Error Index Research Articles

Numerical and Dynamic Features for Heat Transfer Through a Longitudinal Rectangular Fin with Temperature-Dependent Thermal Conductivity

In the work reported herein, we adopt a Newton-Richtmeyer iterative scheme to arrive at solutions describing heat transfer in a longitudinal rectangular fin. Both the thermal conductivity and heat transfer coefficients are assumed to be temperature dependent and the governing partial differential equation highly nonlinear. In order to validate the numerical formulation, we consider some analytical results for this class of problems at steady state .Comparisons show convergence to exact solutions as demonstrated by local and global error indicators. In addition,various fin parameters which play a key role for efficient fin operation and design are investigated by carrying out a comprehensive dynamical qualitative study.

Residual Generative Adversarial Adaptation Network For The Classification Of Melanoma

The capability of recognizing skin cancer in its earliest stages has the potential to be a component that saves lives. It is of the utmost importance to devise an autonomous technique that can be relied upon for accurate melanoma detection using image analysis. In this paper, Generative adversarial network (GAN) with suitable preprocessing is used to classify the labels for the detection of melanoma skin types. The simulation is run to evaluate the effectiveness of the model about several performance measures, such as accuracy, precision, recall, f-measure, percentage error, Dice coefficient, and Jaccard index. These are all performance measures that are taken into consideration. These metrics for measuring achievement are as follows: The results of the simulations make it exceedingly clear that the proposed TE-SAAGAN is more effective than the existing GAN protocols when it comes to recognizing the test images.

Dependency of errors for four global reanalysis and satellite precipitation estimates on four crucial factors

Errors in the reanalysis and satellite precipitation products are closely related to four impacting factors, i.e., seasonality, topography, rainfall intensity, and climate type. Therefore, revealing the dependency of the errors of precipitation products on seasonality, topography, rainfall intensity, and climate type is important for data users and developers to improve the quality of precipitation products and enhance their applications in hydrometeorology. In this study, the links between errors and four impacting factors were used to investigate the dependency of errors in the ERA5 reanalysis and three satellite-only precipitation products (i.e., IMERG-Late, GSMaP-MVK, and PERSIANN-CCS) on the four impacting factors. Results from mainland China show that the errors of the four products depend on the four factors, whereas the dependency of different error indicators on the four factors differs significantly. In all seasons, ERA5 outperformed the three satellite-only precipitation products in most cases. In terms of topographic dependency, the probability of detection (POD) of ERA5 increases with topographic complexity but the opposite is true for the satellite-only precipitation products. Compared with purely infrared (IR) data, the fusion of passive microwave and IR data enhances the quality of precipitation estimates and reduces the topographical dependency of the errors. Regarding intensity-based performance, the performance of the four products in terms of the POD and normalized root-mean-squared error improves as the rain rate increases, whereas that of the three bias metrics (i.e., total bias, hit bias, and miss bias) deteriorates. In terms of the climatic dependency of the errors, the errors of the four products increase as the aridity increases in most cases. False bias contributes primarily to the total bias for the four products. More importantly, we found that the relationship between the false alarm ratio (FAR) and climate type cannot accurately characterize the dependency of false alarms based on climate type because of the interference of hit precipitation events. Based on this finding, the mean number of false alarms is recommended to replace the FAR to objectively investigate the false precipitation of various precipitation products.

A multi-variable multi-step Seq2seq networks for the state of charge estimation of lithium-ion battery

Due to the complexity and changeable of lithium-ion batteries, we propose a multi-variable and multi-step Temporal neural network to cover this task. Specially, a novel multi-step training strategy is applied to deal with long time sequences, and multi-variables is added to supervise the prediction. In addition, the Seq2seq net with long short term memory (LSTM) modules is employed to improve the prediction accuracy in various lithium-ion battery operating environments of −10 °C, 10 °C, 25 °C and 40 °C. The A123 lithium-ion batteries’ database collected by University of Maryland for the real scenarios has been used in the training process. The ablation studies indicate that the multi-step module is necessary under the root mean square error, mean absolute error and mean absolute percentage error index. The prediction error of comparison experiment under our proposed algorithms is 0.45 %@ root mean square error (RMSE), 0.30 %@ mean absolute error (MAE) and 1.11 %@ mean absolute percentage error (MAPE) at 10 °C. Our study introduces a novel and accurate SOC prediction method, which can provide accurate SOC estimates in a wide range of scenarios, emphasizing its novelty and relevance in addressing real-world challenges.

PM2.5 Concentration Prediction Based on LightGBM Optimized by Adaptive Multi-Strategy Enhanced Sparrow Search Algorithm

The atmospheric environment is of great importance to human health. However, its influencing factors are complex and variable. An efficient technique is required to more precisely estimate PM2.5 concentration values. In this paper, an enhanced Sparrow Search Algorithm (LASSA)-optimized Light Gradient Boosting Machine (LightGBM) is proposed for PM2.5 concentration prediction. This approach can provide accurate predictions while also reducing potential losses resulting from unexpected events. LightGBM is regarded as an outstanding machine learning approach; however, it includes hyperparameters that must be optimally mixed in order to achieve the desired results. We update the Sparrow Search Algorithm (SSA) and utilize it to identify the optimal combination of the most crucial parameters, using cross-validation to increase the reliability. Using limited air quality data and meteorological data as inputs, PM2.5 concentration values were predicted. The LASSA-LGB’s output was compared to normal LGB, SSA-LGB and ISSA-LGB. The findings demonstrate that LASSA-LGB outperforms the other models in terms of prediction accuracy. The RMSE and MAPE error indices were lowered from 3% to 16%. The concordance correlation coefficient is not less than 0.91, and the R2 reached 0.96. This indicates that the proposed model has potential advantages in the field of PM2.5 concentration prediction.

Impact of using sinogram domain data in the super-resolution of CT images on diagnostic information.

In recent times, deep-learning-based super-resolution (DL-SR) techniques for computed tomography (CT) images have shown outstanding results in terms of full-reference image quality (FR-IQ) metrics (e.g., root mean square error and structural similarity index metric), which assesses IQ by measuring its similarity to the high-resolution (HR) image. In addition, IQ can be evaluated via task-based IQ (Task-IQ) metrics that evaluate the ability to perform specific tasks. Ironically, most proposed image domain-based SR techniques are not possible to improve a Task-IQ metric, which assesses the amount of information related todiagnosis. In the case of CT imaging systems, sinogram domain data can be utilized for SR techniques. Therefore, this study aims to investigate the impact of utilizing sinogram domain data on diagnostic information restorationability. We evaluated three DL-SR techniques: using image domain data (Image-SR), using sinogram domain data (Sinogram-SR), and using sinogram as well as image domain data (Dual-SR). For Task-IQ evaluation, the Rayleigh discrimination task was used to evaluate diagnostic ability by focusing on the resolving power aspect, and an ideal observer (IO) can be used to perform the task. In this study, we used a convolutional neural network (CNN)-based IO that approximates the IO performance. We compared the IO performances of the SR techniques according to the data domain to evaluate the discriminative information restorationability. Overall, the low-resolution (LR) and SR exhibit lower IO performances compared with that of HR owing to their degraded discriminative information when detector binning is used. Next, between the SR techniques, Image-SR does not show superior IO performances compared to the LR image, but Sinogram-SR and Dual-SR show superior IO performances than the LR image. Furthermore, in Sinogram-SR, we confirm that FR-IQ and IO performance are positively correlated. These observations demonstrate that sinogram domain upsampling improves the representation ability for discriminative information in the image domain compared to the LR andImage-SR. Unlike Image-SR, Sinogram-SR can improve the amount of discriminative information present in the image domain. This demonstrates that to improve the amount of discriminative information on the resolving power aspect, it is necessary to employ sinogram domainprocessing.

Performance of equations for the longitudinal dispersion coefficient: a case study in the Orashi River

Abstract Investigation of the water quality of rivers is a key point in Water Resources Engineering. The longitudinal dispersion coefficient is one of the foremost significant parameters in river water quality monitoring. Several parameters such as hydraulic, morphology, total dissolved solids, and total suspended solids are effective parameters in the determination of the longitudinal dispersion coefficient as revealed by this study. The assessment of the river shows mean hydraulic and geometric properties such as flow, depth, velocity, longitudinal slope, and width to be 354.17 m3/s, 9.61 m, 0.69 m/s, 0.0079,101.63 m and the range of the longitudinal dispersion coefficient as (72–104.4) m2/s. Results obtained by employing the established equations revealed standard error indices and RMSE of the developed equation, and Kashefipour and Falconer equation gives correlation coefficient of about 0.819 and 4.182 and 0.421 and 12.186, respectively, as coefficient of determination and RMSE, and they are more accurate among the empirical equations. However, the newly derived equation for the longitudinal dispersion coefficient performed better when compared with others, indicating the fitness of the developed equation to estimate longitudinal dispersion coefficient.

Intelligent prediction model of mechanical properties of ultrathin niobium strips based on XGBoost ensemble learning algorithm

Ultrathin niobium strips with different thicknesses are prepared by an accumulative rolling process. The tensile test of the ultrathin niobium strips is carried out, and the microstructure of each niobium strip is characterized by electron backscattered diffraction (EBSD). The process parameters, mechanical properties and microstructure characterization data of rolled ultrathin niobium strips with different thicknesses are collected, analyzed and sorted. A data-driven intelligent prediction model for the mechanical properties of ultrathin niobium strips is established by deeply integrating the mechanical properties of ultrathin niobium strips with the microstructure evolution mechanism and combining the integrated data with the XGBoost ensemble learning algorithm. The optimal parameters of the XGBoost model are determined by a grid search and used for mechanical performance prediction. The overall generalization performance of the model is evaluated by the coefficient of determination (R2), mean absolute error (MAE), root mean square error (RMSE) and mean absolute percentage error (MAPE). To reflect the advancement of the proposed model, the prediction results of this model are compared with those of the random forest (RF), multi-layer perceptron (MLP) and gradient boosting decision tree (GBDT) prediction model. The research results show that, on the test set, the R2 in terms of the tensile strength and yield strength predicted values based on the XGBoost algorithm were higher than those of other models, reaching 0.944 and 0.964, respectively. The three error indicators corresponding to the XGBoost model were also at the lowest level. This means that the model based on the XGBoost algorithm has the optimal generalization performance and can thus realize the accurate prediction of the mechanical properties of ultrathin niobium strips. This research provides a new method and idea for the optimal design of rolling process and the prediction of their mechanical properties.

A Novel Order Abatement Technique for Linear Dynamic Systems and Design of PID Controller

This article proposes a novel hybrid technique of order abatement for large-scale models that combines the Mihailov stability method (MSM) and the stability equation method (SEM). In this approach, the denominator coefficients of the higher-order system (HOS) are estimated using the MSM, while the numerator coefficients are computed using the SEM. The suggested approach is based on the MSM, which guarantees the stability of the estimated model if the actual model is stable. The MSM also makes sure that important factors of the original plant, such as dominant poles and stability, are retained in the reduced order system (ROS). The suggested approach is compared to several current conventional reduction methods using error indicators, and the smallest performance error indices values reflect the supremacy of the method. The transfer function (TF) of the ROS is then used to design controllers by employing the moment matching technique. When the controller designed with the approximated model is applied to the real HOS, it indicates that the response of the closed-loop system of the real model entirely overlaps with the response of the reference plant. To further demonstrate the efficiency of the proposed schemes, time-domain specifications are produced and time responses are plotted.

Performance Benchmarking of Different Methods to Solve Gauss-Newton Trust Region Subproblems

Summary The Gauss-Newton (GN) trust region optimization methods perform robustly but may introduce significant overhead cost when using the conventional matrix factorization method to solve the associated GN trust region subproblem (GNTRS). Solving a GNTRS involves solving a nonlinear equation using an iterative Newton-Raphson (NR) method. In each NR iteration, a symmetric linear system can be solved by different matrix factorization methods, including Cholesky decomposition (CD), eigenvalue decomposition (EVD), and singular value decomposition (SVD). Because CD fails to factorize a singular symmetric matrix, we propose solving a GNTRS using the robust EVD method. In this paper, we analyze the performances of different methods to solve a GNTRS using different matrix factorization subroutines in LAPACK with different options and settings. The cost of solving a GNTRS mainly depends on the number of observed data (m) and the number of uncertainty parameters (n). When n≤m, we recommend directly solving the original GNTRS with n variables. When n>m, we propose an indirect method that transforms the original GNTRS with n variables to a new problem with m unknowns. The proposed indirect method can significantly reduce the computational cost by dimension reduction. However, dimension reduction may introduce numerical errors, which, in turn, may result in accuracy degradation and cause failure of convergence using the popular iterative NR method. To further improve the overall performance, we introduce a numerical error indicator to terminate the iterative NR process when numerical errors become dominant. Finally, we benchmarked the performances of different approaches on a set of testing problems with different settings. Our results confirm that the GNTRS solver using the EVD method together with the modified NR method performs the best, being both robust (no failure for all testing problems) and efficient (consuming comparable CPU time to other methods).

An approach for optimal tolerance allocation of five-axis machine tools by simultaneously considering volumetric error and processing simplicity index

Optimal tolerance allocation (OTA) is one of the most effective ways to improve the machining precision of machine tools. However, the existing OTA methods have the problem that tolerance-cost models are particularly vulnerable to subjective factors, which lead to tolerance allocation scheme with poor applicability and reliability. For this reason, a novel OTA method that simultaneously considers volumetric error and processing simplicity index (PSI) is proposed in this paper. Based on the multi-body system theory and homogeneous transform matrix, the volumetric error prediction model based on tolerance of machine tools’ key parts is firstly established by taking the geometric error as a bridge between tolerance and volumetric error of machine tools. Then, the weight coefficient of each tolerance parameter is calculated based on sensitivity analysis method. Moreover, PSI, which denotes the degree of processing simplicity to reach the required tolerance value, is innovatively proposed to replace manufacturing cost. And the tolerance-PSI model is established to replace tolerance-cost model. Then, an OTA model is established by minimizing volumetric error and maximizing PSI. The NSGA-II is employed to obtain OTA scheme. Finally, simulations and experiments are conducted to validate the feasibility and effectiveness of the presented method.

Estimating CO2 solubility in ionic liquids by using machine learning methods

Ionic liquids (ILs) can be used to absorb a greater quantity of carbon dioxide (CO2) by adjusting the ratio of anions and cations.The methods to obtain CO2 solubility in ILs are as follows: Experiment, Equation of State (EOS) and Molecular dynamics simulation (MD). The experiment is time-consuming and labor-intensive, EOS requires critical parameters, and MD calculation is complicated. However, Machine Learning (ML) methods are embraced with high prediction accuracy and convenience by the chemical and petroleum industry. In this work, 1517 solubility data were collected based on 20 different ILs. Three different machine learning methods (Optimization (PSO), Grey Wolf Optimization (GWO) and Sparrow Search Algorithm (SSA) based on Support Vector Machine (SVR)), using acentric factor (ω), critical temperature (Tc), critical pressure (pc) of ILs accompanied by pressure (p), and temperature (T), as input parameters, were employed to predict CO2 solubility in ILs. Meanwhile, three error indexes (namely root mean square error (RMSE), correlation coefficient (R2) and average absolute relative deviation (AARD)), and the duration of time each specified model (PSO-SVR, GWO-SVR and SSA-SVR) takes in order to evaluate the effectiveness of each prediction model.Although the results show that the three different optimization models (PSO-SVR, GWO-SVR and SSA-SVR) have viable prediction effects, the performance of PSO-SVR model has high accuracy and is the lowest time-consuming among them with RMSE and R2 of 0.01881 and 0.9824, respectively. For the SSA-SVR, the estimated RMSE and R2 are respectively 0.01944 and 0.9824 while they are 0.01889 and 0.9822 for the GWO-SVR, respectively. The results imply that all of the models can give reliable predictions on the CO2 solubilities in ILs and the PSO-SVR model performs slightly better than the SSA-SVR and GWO-SVR models.

Machine learning prediction of tree species diversity using forest structure and environmental factors: a case study from the Hyrcanian forest, Iran.

The Hyrcanian forest is a global biodiversity hotspot that harbors many endemic and endangered tree species, but its tree diversity is threatened by various human-induced disturbances, such as logging, grazing, and urbanization. To address this issue, we conducted a study using three machine learning methods, i.e., linear regression (LR), random forest (RF), and support vector machine (SVM), to assess and predict tree species diversity within the forest. To do so, we collected an extensive dataset of forest structure and environmental factors from 2725 sample plots located throughout the forest. The Shannon-Wiener diversity index was used to quantify the tree species diversity for each plot. We found that basal area, tree density, and height of trees were the most important predictors of tree diversity, followed by diameter at breast height, elevation, slope, and aspect. We measured the performance of the models using the coefficient of determination (R2), root mean square error (RMSE), and percent of relative error index (PREI), and found RF as the best-performing model in both the training (RMSE = 0.143, R2 = 0.94, and PREI = - 0.09) and validation (RMSE = 0.15, R2 = 0.94, and PREI = - 0.09) phases. RF was able to generalize effectively to new data without losing much accuracy or explanatory power. SVM demonstrated a moderate performance training (training phase: RMSE = 0.23, R2 = 0.57, and PREI = - 0.17) and (validation phase: RMSE = 0.36, R2 = 0.34, and PREI = - 0.21) among the models, while LR performed the worst (training phase: RMSE = 0.41, R2 = 0.13, and PREI = - 0.19) and (validation phase: RMSE = 0.41, R2 = 0.11, and PREI = - 0.36). These findings have broad applications beyond this specific region and can contribute to promoting sustainable land use practices and conservation efforts in other ecosystems facing similar challenges.

Quality control prediction of electrolytic copper using novel hybrid nonlinear analysis algorithm

Traditional linear regression and neural network models demonstrate suboptimal fit and lower predictive accuracy while the quality of electrolytic copper is estimated. A more dependable and accurate model is essential for these challenges. Notably, the maximum information coefficient was employed initially to discern the non-linear correlation between the nineteen factors influencing electrolytic copper quality and the five quality control indicators. Additionally, the random forest algorithm elucidated the primary factors governing electrolytic copper quality. A hybrid model, integrating particle swarm optimization with least square support vector machine, was devised to predict electrolytic copper quality based on the nineteen factors. Concurrently, a hybrid model combining random forest and relevance vector machine was developed, focusing on primary control factors. The outcomes indicate that the random forest algorithm identified five principal factors governing electrolytic copper quality, corroborated by the non-linear correlation analysis via the maximum information coefficient. The predictive accuracy of the relevance vector machine model, when accounting for all nineteen factors, was comparable to the particle swarm optimization—least square support vector machine model, and surpassed both the conventional linear regression and neural network models. The predictive error for the random forest-relevance vector machine hybrid model was notably less than the sole relevance vector machine model, with the error index being under 5%. The intricate non-linear variation pattern of electrolytic copper quality, influenced by numerous factors, was unveiled. The advanced random forest-relevance vector machine hybrid model circumvents the deficiencies seen in conventional models. The findings furnish valuable insights for electrolytic copper quality management.

Prediction of rural tourism suitability based on multi-dimensional evaluation model

There is an increased focus on how to improve tourism quality in rural areas. To provide reference and guidance for both tourists and tourism departments, a multi-dimensional tourism suitability model is proposed. Meteorological, travel and other data related to a tourism area were analysed, and a tourism suitability evaluation architecture model was developed. From February to September, when temperature fluctuations were more clearly defined, the prediction accuracy of the model was higher, while the test results of the root mean square error and other indicators of the model in meteorological prediction were good. The model had the highest prediction accuracy of 96.8% under multi-dimensional conditions. The model could provide accurate guidance for tourists to choose travel dates and destinations, further promoting rural tourism.

Visual stimuli in the peripersonal space facilitate the spatial prediction of tactile events-A comparison between approach and nearness effects.

Previous studies reported that an object in one's peripersonal space (PPS) attracts attention and facilitates subsequent processing of stimuli. Recent studies showed that visual stimuli approaching the body facilitated the spatial prediction of subsequent tactile events, even if these stimuli were task-irrelevant. However, it is unclear whether the approach is important for facilitating this prediction or if the simple existence of stimuli within the PPS is what matters. The present study aimed to scrutinize the predictive function of visuo-tactile interaction in the PPS by examining the effects of visual stimuli approaching the hand and of visual stimuli near the hand. For this purpose, we examined electroencephalograms (EEGs) during a simple reaction time task for tactile stimuli when visual stimuli were presented approaching the hand or were presented near the hand, and we analyzed event-related spectral perturbation (ERSP) as an index of prediction and event-related brain potentials (ERPs) as an index of attention and prediction error. The tactile stimulus was presented to the left (or right) wrist with a high probability (80%) and to the opposite wrist with a low probability (20%). In the approach condition, three visual stimuli were presented approaching the hand to which the high-probability tactile stimulus was presented; in the near condition, three visual stimuli were presented repeatedly near the hand with the high-probability tactile stimulus. Beta-band activity at the C3 and C4 electrodes, around the primary somatosensory area, was suppressed before the onset of the tactile stimulus, and this suppression was larger in the approach condition than in the near condition. The P3 amplitude for high-probability stimuli in the approach condition was larger than that in the near condition. These results revealed that the approach of visual stimuli facilitates spatial prediction and processing of subsequent tactile stimuli compared to situations in which visual stimuli just exist within the PPS. This study indicated that approaching visual stimuli facilitates the prediction of subsequent tactile events, even if they are task-irrelevant.

Sequential Geometric Programming Method for Parameter Estimation of a Nonlinear System in Microbial Continuous Fermentation

This paper addresses the problem of parameter estimation for the microbial continuous fermentation of glycerol to 1,3-propanediol. A nonlinear dynamical system is first presented to describe the microbial continuous fermentation. Some mathematical properties of the dynamical system in the microbial continuous fermentation are also presented. A parameter estimation model is proposed to estimate the parameters of the dynamical system. The proposed estimation model is a large-scale, nonlinear, and nonconvex optimization problem if the number of experimental groups is large. A sequential geometric programming (SGP) method is proposed to efficiently solve the parameter estimation problem. The results indicated that our proposed SGP method can yield smaller errors between the experimental and calculated steady-state concentrations than the existing seven methods. For the five error indices considered, that is, the concentration errors of biomass, glycerol, 1,3-propanediol, acetic acid, and ethanol, the results obtained using the proposed SGP method are better than those obtained using the methods in the literature (Xiu et al., Gao et al., Sun et al., Sun et al., Li and Qu, Wang et al., and Zhang and Xu), with improvements of approximately 71.86–95.03%, 52.08–94.87%, 99.70–99.98%, 5.39–90.29%, and 12.67–80.83%, respectively. This concludes that the established dynamical system can better describe the microbial continuous fermentation. We also present that our established dynamical system has multiple positive steady states in some fermentation conditions. We observe that there are two regions of multiple positive steady states at relatively high values of substrate glycerol concentration in feed medium.

Replacement of the part of gravity model and of remaining dynamic models by empirical accelerations in the fit processes of a low-Earth satellite orbit and factors limiting their accuracy

This work contains the results of calculations performed to prove the ability of estimated orbital parameters for the replacement of dynamic models in the orbit determination of a sample low-Earth-orbiting satellite. The obtained solutions include two cases of the absorption of dynamic models. In the first case, the contribution of dynamic models, apart from the gravity field, was absorbed, i.e., the satellite motion was described by the gravity field and estimated parameters. In the second case, the contributions of all dynamic models, including the gravity field, were absorbed. For the gravity field model, the absorption concerned its selected parts. In this case, the satellite motion was modeled only by the gravity model truncated to different degrees and orders and an appropriate set of orbital parameters. In both aforementioned cases, the initial conditions were also improved. Cartesian coordinates of the Gravity Field and Steady-State Ocean Circulation Explorer Mission satellite along selected reference arcs of the official reduced-dynamic orbit served as pseudo-observations in this study. The orbital parameters, also known as empirical accelerations, were determined using the least-squares method by a dedicated orbital package. The results were presented and compared in the form of the root-mean-square (RMS) values of the differences between the estimated orbits and the reference orbits, as well as the corresponding values of the obtained empirical accelerations for selected variants of solutions. The obtained accuracy of the process of the fit of the satellite orbit expressed by the corresponding RMS values, reached a millimeter level. For selected typical solutions, the distribution of residuals and power spectra are presented with an indication of characteristic errors: random and systematic periodic components. Key factors influencing the obtained fit accuracies of estimated orbits are given. Contributions of these factors in the error budget of fits of estimated orbits are also presented. Additionally, in the fit process, the performance of selected gravity models coming from different years is compared to assess the impact of gravity field errors on the results of aforementioned process.

Adaptive neuro-fuzzy inference system model driven by the non-negative matrix factorization-extracted muscle synergy patterns to estimate lower limb joint movements

Background and objectiveFor patients with movement disorders, the main clinical focus is on exercise rehabilitation to help recover lost motor function, which is achieved by relevant assisted equipment. The basis for seamless control of the assisted equipment is to achieve accurate inference of the user's movement intentions in the human-machine interface. This study proposed a novel movement intention detection technology for estimating lower limb joint continuous kinematic variables following muscle synergy patterns, to develop applications for more efficient assisted rehabilitation training. MethodsThis study recruited 16 healthy males and 16 male patients with symptomatic patellar tendinopathy (VISA-P: 59.1 ± 8.7). The surface electromyography of 12 muscles and lower limb joint kinematic and kinetic data from healthy subjects and patients during step-off landings from 30 cm-high stair steps were collected. We subsequently solved the preprocessed data based on the established recursive model of second-order differential equation to obtain the muscle activation matrix, and then imported it into the non-negative matrix factorization model to obtain the muscle synergy matrix. Finally, the lower limb neuromuscular synergy pattern was then imported into the developed adaptive neuro-fuzzy inference system non-linear regression model to estimate the human movement intention during this movement pattern. ResultsSix muscle synergies were determined to construct the muscle synergy pattern driven ANFIS model. Three fuzzy rules were determined in most estimation cases. Combining the results of the four error indicators across the estimated variables indicates that the current model has excellent estimated performance in estimating lower limb joint movement. The estimation errors between the healthy (Angle: R2=0.98±0.03; Torque: R2=0.96±0.04) and patient (Angle: R2=0.98±0.02; Torque: R2=0.96±0.03) groups are consistent. ConclusionThe proposed model of this study can accurately and reliably estimate lower limb joint movements, and the effectiveness will also be radiated to the patient group. This revealed that our models also have certain advantages in the recognition of motor intentions in patients with relevant movement disorders. Future work from this study can be focused on sports rehabilitation in the clinical field by achieving more flexible and precise movement control of the lower limb assisted equipment to help the rehabilitation of patients.

Design and performance of a space–time virtual element method for the heat equation on prismatic meshes

We present a space–time virtual element method for the discretization of the heat equation, which is defined on general prismatic meshes and variable degrees of accuracy. Strategies to handle efficiently the space–time mesh structure are discussed. We perform convergence tests for the h- and hp-versions of the method in case of smooth and singular solutions, and test space–time adaptive mesh refinements driven by a residual-type error indicator.