Error Index Research Articles

Life prediction method of rolling bearing based on CNN-LSTM-AM

Bearing is the key component to determine the health of machinery, and it is of great significance to monitor its working status in real time and predict its remaining useful life. In recent years, the RUL prediction method based on deep learning has been widely used and achieved good prediction results. Here, a bearing life prediction method based on convolution neural network (CNN), long short term memory (LSTM) and attention mechanism (AM) is proposed. First of all, the time domain and frequency domain features of the original vibration signals of rolling bearings are extracted, and the extracted feature set is normalized as the input of CNN. The main function of CNN is to extract spatial features and reduce the dimension of the data. Then, using LSTM to extract the information that may be ignored by CNN, the feature information extracted by CNN-LSTM is input to the attention mechanism for weighting, and the key information is screened. And then more accurately represent the degradation characteristics of the equipment, and finally get the bearing remaining life. The performance of the model is verified by two sets of public data sets, and the experimental results show that it is compared with the CNN-LSTM method. The root mean square error (RMSE) index based on CNN-LSTM-AM method is reduced by 14.6 % and 13.8 % respectively, and the score index is increased by 2.0 % and 2.4 % respectively. The results show that the proposed method has higher accuracy in bearing RUL prediction.

Joint constraints from cosmic shear, galaxy-galaxy lensing and galaxy clustering: internal tension as an indicator of intrinsic alignment modelling error

In cosmological analyses it is common to combine different types of measurement from the same survey. In this paper we use simulated DES Y3 and LSST Y1 data to explore differences in sensitivity to intrinsic alignments (IA) between cosmic shear and galaxy-galaxy lensing. We generate mock shear, galaxy-galaxy lensing and galaxy clustering data, contaminated with a range of IA scenarios. Using a simple 2-parameter IA model (NLA) in a DES Y3 like analysis, we show that the galaxy-galaxy lensing + galaxy clustering combination ( 2×2pt) is significantly more robust to IA mismodelling than cosmic shear. IA scenarios that produce up to 5σ biases for shear are seen to be unbiased at the level of ∼1σ for 2×2pt. We demonstrate that this robustness can be largely attributed to the redshift separation in galaxy-galaxy lensing, which provides a cleaner separation of lensing and IA contributions. We identify secondary factors which may also contribute, including the possibility of cancellation of higher-order IA terms in 2×2pt and differences in sensitivity to physical scales. Unfortunately this does not typically correspond to equally effective self-calibration in a 3×2pt analysis of the same data, which can show significant biases driven by the cosmic shear part of the data vector. If we increase the precision of our mock analyses to a level roughly equivalent to LSST Y1, we find a similar pattern, with considerably more bias in a cosmic shear analysis than a 2×2pt one, and significant bias in a joint analysis of the two. Our findings suggest that IA model error can manifest itself as internal tension between ξ± and γt+w data vectors. We thus propose that such tension (or the lack thereof) can be employed as a test of model sufficiency or insufficiency when choosing a fiducial IA model, alongside other data-driven methods.

Intelligent PID Controller Based on Neural Network for AI-Driven Control Quadcopter UAV

Unmanned Aerial Vehicle (UAV), specifically a quadcopter is publicly popular which it provides services in different applications such as aerial delivery, aerial photography, military, weather forecasting and more examples to date. A Proportional-Integral-Derivative (PID) controller is one of the control techniques that can provide stabilization and reliable trajectory tracking. However, proper PID gains are needed to ensure a stable flight and it should be hybridized or improved to increase the robustness, reliability, and stabilization during flight. In this paper, an intelligent PID controller using neural network is proposed based on Levenberg-Marquardt feedforward neural network training method. The PID gains are initialized using different ranges according to the optimal gains generated by Particle Swarm Optimization, and this contributes towards a good training performance using Mean Square Error (MSE) evaluation. The trained network takes desired output and references as input data to calculate the required combination of PID gains as the output. The including of the response characteristics as the input data for the network, together with reference, error, and control input is the significance of the work. The performance of this work is presented using MSE performances, attitudes and altitude stabilization, and trajectory tracking reliability through error index performances. The simulation results graphically prove that the proposed controller provides better stability with reduced overshoot and settling times. Disturbance rejection is also enhanced by 1.7% compared to manual tuned PID controller. The reliability of the proposed controller highlights avenues for further exploration in AI-driven control strategies for quadcopter systems.

An Innovative Correction–Fusion Approach for Multi-Satellite Precipitation Products Conditioned by Gauge Background Fields over the Lancang River Basin

Satellite precipitation products can help improve precipitation estimates where ground-based observations are lacking; however, their relative accuracy and applicability in data-scarce areas remain unclear. Here, we evaluated the accuracy of different satellite precipitation datasets for the Lancang River Basin, Western China, including the Tropical Rainfall Measuring Mission (TRMM) 3B42RT, the Global Precipitation Measurement Integrated Multi-satellitE Retrievals (GPM IMERG), and Fengyun 2G (FY-2G) datasets. The results showed that GPM IMERG and FY-2G are superior to TRMM 3B42RT for meeting local research needs. A subsequent bias correction on these two datasets significantly increased the correlation coefficient and probability of detection of the products and reduced error indices such as the root mean square error and mean absolute error. To further improve data quality, we proposed a novel correction–fusion method based on window sliding data correction and Bayesian data fusion. Specifically, the corrected FY-2G dataset was merged with GPM IMERG Early, Late, and Final Runs. The resulting FY-Early, FY-Late, and FY-Final fusion datasets showed high correlation coefficients, strong detection performances, and few observation errors, thereby effectively extending local precipitation data sources. The results of this study provide a scientific basis for the rational use of satellite precipitation products in data-scarce areas, as well as reliable data support for precipitation forecasting and water resource management in the Lancang River Basin.

Study on the applicability of the Brief Job Stress Questionnaire based on classical test theory and item response theory

Objective: To evaluate the quality and item characteristics of the Brief Job Stress Questionnaire (BJSQ) among employees in manufacturing and service industries. Methods: From December 2021 to December 2022, a total of 2077 employees from 4 manufacturing and service enterprises in Beijing were selected by the method of combining purpose sampling and convenience sampling. The Chinese version of BJSQ was used to carry out a survey on occupational stress from 57 items in 4 dimensions including job stress factors, stress response, social support factors and satisfaction. Classical test theory (CTT) was used to analyze the validity and reliability of the questionnaire. The Semejima hierarchical response model in item response theory (IRT) was used to analyze the differentiation a, difficulty coefficient b and information content of each item. Results: Among the 2077 subjects, the age M (Q(1), Q(3)) was 33 (28, 37) years old, and the working age M (Q(1), Q(3)) was 4 (2, 8) years. There were 723 (34.8%) people in manufacturing industry and 1354 (65.2%) people in service industry. Eleven common factors were extracted by exploratory factor analysis, with a cumulative variance contribution rate of 62.823%, the variance of the common factors of each entry ranging from 0.451 to 0.865, and the range of factor loading values from 0.413 to 0.825, with 5 items having cross-loadings. The results of the validation factor analysis showed that the model fit indexes of root means square error of approximation was 0.055, comparative fit index was 0.950, Tucker Lewis index was 0.948, and standardized root mean square was 0.066. Content validity results showed that the total scores of the Chinese version of the BJSQ were positively correlated with the scores of the 4 dimensions (r(s)=0.487-0.936, P<0.05) . The results of the reliability analysis showed that the Cronbach's alpha coefficient for the total questionnaire was 0.945, and the Cronbach's alpha coefficients of job stress factors, stress response and social support factors were 0.775, 0.957, and 0.830, respectively. The Spearman-Brown coefficient for the total questionnaire was 0.866, and for the 3 dimensions, it was 0.572, 0.882 and 0.772. The results of IRT analysis showed that only 1 of the 57 items had a differentiation a-value<0.30, the difficulty coefficient b-value of each item ranged from -12.02 to 11.09, of which 8 items had a difficulty coefficient that was too high, 3 items had a difficulty coefficient that was too low, and 3 items did not meet the requirements, and the average amount of information in each item ranged from 0.022 to 2.566, and there were 47 items with average amount of information>0.088 (5/57) . Conclusion: The Chinese version of BJSQ has good reliability and validity in the typical occupational groups of manufacturing and service industries in China, and most of the items have good performance, but some items still need to be further improved and optimized or deleted.

An improved model for primary prediction of performance map for turbocharger radial turbine

In the contemporary landscape, possessing an intricate understanding of the performance characteristics of turbocharger radial turbine proves invaluable during engine development phases, to improve predictive capabilities of calculation codes and enhance the critical process of matching engines with turbochargers. This research deals with offering two precise yet straightforward analytical functions intended to generate comprehensive performance maps of turbocharger turbines. This is achieved through a refined adjustment of a preexisting analytical function, after introducing an inventive multiplication factor that aligns numerical calculations with experimental data to predict the turbine’s expansion ratio. Besides, a second analytical function forecasts the turbine’s thermo-mechanical efficiency by establishing a power balance equation between the turbine and supplied compressor map. The outcome of the developed model is compared with existing method on two distinct turbochargers, encompassing various rotational speeds. Additionally, a sensitive analysis aiming to detect the most important factors affecting our developed model while exploring it possible validity range for different thermodynamic parameters. The results indicate that the two functions yield reliable estimations of turbine performance, with maximum; root mean square error, R2, and mean absolute percentage error indices find around 9.47%, 0.993, and 9.03% for the turbine expansion ratio, and about 4.42%, 0.612, and 19.78% for efficiency prediction. This novel model enhances simulation accuracy while preserving user-friendliness and robustness based on the prerequisite of limited geometric and thermodynamic parameters at the turbocharger boundaries. Finally, the main advantages of the proposed model is its adaptability for the implementation in calculation codes, turbomachinery optimization strategies and assessments of the design and performance, addressing scenarios where the original turbine maps are rarely provided by turbocharger manufacturers.

The posteriori analysis of the spectral element discretization of the wave equation

This work focuses on discretizing a second-order linear wave equation using the implicit Euler scheme for time discretization and the spectral element method for spatial discretization. We prove that optimal adaptivity can be achieved by combining adaptive time steps with adaptive spectral mesh. We introduce two sets of error indicators for time and space, respectively, and derive optimal estimates.

Generalized 3D registration algorithm for enhancing retinal optical coherence tomography images.

Optical coherence tomography (OCT) has emerged as the standard of care for diagnosing and monitoring the treatment of various ocular disorders due to its noninvasive nature and in vivo volumetric acquisition capability. Despite its widespread applications in ophthalmology, motion artifacts remain a challenge in OCT imaging, adversely impacting image quality. While several multivolume registration algorithms have been developed to address this issue, they are often designed to cater to one specific OCT system or acquisition protocol. We aim to generate an OCT volume free of motion artifacts using a system-agnostic registration algorithm that is independent of system specifications or protocol. We developed a B-scan registration algorithm that removes motion and corrects for both translational eye movements and rotational angle differences between volumes. Tests were carried out on various datasets obtained from two different types of custom-built OCT systems and one commercially available system to determine the reliability of the proposed algorithm. Additionally, different system specifications were used, with variations in axial resolution, lateral resolution, signal-to-noise ratio, and real-time motion tracking. The accuracy of this method has further been evaluated through mean squared error (MSE) and multiscale structural similarity index measure (MS-SSIM). The results demonstrate improvements in the overall contrast of the images, facilitating detailed visualization of retinal vasculatures in both superficial and deep vasculature plexus. Finer features of the inner and outer retina, such as photoreceptors and other pathology-specific features, are discernible after multivolume registration and averaging. Quantitative analyses affirm that increasing the number of averaged registered volumes will decrease MSE and increase MS-SSIM as compared to the reference volume. The multivolume registered data obtained from this algorithm offers significantly improved visualization of the retinal microvascular network as well as retinal morphological features. Furthermore, we have validated that the versatility of our methodology extends beyond specific OCT modalities, thereby enhancing the clinical utility of OCT for the diagnosis and monitoring of ocular pathologies.

Data-based adaptive refinement of finite element thin plate spline

The thin plate spline, as introduced by Duchon, interpolates a smooth surface through scattered data. It is computationally expensive when there are many data points. The finite element thin plate spline (TPSFEM) possesses similar smoothing properties and is efficient for large data sets. Its efficiency is further improved by adaptive refinement that adapts the precision of the finite element grid. Adaptive refinement processes and error indicators developed for partial differential equations may not apply to the TPSFEM as it incorporates information about the scattered data. This additional information results in features not evident in partial differential equations. An iterative adaptive refinement process and five error indicators were adapted for the TPSFEM. We give comprehensive depictions of the process in this article and evaluate the error indicators through a numerical experiment with a model problem and two bathymetric surveys in square and L-shaped domains.

Motion-robust free-running volumetric cardiovascular MRI.

To present and assess an outlier mitigation method that makes free-running volumetric cardiovascular MRI (CMR) more robust to motion. The proposed method, called compressive recovery with outlier rejection (CORe), models outliers in the measured data as an additive auxiliary variable. We enforce MR physics-guided group sparsity on the auxiliary variable, and jointly estimate it along with the image using an iterative algorithm. For evaluation, CORe is first compared to traditional compressed sensing (CS), robust regression (RR), and an existing outlier rejection method using two simulation studies. Then, CORe is compared to CS using seven three-dimensional (3D) cine, 12 rest four-dimensional (4D) flow, and eight stress 4D flow imaging datasets. Our simulation studies show that CORe outperforms CS, RR, and the existing outlier rejection method in terms of normalized mean square error and structural similarity index across 55 different realizations. The expert reader evaluation of 3D cine images demonstrates that CORe is more effective in suppressing artifacts while maintaining or improving image sharpness. Finally, 4D flow images show that CORe yields more reliable and consistent flow measurements, especially in the presence of involuntary subject motion or exercise stress. An outlier rejection method is presented and tested using simulated and measured data. This method can help suppress motion artifacts in a wide range of free-running CMR applications.

Efficient pulse sequence design framework for high-dimensional MR fingerprinting scans using systematic error index.

For effective optimization of MR fingerprinting (MRF) pulse sequences, estimating and minimizing errors from actual scan conditions are crucial. Although virtual-scan simulations offer an approximation to these errors, their computational demands become expensive for high-dimensional MRF frameworks, where interactions between more than two tissue properties are considered. This complexity makes sequence optimization impractical. We introduce a new mathematical model, the systematic error index (SEI), to address the scalability challenges for high-dimensional MRF sequence design. By eliminating the need to perform dictionary matching, the SEI model approximates quantification errors with low computational costs. The SEI model was validated in comparison with virtual-scan simulations. The SEI model was further applied to optimize three high-dimensional MRF sequences that quantify two to four tissue properties. The optimized scans were examined in simulations and healthy subjects. The proposed SEI model closely approximated the virtual-scan simulation outcomes while achieving hundred- to thousand-times acceleration in the computational speed. In both simulation and in vivo experiments, the optimized MRF sequences yield higher measurement accuracy with fewer undersampling artifacts at shorter scan times than the heuristically designed sequences. We developed an efficient method for estimating real-world errors in MRF scans with high computational efficiency. Our results illustrate that the SEI model could approximate errors both qualitatively and quantitatively. We also proved the practicality of the SEI model of optimizing sequences for high-dimensional MRF frameworks with manageable computational power. The optimized high-dimensional MRF scans exhibited enhanced robustness against undersampling and system imperfections with faster scan times.

A decision-making approach on control techniques for an inverted pendulum based on, neuro-fuzzy, indirect adaptive and PID controllers

The operation of an inverted pendulum and its respective type of control are affected by the change of the values of its internal parameters. Changes with high uncertainty result in responses with undesirable outputs. In this work, a comparison is presented for the control of an inverted pendulum to determine the operation and characteristics of three types of control systems: Neuro-Fuzzy Control (NFC), Indirect Adaptive Control (IAC) and a Proportional Integral Derivative control (PID). The study considers several indices such as stabilization time, rise time, mean square error, overshoots, convergence, computational load, error, mathematical requirements, and performance indices for control systems. To demonstrate its operation, the controls are implemented in hardware, one for the NFC and another for the IAC under an Arduino UNO platform. The results indicate that the NFC and IAC controls do not generate a transient or impulse response, only a small delay and the rise and stabilization time are minimal. While PID presents a transient response and overshoot, as well as a stabilization time to reach the steady state response.

Deep learning for high-resolution seismic imaging

Seismic imaging techniques play a crucial role in interpreting subsurface geological structures by analyzing the propagation and reflection of seismic waves. However, traditional methods face challenges in achieving high resolution due to theoretical constraints and computational costs. Leveraging recent advancements in deep learning, this study introduces a neural network framework that integrates Transformer and Convolutional Neural Network (CNN) architectures, enhanced through Adaptive Spatial Feature Fusion (ASFF), to achieve high-resolution seismic imaging. Our approach directly maps seismic data to reflection models, eliminating the need for post-processing low-resolution results. Through extensive numerical experiments, we demonstrate the outstanding ability of this method to accurately infer subsurface structures. Evaluation metrics including Root Mean Square Error (RMSE), Correlation Coefficient (CC), and Structural Similarity Index (SSIM) emphasize the model's capacity to faithfully reconstruct subsurface features. Furthermore, noise injection experiments showcase the reliability of this efficient seismic imaging method, further underscoring the potential of deep learning in seismic imaging.

A Novel Accelerated Multistage Learning Control Mechanism via Virtual Performance Reduction.

This study uses a multistage learning mechanism concept to investigate the accelerated learning control for stochastic systems. In this mechanism, the learning iterations are divided into successive stages, with each stage comprising several iterations. The learning gain is constant in each stage to accelerate the learning process and decreases it from one stage to another to eliminate the noise effect asymptotically. The critical issue is determining the switching iteration when a new stage starts. This study resolves this issue by calculating a virtual performance index of the mean-squared input error and its estimated upper bound. Specifically, the ideal, practical, and improved multistage learning control schemes are proposed to determine the switching iteration and generate the learning gain sequence. The ideal scheme achieves the best performance at the cost of a large computation burden, and the practical scheme saves computation cost, but the performance is not excellent. The improved scheme significantly approximates the best performance by introducing additional stretching parameters to the performance index. Illustrative simulations are provided to verify the theoretical results.

Appropriate indicator of modeling error for threshold-based model selection in statistics-based ultrasound tissue characterization

Analysis of the envelope statistics of ultrasound echo signals contributes to quantitative tissue characterization in medical ultrasound. Many probability distribution model functions have been studied, and the model function that should be used for tissue characterization depends on the type of disease, even in the same organ. Thus, an appropriate model selection is important for an accurate diagnosis. In this study, we aimed to select a model using threshold processing for modeling errors instead of a simple selection by minimizing the modeling error. For this purpose, we compared several indicators of modeling errors using random number simulations, ultrasonic simulation, and phantom experiment. The results validated that the Mahalanobis distance of moments is an appropriate indicator because it enables the use of a constant threshold value, regardless of the type of model function and data length.

Groundwater Level Forecasting Using Machine Learning: A Case Study of the Baekje Weir in Four Major Rivers Project, South Korea

AbstractUnderstanding the impact of human‐made structures on groundwater levels is essential, with structures like dams or weirs presenting unique challenges and opportunities for study. The Baekje weir in South Korea presents an interesting case as the weir has undergone full gate opening, which is generally not the case for weirs and reservoirs, providing valuable opportunity for simulating weir removal conditions. The main objectives are investigation of groundwater level fluctuations under various weir operations, distances from the weir, and seasonal variations. The study utilizes observed data that simulates conditions with and without the weir, including scenarios of full gate opening. Multiple machine learning algorithms—Random Forest (RF), Artificial Neural Network, Support Vector Regression (SVR), Gradient Boosting, and Extreme Gradient Boosting (XGBoost)—are used to develop accurate groundwater level prediction models. The models' performance is assessed using coefficient of determination, Root mean square error (RMSE), Mean Absolute Error (MAE) indices, and visualized through Taylor diagrams. Results indicate that XGBoost outperforms other models in all three groups during both training and testing phases. Specifically, XGBoost surpasses RF by 2.09% (R2), 5.66% (RMSE), and 10.1% (MAE) in training, and outperforms SVR by 11.2% (R2), 42.0% (RMSE), and 129.2% (MAE) in testing. Additionally, the study generates groundwater level maps, providing a practical tool for managing groundwater systems and informing decision‐making in weir operations. This study not only sheds light on the dynamic relationship between weir operations and groundwater levels but also provides actionable insights for effective water management in similar hydrological settings.

Application of Tropical Rainfall Measuring Mission (TRMM) Data for Flood Estimation in Lack Data Catchment

Providing real-time hydrological data for the design, development and management of water resources is a fundamental issue that is still being faced by hydrologists and practitioners. This data limitation is not only caused by the uneven distribution of hydrological measuring instruments, but also due to the inability of measuring instruments to present the data in real time. This paper aims to evaluate hydrological data, especially spatial-based rainfall data known as Tropical Rainfall Measuring Mission (TRMM) data as an alternative to rainfall data to predict flood hydrographs in a catchment with limited data. The study was initiated by selecting pairs of automatic rainfall data (ARG) and water level (AWLR) and combined with TRMM rainfall data for the same time series. These two types of rainfall data are then used as input for the HEC-HMS hydrological model involving a number of catchment parameters, such as: basin area, stream network, land use/land cover (LULC), soil characteristics and several other parameters. Three analytical methods are assigned to determine the shape of the hydrograph which include: Snyder UH (transformation method), SCS-CN (loss method), and recession (baseflow method). Discharge data converted from water level data is input at the catchment outlet as a reference for setting calibration parameters which are evaluated with the RMSE error indicator. The simulation results show that the predicted discharge deviation from TRMM rainfall data is higher than the predicted discharge from ARG rainfall data with RMSE 0.979 and 1.731 respectively. However, basically this TRMM data can be an alternative data by validating it with ARG rain data to be applied to lack of catchment data.

Modeling and simulation of pollution transport in the Mediterranean Sea using enriched finite element method

This paper presents a novel numerical method for simulating the transport and dispersion of pollutants in the Mediterranean sea. The governing mathematical equations consist of a barotropic ocean model with friction terms, bathymetric forces, Coriolis and wind stresses coupled to an advection–diffusion equation with anisotropic dispersion tensor and source terms. The proposed numerical solver uses a multilevel adaptive semi-Lagrangian finite element method that combines various techniques, including the modified method of characteristics, finite element discretization, coupled projection scheme based on a rotational pressure correction algorithm, and an adaptive L2-projection. The approach employs the gradient of the concentration as an error indicator for enrichment adaptations and increasing the number of quadrature points where needed without refining the mesh. The method is shown to provide accurate and efficient simulations for pollution transport in the Mediterranean sea. The proposed approach distinguishes itself from the well-established adaptive finite element methods for incompressible viscous flows by retaining the same structure and dimension of linear systems during the adaptation process.

Multigoal-oriented a posteriori error control for heated material processing using a generalized Boussinesq model

In this work, we develop a posteriori error control for a generalized Boussinesq model in which thermal conductivity and viscosity are temperature-dependent. Therein, the stationary Navier–Stokes equations are coupled with a stationary heat equation. The coupled problem is modeled and solved in a monolithic fashion. The focus is on multigoal-oriented error estimation with the dual-weighted residual method in which an adjoint problem is utilized to obtain sensitivity measures with respect to several goal functionals. The error localization is achieved with the help of a partition-of-unity in a weak formulation, which is specifically convenient for coupled problems as we have at hand. The error indicators are used to employ adaptive algorithms, which are substantiated with several numerical tests such as one benchmark and two further experiments that are motivated from laser material processing. Therein, error reductions and effectivity indices are consulted to establish the robustness and efficiency of our framework.

Prediction of water consumption in Beijing based on the multi-variable grey model with adjacent accumulation

Abstract With the rapid development of the social economy, the importance of water resources is becoming increasingly prominent. Urban water demand in Beijing has been growing rapidly. Accurate water consumption forecasting is of utmost importance for reasonable allocation and optimization of water supply systems. In this study, an innovative multi-variable grey prediction model with adjacent accumulation (AOGM(1,N)) is proposed to predict Beijing's annual water consumption for four different water usage scenarios (domestic water, agricultural water, industrial water, and environmental water) by incorporating the adjacent accumulation into the optimized grey model. Grey relational analysis is used to select the key influence factors. The adjustable parameter of the prediction model is chosen by using the particle swarm optimization algorithm. By comparing with other models in the existing literature, the proposed AOGM(1,N) model has evidently superior prediction performance based on the error indicators, which supports the novel method's merits and validity. This study could help us better understand water usage and be applied to the planning and management problems of urban water supply systems.