Average Root Mean Square Research Articles

Bathymetry reconstruction from experimental data using PDE-constrained optimisation

Knowledge of the bottom topography, also called bathymetry, of rivers, seas or the ocean is important for many areas of maritime science and civil engineering. While direct measurements are possible, they are time consuming, expensive and inaccurate. Therefore, many approaches have been proposed how to infer the bathymetry from measurements of surface waves. Mathematically, this is an inverse problem where an unknown system state needs to be reconstructed from observations with a suitable model for the flow as constraint. In many cases, the shallow water equations can be used to describe the flow. While theoretical studies of the efficacy of such a PDE-constrained optimisation approach for bathymetry reconstruction exist, there seem to be few publications that study its application to data obtained from real-world measurements. This paper shows that the approach can, at least qualitatively, reconstruct a Gaussian-shaped bathymetry in a wave flume from measurements of the free surface level at up to three points. Achieved normalised root mean square errors (NRMSE) are in line with other approaches.

Assessment of the accuracy of 3D printed medical models through reverse engineering

The dimensional accuracy of additively manufactured (3D printed) medical models can be affected by various parameters. Although different methods are used to evaluate the accuracy of additively manufactured models, this study focused on the investigation of the dimensional accuracy of the medical model based the combination of reverse engineering (RE) and additive manufacturing (AM) technologies. Human femur bone was constructed from CT images and manufactured, using Fortus 450mc Industrial material extrusion 3D Printer. The additive manufactured femur bone was subsequently 3D scanned using three distinct non-contact 3D scanners. MeshLab was used for mesh analysis, while VX Elements was used for post-processing of the point cloud. A combination of the VX Inspect environment and MeshLab was used to evaluate the scanning performance. The deviation of the 3D scanned 3D models from the reference mesh was determined using relative metrics and absolute measurements. The scanners reported deviations ranging from −0.375 mm to 0.388 mm, resulting in a total range of approximately 0.763 mm with average root mean square (RMS) deviation of 0.22 mm. The results indicate that the additively manufactured model, as measured by 3D scanning, has a mean deviation with an average range of approximately 0.46 mm and an average mean value of around 0.16 mm.

Deep learning-based inversion framework by assimilating hydrogeological and geophysical data for an enhanced geothermal system characterization and thermal performance prediction

Enhanced geothermal systems (EGS), which are developed by creating artificial fractures to enhance the permeability of deep reservoir, show their its advantage in power generation. However, due to the limited wells in deep depth, characterizing fractured geothermal reservoirs with sparse data is difficult and poses challenges for long-term thermal performance prediction. Interpreting observation data through inversion to characterize the fracture aperture and predict EGS long-term thermal performance is a hopeful scheme. Thus, a joint inversion framework, convolutional variational autoencoder-ensemble smoother with multiple data assimilation (CVAE-ESMDA), is proposed with the following aspects: (i) CVAE is trained to parameterize the high-dimensional Non-Gaussian aperture field, (ii) ESMDA is applied to integrate hydrogeological and geophysical data for aperture characterization. Based on the inversion results, the long-term performance is predicted. The normalized root mean square errors (NRMSEs) of inversion results decrease from 27.66 % to 24.52 % after multi-type data are integrated for CVAE-ESMDA. Furthermore, the NRMSEs of long-term thermal prediction of two production wells also decrease to only 2.3 % and 8.2 %. To further exhibit the advantages of CVAE-ESMDA, another joint inversion framework, principal component analysis (PCA)-ESMDA, is also compared. However, PCA is limited in addressing Non-Gaussian aperture field and its long-term thermal prediction performance is unsatisfactory.

An Artificial Intelligence Approach for Estimating the Turbidity of Artisanal Wine and Dosage of Clarifying Agents

Red wine is a beverage consumed worldwide and contains suspended solids that cause turbidity. The study’s purpose was to mathematically model estimated turbidity in artisanal wines concerning the dosage and types of fining agents based on previous studies presenting positive results. Burgundy grape wine (Vitis lambrusca) was made and clarified with ‘yausabara’ (Pavonia sepium) and bentonite at different concentrations. The system was modelled using several machine learning models, including MATLAB’s Neural Net Fitting and Regression Learner applications. The results showed that the validation of the neural network trained with the Levenberg–Marquardt algorithm obtained significant statistical indicators, such as the coefficient of determination (R2) of 0.985, mean square error (MSE) of 0.004, normalized root mean square error (NRSME) of 6.01 and Akaike information criterion (AIC) of −160.12, selecting it as the representative model of the system. It presents an objective and simple alternative for measuring wine turbidity that is useful for artisanal winemakers who can improve quality and consistency.

Measurement and correlation of solubility data for sodium picosulphate in selected pure solvents and mixed-solvent systems from 298.15 K to 328.15 K

An investigation was carried out to determine the solubility of the stimulant laxative drug Sodium Picosulphate (SP). A wide range of pure solvents were studied, including methanol, ethanol, 1-propanol, 1-butanol, dimethyl formamide, dimethyl sulfoxide, acetonitrile, 1,4-dioxane, acetic acid, and water. More to the point, the solubility of the compound was determined using mixed solvent systems; methanol + acetonitrile and water + acetonitrile. Experimental mole fraction solubility of SP was determined by the gravimetric method over a range of temperatures (298.15 K to 328.15 K) under atmospheric pressure (p=0.1MPa). According to experimental results, a temperature-dependent relationship exists between solubility and temperature. Further, we correlated the experimental mole fraction solubility data with theoretical models including Apelblat, Yaws, Van't Hoff, Modified Jouyban-Acree, CNIBS/R-K models. It appears that the results are well in agreement with the experimental results due to the small values of relative average deviation (RAD) and root mean square deviation (RMSD).The solubility data might be useful in the various areas such as modification, production, crystallization, and separation of SP.

Transportation Simulation Modeling and Location-Based Services Data Completion Based on a Data and Model Dual-Driven Approach

The evolving economic and technological landscape has brought about significant changes in travel behaviors and traffic patterns. These changes have led to the emergence of complex, multi-modal travel demands that interact with transportation networks, posing new challenges in transportation analysis and control. The primary objective of this study is to address these challenges by improving transportation modeling and data completeness using advanced modeling tools and transportation big data. We propose a dual-driven simulation model that integrates transportation simulation and big data. The approach begins by utilizing initial Location-Based Services (LBS) data to establish a mesoscopic multi-modal simulation model, which is then calibrated. This calibrated model is then employed to complete the missing trajectories of the LBS data. The innovative aspect of this dual-driven simulation model lies in its novel approach to constructing transportation models and completing LBS data, thereby enhancing both the simulation accuracy and the results of missing path completion. We conduct tests using the urban area of Hangzhou as an example, and the results show that the Normalized Root Mean Square Error (NRMSE) between the average link speeds in the simulation model and in real world observation is reduced to 24.1%. In the LBS data completion process, our proposed method achieves a travel mode identification accuracy of 95.3% for private car travel. Compared to the two baseline methods, the average accuracy of completed trajectories increases by 6.31% and 2.46%, respectively.

Integrating gated recurrent unit in graph neural network to improve infectious disease prediction: an attempt.

This study focuses on enhancing the precision of epidemic time series data prediction by integrating Gated Recurrent Unit (GRU) into a Graph Neural Network (GNN), forming the GRGNN. The accuracy of the GNN (Graph Neural Network) network with introduced GRU (Gated Recurrent Units) is validated by comparing it with seven commonly used prediction methods. The GRGNN methodology involves multivariate time series prediction using a GNN (Graph Neural Network) network improved by the integration of GRU (Gated Recurrent Units). Additionally, Graphical Fourier Transform (GFT) and Discrete Fourier Transform (DFT) are introduced. GFT captures inter-sequence correlations in the spectral domain, while DFT transforms data from the time domain to the frequency domain, revealing temporal node correlations. Following GFT and DFT, outbreak data are predicted through one-dimensional convolution and gated linear regression in the frequency domain, graph convolution in the spectral domain, and GRU (Gated Recurrent Units) in the time domain. The inverse transformation of GFT and DFT is employed, and final predictions are obtained after passing through a fully connected layer. Evaluation is conducted on three datasets: the COVID-19 datasets of 38 African countries and 42 European countries from worldometers, and the chickenpox dataset of 20 Hungarian regions from Kaggle. Metrics include Average Root Mean Square Error (ARMSE) and Average Mean Absolute Error (AMAE). For African COVID-19 dataset and Hungarian Chickenpox dataset, GRGNN consistently outperforms other methods in ARMSE and AMAE across various prediction step lengths. Optimal results are achieved even at extended prediction steps, highlighting the model's robustness. GRGNN proves effective in predicting epidemic time series data with high accuracy, demonstrating its potential in epidemic surveillance and early warning applications. However, further discussions and studies are warranted to refine its application and judgment methods, emphasizing the ongoing need for exploration and research in this domain.

Experimental validation of a PNS-optimized whole-body gradient coil.

Peripheral nerve stimulation (PNS) limits the usability of state-of-the-art whole-body and head-only MRI gradient coils. We used detailed electromagnetic and neurodynamic modeling to set an explicit PNS constraint during the design of a whole-body gradient coil and constructed it to compare the predicted and experimentally measured PNS thresholds to those of a matched design without PNS constraints. We designed, constructed, and tested two actively shielded whole-body Y-axis gradient coil winding patterns: YG1 is a conventional symmetric design without PNS-optimization, whereas YG2's design used an additional constraint on the allowable PNS threshold in the head-imaging landmark, yielding an asymmetric winding pattern. We measured PNS thresholds in 18 healthy subjects at five landmark positions (head, cardiac, abdominal, pelvic, and knee). The PNS-optimized design YG2 achieved 46% higher average experimental thresholds for a head-imaging landmark than YG1 while incurring a 15% inductance penalty. For cardiac, pelvic, and knee imaging landmarks, the PNS thresholds increased between +22% and +35%. For abdominal imaging, PNS thresholds did not change significantly between YG1 and YG2 (-3.6%). The agreement between predicted and experimental PNS thresholds was within 11.4% normalized root mean square error for both coils and all landmarks. The PNS model also produced plausible predictions of the stimulation sites when compared to the sites of perception reported by the subjects. The PNS-optimization improved the PNS thresholds for the target scan landmark as well as most other studied landmarks, potentially yielding a significant improvement in image encoding performance that can be safely used in humans.

Optimizing recombinant antibody fragment production: A comparison of artificial intelligence and statistical modeling.

Maximizing the recombinant protein yield necessitates optimizing the production medium. This can be done using a variety of methods, including the conventional "one-factor-at-a-time" approach and more recent statistical and mathematical methods such as artificial neural network (ANN), genetic algorithm, etc. Every approach has advantages and disadvantages of its own, yet even when a technique has flaws, it is nevertheless used to get the best results. Here, one categorical variable and four numerical parameters, including post-induction time, inducer concentration, post-induction temperature, and pre-induction cell density, were optimized using the 232 experimental assays of the central composite design. The direct and indirect effects of factors on the yield of anti-epithelial cell adhesion molecule extracellular domain fragment antibody were examined using statistical methods. The analysis of variance results indicate that the response surface methodology (RSM) model is effective in predicting the amount of produced single-chain fragment variable (p-value = 0.0001 and R2 = 0.905). For ANN modeling, the evaluation using normalized root mean square error (NRMSE) and R2 values shows a good fit (R2 = 0.942) and accurate predictions (NRMSE = 0.145). The analysis of error parameters and R2 of a dataset, which contained 30 data points randomly selected from the complete dataset, showed that the ANN model had a higher R2 value (0.968) compared to the RSM model (0.932). Furthermore, the ANN model demonstrated stronger predictive ability with a lower NRMSE (0.048vs. 0.064). Induction at the cell density of 0.7 and an isopropyl β-D-1-thiogalactopyranoside concentration of 0.6mM for 32 h at 30°C in BW25113 was the ideal culture condition leading to the protein yield of 259.51mg/L. Under the optimum conditions, the output values predicted by the ANN model (259.83mg/L) were more in line with the experimental data (259.51mg/L) than the RSM (276.13mg/L) expected value. This outcome demonstrated that the ANN model outperforms the RSM in terms of prediction accuracy.

LEO-Enhanced GNSS/INS Tightly Coupled Integration Based on Factor Graph Optimization in the Urban Environment

Precision point positioning (PPP) utilizing the Global Navigation Satellite System (GNSS) is a traditional and widely employed technology. Its performance is susceptible to observation discontinuities and unfavorable geometric configurations. Consequently, the integration of the Inertial Navigation System (INS) and GNSS makes full use of their respective advantages and effectively mitigates the limitations of GNSS positioning. However, the GNSS/INS integration faces significant challenges in complex and harsh urban environments. In recent years, the geometry between the user and the satellite has been effectively improved with the advent of lower-orbits and faster-speed Low Earth Orbit (LEO) satellites. This enhancement provides more observation data, opening up new possibilities and opportunities for high-precision positioning. Meanwhile, in contrast to the traditional extended Kalman filter (EKF) approach, the performance of the LEO-enhanced GNSS/INS tightly coupled integration (TCI) can be significantly improved by employing the factor graph optimization (FGO) method with multiple iterations to achieve stable estimation. In this study, LEO data and the FGO method were employed to enhance the GNSS/INS TCI. To validate the effectiveness of the method, vehicle data and simulated LEO observations were subjected to thorough analysis. The results suggest that the integration of LEO data significantly enhances the positioning accuracy and convergence speed of the GNSS/INS TCI. In contrast to the FGO GNSS/INS TCI without LEO enhancement, the average enhancement effect of the LEO is 22.16%, 7.58%, and 10.13% in the north, east, and vertical directions, respectively. Furthermore, the average root mean square error (RMSE) of the LEO-enhanced FGO GNSS/INS TCI is 0.63 m, 1.21 m, and 0.85 m in the north, east, and vertical directions, respectively, representing an average improvement of 41.91%, 13.66%, and 2.52% over the traditional EKF method. Meanwhile, the simulation results demonstrate that LEO data and the FGO method effectively enhance the positioning and convergence performance of GNSS/INS TCI in GNSS-challenged environments (tall buildings, viaducts, underground tunnels, and wooded areas).

Seismo-ionospheric precursory detection using hybrid Bayesian-LSTM network model with uncertainty-boundaries and anomaly-intensity

Several efforts have been made to understand the complex physical processes involved in a seismic process, but the findings are vague considering prediction capabilities. Nevertheless, recent seismo-ionosphere precursory research has enlightened new pathways toward building an earthquake (EQ) forecasting system. Previously, some conventional mathematical/statistical approaches have been proposed for detecting an anomalous value as a potential precursor. We propose a hybrid Bayesian-based Long Short-Term Memory (B-LSTM) Network model to forecast the Total Electron Content (TEC) data. We applied B-LSTM on different Vertical TEC (VTEC) datasets of two EQs (Mw7.7 Awaran EQ and Mw7.1 Van EQ) by forecasting VTECs with Normalised Root Mean Square Error (NRMSE) scores of 0.15 and 0.10, respectively. We calculated errors and estimated the 99 % confidence interval to extract the VTEC anomalies. The model detects VTEC anomalies successfully but these anomalies may still have some biases and may lead to a false alarm. In order to minimize possible false alarms, we calculated the intensity of each anomaly and found a strong anomaly that occurred 2–3 days before the EQs. To strengthen the relationship of the detected VTEC anomalies with the investigated earthquakes, we examined the state of space weather conditions during and before the event. Our analysis expands the use of deep learning methods in EQ prediction and VTEC forecasting that can be used for various applications e.g. space weather and navigation.

SVM-assisted ANN model with principal component analysis based dimensionality reduction for enhancing state-of-charge estimation in LiFePO4 batteries

Accurate estimation of state-of-charge (SoC) is significant for monitoring the operation of LiFePO4 batteries. This paper addresses the challenges posed by the nonlinear characteristics of LiFePO4 batteries, which adversely affect the accuracy of SoC estimation. The proposed novel methodology for SoC estimation in LiFePO4 batteries involves a Support Vector Machine (SVM) assisted Artificial Neural Network (ANN) model incorporating principal component analysis (PCA) to efficiently interpret the input data. To improve the prediction accuracy, the non-linear characteristics of LiFePO4 are divided into three parts and each of these parts is used to train a separate ANN model. Further, an optimal number of hidden layers and neurons are selected for each ANN model to minimize the prediction errors. The usage of dedicated smaller datasets for each ANN model simplifies the structure. SVM classifies the battery operating regions and selects the most suitable ANN model for SoC estimation. PCA is applied to process the obtained experimental data resulting in three principal components serving as inputs for the SVM-assisted ANN model. Further, with PCA the input dimensions are reduced from four to three, thereby leading to computational simplicity. The input data comprises of current, voltage, open-circuit voltage and temperature of the battery. An experimental prototype, comprising a customized battery pack and sensing mechanisms, is developed for data collection for training SVM and ANN models. With the proposed SVM-assisted ANN involving PCA, the loss function is minimized and an average Root Mean Square Error (RMSE) of 0.3133 is achieved. This demonstrates the feasibility, accuracy and applicability of SoC estimation with the developed SVM-assisted ANN model for LiFePO4 batteries.

Cooperative Localization under Ionospheric Scintillation Events

Ionospheric scintillation causes major impairments to Global Navigation Satellite System (GNSS) in low-latitude regions. In severe scenarios, this event can lead to complete loss of lock, thus making GNSS measurements unusable for navigation. In this paper, we derive a cooperative localization algorithm where a set of partially connected aircraft exchange messages with neighboring nodes on the network to improve their own position estimates. We consider the scintillation events as abrupt changes in the measurement variance, which are modeled by a discrete-valued Markov process at the nodes which have access to GNSS measurements. Simulation results show that Markovian modeling and cooperation via factor graph message passing reduce the average 3D root mean square localization error and yield an average vertical position error that meets civil aviation standards for approach and landing.

Kalman filter based on a fractional discrete-time stochastic augmented CoVid-19 model

In this paper, we study the dynamics of the CoVid-19 outbreak in Semarang, Indonesia, using a fractional CoVid-19 model. We first determine the effects of the isolation rate ∊ and infection rate β on the reproduction number R0 and infected number V. We find that R0 is directly proportional to β and inversely proportional to ∊. For V, the effect of physical distancing is not as significant as changing ∊. As ∊ increases, V decreases, the number of susceptible individuals increases, the number of quarantined individuals decreases sharply, and the number of recovered individuals decreases. Moreover, the effect of vaccination is also considered. The combination of physical distancing, isolation, and vaccination has a significant impact on reducing the number of infected individuals. Analysis of dynamical systems allows us to understand the characteristics of our model, such as its boundedness and non-negativity, the existence of equilibrium points, the existence and uniqueness of solutions, and the local and global stability. To validate our fractional CoVid-19 model, we introduce the fractional extended Kalman filter (FracEKF) as a prediction method and compare the results against reported CoVid-19 data. FracEKF is a modified version of the basic extended Kalman filter with a time-fractional memory effect. The prediction results illustrate the accuracy of this model in terms of the root mean square error (RMSE), normalized root mean square error (NRMSE), and mean absolute percentage error (MAPE) for each fractional-order. Varying ∊ reproduces the trends observed in the reported data for the number of infected individuals, i.e., when ∊ increases, the infected number decreases. Moreover, a higher fractional-order results in higher model accuracy. Furthermore, higher values of the process noise Qf give smaller errors, whereas higher values of the observation noise Rf produce higher errors. Qf and the fractional-order α are inversely proportional to RMSE,NRMSE, and MAPE, whereas Rf is directly proportional to RMSE,NRMSE, and MAPE.

Application of improved DBN and GRU based on intelligent optimization algorithm in power load identification and prediction

Non intrusive load monitoring belongs to the key technologies of intelligent power management systems, playing a crucial role in smart grids. To achieve accurate identification and prediction of electricity load, intelligent optimization algorithms are introduced into deep learning optimization for improvement. A load recognition model combining sparrow search algorithm and deep confidence network is designed, as well as a gated recurrent network prediction model on the grounds of particle swarm optimization. The relevant results showed that the sparrow search algorithm used in the study performed well on the solution performance evaluation metrics with a minimum value of 0.209 for the inverse generation distance and a maximum value of 0.814 for the hyper-volume. The accuracy and recall values of the optimized load identification model designed in the study were relatively high. When the accuracy was 0.9, the recall rate could reach 0.94. The recognition accuracy of the model on the basis of the test set could reach up to 0.924. The lowest classification error was only 0.05. The maximum F1 value of the harmonic evaluation index of the bidirectional gated recurrent network optimized by particle swarm optimization converged to 90.06%. The loss function had been optimized by particle swarm optimization, and both the convergence value and convergence speed had been markedly enhanced. The average absolute error and root mean square error of the prediction model were both below 0.3. Compared to the bidirectional gated recurrent model before optimization, the particle swarm optimization strategy had a significant improvement effect on prediction details. In addition, the research method had superior recognition response speed and adaptability in real application environments. This study helps to understand the load demand of the power system, optimize the operation of the power grid, and strengthen the reliability, efficiency, and sustainability of the power system.

Assessing Spatiotemporal Behavior of Human Gait: A Comparative Study Between Low-Cost Smartphone-Based Mocap and OptiTrack Systems

AbstractThis study assessed the accuracy of a low-cost marker-based motion capture system with smartphone devices to estimate the spatiotemporal behavior of human gait in comparison with the performance of the commercial OptiTrack system. Initially, three test subjects were selected for the study, and after equipping them with passive retroreflective markers, they were recorded for gait velocities of 1.50, 1.90, and 2.30 $$m\bullet {s}^{-1}$$ m ∙ s - 1 while collecting kinematic data and videos. The results showed that the smartphone motion capture system exhibited significant spatiotemporal tracking and accuracy in the x-y trajectories and estimation of joint relative angles of the hip, knee, and ankle joints (θ1, θ2, and θ3, respectively) compared to the commercial OptiTrack system. In this comparison, an average goodness-of-FIT and normalized root mean square error of over 88.93% and 2.71% were obtained, respectively, for the joint relative angles of the hip and knee (θ1 and θ2) in all tests performed. However, the accuracy of the joint relative angle of the ankle (θ3, average FIT: 71.04% and nRMSE: 4.26%) was lower because of the low capture rate of the retroreflective markers in the smartphone system and the higher relative velocity in the lower extremities of the test subjects, which generated noise in the calculation of x-y trajectories. This decrease in accuracy has been reported in other studies. However, both motion capture systems experienced marker data loss at the hip, highlighting the need for improvement in the spatial distribution of the optical devices. The OptiTrack system demonstrated better optical redundancy but still required improvements. In contrast, the smartphone system, with its inherent limitations in terms of optical redundancy and spatial distribution, can be enhanced by incorporating multiple cameras for a three-dimensional view. Despite these limitations, the low-cost smartphone system showed optimal performance with minimal errors compared with the commercial system, making it a cost-effective option with potential for further development. The rapid advancement of smartphone technology and its accessibility make it an attractive choice for motion capture applications.

Estimating soil moisture content in citrus orchards using multi-temporal sentinel-1A data-based LSTM and PSO-LSTM models

Soil moisture content is a vital variable in agricultural, hydrological, ecological and climatological processes. However, susceptible to soil type, soil structure, topography, vegetation and human activities, soil moisture content exhibits strong spatial heterogeneity in spatial distribution, which makes it difficult to accurately estimate the soil moisture content distribution information at a large scale using conventional methods. To solve the problem, this study proposed a novel hybrid model (PSO-LSTM) based on the particle swarm optimization (PSO) and long short-term memory (LSTM) network model to accurately predict soil moisture content at a large scale. Five different input combinations were constructed based on the vertical polarization (VV) and cross-polarization (VH) of multi-phase Sentinel-1A data, and the soil moisture content at depths of 5 cm, 10 cm, 20 cm and 40 cm in citrus orchards were estimated using the standalone LSTM and hybrid PSO-LSTM models. The results showed that the estimation accuracy of the hybrid PSO-LSTM model was greater than that of the standalone LSTM model at different depths, with the normalized root mean square error (NRMSE) of 4.568–11.023 % and 18.056–30.156 %, respectively. With the VV polarization as the only inputs, the PSO-LSTM model obtained high prediction accuracy, with the normalized root mean square error (NRMSE) of 5.458–10.125 %, respectively. Therefore, the PSO-LSTM model with VV polarization input was recommended to estimate the soil moisture content at different depths in citrus orchards, which provides important data for decision-making on distributed precision irrigation at a large scale.

Effect of different constraining boundary conditions on simulated femoral stresses and strains during gait

Finite element analysis (FEA) is commonly used in orthopaedic research to estimate localised tissue stresses and strains. A variety of boundary conditions have been proposed for isolated femur analysis, but it remains unclear how these assumed constraints influence FEA predictions of bone biomechanics. This study compared the femoral head deflection (FHD), stresses, and strains elicited under four commonly used boundary conditions (fixed knee, mid-shaft constraint, springs, and isostatic methods) and benchmarked these mechanics against the gold standard inertia relief method for normal and pathological femurs (extreme anteversion and retroversion, coxa vara, and coxa valga). Simulations were performed for the stance phase of walking with the applied femoral loading determined from patient-specific neuromusculoskeletal models. Due to unrealistic biomechanics observed for the commonly used boundary conditions, we propose a novel biomechanical constraint method to generate physiological femur biomechanics. The biomechanical method yielded FHD (< 1 mm), strains (approaching 1000 µε), and stresses (< 60 MPa), which were consistent with physiological observations and similar to predictions from the inertia relief method (average coefficient of determination = 0.97, average normalized root mean square error = 0.17). Our results highlight the superior performance of the biomechanical method compared to current methods of constraint for both healthy and pathological femurs.

Quantitative Relationship of Plant Height and Leaf Area Index of Spring Maize under Different Water and Nitrogen Treatments Based on Effective Accumulated Temperature

To optimize the growth management of spring maize, it is essential to understand the dynamics of plant height and leaf area index (LAI) under controlled water and nitrogen supply. This study conducted two-year field experiments (2022–2023) in Karamay, Xinjiang. Three irrigation levels (75%, 100%, and 125% of Crop Evapotranspiration (ETc)) and four nitrogen application rates (0, 93, 186, and 279 kg N/ha) were set. A logistic growth model was fitted using accumulated effective temperature as the independent variable to analyze the growth and development characteristics of spring maize under various water and nitrogen conditions. The results demonstrated that the logistic models, based on relative effective accumulated temperature, had a determination coefficient (R2) of over 0.99 and a Normalized Root Mean Square Error (NRMSE) of less than 10%. Irrigation extended the rapid growth phase of plant height, whereas nitrogen application shortened the time to enter this rapid growth phase and prolonged its duration. Irrigation increased the maximum LAI growth rate and shortened and prolonged the rapid growth phase, while nitrogen extended the duration of the rapid growth phase for LAI. The W2N2 treatment, consisting of 100% ETc irrigation and 186 kg N/ha, was identified as the optimal drip irrigation water–nitrogen combination for spring maize in the study area. Under optimal water and nitrogen supply, both the maximum growth rate and the average growth rate during the rapid growth phase were higher, requiring accumulated effective temperatures of 825.16–845.74 °C·d and 856.68–890.00 °C·d, respectively, to reach these rates. The appropriate water and nitrogen supply significantly enhanced the synergistic promotion of growth and development in spring maize. This study provides a theoretical basis for the quantitative analysis of growth dynamics in summer maize using effective accumulated temperature.

Relative truth value acquisition method of heterogeneous surface based on the Improved Point Spread Function

Abstract. The acquisition of pixel-scale relative truth value is important for remote sensing validation.The Point Spread Function (PSF) has been widely used in the field of the acquisition of relative truth value of heterogeneous surface. In this study, we propose an Improved Point Spread Function (IPSF) based on the Median Pixel Variability Weighted (MPVW) method and PSF to acquire relative truth value of heterogeneous surface. Firstly, the size of variance and clustering window are confirmed based on the pixel scale information of the satellite product to be validated. Secondly, the PSF suitable for heterogeneous surface is selected from 5 PSFs. Thirdly, the IPSF is constructed according to the MPVW and the PSF suitable for heterogeneous surface. Finally, the IPSF is used to acquire relative true value at pixel-scale of heterogeneous surface from airborne hyperspectral image. This study shows: (1) Good correlation between relative true value obtained using IPSF and reference value is indicated as R2 values among 256 channels reach 0.985, structural similarity (SSIM) ranges from 0.992 to 0.998, and peak signal noise ratio (PSNR) more than 35dB. (2) Better accuracy performance is observed in the acquisition of relative truth value of heterogeneous surface for IPSF than PSF. Compared with conventional PSF, the R2, PSNR and SSIM of the result of IPSF are increased by about 1.34%, 9% and 0.7% on the average. (3) Significant advantage of IPSF is also reported in reducing the deviation compared to PSF, as the average root mean square error (RMSEave) is reduced by 30.37% and the average mean absolute error (MAEave) is reduced by 35.98%, respectively. (4) Comparing the RMSE and MAE of PSF and IPSF result, the RMSE and MAE of the result of IPSF become smaller. The RMSE decreases from 3 ~ 195 to 2 ~ 131. The MAE changes from 2 ~ 138 to 1 ~ 89. Overall, the IPSF proposed in this paper can effectively calculate the relative true value of heterogeneous surface, which can provide reference for the validation of multi-spectral and hyper-spectral satellite products.