Absolute Estimation Error Research Articles

Construction of an analytical method for limiting the complexity of neural-fuzzy models with guaranteed accuracy

We have proposed an analytical method for limiting the complexity of neural-fuzzy models that provide for the guaranteed accuracy of their implementation when approximating functions with two or more derivatives. The method makes it possible to determine the required minimal number of parameters for systems that employ fuzzy logic, as well as neural models. We have estimated the required number of neurons (terms) in a model, which ensure the accuracy required for the area of a model curve to approach the system one along the sections of function approximation. The estimate for an approximation error was obtained based on the residual members of decomposition, in the Lagrangian form, of areas of the approximated system function into a Maclaurin series. The results received make it possible to determine the required number of approximation sections and the number of neurons (terms) in order to ensure the assigned relative and absolute error of approximation. We have estimated the required number of neurons (terms) that provide for the necessary accuracy of model implementation based on the maximum deviation between the system and model curves along the section of approximation. This makes it possible to select, depending on the assigned required accuracy, the number of terms of fuzzy variables, input and output variables, linguistic rules, coordinates of modal values along the axes of input and output variables. To verify validity of the proposed solutions, we modeled the system curves in the Matlab/Simulink environment, which confirmed the guaranteed accuracy of their implementation in accordance with the analytical calculations reported earlier. The results obtained could be applied in modern intelligent technical systems of management, control, diagnosis, and decision-making. Using the proposed methods for selecting and applying the minimal number of terms (neurons) would help reduce the required computing power in nonlinear systems

Design and Evaluation of a Multidirectional Thermal Flow Sensor on Flexible Substrate

The development and the corresponding evaluation of a multidirectional thermal flow sensor are presented in this work. The sensor was fabricated on a flexible substrate, allowing for new applications, since it provides the possibility of installation in nonplanar surfaces such as pipelines. Furthermore, the sensing elements are not in direct contact with the fluid, which increases the device reliability, extends its application range, and allows the noncontact monitoring of fluids. This was achieved by utilizing the substrate as a protective layer between the sensing elements and the fluid under measurement. The operation principle is based on the determination of the flow-induced temperature profile variations. A dedicated experimental setup was designed and used for the device evaluation. Both flow velocity value and direction were successfully extracted, while the results were consistent with the predicted theoretical values. A single-layer back propagation neural network that correlates the sensors’ readouts to the angle of rotation was implemented, which leads to a mean absolute direction estimation error in the order of 2.7 degrees independent to the training procedure datasets.

Estimation of Leaf Inclination Angle in Three-Dimensional Plant Images Obtained from Lidar

The leaf inclination angle is a fundamental variable for determining the plant profile. In this study, the leaf inclination angle was estimated automatically from voxel-based three-dimensional (3D) images obtained from lidar (light detection and ranging). The distribution of the leaf inclination angle within a tree was then calculated. The 3D images were first converted into voxel coordinates. Then, a plane was fitted to some voxels surrounding the point (voxel) of interest. The inclination angle and azimuth angle were obtained from the normal. The measured leaf inclination angle and its actual value were correlated and indicated a high correlation (R2 = 0.95). The absolute error of the leaf inclination angle estimation was 2.5°. Furthermore, the leaf inclination angle can be estimated even when the distance between the lidar and leaves is about 20 m. This suggests that the inclination angle estimation of leaves in a top part is reliable. Then, the leaf inclination angle distribution within a tree was calculated. The difference in the leaf inclination angle distribution between different parts within a tree was observed, and a detailed tree structural analysis was conducted. We found that this method enables accurate and efficient leaf inclination angle distribution.

Lithium-ion battery modeling based on Big Data

Battery is the bottleneck technology of electric vehicles. The complex chemical reactions inside the battery are difficult to monitor directly. The establishment of a precise mathematical model for the battery is of great significance in ensuring the secure and stable operation of the battery management system. First of all, a data cleaning method based on machine learning is put forward, which is applicable to the characteristics of big data from batteries in electric vehicles. Secondly, this paper establishes a lithium-ion battery model based on deep learning algorithm and the error of model based on different algorithms is compared. The data of electric buses are used for validating the effectiveness of the model. The result shows that the data cleaning method achieves good results, in the case of the terminal voltage missing, the mean absolute percentage error of filling is within 4%, and the battery modeling method in this paper is able to simulate the battery characteristics accurately, and the mean absolute percentage error of the terminal voltage estimation is within 2.5%.

Three-Dimensional Monitoring of Plant Structural Parameters and Chlorophyll Distribution.

Image analysis is widely used for accurate and efficient plant monitoring. Plants have complex three-dimensional (3D) structures; hence, 3D image acquisition and analysis is useful for determining the status of plants. Here, 3D images of plants were reconstructed using a photogrammetric approach, called “structure from motion”. Chlorophyll content is an important parameter that determines the status of plants. Chlorophyll content was estimated from 3D images of plants with color information. To observe changes in the chlorophyll content and plant structure, a potted plant was kept for five days under a water stress condition and its 3D images were taken once a day. As a result, the normalized Red value and the chlorophyll content were correlated; a high R2 value (0.81) was obtained. The absolute error of the chlorophyll content estimation in cross-validation studies was 4.0 × 10−2 μg/mm2. At the same time, the structural parameters (i.e., the leaf inclination angle and the azimuthal angle) were calculated by simultaneously monitoring the changes in the plant’s status in terms of its chlorophyll content and structural parameters. By combining these parameters related to plant information in plant image analysis, early detection of plant stressors, such as water stress, becomes possible.

A New State of Charge Estimation Method for Lithium-Ion Battery Based on the Fractional Order Model

This paper presents that the fractional order Kalman filter (FOKF) method is used to estimate the state of charge (SOC) for lithium-ion battery based on the fractional order model. First, a fractional order battery model was established which can better reflect the dynamic characteristics of the battery. The fractional orders were identified by genetic algorithm. Then, compared with three other modeling methods in four aspects: maximum absolute error, maximum relative error, computational complexity and number of model parameters, it is shown that the fractional order model proposed in this paper is more accurate and reliable. The results shows that the maximum absolute error of the terminal voltage is 0.014 V under constant current discharge test. The accuracy improves 0.058 V comparing to the integer order model. Finally, the SOC was estimated through two methods. The results shows that the maximum absolute estimation error of SOC is under 0.02 by FOKF, which has higher accuracy and faster convergence speed compared with extend Kalman filter (EKF) method.

A system for supporting practice of lure casting using acceleration and gyroscope sensors

For practice of lure casting, information on fly distance of lure and information on rod motion are helpful. In this letter, we propose a system for supporting practice of lure casting. In our system, a sensor device with acceleration and gyroscope sensors is attached at a rod and it collects sensor data during casting motion to estimate fly distance. The estimated fly distance and sensor data are displayed at a user's mobile device. Through experimental evaluations, we confirmed that the mean absolute error of fly distance estimation of our proposed system is 1.376 m. © 2018 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

CFD-PBM simulations of a pulsed sieve plate column

A 2D computational model coupling two-phase CFD and population balance equations is used to predict dispersed phase holdup and Sauter mean drop diameter in a pulsed sieve plate column which is relevant for solvent extraction in nuclear fuel cycle. Spatial and temporal variations of drop diameter are captured by the model. Population balance equations consider both drop breakage and coalescence in the column. Standard breakage and coalescence kernels are used to model breakage and coalescence rates. The model is validated using reported experimental data of dispersed phase holdup and Sauter mean drop diameter. In the first round of simulations standard Kumar-Hartland drag model is used to model the interphase momentum exchange. The average absolute relative error in estimation of dispersed phase holdup and Sauter mean diameter are found to be 13.6% and 8.5%, respectively. Optimization of the model constants of Kumar-Hartland drag model is done to reduce the error in dispersed phase holdup prediction to 5.6%.

Regional risks of artificial forestation in the steppe zone of Kazakhstan (case study of the green belt of Astana)

This article deals with results of research on artificial forest in a green zone around the city of Astana. The authors of the article established temporary sample plots where condition, capacity for survival, and growth of trees were observed by standard techniques adapted to conditions of the forest-steppe subzone of Northern Kazakhstan. The reasons for the unsatisfactory condition of the planted forest were found and recommendations on improvement were made. The conclusion was drawn that to establish forest plantations it is necessary to select such species of trees and shrubs that will be resistant in specific conditions to the negative factors of urban lands. A possibility of replanting adult trees to intensify reforestation was also studied. The authors analyzed the dynamics of Silver birch preservation in 2011-2017. The Mann-Whitney-Wilcoxon U test was used to prove the presence of differences between the types of trees’ average preservations. Based on the data thus obtained, it was concluded that the forest plantations created by the different methods differed significantly in terms of the preservation rate, as well as in the heights and diameters of the trees. Forecasts of tree preservations in 2018 were made using moving average and linear regression methods. The best forecasts were chosen in terms of the mean relative absolute error of approximation. The results confirmed an initial hypothesis predicting significant differences between the methods used for artificial reforestation: the non-replanted trees are expected to have the highest rate of preservation, whereas the trees replanted to a low location, the lowest preservation rate. The prediction of the preservation rate of forest plantations of Silver birch created by the different methods will allow reducing the risks when conducting forestry activities on artificial reforestation. Regional features must be taken into account in the development of recommendations for a comprehensive system of measures which are based on the scientific forestry techniques to ensure optimum reforestation.

Distortions of perceived volume and length of body parts

We experience our body as a 3D, volumetric object in the world. Measures of our conscious body image, in contrast, have investigated the perception of body size along one or two dimensions at a time. There is, thus, a discrepancy between existing methods for measuring body image and our subjective experience of having 3D body. Here we assessed in a sample of healthy adults the perception of body size in terms of its 1D length and 3D volume. Participants were randomly assigned to two groups using different measuring units (other body part and non-body object). They estimated how many units would fit in a perceived size of body segments and the whole body. The patterns of length and volume misperception across judged segments were determined as their perceived size proportional to their actual size. The pattern of volume misperception paints the representation of 3D body proportions resembling those of a somatosensory homunculus. The body parts with a smaller actual surface area relative to their volume were underestimated more. There was a tendency for body parts underestimated in volume to be overestimated in length. Perceived body proportions thus changed as a function of judgement type while showing a similarity in magnitude of the absolute estimation error, be it an underestimation of volume or overestimation of length. The main contribution of this study is assessing the body image as a 3D body representation, and thus extending beyond the conventional ‘allocentric’ focus to include the body on the inside. Our findings highlight the value of studying the perceptual distortions “at the baseline”, i.e., in healthy population, so as to advance the understanding of the nature of perceptual distortions in clinical conditions.

On modeling reference crop evapotranspiration under lack of reliable data over Iran

This study was conducted to evaluate the performance of temperature-based models i.e. temperature-based Penman-Monteith FAO 56 fed with average wind speed (U) value (TPMU) and default U quantity (TPM2), Hargreaves-Samani (HS) and FAO Blaney-Criddle (FBC) against Penman-Monteith FAO 56 (PM) using data recorded in 1993–2015 at 146 sites over Iran. Two statistics i.e. normalized Root Mean Square (nRMSE) and relative Mean Bias Error (rMBE) were calculated to analyze the absolute error and bias magnitude of the temperature-based ET0 estimation, respectively. Except for the December-January-February (DJF), the models gave reliable seasonal estimates (i.e. nRMSE of 30 > %) for the majority of studied areas. At monthly scale, FBC gave poor estimates of ET0 in DJF for more than 60% of semi-arid and sub/humid-humid sites. ET0 in December and January was not also modeled reliably by TPM2 for 61 and 52% of the semi-arid and sub/humid-humid sites, respectively. Hence, application of FBC and TPM2 appears not to be recommendable in cold areas and months over Iran. Overall, TPMU and HS are better suited at all temporal scales under data limitation over the studied areas. In the case of data availability, calculation of TPM with local average U (instead of default quantity of 2 m s−1) is highly likely to improve the estimation accuracy. Seasonal and monthly ET0 were mostly underestimated over the hyper-arid/arid sites during the March-April-May (MAM) and June-July-August (JJA). However, TPM2 and HS overestimated ET0 for the majority of semi-arid and sub-humid/humid areas. The U anomalies were identified as the primary contributing factor to the error in temperature-based ET0 estimation for most cases. TPM2, HS and FBC provided more accurate estimates for the U range of 1.5–2.5 m s−1. These findings are of significant practical importance for agricultural, hydrological and climatic studies and applications under data sparse condition.

A numerical solution for the inhomogeneous Dirichlet boundary value problem on a non-convex polygon

In this paper, we introduce an effective finite element scheme for the Poisson problem with inhomogeneous Dirichlet boundary condition on a non-convex polygon. Due to the corner singularities, the solution is composed of a singular part not belonging to the Sobolev space H2 and a smoother regular part. We first provide a generalized extraction formula for the coefficient of singular part, which is depending on the inhomogeneous boundary condition and the regular part. We then propose a stable finite element method for the regular part by the use of the derived formula. We show the H1 and L2 error estimates of the finite element solution for the regular part and the absolute error estimate of the approximation for the coefficient of singular part. Finally, we give some numerical examples to confirm the efficiency and reliability of the proposed method.

Predicting models of leaf area for trees in Larix olgensis plantation.

Leaf area influences dry matter production of trees, as well as the growth of trees and forest stands. The accurate estimation of leaf area plays an important role in analyzing the growth of trees and forest stands. Based on data of 76 Larix olgensis trees in a plantation of Heilongjiang Province, predicting models of branch leaf area (BLA) and crown leaf area (CLA) were constructed, respectively. The results showed that a form of lnBLA=β1+(β2+b2)lnBD+(β3+b3)lnRDINC+β4lnDBH+β5lnHT/DBH+(β6+b6)lnCR was selected as the optimal BLA mixed-effect model with the considera-tion of tree-level random effects, composed of three random-effect on lnBD, lnRDINC and lnCR (βi represented model fixed parameters, bi represented model random-effect parameters, BD was branch diameter, RDINC was the relative depth into crown from tree apex, DBH was tree diameter at breast height, HT/DBH represented the ratio of tree height to DBH, and CR represented the ratio of crown length to tree height). The adjusted coefficient of determination (Ra2), residual mean squares error (RMSE), mean error (ME), mean absolute error (MAE) and precision estimation (P) of the optimal BLA mixed model were 0.90, 0.5477, -0.03, 0.24 and 91%, respectively, indicating the model had a good performance in predicting. The CLA was calculated by predicted values of all branches based on developed BLA model and the final form of CLA model was as follows: lnCLA=γ0+γ1lnDBH+γ2CR (γi, model parameters). Results of likelihood ratio test (P>0.05) showed that plot-level random effect had no influence on the model performance, which can be ignored. The CLA model got a good-fitting effect with R2 and RMSE being 0.87 and 0.3847, respectively. The CLA predicting model developed in this study could provide a good prediction of CLA for L. olgensis trees and provided a theoretical basis for the research on distribution of leaf area and photosynthesis.

Estimation of Energy Expenditure in Wheelchair-Bound Spinal Cord Injured Individuals Using Inertial Measurement Units

A healthy lifestyle reduces the risk of cardio-vascular disease. As wheelchair-bound individuals with spinal cord injury (SCI) are challenged in their activities, promoting and coaching an active lifestyle is especially relevant. Although there are many commercial activity trackers available for the able-bodied population, including those providing feedback about energy expenditure (EE), activity trackers for the SCI population are largely lacking, or are limited to a small set of activities performed in controlled settings. The aims of the present study were to develop and validate an algorithm based on inertial measurement unit (IMU) data to continuously monitor EE in wheelchair-bound individuals with a SCI, and to establish reference activity values for a healthy lifestyle in this population. For this purpose, EE was measured in 30 subjects each wearing four IMUs during 12 different physical activities, randomly selected from a list of 24 activities of daily living. The proposed algorithm consists of three parts: resting EE estimation based on multi-linear regression, an activity classification using a k-nearest-neighbors algorithm, and EE estimation based on artificial neural networks (ANNs). The mean absolute estimation error for the ANN-based algorithm was 14.4% compared to indirect calorimeter measurements. Based on reference values from the literature and the data collected within this study, we recommend wheeling 3 km per day for a healthy lifestyle in wheelchair-bound SCI individuals. Combining the proposed algorithm with a recommendation for physical activity provides a powerful tool for the promotion of an active lifestyle in the SCI population, thereby reducing the risk for secondary diseases.

In-Home Sleep Apnea Severity Classification using Contact-free Load Cells and an AdaBoosted Decision Tree Algorithm.

We present a method for automated diagnosis and classification of severity of sleep apnea using an array of non-contact pressure-sensitive sensors placed underneath a mattress as an alternative to conventional obtrusive sensors. Our algorithm comprises two stages: i) A decision tree classifier that identifies patients with sleep apnea, and ii) a subsequent linear regression model that estimates the Apnea-Hypopnea Index (AHI), which is used to determine the severity of sleep disordered breathing. We tested our algorithm on a cohort of 14 patients who underwent overnight home sleep apnea test. The machine learning algorithm was trained and performance was evaluated using leave-one-patient-out cross-validation. The accuracy of the proposed approach in detecting sleep apnea is 86.96%, with sensitivity and specificity of 81.82% and 91.67%, respectively. Moreover, classification of severity of the sleep disorder was correctly assigned in 11 out of 14 cases, and the mean absolute error in the AHI estimation was calculated to be 3.83 events/hr.

Robust Heart Rate Estimation During Physical Exercise Using Photoplethysmographic Signals.

A method for estimating heart rate (HR) from photoplethysmographic (PPG) signal, during physical exercise, is presented in this paper. Accurate and reliable estimation of HR from PPG during intensive physical activity is challenging because intense motion artifacts can easily mask the true HR. If PPG signal is contaminated by intense motion artifacts, the highest peak of PPG spectrum is shifted from true HR due to motion artifacts. The proposed method employs a simple technique using spectral estimation and median filtering for HR estimation from intensely motion artifacts corrupted PPG signal. Experimental result for a database of 12 subjects recorded during fast running showed that the average absolute estimation error was 1.31 beats/minute.

Spacecraft localization by indirect linear measurements from a single antenna

PurposeThe purpose of this paper is to present a two-stage approach for estimation of spacecraft’s position and velocity by indirect linear measurements from a single antenna.Design/methodology/approachIn the first stage, direct nonlinear antenna measurements are transformed to linear x-y-z coordinate measurements of spacecraft’s position, and statistical characteristics of orbit determination errors are analyzed. Variances of orbit parameters’ errors are chosen as the accuracy criteria. In the second stage, the outputs of the first stage are improved by the designed Extended Kalman Filter for estimation of the spacecraft’s position and velocity on indirect linear x-y-z measurements.FindingsThe complex content of the measurement matrix in the conventional method causes periodic singularities in simulation results. In addition, the convergence of the filter using direct measurements is highly dependent on the initialization parameters’ values due to the nonlinear partial derivatives in the Jacobian measurement matrix. The comparison of the accuracy of both methods shows that the estimation by using indirect measurements reduces the absolute estimation errors. The simulation results show that the proposed two-stage procedure performs both with better estimation accuracy and better convergence characteristics. The method based on indirect measurements provides an unnoticeably short transient duration.Practical implicationsThe proposed method can be recommended for satellite orbit estimation regarding its presented superiorities.Originality/valueInputting the single antenna measurements to the filter indirectly results in a quite simpler measurement matrix. As a result, the convergence of the filter is faster and estimation errors are lower.

Pedestrian Dead Reckoning Based on Motion Mode Recognition Using a Smartphone.

This paper presents a pedestrian dead reckoning (PDR) approach based on motion mode recognition using a smartphone. The motion mode consists of pedestrian movement state and phone pose. With the support vector machine (SVM) and the decision tree (DT), the arbitrary combinations of movement state and phone pose can be recognized successfully. In the traditional principal component analysis based (PCA-based) method, the obtained horizontal accelerations in one stride time interval cannot be guaranteed to be horizontal and the pedestrian’s direction vector will be influenced. To solve this problem, we propose a PCA-based method with global accelerations (PCA-GA) to infer pedestrian’s headings. Besides, based on the further analysis of phone poses, an ambiguity elimination method is also developed to calibrate the obtained headings. The results indicate that the recognition accuracy of the combinations of movement states and phone poses can be 92.4%. The 50% and 75% absolute estimation errors of pedestrian’s headings are 5.6° and 9.2°, respectively. This novel PCA-GA based method can achieve higher accuracy than traditional PCA-based method and heading offset method. The localization error can reduce to around 3.5 m in a trajectory of 164 m for different movement states and phone poses.

Regression by Integration demonstrated on Ångström-Prescott-type relations

Abstract We present a novel approach for the determination of the relationship between two random variables, which we call Regression by Integration. The resulting curve is a least absolute error estimate. Compared to other regression methods, it has the advantage that, instead of a sample of simultaneously taken pairs of the two random variables, only a separate sample of each of the random variables is required. We demonstrate the practicability of the method on Angstrom-Prescott-type relations and compare the results with those obtained by least square error fits. We present supporting theoretical background information based on copulas. We show that Regression by Integration leads to the strict interdependence of the two random variables; Spearman's rho is equal to one.

Does Selecting Covariates Using Factor Analysis in Mapping Algorithms Improve Predictive Accuracy? A Case of Predicting EQ-5D-5L and SF-6D Utilities from the Women’s Health Questionnaire

BackgroundIn addition to theoretical justifications, many statistical methods have been used for selecting covariates to include in algorithms mapping nonutility measures onto utilities. However, it is not clear whether using exploratory factor analysis (EFA) as one such method improves the predictive ability of these algorithms. ObjectiveThis question is addressed within the context of mapping a non–utility-based outcome, the core 23-item Women’s Health Questionnaire (WHQ-23), onto two utility instruments: five-level EuroQol five-dimensional questionnaire (EQ-5D-5L) and the six-dimensional health state short form (derived from short form 36 health survey) (SF-6D). MethodsData on all three outcomes were collected from 455 women from the Australian general population participating in a study assessing attitudes toward in vitro fertilization. Statistical methods for selecting covariates included stepwise regression (SW), including all covariates (Include all), multivariable fractional polynomial (MFP), and EFA. The predictive accuracy of 108 regression models was assessed using five criteria: mean absolute error, root mean squared error, correlation, distribution of predicted utilities, and proportion of predictions with absolute errors of less than 0.0.5. Validation of “primary” models was carried out on random samples of the in vitro fertilization study. ResultsThe best results for EQ-5D-5L and SF-6D predictions were obtained from models using SW, “Include all,” and MFP covariate-selection approaches. Root mean squared error (0.0762–0.1434) and mean absolute error (0.0590–0.0924) estimates for these models were within the range of published estimates. EFA was outperformed by other covariate-selection methods. ConclusionsIt is possible to predict valid utilities from the WHQ-23 using regression methods based on SW, “Include all,” and MFP covariate-selection techniques.