Error Model Research Articles

Machine Learning for Mapping and Forecasting Poverty in North Sumatera: A Data-Driven Approach

Discussing poverty is crucial because it affects many facets of society, including socioeconomic disparity, crime, and the inability to obtain high-quality education. One of the provinces with the highest poverty rate in Indonesia is North Sumatra. A strategy is required to gather accurate data to effectively reduce poverty. Poverty mapping and prediction were conducted in North Sumatra to get a precise spatial distribution of poverty, the operation of the poverty model, and forecasting using machine learning (ML). Poverty prediction was conducted using a random forest (RF) algorithm and poverty mapping was conducted using the K-Means algorithm. The poverty mapping showed a significant inertia value decline in the third and fourth clusters of the elbow graph. The third cluster (0.313) was superior to the fourth cluster (0.244) in the silhouette index. Thus, there were three poverty clusters - low, medium, and high - that were used in the model. The best model was created using the grid search cross-validation, while the best prediction results were created using the RF algorithm, with the following parameters: n-estimator = 50, max depth = 10, min samples split = 2, and min samples leaf = 1. The mean squared error (MSE) of the RF model's predictions was 0.002617, or satisfactory precision.

Deep learning-based GLOF modelling for hazard assessment and risk management

ABSTRACT Glacial Lake Outburst Flood (GLOF) has become a crucial aspect as the increase in the meltdown of glaciers results in the breach of unstable debris dams. Hence, it is essential to understand the nature of the glacial lakes for proper planning and development of the region in the long term. In this paper, a deep learning network is developed for GLOF hazard and risk assessment. The Shepard Convolutional Neural Network Fused Deep Maxout Network (ShCNNFDMN) is developed by fusing the Shepard Convolutional Neural Networks (ShCNN) and the Deep Maxout Network (DMN) based on regression analysis. Here, various data and feature attributes, like geometric properties, location properties, lake-based properties, and global properties are determined from the glacial lake data. Afterthat, hazard assessment is carried out based on these parameters by the ShCNNFDMN. Then, risk assessment is performed based on the hazard levels and the feature attributes. The ShCNNFDMN is analyzed based on metrics, such as Hazard modelling error, Risk prediction error, Mean Average Error (MAE), and R-Squared are found to produce values of 0.462, 0.423, 0.358, and 0.288, respectively. The proposed method is useful in applications, like infrastructure planning, taking preventive and mitigative actions in downstream areas of glacier lakes.

Quantitative structure‐property relationship techniques for predicting carbon dioxide solubility in ionic liquids using machine learning methods

AbstractIonic liquids (ILs) are considered unique and attractive types of solvents with great potential to capture carbon dioxide (CO2) and reduce its emissions into the atmosphere. On the other hand, carrying out experimental measurements of CO2 solubility for each new IL is time‐consuming and expensive. Whereas, the possible combinations of cations and anions are numerous. Therefore, the preparation and design of such processes requires simple and accurate models to predict the solubility of CO2 as a greenhouse gas. In the present study, two different models, namely: artificial neural network (ANN) and support vector machine optimized with dragonfly algorithm (DA‐SVM) were used in order to establish a quantitative structure–property relationship (QSPR) between the molecular structures of cations and anions and the CO2 solubility. More than 10 116 CO2 solubility data measured in various ionic liquids (ILs) at different temperatures and pressures were collected. 13 significant PaDEL descriptors (E2M, MATS8S, TDB6I, TDB1S, ATSC4V, MATS8M, ATSC7V, Gats2S, Gats5S, Gats5C, ATSC6V, DE, and Lobmax), temperature and pressure were considered as the model input data. For the test set data (2023 data point), the estimated mean absolute error (MAE) and R2 for the ANN model are of 0.0195 and 0.9828 and 0.0219 and 0.9745 for the DA‐SVM model. The results obtained showed that both models can reliably predict the solubility of CO2 in ILs with a slight superiority of the ANN model. Examination of sensitivity and outlier diagnosis examinations confirmed that the QSPR model optimized using the ANN algorithm is better suited to correlate and predict this property.

An accelerated sequential function specification method based on LM gradient for transient inverse heat conduction problem

The sequential function specification method (SFSM) and the Levenberg-Marquardt method (LM) are two typical methods for inverse heat conduction problems (IHCP). However, these two methods have poor convergence and low convergence speed. Therefore, the combination of LM with SFSM is depended on to propose a modified Sequential Levenberg-Marquardt gradient method (SLM). The computation results of three shapes of heat fluxes with noise show the SLM is averagely improved over 16.3% more than SFSM in computation accuracy, but equally reduced over 39.9% less than in computation time. On other hand, when the emphasis is on the effect of the Aitken acceleration method, Tikhonov regularization and polynomial order on SLM, a neural network prediction model of the root mean square error is trained by regularization factor, polynomial order and the number of future time steps. Subsequently, the genetic algorithm optimization method is proposed for the minimum root mean square error so that it can improve the computation accuracy and efficiency of IHCP to the maximum extent. Finally, Second-order polynomial order and small order-of-magnitude regularization factor are highly recommended for parameter selection with multiple choices. The ASLM only needs to determine the optimal number of future time steps.

Model Predictive Control based on Long-Term Memory neural network model inversion

Long Short-Term Memory (LSTM) neural networks are well suited for representing time series as, compared to other neural networks, their structure avoids vanishing or exploding gradients. LSTM has been embedded into Model Predictive Control algorithms in order to forecast the behavior of nonlinear systems. The new algorithm presented in the paper is of a different nature, as the LSTM network approximates the inverse of the system over a receding horizon and provides a sequence of future inputs as a function of a specified output trajectory. The main advantage of the method appears when the desired output trajectory is generated from a small set of parameters, for example, a convergence rate. The Model Predictive control optimizes its criterion with respect to this small set of variables, and the LSTM supplies the corresponding future control inputs. Eventually, the modeling error of the LSTM can be compensated by feeding the control sequence to the forward model and updating the controller according to the output deviation. The algorithm allows to design Model Predictive controllers for nonlinear systems in a generic way, using a very small number of decision variables even with a long receding horizon.

Subspace-based noise covariance estimation for Kalman filter in virtual sensing applications

The accuracy of the Kalman filter in state estimation depends on the knowledge of the process and measurement noise covariances. These are usually treated as tuning parameters and adjusted in a heuristic manner to fine-tune the state predictions. While several methods to identify the noise covariance from data exist, some require the use of optimization algorithms, or inversion of large matrices, which is numerically inefficient. In this work we explore a direct approach to estimate the covariance of possibly correlated process and measurement noises, which is based on subspace identification. It is shown that the subspace-based method outperforms the established autocovariance least-squares scheme and provides a good initial guess on the noise covariance in case the system is subjected to model errors. We validate the proposed scheme on a laboratory experiment, where it is shown that the predictions of the system outputs at sensor locations that are not used as observations in the identification procedure match well with the actual measurements.

Formulating approximation error as noise in surrogate-assisted multi-objective evolutionary algorithm

Many real multi-objective optimization problems with 20-50 decision variables often have only a small number of function evaluations available, because of their heavy time/money burden. Therefore, surrogate models are often utilized as alternatives for expensive function evaluations. However, the approximation error of the surrogate model is inevitable compared to the real function evaluation. The approximation error has a similar impact on the algorithm as noise, i.e., different optimization stages suffer from various impacts. Therefore, the current optimization stage can be indirectly detected via measuring the impact of the noise formulated by the approximation error. In addition, the rising dimension of the search space leads to an increase in the approximation errors of the surrogate models, which poses a huge challenge for existing surrogate-assisted multi-objective evolutionary algorithms. In this work, we propose a stage-adaptive surrogate-assisted multi-objective evolutionary algorithm to solve the medium-scale optimization problems. In the proposed algorithm, the ensemble model consisting of the latest and historical models is used as the surrogate model, on the basis of which a set of potential candidates can be discovered. Then, a stage-adaptive infill sampling strategy selects the most suitable sampling strategy by analyzing the demand of the current optimization stage on convergence, diversity, model accuracy to sample from the candidates. As for the current optimization stage, it is detected by a noise impact indicator, where the approximation errors of surrogate models are formulated as noise. The experimental results on a series of medium-scale expensive test problems demonstrate the superiority of the proposed algorithm over six state-of-the-art compared algorithms.

Pose Selection Based on a Hybrid Observation Index for Robotic Accuracy Improvement

The problem of the insufficient accuracy performance of industrial robots in high-precision manufacturing is addressed in this paper. Firstly, a kinematic error model based on an M-DH model was presented. Secondly, a hybrid observability index O6 was proposed to select the optimal poses for parameter identification. O6 is the combination of O1 and O3. The optimal poses were obtained by using the IOOPS algorithm. Thirdly, the fitness function for parameter identification was established, and the Levenberg–Marquardt (LM) algorithm was applied for the accurate identification of kinematic parameter errors. Finally, several experiments were conducted to evaluate the performance of the proposed hybrid observability index O6. The average position error and average attitude error of Staubli TX60 robot were reduced by 89% and 49%. The results show that the proposed hybrid observability index O6 has great stability and effectiveness for robot calibration.

A Spin-Optical Quantum Computing Architecture

We introduce an adaptable and modular hybrid architecture designed for fault-tolerant quantum computing. It combines quantum emitters and linear-optical entangling gates to leverage the strength of both matter-based and photonic-based approaches. A key feature of the architecture is its practicality, grounded in the utilisation of experimentally proven optical components. Our framework enables the execution of any quantum error correcting code, but in particular maintains scalability for low-density parity check codes by exploiting built-in non-local connectivity through distant optical links. To gauge its efficiency, we evaluated the architecture using a physically motivated error model. It exhibits loss tolerance comparable to existing all-photonic architecture but without the need for intricate linear-optical resource-state-generation modules that conventionally rely on resource-intensive multiplexing. The versatility of the architecture also offers uncharted avenues for further advancing performance standards.

Prediction of Surface Subsidence in Mining Areas Based on Ascending-Descending Orbits Small Baseline Subset InSAR and Neural Network Optimization Models

Surface subsidence hazards in mining areas are common geological disasters involving issues such as vegetation degradation and ground collapse during the mining process, which also raise safety concerns. To address the accuracy issues of traditional prediction models and study methods for predicting subsidence in open-pit mining areas, this study first employed 91 scenes of Sentinel-1A ascending and descending orbits images to monitor long-term deformations of a phosphate mine in Anning City, Yunnan Province, southwestern China. It obtained annual average subsidence rates and cumulative surface deformation values for the study area. Subsequently, a two-dimensional deformation decomposition was conducted using a time-series registration interpolation method to determine the distribution of vertical and east–west deformations. Finally, three prediction models were employed: Back Propagation Neural Network (BPNN), BPNN optimized by Genetic Algorithm (GA-BP), and BPNN optimized by Artificial Bee Colony Algorithm (ABC-BP). These models were used to forecast six selected time series points. The results indicate that the BPNN model had Mean Absolute Errors (MAE) and Root Mean Squared Errors (RMSE) within 7.6 mm, while the GA-BP model errors were within 3.5 mm, and the ABC-BP model errors were within 3.7 mm. Both optimized models demonstrated significantly improved accuracy and good predictive capabilities.

An improved transmission efficiency prediction method for nonlinear characteristics of the cycloid reducer

This study aims to accurately predict the nonlinear characteristics of transmission efficiency of cycloid reducers under different operating conditions. Firstly, equivalent modeling of the multi-source errors (MSEs) in the designed cycloid reducer is conducted. Force analysis algorithms considering MSEs are proposed for the cycloid drive mechanism, the output mechanism, and the bearings. Secondly, mathematical models are established for the load-dependent power losses, while an equivalent test is used for modeling load-independent power losses. Subsequently, an improved transmission efficiency prediction (TEP) method for cycloid reducers is proposed, which is then applied to the performance prediction of a prototype under different operating conditions. The advantages of the improved TEP method over the conventional method are discussed, and the influences of MSEs and load-independent power losses on the nonlinear characteristics of transmission efficiency are summarized. Finally, tests are conducted for the reducer prototype, and the test results are found to be in good agreement with the results obtained by the proposed TEP method. The main contribution of this study is to establish a solid algorithmic and modeling foundation for the optimal design of nonlinear transmission efficiency in cycloid reducers and provide reliable guidance for their engineering applications.

Residual stresses prediction in transition metal nitrides sputtered coatings using artificial neural network and experimental evaluation of surface morphology

In the production of transition metal nitride hard coatings under specific deposition conditions, the resulting residual stresses play a critical role in determining the mechanical properties, adhesion, and overall performance of the coatings. In this work, an artificial neural network (ANN) that utilizes feed-forward architecture is used to predict the average residual stress in titanium nitride (TiN) coatings with different coating thickness. These coatings are manufactured under varying bias voltages and temperature on substrate. The impact of variations in coating thickness, bias voltage, and temperature on development of internal residual stresses and changes in microstructure within sputtered coatings have been gathered from existing literature. The data collected is within the context of fibrous (zone I) and mix columnar and fibrous structure (combined zone) as defined by an existing structure zone model. The model is trained with experimental data from literature. The model is trained with experimental data from literature. The validation of the ANN model is carried out by comparing the predictions with experimental results. X-ray diffraction is used to analyze the residual stresses, preferred orientation, and the structure (zone I and combined zone) of produced coatings under different sputtering parameters. The regression and performance curves are used to assess the efficacy of ANN model. The coefficient of determination of trained model and mean square error are 0.9918 and 0.35, respectively. The predicted results show good agreement with experimental and subsequently AFM grain morphology analysis captures the growth mechanisms involved in the residual stresses evolution.

Spatial dependence and poverty factors: A study of Pantura Regions in East Java Province, Indonesia

Poverty is still a problem in various countries in the world, so eradicating poverty and hunger by 2030 is the backbone of the goals of the sustainable development agenda. Poverty, which is the main goal of the Millennium Development Goals (MDGs), is again the main goal in the Sustainable Development Goals (SDGs). This research aims to determine the spatial dependence of poverty in the Pantura Region of East Java Province and to determine the influence of economic growth, education, unemployment, natural resources, health and accessibility on poverty in the Pantura Region of East Java Province. This research uses a quantitative approach, with data analysis methods using Moran’s index analysis, and spatial panel regression by selecting the best model from four models, namely the spatial autoregressive model (SAR), the spatial error model (SEM), the spatial Durbin model (SDM), and spatial autoregressive combined (SAC) model. The research results show that there is spatial interaction between coastal areas through endogenous and exogenous interactions between independent variables. Based on the selection of the best model, the spatial Durbin model (SDM) was selected for the Pantura Region. Economic growth has a negative effect on poverty. Education has a negative effect on poverty. Unemployment has no effect on poverty. Natural resources have a positive effect on poverty. Health has no effect. Accessibility has a negative effect on poverty in the Pantura Region. This research provides a new and important contribution in understanding the spatial patterns of poverty and the factors that influence it in the Pantura Region, which is a strategic and vulnerable area in East Java. This research also faces several limitations and challenges, such as data quality, model assumptions, and spatial validity. Future research could expand this analysis using more complete data, more flexible models, and more sophisticated techniques.

A Comprehensive Evaluation of Black Carbon in Snow and Its Radiative Forcing in CMIP5 and CMIP6 Models Based on Global Field Observations

AbstractBlack carbon in snow (BCS) is a crucial parameter in Earth System modeling, as it influences global radiative balance. Here, simulated BCS from Coupled Model Intercomparison Project Phase 5 and 6 (CMIP5 and CMIP6) that provided BCS as a model output were evaluated. In comparison with global BCS observations, CMIP5/6 models successfully reproduced long‐term historical trends linked to human activities, but struggled capturing decadal variability caused by natural climate variability. CMIP6 models NorESM2‐MM, NorESM2‐LM, and TaiESM1 yielded the most accurate simulations of BCS concentration with modest overestimation of <50%, while the four CESM2 models underestimated concentrations by up to ∼80%. These errors effectively balanced for the CMIP6 multi‐model ensemble mean (MME), which had a relative error (RE) of −37%. However, the CMIP5 MME was less reliable due to extreme overestimation by up to 8,000% in the three MIROC models. The significant BCS concentration errors in the MIROC and CESM2 models were linked mainly to errors in handling of BC in snow processes. Conversely, marked improvements in NorESM, the only common to both CMIP5 and CMIP6, were due to improved simulation of black carbon deposition. BCS errors significantly impacted radiative forcing estimates, particularly at the poles, where model errors reached several thousandfold. CMIP6 exhibited superior results compared to CMIP5, achieving global MME RE of −33% in radiative forcing estimates. However, it's worth noting BCS output is currently limited, with only seven models available for each of CMIP5 and CMIP6 here. Additional models simulating BCS are desirable in the next CMIP generations.

Dynamics Modeling and Parameter Identification for a Coupled-Drive Dual-Arm Nursing Robot

A dual-arm nursing robot can gently lift patients and transfer them between a bed and a wheelchair. With its lightweight design, high load-bearing capacity, and smooth surface, the coupled-drive joint is particularly well suited for these robots. However, the coupled nature of the joint disrupts the direct linear relationship between the input and output torques, posing challenges for dynamic modeling and practical applications. This study investigated the transmission mechanism of this joint and employed the Lagrangian method to construct a dynamic model of its internal dynamics. Building on this foundation, the Newton-Euler method was used to develop a dynamic model for the entire robotic arm. A continuously differentiable friction model was incorporated to reduce the vibrations caused by speed transitions to zero. An experimental method was designed to compensate for gravity, inertia, and modeling errors to identify the parameters of the friction model. This method establishes a mapping relationship between the friction force and motor current. In addition, a Fourier series-based excitation trajectory was developed to facilitate the identification of the dynamic model parameters of the robotic arm. Trajectory tracking experiments were conducted during the experimental validation phase, demonstrating the high accuracy of the dynamic model and the parameter identification method for the robotic arm. This study presents a dynamic modeling and parameter identification method for coupled-drive joint robotic arms, thereby establishing a foundation for motion control in humanoid nursing robots.

Research on stochastic error suppression method of FOG based on quasi-proportional information

Abstract In order to improve the precision of fiber optic gyro (FOG), it is necessary to suppress the stochastic error effectively. Therefore, the stochastic error suppression of FOG is studied. Firstly, the data of FOG at room temperature and variable temperature are analyzed. Then, a general form of FOG random error model is derived, and an adaptive filtering method based on quasi-proportional information is proposed to estimate the process noise covariance effectively. At last, the room temperature experiment, the variable temperature experiment and the dynamic experiment are carried out. Compared with the recently proposed adaptive filter algorithm, the variance reduction of the proposed algorithm at the average time of 33 s, 54 s and 55 s is more than 70%, and the suppression effect of the algorithm on the random walk coefficient is improved by more than 2%, showing strong robustness.

MOB-Net: Limb-modularized uncertainty torque learning of humanoids for sensorless external torque estimation

Momentum observer (MOB) can estimate external joint torque without requiring additional sensors, such as force/torque or joint torque sensors. However, the estimation performance of MOB deteriorates due to the model uncertainty which encompasses the modeling errors and the joint friction. Moreover, the estimation error is significant when MOB is applied to high-dimensional floating-base humanoids, which prevents the estimated external joint torque from being used for force control or collision detection in the real humanoid robot. In this paper, the pure external joint torque estimation method named MOB-Net, is proposed for humanoids. MOB-Net learns the model uncertainty torque and calibrates the estimated signal of MOB, substantially reducing the estimation errors of MOB. The external joint torque can be estimated in the generalized coordinate including whole-body and virtual joints of the floating-base robot with only internal sensors (an IMU on the pelvis and encoders in the joints). Furthermore, MOB-Net shows more robust performance for the unseen data compared to the end-to-end learning method, and the robustness of MOB-Net is validated through extensive simulations, real robot experiments, and ablation studies. Finally, various collision handling scenarios are presented to show the versatility of MOB-Net: contact wrench feedback control for locomotion, collision detection, and collision reaction for safety.

Simultaneous compensation of geometric and compliance errors for robotics with consideration of variable payload effects

In order to satisfy the high accuracy requirements of robotic applications, it is necessary to consider not only the geometric errors but also the compliance errors which are caused by the self-gravity of the link and the external payloads. A general error model is developed based on the modified Denavit-Hartenberg (DH) model. For the parameters in the error model, there is a coupling between the compliance coefficients and the link parameters, making it difficult to use only the compliance coefficients to compute the compliance errors due to external payloads. As the external payload for the robot manipulator varies, the parameter identification of the model should be conducted again. In this paper, a novel algorithm using a variable payload method is proposed to first identify the compliance coefficients using different payloads and end effector position information. Second, the kinematic parameter errors and link parameters are identified with the given compliance coefficients. Then, the algorithm generates a modified trajectory using the calibrated DH tables for the precision compensation. Simulation and experimental results demonstrate that the positioning accuracy can be improved by 80 % to 90 % even under different payloads. The root mean square, mean, maximum, and standard deviation of the residual errors by using the proposed algorithm could outperform the conventional kinematic algorithm.

Learning from models: high-dimensional analyses on the performance of machine learning interatomic potentials

Machine learning interatomic potential (MLIP) has been widely adopted for atomistic simulations. While errors and discrepancies for MLIPs have been reported, a comprehensive examination of the MLIPs’ performance over a broad spectrum of material properties has been lacking. This study introduces an analysis process comprising model sampling, benchmarking, error evaluations, and multi-dimensional statistical analyses on an ensemble of MLIPs for prediction errors over a diverse range of properties. By carrying out this analysis on 2300 MLIP models based on six different MLIP types, several properties that pose challenges for the MLIPs to achieve small errors are identified. The Pareto front analyses on two or more properties reveal the trade-offs in different properties of MLIPs, underscoring the difficulties of achieving low errors for a large number of properties simultaneously. Furthermore, we propose correlation graph analyses to characterize the error performances of MLIPs and to select the representative properties for predicting other property errors. This analysis process on a large dataset of MLIP models sheds light on the underlying complexities of MLIP performance, offering crucial guidance for the future development of MLIPs with improved predictive accuracy across an array of material properties.

Short-Term Photovoltaic Power Prediction Based on a Digital Twin Model

Due to the influence of meteorological conditions, shipboard photovoltaic (PV) systems have problems such as large fluctuation and inaccurate prediction of the output power. In this paper, a short-term PV power prediction method based on a novel digital twin (DT) model and BiLSTM is proposed. Firstly, a PV mechanism model and a data-driven model were established, in which the data-driven model was updated iteratively in real time using the sliding time window update method; then, these two models were converged to construct a PV DT model according to the DS evidence theory. Secondly, a BiLSTM model was built to make short-term predictions of the PV power using the augmented dataset of the DT model as an input. Finally, the method was tested and verified by experiments and further compared with main PV prediction methods. The research results indicate the following: firstly, the absolute error of the DT model was smaller than that of the mechanism model and the data-driven model, being as low as 5.62 W after the data update of the data-driven model; thus, the DT model realized data augmentation and high fidelity. Secondly, compared to several main PV prediction models, the PV DT model combined with BiLSTM had the lowest RMSE, MAE, and MAPE; the best followability; and the smallest absolute error under different weather conditions, which was especially obvious under cloudy weather conditions. In summary, the method can accurately predict the shipboard PV power, which has great theoretical significance and application value for improving the economy and reliability of solar ship operation.