Error Measures Research Articles

A novel systematically optimized tabular neural network (TabNet) algorithm for predicting the tensile modulus of additively manufactured PLA parts

Assessing the elastic modulus of 3D-printed polylactic acid (PLA) components is essential for understanding their stiffness and load capacity, which are crucial for predicting product performance and durability. In this study, the predictive accuracy of a Tabular Neural Network (TabNet) algorithm for determining the elastic modulus of 3D-printed PLA components via fused deposition modeling (FDM) was investigated. Utilizing a comprehensive dataset of 128 literature-sourced data points, divided into 80 % for training and 20 % for validation, the study proposed a new Taguchi-based method for efficient hyperparameter optimization of the TabNet algorithm. This optimization revealed that a configuration of 8 decision blocks, 16 attention blocks, and 5 decision steps, along with the "Adam" optimizer, a gamma of 1, learning rate of 0.1, and lambda-sparse of 0.01, yielded the highest prediction accuracy for the elastic modulus of PLA parts. The performance of the optimized TabNet model was evaluated using R-squared (R²), Mean Absolute Error (MAE), Mean Squared Error (MSE), and Root Mean Squared Error (RMSE) measures. The findings highlighted an R² of 96.855 %, an MAE of 0.158, an MSE of 0.037, and an RMSE of 0.193 in the validation dataset, demonstrating substantial predictive reliability. To further test the model’s robustness, fourteen unseen data points were analyzed. The observed discrepancies between predicted and actual values were under 10 %, affirming the Taguchi-optimized TabNet algorithm’s effectiveness in forecasting the elastic modulus of FDM 3D-printed PLA components. This investigation provides a significant advancement in additive manufacturing, introducing a precise and reliable method for predicting the mechanical properties of 3D-printed materials.

Intelligent computing applications to study the tri-hybrid nanofluid past over the stretched surface

In this study, a recurrent neural network with the Levenberg-Marquardt backpropagation algorithm is used to examine the effects of various parameters on cooling mechanisms involving tri-hybrid nanofluid consisting of Al2O3, Cu, TiO2 and magnetohydrodynamic stagnation point flow. This research focus on nanofluid in the existence of an asymmetrically stretched disc in water, which plays an imprortant role for understanding heat transfer in addition to the dynamics of momentum and thermal boundary surface. Transform the complex partial differential system through suitable similarity transformations into the ordinary differential equations for numerical computing. These equations have been solved numerically by using the Adams method in Mathematica to generate datasets for various parameters.The current study demonstrates that the velocity profile rises with higher magnetic, velocity slip, and mass suction parameters. The fluid thermal level tends to decrease with an increase in mass suction parameters, whereas an increase in the magnetic parameter and Eckert number raises the fluid’s thermal level. Furthermore, it is noticed that the flow resistance and internal friction of the fluid are proportional to the viscosity parameter. The proposed scheme has shown its effectiveness in a wide range of scenarios and cases. This was achieved by comparing the mean square error metric for the squeezing flow tri-hybrid nanofluid problem with the obtained results. In addition, various statistical measures like state transitions, fitness assessments, error histograms, and regression analyses, provide further evidence of the solver’s robustness and reliability. The excellent agreement between the reference datasets and refined numerical solutions through the scheme showcases the method’s effectiveness, achieving remarkable accuracy levels ranging from 10-6 to 10-12.

An on-machine measurement and calibration method for incident laser error in dual-swing laser heads

The dual-swing laser head is essential for five-axis laser machining, yet its precision is greatly affected by the incident laser beam. Any positional or angular deviation in the laser can cause the focus spot position of the head to change continuously during rotation, thereby severely compromise the manufacturing performance of the head. However, the current calibration methods for the incident beam of dual-swing laser heads have issues with low accuracy and insufficient engineering applicability. This paper proposes an on-machine measurement and calibration method for incident laser error in dual-swing laser heads. An error model for the incident beam with a dual-swing laser head was established, from which the law of spot position changes caused by incident beam errors during the head's rotation was derived. Subsequently, following this law, a precision calibration method for the laser head's incident beam error was proposed, based on the theory of optical image height. Afterwards, an on-machine error measurement system was established on the dual-swing laser head, and the calibration method was verified through experiments. The results show that the use of this calibration method can improve the accuracy of the incident beam for dual-swing laser head to 0.071 mm, which is approximately 3–4 times better than traditional calibration methods, thereby significantly enhancing the manufacturing precision of the laser head.

Measuring error in the Demographic Index – steps towards a future population statistics system in England and Wales

ObjectiveWe are developing methods to measure the quality of the Demographic Index at a National Statistics Institute. The Demographic Index is the foundational dataset for a future, transformed, population statistics system for England and Wales. It clusters records for individuals across many years of health, education, and tax data, and assigns them a unique ID. Previous research has helped us to conceptualise three types of error in the Demographic Index: clustering error, coverage error, and data measurement error. We are currently working on estimating one type of clustering error, whereby records for two individuals are mistakenly assigned the same ID (“false positive clusters”). ApproachPrevious work has allowed us to identify variables associated with false positive clusters. We are now working on a stratification method, whereby each ID in the Demographic Index is scored according to how likely it is to contain this error. We plan to measure uncertainty using bootstrapping. Results and ConclusionsThis work is ongoing, and we hope to obtain results by summer 2024. ImplicationsIt is vital for us to understand and measure error in the Demographic Index because this is necessary for measuring error in any statistics derived from the Index. And it is crucial that population statistics made by any future system should have measures of error. Assuming that our work shows promise, we will continue by measuring other types of error, and by creating use cases to test how these measures can be fed forward into secondary analyses (e.g. population estimation).

The Comparison of Performance Double Exponential Smoothing and Double Moving Average Methods in Seasonal Meat Stock Demand

The demand for beef supplies depended on seasonal patterns because it depends on feed supplies, especially in rural areas that still rely on natural feed. Beef supplies were part of government regulations because they were highly demanded commodities. They are livestock products that contain nutritional value to meet the protein needs of the community. Beef stocks were influenced by factors such as beef production, beef consumption, and people's income levels. In anticipating the increasing demand for beef, it is necessary to carry out forecasting to estimate the demand for meat in the future. In forecasting, various methods were used to choose the method with the lowest error rate. This research will compare the Double Exponential Smoothing (DES) with the Double Moving Average (DMA) based on the Mean Absolute Percentage Error (MAPE) measurement, one method for finding the minor error value. Based on the test results with beef supplies in Madura and conducting analysis, it can be concluded that the method with the smallest MAPE value is the Double Exponential Smoothing method, with the smallest MAPE value of 9.50% at an alpha parameter of 0.5. In testing with the Double Moving Average method, by determining the best MAPE value, the best time order in the Double Moving Average method is at time order parameter 2 with a MAPE value of 29.8408%. After finding the parameter with the smallest MAPE value, that parameter is used for data testing. In the measurement, data testing for data of 1 year, two years, three years, and four years. Each method has a level of error value that increases the same; a lot of data entered can affect the size of the MAPE value. So, the more data entered, the smaller the resulting error value.

Cervical Sensorimotor Function Tests Using a VR Headset-An Evaluation of Concurrent Validity.

Sensorimotor disturbances such as disturbed cervical joint position sense (JPS) and reduced reaction time and velocity in fast cervical movements have been demonstrated in people with neck pain. While these sensorimotor functions have been assessed mainly in movement science laboratories, new sensor technology enables objective assessments in the clinic. The aim was to investigate concurrent validity of a VR-based JPS test and a new cervical reaction acuity (CRA) test. Twenty participants, thirteen asymptomatic and seven with neck pain, participated in this cross-sectional study. The JPS test, including outcome measures of absolute error (AE), constant error (CE), and variable error (VE), and the CRA test, including outcome measures of reaction time and maximum velocity, were performed using a VR headset and compared to a gold standard optical motion capture system. The mean bias (assessed with the Bland-Altman method) between VR and the gold standard system ranged from 0.0° to 2.4° for the JPS test variables. For the CRA test, reaction times demonstrated a mean bias of -19.9 milliseconds (ms), and maximum velocity a mean bias of -6.5 degrees per seconds (°/s). The intraclass correlation coefficients (ICCs) between VR and gold standard were good to excellent (ICC 0.835-0.998) for the JPS test, and excellent (ICC 0.931-0.954) for reaction time and maximum velocity for the CRA test. The results show acceptable concurrent validity for the VR technology for assessment of JPS and CRA. A slightly larger bias was observed in JPS left rotation which should be considered in future research.

Evaluation of GEDI footprint level biomass models in Southern African Savannas using airborne LiDAR and field measurements

Savannas cover more than 20% of the Earth and account for the third largest stock of global aboveground biomass yet estimates of their above ground biomass density (AGBD) are very inaccurate. The Global Ecosystem Dynamic Investigation (GEDI) sensor provides near-global full-waveform LiDAR data with 25 m footprints, from which various structural metrics are derived that are used to predict footprint level AGBD. The current GEDI L4A AGBD product uses a comprehensive Forest Structure and Biomass Database (FSBD) to develop models for specific plant functional types and geographic regions, but southern African savannas have been underrepresented in the reference data. The objectives of this study were to (i) validate GEDI L4A AGBD in South African savannas using field measurements and ALS datasets and (ii) develop and evaluate local GEDI footprint-level AGBD estimates from multiple L2A and L2B metrics. The local GEDI AGBD models outperformed GEDI L4A AGBD (R2 = 0.42, RMSE = 12 Mg/ha, %RMSE = 79.5%) with higher R2 and smaller error measures. The local GEDI AGBD using a random forest model (RF) had the highest R2 of 0.71 and lowest %RMSE of 53.3%, while the generalized linear model (GLM) results provided the lowest Relative Mean Systematic Deviation (RMSD) of 9.2%, which was half that of RF model. L4A significantly underestimated AGBD with an RMSD up to −37%. This highlights the importance and benefits of local calibration of biomass models to unlock the full potential of GEDI metrics for estimating AGBD. The field and ALS data have subsequently been contributed to the GEDI FSBD and should be used in calibration of future versions of GEDI L4A AGBD product. This research paves the way for the integration of the local GEDI AGBD estimates with other sensors, notable the eminent NISAR mission, to derive regional to global gridded AGBD products that will enable the monitoring of savanna carbon stocks.

Analysis of models of measurement and correction of volumetric error of three-axis metal-cutting machine tool

The paper considers the improvement of the quality of products of machined production in connection with the quality of machining of various products and, accordingly, with the accuracy of the equipment used. It is noted that geometrical errors, which account for up to 40 % of the total error of a multi-axis, especially three-axis, metal-cutting machine tool, have the greatest influence on the accuracy of product machining. In order to improve the quality of product machining, it is necessary to correct its parameters according to the measurement information received during machine tool operation, for which the methods of mathematical modelling are used. Models of the volumetric error of a three-coordinate metal-cutting machine tool are developed, taking into account the summands of the first (linear) and second (quadratic) order of smallness. A comparative analysis of the developed models is carried out. The results of experiments on measurement of volumetric errors of the STAN S500 complex and their correction on the basis of the nonlinear theoretical model are given. It is found that in the range of angular errors 0–2.5′ the consideration of quadratic terms of the model in addition to linear ones does not lead to a significant reduction of the volumetric error. It is shown that when processing measurement information of multi-axis metal-cutting machines it is sufficient to limit the consideration of components of the volumetric error not higher than the first order of smallness. The research results are useful for the acceptance and periodic control of the volumetric error of metal-cutting machines, as well as for the programme reduction of the volumetric error.

A reliable ensemble forecasting modeling approach for complex time series with distributionally robust optimization

Accurate ensemble forecast results provide strong support for management decisions. While the existing ensemble forecasting model ignores the requirement of directional accuracy making its prediction direction is usually error-prone. To address this issue, we develop a convex directional prediction error measure and subsequently construct a reliable ensemble forecasting model that minimizes the horizontal prediction error with the bounded directional prediction error. Mathematically, we provided the proper range of the required directional error level. Furthermore, we find the classical ensemble forecasting model is a special case of our study when the directional error level is larger than the upper bound we gave in this study. To deal with the possible deterioration of the individual model over time, we also considered its worst possible prediction performance by introducing the distributionally robust optimization (DRO) technique into the proposed reliable ensemble forecasting model. Technically, we showed that the DRO-based reliable ensemble forecasting model is convex and can be reformulated into a second-order cone problem which can be readily solved by off-the-shelf solvers. Finally, the effectiveness of the proposed reliable ensemble forecasting model and the DRO-based reliable ensemble forecasting model were validated on three different datasets, e.g., the exchange rate, the oil price, and the country risk index. To sum up, we construct a reliable ensemble forecasting model to simultaneously control the horizontal prediction error and directional prediction error of ensemble forecasting, and thus enhance the reliability of ensemble forecasting.

Swarm intelligence-based optimization of machine learning models for diverse industrial problems: a comparative study

Abstract With the rapid development of artificial intelligence, machine learning has emerged as a promising approach to tackle complex problems in various industries. It is particularly evident in situations where limited data samples are available, such as when developing new materials, or in high-speed machining scenarios where computational efficiency and result reliability are equally crucial. In this work, we have selected five widely recognized machine learning models (e-SVR, v-SVR, BP, Random Forest, Extreme Learning Machines) as baseline methods. We employ Snake Optimizer, a recently popular swarm intelligence algorithm, to optimize the parameters of each model individually. The Mean Squared Error is utilized as an evaluation fitness measure to adaptively optimize and determine the optimal hyperparameter combination for each method. Consequently, five hybrid models are established. To thoroughly evaluate the performance and applicability of these models, predictive experiments are conducted using temperature data of permanent magnet synchronous motors, energy consumption data from steel companies and real-estate price data of Chicago, representing three distinct scenarios. The learning ability and generalization capability of these models are tested and assessed using four error measures: Mean Absolute Error, R-Squared, Root Mean Squared Error, and Computation Time. Moreover, comparison and discussion between the hybrid models and their respective basic models are also conducted, analysing the effectiveness of SO algorithm in optimization. Through analysis and discussion, a comprehensive understanding of the characteristics and applicability of them is provided. Our objective is to provide scientific researchers and engineers with valuable insights into different methods and their characteristics.

New Results on Rapid Dynamical Pattern Recognition via Deterministic Learning From Sampling Sequences.

Rapid dynamical pattern recognition based on the deterministic learning method (DLM-based RDPR) aims to rapidly recognize the most similar dynamical pattern pair from perspectives of differences in inherent system dynamics. The basic mechanism is to use available recognition errors to reflect the differences in the dynamics of dynamical pattern pairs and then to make a decision based on a minimal recognition error (MRE) principle. This article focuses on providing a rigorous theoretical analysis of the MRE principle in DLM-based RDPR under the sampled-data framework. Specifically, we seek a unified methodology from the similarity definition to the measure implementation and then to derive general sufficient conditions and necessary conditions for the MRE principle. The main idea is to: 1) from the average signal energy aspect, define a time-dependent dynamics-based similarity in dynamical pattern pairs and reestablish the measure of recognition errors generated from the DLM-based RDPR; 2) introduce the energy-based Lyapunov method to establish the interrelation between the dynamical distance and the recognition error; and 3) derive sufficient conditions and necessary conditions from two directions of the interrelation. The proposed conditions distinguish themselves from virtually all of the existing DLM-based RDPR works with only sufficient conditions in the sense that it is shown in a rigorous analysis that under what conditions, the pattern pair recognized based on the MRE principle is indeed the most similar one. Therefore, the proposed work makes the DLM-based RDPR possess good interpretability and provides strong theoretical guidance in engineering applications.

Associations between ocular biometry and anthropometric measurements among Sudanese adults.

Correlations between body parameters and ocular parameters are essential to emphasize the diagnosis and management of ocular and systemic diseases. This study aimed to assess the associations between ocular parameters and anthropometric parameters in adult Sudanese individuals. A cross-sectional hospital-based study was conducted with 250 young volunteers (250 eyes) at Al-Neelain University Eye Hospital from January to June 2019. Clinical examinations included demographic data, medical history, visual acuity assessment, refractive error, and anterior corneal power (ACP) measurement using an autorefkeratometer and ocular biometry via A-scan ultrasound. Anthropometric assessments included height (measured using a wall-mounted metric ruler), weight (measured with a digital scale), and body mass index (BMI), calculated as weight divided by height squared. Data analysis was performed using SPSS version 25. There were 64 (25.6%) men and 186 (74.4%) women. The mean age was 21.29 ± 1.18 years. The mean body height, weight, and BMI were 1.62 ± 0.07 m, 58.56 ± 11.93 kg, and 22.38 ± 4.80 kg/m2, respectively. The mean axial length (AL), ACP, anterior chamber depth (ACD), and vitreous depth (VD) were 22.81 ± 0.74 mm, 43.30 ± 1.40 D, 3.20 ± 0.33 mm, and 15.97 ± 0.67 mm, respectively. Body height was positively correlated with AL, ACD, and VD and negatively correlated with ACP (P < 0.001). Body weight was significantly positively correlated with AL and VD (P < 0.05). BMI was not correlated with any ocular parameters (P > 0.05). The study concluded that taller subjects had significantly longer axial lengths, deeper vitreous cavities, and flatter corneas. However, body weight was positively associated with axial length and vitreous depth.

Random forests regression for soft interval data

Analyzing soft interval data for uncertainty quantification has attracted much attention recently. Within this context, regression methods for interval data have been extensively studied. As most existing works focus on linear models, it is important to note that many problems in practice are nonlinear in nature and the development of nonlinear regression tools for interval data is crucial. This paper proposes an interval-valued random forests model that defines the splitting criterion of variance reduction based on an L 2 type metric in the space of compact intervals. The model simultaneously considers the centers and ranges of the interval data as well as their possible interactions. Unlike most linear models that require additional constraints to ensure mathematical coherences, the proposed random forests model estimates the regression function in a nonparametric way, and so the predicted interval length is naturally nonnegative without any constraints. Simulation studies show that the new method outperforms typical existing regression methods for various linear, semi-linear, and nonlinear data archetypes and under different error measures. To demonstrate the applicability, a real data example is presented where the price range data of the Dow Jones Industrial Average index and its component stocks are analyzed.

Functional Time Series Models for K-Step Prediction of Sugar Production: A Case Study of Eswatini, Kenya, and South Africa

Sugar, produced from cane or beet, is a vital energy source and a globally traded commodity. Most business happens in a futures exchange market where speculators, hedgers, and institutional consumers and producers, make decisions based on their understanding of the future supply and demand situation. Sugar is sometimes bought and sold before the cane or beet is planted. Hence, improving sugar production forecast accuracy is vital to maximize gains and enable effective planning. The study considered the annual sugar production total as a function of the monthly output rather than a scalar quantity and analyzed historical data using three functional time series techniques. In particular, the methods used for k-steps and dynamic updating prediction of sugar production include Local Polynomial Regression (LPR), Ridge Regression (RR), and Penalized Least Squares (PLS). The performance of the three models was compared to that of the automatic ARIMA method using the Mean Squared Error (MSE) and the Mean Absolute Percentage Error (MAPE) measures to establish the suitability of each technique in sugar production forecasting. The LPR, RR, and PLS outperformed the ARIMA method in all three cases. However, the prediction accuracy was lower for highly volatile datasets from countries that overly depend on rainfall for cane development.

Differentially private and explainable boosting machine with enhanced utility

In this paper, we introduce DP-EBM*, an enhanced utility version of the Differentially Private Explainable Boosting Machine (DP-EBM). DP-EBM* offers predictions for both classification and regression tasks, providing inherent explanations for its predictions while ensuring the protection of sensitive individual information via Differential Privacy. DP-EBM* has two major improvements over DP-EBM. Firstly, we develop an error measure to assess the efficiency of using privacy budget, a crucial factor to accuracy, and optimize this measure. Secondly, we propose a feature pruning method, which eliminates less important features during the training process. Our experimental results demonstrate that DP-EBM* outperforms the state-of-the-art differentially private explainable models.

Forecasting Maximum Temperature Trends with SARIMAX: A Case Study from Ahmedabad, India

Globalization and industrialization have significantly disturbed the environmental ecosystem, leading to critical challenges such as global warming, extreme weather events, and water scarcity. Forecasting temperature trends is crucial for enhancing the resilience and quality of life in smart sustainable cities, enabling informed decision-making and proactive urban planning. This research specifically targeted Ahmedabad city in India and employed the seasonal autoregressive integrated moving average with exogenous factors (SARIMAX) model to forecast temperatures over a ten-year horizon using two decades of real-time temperature data. The stationarity of the dataset was confirmed using an augmented Dickey–Fuller test, and the Akaike information criterion (AIC) method helped identify the optimal seasonal parameters of the model, ensuring a balance between fidelity and prediction accuracy. The model achieved an RMSE of 1.0265, indicating a high accuracy within the typical range for urban temperature forecasting. This robust measure of error underscores the model’s precision in predicting temperature deviations, which is particularly relevant for urban planning and environmental management. The findings provide city planners and policymakers with valuable insights and tools for preempting adverse environmental impacts, marking a significant step towards operational efficiency and enhanced governance in future smart urban ecosystems. Future work may extend the model’s applicability to broader geographical areas and incorporate additional environmental variables to refine predictive accuracy further.

A non-parametric model of ground motion parameters for shallow crustal earthquakes in Europe

The current study focuses on deriving ground motion models (GMMs) for 21 ground motion parameters derived from data sourced from the Engineering Strong Motion (ESM) database. These parameters include Peak Ground Acceleration (PGA), Peak Ground Velocity (PGV), Peak Ground Displacement (PGD), PGV-to-PGA ratio, (V/H) PGA ratio Predominant Frequency (Fp), Central Frequency (Ω), Spectral Parameter (q), Significant Duration (TSig), Root Mean Square Acceleration (Arms), Arias Intensity (Ia), Cumulative Absolute Velocity (CAV), Characteristic Intensity (IC), Acceleration Spectrum Intensity (ASI), Velocity Spectrum Intensity (VSI), Total Energy (Eacc), Spectral Centroid (Ew), Spectral Standard Deviation (Sw), Temporal Centroid (Et), Temporal Standard Deviation (St), and Correlation between time and frequency [ρ(t,ω)]. Both horizontal and vertical components are considered in this study. The inherent random effects within ground motion regression, encompassing inter-event, inter-site, inter-locality, and inter-region variabilities, are addressed using cross-nested mixed effect regression utilizing a non-parametric GMM approach employing Artificial Neural Network (ANN). Quantitative assessment of the models involves correlation coefficients for regression through the origin and error measures like mean squared error and mean absolute error. These findings of the assessment confirm reliable estimates of Ground Motion Parameters (GMPs). A comparison of GMPs computed using the proposed model and those reported in the literature indicated model's superior performance. Furthermore, satisfactory performance of the proposed GMM in ground motion simulation for the ESM region is demonstrated.

Evaluating the effectiveness of safety countermeasures at highway–railway grade crossing based on a machine learning framework

Objective This research aims to cluster similar highway–railway grade crossings (HRGCs) to examine the safety countermeasures at HRGCs. Methods The methodology integrates inventory and collision data from Federal Railroad Association (FRA) data set during years 2010 to 2022 . The XGBoost and random forest (RF) algorithms are employed to identify influential collision severity factors. Then, the deep latent class analysis (DLCA) method is utilized on selected inventory factors as important features to cluster similar HRGCs. Afterward, collision modification factor (CMF) and standard error (SE) measures are computed for each countermeasure through collisions within each HRGC cluster. Results XGBoost successfully identified 20 important collision and inventory factors with importance levels exceeding 94%, such as the number of daily trains and the surface material. Then, the DCLA method achieved 4 distinct clusters optimized by high similarity within each cluster and significant independence among clusters. The effectiveness of countermeasures was computed in terms of CMF and SE. The CMF results demonstrated that bells achieved superior safety compared to other countermeasures in clusters with sharper track angles and high maximum train speeds. Implementing bells decreased collisions across Clusters 1 and 4, with reductions of 53% (CMF = 0.47) and 46% (CMF = 0.54), respectively. Conclusions The results highlight XGBoost’s capability to identify important collision and inventory factors, successfully uncovering 20 of the most important factors. The DCLA clustering method forms 4 distinct groups marked by substantial internal similarity within each cluster. This approach contributes to a clearer understanding of how each countermeasure impacts collision frequency. The findings highlight the varying effectiveness of different countermeasures across clusters, improving decision making for safety at HRGCs. The study highlights the efficacy of crossbucks in addressing safety concerns during moderate traffic conditions, particularly evident in environments with a highway speed limit between 100 and 125 mph. Additionally, bells demonstrate notable effectiveness in areas with sharper track angles.

High Spatial-Resolution and Acquisition-Efficiency Cardiac MR T1 Mapping Based on Radial bSSFP and a Low-Rank Tensor Constraint.

Cardiac T1 mapping is valuable for evaluating myocardial fibrosis, yet its resolution and acquisition efficiency are limited, potentially obscuring visualization of small pathologies. To develop a technique for high-resolution cardiac T1 mapping with a less-than-100-millisecond acquisition window based on radial MOdified Look-Locker Inversion recovery (MOLLI) and a calibrationless space-contrast-coil locally low-rank tensor (SCC-LLRT) constrained reconstruction. Prospective. Sixteen healthy subjects (age 25 ± 3 years, 44% females) and 12 patients with suspected cardiomyopathy (age 57 ± 15 years, 42% females), NiCl2-agar phantom. 3-T, standard MOLLI, radial MOLLI, inversion-recovery spin-echo, late gadolinium enhancement. SCC-LLRT was compared to a conventional locally low-rank (LLR) method through simulations using Normalized Root-Mean-Square Error (NRMSE) and Structural Similarity Index Measure (SSIM). Radial MOLLI was compared to standard MOLLI across phantom, healthy subjects, and patients. Three independent readers subjectively evaluated the quality of T1 maps using a 5-point scale (5 = best). Paired t-test, Wilcoxon signed-rank test, intraclass correlation coefficient analysis, linear regression, Bland-Altman analysis. P < 0.05 was considered statistically significant. In simulations, SCC-LLRT demonstrated a significant improvement in NRMSE and SSIM compared to LLR. In phantom, both radial MOLLI and standard MOLLI provided consistent T1 estimates across different heart rates. In healthy subjects, radial MOLLI exhibited a significantly lower mean T1 (1115 ± 39 msec vs. 1155 ± 36 msec), similar T1 SD (74 ± 14 msec vs. 67 ± 23 msec, P = 0.20), and similar T1 reproducibility (28 ± 18 msec vs. 22 ± 15 msec, P = 0.34) compared to standard MOLLI. In patients, the proposed method significantly improved the sharpness of myocardial boundaries (4.50 ± 0.65 vs. 3.25 ± 0.43), the conspicuity of papillary muscles and fine structures (4.33 ± 0.74 vs. 3.33 ± 0.47), and artifacts (4.75 ± 0.43 vs. 3.83 ± 0.55). The reconstruction time for a single slice was 5.2 hours. The proposed method enables high-resolution cardiac T1 mapping with a short acquisition window and improved image quality. 1 TECHNICAL EFFICACY: Stage 1.

Development of fixed-point two-degree-of-freedom positioning errors measurement system with precision improvement function

A two-degree-of-freedom (2-DOF) error measurement system is proposed for assessing the positioning errors of a rotary stage. Additionally, this study introduces a compensation method for addressing four-degree-of-freedom (4-DOF) laser drift errors and presents a refined approach for correcting the decoupling matrix. Initially, passive compensation is utilized to address the 4-DOF laser drift errors, and the impact of laser drifts is minimized through an averaging technique. Subsequently, the identified laser drift errors are analyzed using a mathematical model to effectively compensate for these errors and enhance the overall accuracy of the measurement system. Concerning the correction of the decoupling matrix, a more precise method is employed in contrast to traditional approaches. Experimental data obtained from commercial interferometers are subjected to linear fitting using the least squares method, facilitating a more accurate refinement of the decoupling matrix. This method enables a better alignment of the decoupling matrix with the experimental conditions.