermal radiation and variable thermal conductivity. The endorsed nanofluid model encompasses both thermophoretic and Brownian diffusions. The Nernst-Planck and Poisson equations are used to characterize electroosmotic process. The mathematical model is then numerically solved using NDSolve in Mathematica. The variation in relevant hemodynamic characteristics concerning key flow parameters is explored through numerous graphical representations. Two distinct artificial neural networks have been developed to estimate values for rates of mass and heat transfer. The Levenberg-Marquardt algorithm is used as the training algorithm in network models with multi-layer perceptron architecture. Graphical inspection of the results demonstrates a decrease in blood flow with an elevated Helmholtz-Smoluchowski velocity. A lower pressure gradient is recorded with a higher electroosmotic parameter. Furthermore, an augmentation in the thermal conductivity parameter leads to a reduction in heat transfer rate at the wall. The concentration profile demonstrates an increase with a rise in the chemical reaction parameter. The results obtained from the neural network models exhibit an ideal harmony with the target values. The developed neural network models demonstrated the ability to predict rates of heat and mass transfer values with average deviations of −0.01% and 0.004%, respectively.

Recovering induced polarization effects from 1-D coupled inversion of transient electromagnetic data

SUMMARY Induced polarization (IP) effects can significantly affect and superimpose the inductive earth response, leading to heavily distorted data and, if overlooked, false geological interpretation. In this paper, we implemented the Levenberg–Marquardt (LM) and very fast simulated annealing (VFSA) algorithms to recover IP effects from central loop transient electromagnetic (TEM) data. To incorporate the IP effect in the TEM response, we used the Cole–Cole parametrization, maximum phase angle (MPA), maximum imaginary conductivity (MIC) and Jeffrey transform of Cole–Cole parameters. The result of 1-D forward calculation and inversion of synthetic TEM data revealed that the Cole–Cole parametrization is more robust and reliable than MPA, MIC and Jeffrey transform, and that the synthetic data were well fitted and IP parameters well recovered using this model. However, the incorporation of the IP effect leads to a highly nonlinear and non-unique inverse problem which requires an accurate starting model, especially for LM inversion. To evaluate the performance of our algorithm using field data, we carried out a 1-D inversion of TEM data acquired along a profile that traverses a waste site located near Cologne, Germany. Furthermore, to obtain a priori information and validate the result of TEM data modelling, we conducted an electrical resistivity tomography (ERT) and time-domain IP (TDIP) survey along the TEM profile. A 2-D inversion was used to retrieve the Cole–Cole parameters as input for TEM interpretation. By including the IP information, the TEM field data can be explained quantitively, and a consistent and improved interpretation of the waste body is achieved.

Dynamics modeling and nonlinear attitude controller design for a rocket-type unmanned aerial vehicle

This paper presents an altitude and attitude control system for a newly designed rocket-type unmanned aerial vehicle (UAV) propelled by a gimbal-based coaxial rotor system (GCRS) enabling thrust vector control (TVC). The GCRS is the only means of actuation available to control the UAV’s orientation, and the flight dynamics identify the primary control difficulty as the highly nonlinear and tightly coupled control distribution problem. To address this, the study presents detailed derivations of attitude flight dynamics and a control strategy to track the desired attitude trajectory. First, a Proportional-Integral-Derivative (PID) control algorithm is developed based on the formulation of linear matrix inequality (LMI) to ensure robust stability and performance. Second, an optimization algorithm using the Levenberg–Marquardt (LM) method is introduced to solve the nonlinear inverse mapping problem between the control law and the actual actuator outputs, addressing the nonlinear coupled control input distribution problem of the GCRS. In summary, the main contribution is the proposal of a new TVC UAV system based on GCRS. The PID control algorithm and LM algorithm were designed to solve the distribution problem of the actuation model and confirm altitude and attitude tracking missions. Finally, to validate the flight properties of the rocket-type UAV and the performance of the proposed control algorithm, several numerical simulations were conducted. The results indicate that the tightly coupled control input nonlinear inverse problem was successfully solved, and the proposed control algorithm achieved effective attitude stabilization even in the presence of disturbances.

Maximum displacement prediction model for steel beams with hexagonal web openings under impact loading based on artificial neural networks

The estimation of the maximum displacement of steel beams with hexagonal web openings under impact loads is crucial for the anti-impact design of structures. The dynamic characteristics are complex, and the maximum displacement can be obtained experimentally, although the time cost, and expense of such experiments are high. In this context, a 6-5-1 artificial neural network model based on the Levenberg-Marquardt backpropagation algorithm was developed, incorporating 5-fold cross-validation techniques. Due to limited experimental data, 324 high-precision finite element models were created in bulk using Python-based ABAQUS software scripts to provide additional numerical data, and 26 specimens were designed for drop hammer tests to validate the finite element models. The artificial neural network model on the test data yielded a mean squared error of 0.0268, a mean absolute error of 0.0014, and a coefficient of determination value of 0.9806, with samples having an error of less than 10% comprising 77.16% of the total samples. Using Garson’s algorithm, the contribution of input features was estimated, and a full parameter analysis of the proposed model was conducted. The results indicate that the most significant factor is the impact mass, which accounts for 37.58%. When the impact mass increased from 530 kg to 630 kg, the maximum displacement of Q235 surged by 93.75%. The factor with the least impact is the opening spacing, accounting for 2%, with an average increase in maximum displacement of only 3.45%. Finally, ANN-based equations that can be used as design tools are established.

A Mathematical Modeling of Computer Numerical Control Skiving Process for Manufacturing Helical Face Gears Using Sensitivity Matrix Combined With Levenberg–Marquardt Algorithm

Abstract Currently, numerous studies have applied gear skiving processes to produce face gear. However, there remains a significant challenge in achieving a flexible computing model for manufacturing a precise tooth surface for face gear. This study proposes a novel mathematical model that combines the cutter modification method and computer numerical control (CNC)-axis motion modification methods within a unified “closed-loop optimization.” This approach aims to enhance the tooth surface accuracy of skived helical face gears by determining optimal coefficients. Applying the Levenberg–Marquardt algorithm and sensitivity matrix enables the calculation of new polynomial coefficients, ensuring the attainment of gear surfaces with an accuracy grade of B6 (according to the ANSI/AGMA 2009-B01 standard) for each target surface. The proposed methodology involves the generation of a helical skiving cutter using a corrected rack. Subsequently, the cutting path on the CNC machine is optimized by incorporating additional motions expressed in polynomials. A comprehensive skiving simulation is conducted to achieve the desired face-gear surface, which is corrected by specified polynomial coefficients. The proposed model is validated through numerical and machining simulations using vericut software. The results affirm the practicality and efficacy of our approach in achieving the desired accuracy in producing helical face gears through power skiving processes.

Teak leaf biochar production for sustainable forest waste management at low temperatures

This study investigates the possibilities of producing biochar from teak leaves as an environmentally beneficial approach to managing forest waste in a sustainable manner. Teak leaves, a readily available forest by-product, were converted into biochar through a low-temperature pyrolysis process using a top-lit updraft mechanism. The results demonstrate the efficiency of this approach, yielding a substantial biochar output of 37.4 wt%, with its thermal field modelled perfectly via Levenberg-Marquardt algorithm in ANN topology. Elemental analysis of the teak leaf biochar revealed a high carbon content of 64.40%, positioning it as a valuable carbon-rich material suitable for various applications. Textural properties analysis indicated a significant surface area of 371.78 m2/g and a total pore volume of 0.175 cm³/g, enhancing its potential for various applications. Scanning Electron Microscopy (SEM) investigations showed a diverse network of pores and a rough surface structure, reinforcing the biochar’s versatility. This study shows the environmental benefits of low-temperature teak leaf biochar production, because it provides a carbon-content-preserving, sustainable alternative for handling forest wastes.

Prediction of seismic performance of a masonry-infilled RC frame based on DEM and ANNs

In this paper, discrete element modelling and artificial neural networks (ANNs) were adopted to evaluate seismic performance of a masonry-infilled reinforced concrete (RC) frame. Discrete element models were developed to simulate quasi-static tests of infilled frames and were validated by using experimental data from the literature in terms of ultimate bearing capacities, initial stiffnesses and hysteresis curves. Parametric analysis was conducted based on the validated models to further investigate the influence factors of infilled RC frames and to collect a database for training ANN models. Subsequently, 440 datasets were divided into a training set (70 %), a validating set (15 %), and a testing set (15 %). Back propagation neural network (BPNN) and radial basis function neural network (RBFNN) were employed to predict the seismic behavior of a masonry-infilled RC frame. The BPNN model used the Levenberg-Marquardt algorithm exhibited the highest coefficient of determination, and it was better than the RBFNN model with more neurons. Eventually, a practical ANN model was proposed to evaluate the seismic performance of a masonry-infilled RC frame.

Lithium Battery SoC Estimation Based on Improved Iterated Extended Kalman Filter

With the application of lithium batteries more and more widely, in order to accurately estimate the state of charge (SoC) of the battery, this paper uses the iterated extended Kalman filter (IEKF) algorithm to estimate the SoC. The Levenberg–Marquardt (LM) method is used to optimize the error covariance matrix of IKEF. Based on the hybrid pulse power characteristics experiment, a second-order Thevenin model with variable parameters is established on the MATLAB platform. The experimental results show that the proposed model is effective under the constant current discharge condition, the Federal Urban Driving Schedule (FUDS) condition, and the Beijing dynamic stress test (BJDST) condition. The results show that the simulation error of the improved LM-IEKF algorithm is less than 2% under different working conditions, which is lower than that of the IKEF algorithm. The improved algorithm has a fast convergence speed to the true value, and it has a good estimation accuracy in the case of large changes in external input current. Additionally, the fluctuation of error is relatively stable, which proves the reliability of the algorithm.

Security monitoring via sound analysis and voice identification with artificial intelligence

The article demonstrates the possibility of monitoring user access through authentication based on voice profiles using the means of Artificial Intelligence. A two-stage approach is proposed for sound analysis and voice recognition using Feed-Forward Neural Networks (FFNNs) and Cascade-Forward Neural Networks (CFNNs). Seven test voice profiles were pre-processed to extract quantitative sound features. The procedure involves registration of a set of sound parameters concerning three categories, respectively, for all audio and acoustic measurements in the entire sound spectrum, measurements up to and above 100 dBA. The neural architectures were trained with Scaled Gradient Descent (SCG) and Levenberg Marquardt (LM) algorithms, using different transfer functions in the output structural layers. In the initial phase of neural training, the entire sound spectrum of registered indicators was used, and high levels of Accuracy around 90.0% were reached. Subsequently, steps were taken to reduce the informative features when searching for similar levels of accuracy in order to limit the necessary computational procedures in neural training, but maintain the threshold of successful user authentication. In the analysis of neural performance, in addition to accuracy, additional criteria were used, namely Mean-Squared Error (MSE) and Root Mean Squared Error (RMSE). About the achieved and analyzed results, a synthesis was conducted of a set of four informative features with the highest significance, respectively LAE (A-weighted, sound exposure level), Laeq (A-weighted, equivalent sound level), LAF (A-weighted, fast time-constant, sound level) and LAS (A-weighted, slow time constant response, sound level). In the course of subsequent neural training processes, unsuitability was found when using the Log-sigmoid activation type with greatly underestimated accuracy readings and errors below 58.0% and above thresholds of 0.2300 and 0.4800. Positive performance indicators of voice recognition were achieved with Softmax and Hyperbolic tangent sigmoid activations in SCG and LM training procedures in levels of accuracy of 98.7 % and 96.1 % at FFNN models. Successful correct recognition of the test voice profiles on access and security personalization with a quantitative equivalent of 100.0 % accuracy was achieved in the Linear transfer function for Cascade-Forward Neural Networks. The proposed method and the synthesized neural models in the research can be used as units and modules in access control systems with biometric diagnostics and intelligent recognition of employees in company departments to electronically store classified information and physical access control.

ANN Algorithms for Parkinson s, ALS, Huntington, and Healthy Walking Detection

In this study, the utilization of artificial neural networks (ANN) algorithms, in the diagnosis of neurodegenerative diseases were examined. Data obtained from the measurement of walking parameters were evaluated for disease diagnosis using the ANN model among individuals with ALS, Parkinson's, Huntington's, and healthy individuals. Comparative analyses conducted using Levenberg-Marquardt, Bayesian Regularization, and Scaled Conjugate Gradient algorithms demonstrate that the Levenberg-Marquardt algorithm provides the most effective diagnosis with a success rate of 99%. This study highlights the potential of artificial neural networks in the early diagnosis of neurodegenerative diseases and lays a foundation for future research. In conclusion, artificial neural networks may play a significant role in the diagnosis of neurodegenerative diseases, but further research and method development in this area are warranted.

RNNPose: 6-DoF Object Pose Estimation via Recurrent Correspondence Field Estimation and Pose Optimization.

6-DoF object pose estimation from a monocular image is a challenging problem, where a post-refinement procedure is generally needed for high-precision estimation. In this paper, we propose a framework, dubbed RNNPose, based on a recurrent neural network (RNN) for object pose refinement, which is robust to erroneous initial poses and occlusions. During the recurrent iterations, object pose refinement is formulated as a non-linear least squares problem based on the estimated correspondence field (between a rendered image and the observed image). The problem is then solved by a differentiable Levenberg-Marquardt (LM) algorithm enabling end-to-end training. The correspondence field estimation and pose refinement are conducted alternately in each iteration to improve the object poses. Furthermore, to improve the robustness against occlusion, we introduce a consistency-check mechanism based on the learned descriptors of the 3D model and observed 2D images, which downweights the unreliable correspondences during pose optimization. We evaluate RNNPose on several public datasets, including LINEMOD, Occlusion-LINEMOD, YCB-Video and TLESS. We demonstrate state-of-the-art performance and strong robustness against severe clutter and occlusion in the scenes. Extensive experiments validate the effectiveness of our proposed method. Besides, the extended system based on RNNPose successfully generalizes to multi-instance scenarios and achieves top-tier performance on the TLESS dataset.

Unleashing the power of artificial neural networks: accurate estimation of monthly averaged daily wind power at Adama wind farm I, Ethiopia

Wind power plays a vital role in the electricity generation of many countries, including Ethiopia. It serves as a valuable complement to hydropower during the dry season, and its affordability is crucial for the growth of industrial centers. However, accurately estimating wind energy poses significant challenges due to its random nature, severe variability, and dependence on wind speed. Numerous techniques have been employed to tackle this problem, and recent research has shown that Artificial Neural Network (ANN) models excel in prediction accuracy. This study aims to assess the effectiveness of different ANN network types in estimating the monthly average daily wind power at Adama Wind Farm I. The collected data was divided into three sets: training (70%), testing (15%), and validation (15%). Four network types, namely Feedforward Backpropagation (FFBP), Cascade Feedforward Backpropagation (CFBP), Error Backpropagation (EBP), and Levenberg–Marquardt (LR), were utilized with seven input parameters for prediction. The performance of these networks was evaluated using Mean Absolute Percentage Error (MAPE) and R-squared (R2). The EBP network type demonstrated exceptional performance in estimating wind power for all wind turbines in Groups GI, GII, and GIII. Additionally, all proposed network types achieved impressive accuracy levels with MAPE ranging from 0.0119 to 0.0489 and R2 values ranging from 0.982 to 0.9989. These results highlight the high predictive accuracy attained at the study site. Consequently, we can conclude that the ANN model’s network types were highly effective in predicting the monthly averaged daily wind power at Adama Wind Farm I. By leveraging the power of ANN models, this research contributes to improving wind energy estimation, thereby enabling more reliable and efficient utilization of wind resources. The findings of this study have practical implications for the wind energy industry and can guide decision-making processes regarding wind power generation and integration into the energy mix.

Transistor modeling based on LM‐BPNN and CG‐BPNN for the GaAs pHEMT

AbstractIn order to address the challenges of complex process and low precision in traditional device modeling, double hidden layer back propagation neural network (BPNN) are trained using the conjugate gradient (CG) algorithm and the Levenberg–Marquardt (LM) algorithm, the CG‐BPNN and LM‐BPNN models of small signal for gallium arsenide (GaAs) pseudomorphic high electron mobility transistor (pHEMT) are obtained and analyzed here. At first, the scattering parameters (S‐parameters) of GaAs pHEMT are divided into training set and test set randomly. Experimental results show that the CG‐BPNN model is better than another S‐parameters when predicting ImS12 with mean square error (MSE) of 7.6632e‐06, while LM‐BPNN model predicts ImS12 with MSE of 2.4672e‐06. Meanwhile, the MSE of CG‐BPNN model is higher than LM‐BPNN model when predicting all the S‐parameters. In addition, it shows a smaller fluctuation range for the error curve of LM‐BPNN model, which is more stable than the CG‐BPNN model. Therefore, the double hidden layer LM‐BPNN model is the better choice to characterize the small signal of GaAs pHEMT.

Investigating Feed-Forward Back-Propagation Neural Network with Different Hyperparameters for Inverse Kinematics of a 2-DoF Robotic Manipulator: A Comparative Study

Inverse kinematics is a significant challenge in robotic manipulators, and finding practical solutions plays a crucial role in achieving precise control. This paper presents a study on solving inverse kinematics problems using the Feed-Forward Back-Propagation Neural Network (FFBP-NN) and examines its performance with different hyperparameters. By utilizing the FFBP-NN, our primary objective is to ascertain the joint angles required to attain precise Cartesian coordinates for the end-effector of the manipulator. To accomplish this, we first formed three input-output datasets (a fixed-step-size dataset, a random-step-size dataset, and a sinusoidal-signal-based dataset) of joint positions and their respective Cartesian coordinates using direct geometrical formulations of a two-degree-of-freedom (2-DoF) manipulator. Thereafter, we train the FFBP-NN with the generated datasets using the MATLAB Neural Network Toolbox and investigate its potential by altering the hyperparameters (e.g., number of hidden neurons, number of hidden layers, and training optimizer). Three different training optimizers are considered, namely the Levenberg-Marquardt (LM) algorithm, the Bayesian Regularization (BR) algorithm, and the Scaled Conjugate Gradient (SCG) algorithm. The Mean Squared Error is used as the main performance metric to evaluate the training accuracy of the FFBP-NN. The comparative outcomes offer valuable insights into the capabilities of various network architectures in addressing inverse kinematics challenges. Therefore, this study explores the application of the FFBP-NNs in tackling the inverse kinematics, and facilitating the choice of the most appropriate network design by achieving a portfolio of various experimental results by considering and varying different hyperparameters of the FFBP-NN.

Research on the Three-Level Integrated Environmental Evaluation Model for Multi-Greenhouse Potatoes

Aiming at the problems of large error and redundancy in the multi-node data acquisition of multi-greenhouse photo growth environmental information, a three-level fusion algorithm based on adaptive weighting, an LMBP network, and an improved D-S theory is proposed. The box-and-line graph method recognizes the original data and then replaces it based on the mean value method; the air temperature, humidity, and light intensity measurements are unbiased estimations of the true value to be estimated, so the first level of fusion chooses the adaptive weighted average algorithm to find the optimal weights of each sensor under the condition of minimizing the total mean-square error and obtains the optimal estimation of the weights of the homogeneous sensors of a greenhouse. The Levenberg–Marquardt algorithm was chosen for the second level of fusion to optimize the weight modification of the BP neural network, i.e., the LMBP network, and the three environmental factors corresponding to “suitable”, “uncertain” and “unsuitable” potato growth environments were trained for the three environmental factors in the reproductive periods. The output of the hidden layer was converted into probability by the Softmax function. The third level is based on the global fusion of evidence theory (also known as D-S theory), and the network output is used as evidence to obtain a consistent description of the multi-greenhouse potato cultivation environment and the overall scheduling of farming activities, which better solves the problem of the difficulty in obtaining basic probability assignments in the evidence theory; in the case of a conflict between the evidence, the BPA of the conflicting evidence is reallocated, i.e., the D-S theory is improved. Example validation shows that the total mean square error of the adaptive weighted fusion value is smaller than the variance of each sensor estimation, and sensors with lower variance are assigned lower weights, which makes the fusion result not have a large deviation due to the failure of individual sensors; when the fusion result of a greenhouse feature level is “unsuitable”, the fusion result of each data level is considered comprehensively, and the remote control agency makes a decision, which makes full use of the complementary nature of multi-sensor information resources and solves the problem of fusion of multi-source environmental information and the problem of combining conflicting environmental evaluation factors. Compared with the traditional D-S theory, the improved D-S theory reduces the probability of the “uncertainty” index in the fusion result again. The three-level fusion algorithm in this paper does not sacrifice data accuracy and greatly reduces the noise and redundancy of the original data, laying a foundation for big data analysis.

Nonlinear Curve Fitting to Measurement Points with WTLS Method Using Approximation of Linear Model

The paper presents an approximate method of fitting measurement points to parameterized arbitrary nonlinear curves described by complex equations, even implicit ones, the most commonly used method of least squares in general WTLS. An approximation of a linear model is used here, in which the laws of propagation of error and propagation of uncertainty are true, so that only the first derivative of the transforming function is relevant. The effectiveness of the method has been demonstrated in several numerical examples. The method was verified on several nonlinear functions using the iterative algorithm by Monte Carlo propagation of distribution and the classical method based on the Levenberg-Marquardt algorithm for nonlinear optimization.

Determination of residual stress field in laser cladding using finite element updating method driven by contour deformation

Laser cladding is a cutting-edge technology widely used in additive manufacturing and surface modification. This process entails rapid melting and solidification driven by laser heating, which induces residual stress within the material. This study presents a data-driven approach to refine the numerical model of laser cladding, simultaneously emphasizing both the temperature characteristics and residual stress distribution within the thermomechanical coupling process. After integrating the residual stress distribution data obtained through the contour method with the molten pool morphology shaped by the thermal effects of laser cladding, a Levenberg-Marquardt optimization algorithm based finite element model updating scheme is proposed to efficiently identify the parameters of double ellipsoid heat source model, which employs parallel computing to reduce the computational time for iterations. The effectiveness of the proposed method is validated using experimental data. Moreover, this approach is adaptable, unaffected by the specimen size and shape, and can accurately predict the residual stress distribution characteristics. Therefore, it offers a robust framework for simulating the mechanisms of residual stress generation in titanium alloy laser cladding.

A Numerical simulation method for analyzing 1H spin diffusion NMR for Multicomponent and multiphase polymer systems

A numerical simulation method, namely, SDNMR-WEBFIT, is reported for simulating proton spin diffusion NMR based on the Levenberg-Marquardt algorithm and a pseudo-2D diffusion model. This method is used for the precise quantification of dynamics heterogeneity of the interphase within multiphase polymer systems. The numerical simulation method provides measurements of spin-lattice relaxation time (T1), proton density (ρH), lamellar thickness (d), and spin diffusion coefficient (D) for each component. The pseudo-2D diffusion model is employed to simulate the proton spin diffusion build-up/decay curves, simultaneously calculating the lateral fraction of island-like structures (x-ratio). Such approach was successfully applied to various polymer systems, such as semi-crystalline polymer (Poly(ε-caprolactone), PCL), block copolymers (Styrene-butadiene-styrene triblock copolymer, SBS), and plasticized semi-polymers (Polvinyl alcohol, PVA).