Normalized Root Mean Square Error Values Research Articles

Image‐based estimation method for field inhomogeneity in brain echo‐planar images with geometric distortion using k‐space textures

ABSTRACTEcho‐planar imaging (EPI) can suffer from geometrical distortion due to magnetic field inhomogeneity. To correct the geometric distortions in EPI, a magnetic field map is used. Our purpose was to develop a novel image‐based method for estimating the field inhomogeneity map from the distorted EPI image and T1‐weighted image of the brain using k‐space textures. Based on magnetic resonance imaging physics, our method synthesizes the distorted image to match the measured EPI image through the generating process of EPI image by updating the estimated field inhomogeneity map. The estimation process was performed to minimize the cost function, which was defined by the synthesized EPI image and the measured EPI image with geometric distortion, using an iterative conjugate gradient algorithm. The proposed method was applied to simulation and human data. To evaluate the performance of the proposed method quantitatively, we used the normalized root mean square error (NRMSE) between the ground truth and the results estimated by our proposed method. In simulation data, the values of the NRMSE between the ground truth and the estimated field inhomogeneity map were <0.08. In both simulation and human data, the estimated EPI images were very similar to input EPI images, and the NRMSE values between them were <0.09. The results of the simulated and human data demonstrated that our method produced a reasonable estimation of the field inhomogeneity map. The estimated map could be used for distortion correction in EPI images. © 2015 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering) 45B: 142–152, 2015

Evaluation of a Modified Hybrid‐Maize Model Incorporating a Newly Developed Module of Plastic Film Mulching

ABSTRACTUnderstanding maize (Zea mays L.) growth, development, and production under plastic film mulching is useful to improve crop management strategies and increase grain yield in areas with limited water and low temperatures. A new plastic film mulching module for the Hybrid‐Maize model was developed to simulate maize development and grain yield. This paper evaluates the performance of the new model at Changwu experimental station, northwest China, and at the 852 farm and Qixing farm in northeast China, compared with the original Hybrid‐Maize model. Compared with measured data, the root mean square error (RMSE) and normalized root mean square error (NRMSE) values for leaf area index (LAI) were 1.0 and 29% for the original model and 0.72 and 20% for the modified model, respectively. The RMSE and NRMSE values for the aboveground dry matter simulated by the original model were 2674 kg ha−1 and 24% compared with 1552 kg ha−1 and 14% by the new model. The RMSE and NRMSE values for the grain dry matter were 495 kg ha−1 and 5.5% by the original model and 441 kg ha−1 and 4.9% by the modified model. The RMSE and NRMSE values for the LAI and aboveground and grain dry matter were all lower for the modified model, indicating improved simulations. With the modified model, simulated aboveground dry matter and LAI increased >14 and 30%, respectively, compared with the original model. However, the modified model overestimated LAI and aboveground dry matter in the maize vegetative stage.

Intercomparison of surface energy flux measurement systems used during the HiWATER‐MUSOEXE

AbstractAgreement among instruments is very important for the Multi‐Scale Observation Experiment on Evapotranspiration over heterogeneous land surfaces of The Heihe Watershed Allied Telemetry Experimental Research (HiWATER‐MUSOEXE), particularly in regard to radiation and turbulent flux measurements. Before HiWATER‐MUSOEXE was conducted, 20 eddy covariance (EC) system sets, 18 radiometer sets, and seven large aperture scintillometers (LASs) sets were intercompared over the Gobi desert between 14 and 24 May 2012. For radiometers, the four‐component radiation measurements exhibited good agreement—the average root‐mean‐square error (RMSE) and mean relative error (MRE) for the net radiation were 10.38 W m−2 and 1.24%, respectively. With regard to the EC systems, the best consistency for sensible heat fluxes was found among CSAT3 sonic anemometers and Li7500A/Li7500/EC150 combinations (average RMSE, 12.30 W m−2 and MRE, −1.36%), followed by Gill sonic anemometers and Li7500A/Li7500 combinations when a proper angle of attack correction method was applied (average RMSE, 16.75 W m−2 and MRE, −5.52%). The sensible heat flux measured using different LASs agreed well with high correlation coefficients—the average RMSE and MRE values were 10.26 W m−2 and 5.48% for boundary layer scintillometer (BLS) 900, 16.32 W m−2 and 10.47% for BLS450, and 14.38 W m−2 and −3.72% for ZZLAS, respectively. The EC and LAS measurements were compared and agreed well over homogeneous underlying surfaces, which also indicated that the EC and LAS measurements would be comparable in the follow‐up experiment. The intercomparison results can be used to determine instrument placement and are very helpful for subsequent data analysis.

Adaptability of APSIM Maize Model in Northeast China

The APSIM (Agricultural Production Systems Simulator) model was introduced to simulate maize growth, development and yields in Northeast China using the field experimental data and climate data collected from six typical agricultural meteorological stations in the studied area. APSIM was calibrated using the first part of data to determine the varietal parameters, then simulated the growing periods, leaf area index (LAI), total above-ground biomass and yields using the second part of data at each site. The results showed that there was a good agreement between the simulated and measured values in growing periods. The difference of growing periods from sowing to emergence, from sowing to flowering and from sowing to maturity between simulated and measured data was 0–2.0, 0.7–2.0, and 0.7–2.3 d, respectively. The Normalized Root Mean Square Error (NRMSE) values for measured and simulated LAI and total above-ground biomass in Harbin station were 33% and 11%, respectively. NRMSE values for measured and simulated yield in Harbin, Hailun, Tailai, Huadian, Tonghua, and Benxi station were 18%, 13%, 4%, 4%, 5%, and 2%, respectively. These re-sults indicated that APSIM model has good ability to simulate the growing periods, dynamic process of LAI, dynamic process of above-ground biomass and yield of maize in Northeast China. This research supports the model application in Northeast China, such as simulating maize potential yield, or prescribing yield limiting factors.

Calibration of Hargreaves–Samani equation for estimating reference evapotranspiration in semiarid and arid regions

The Penman–Monteith (FAO-56 PM) equation is suggested as the standard method for estimating evapotranspiration (ET0) by the International Irrigation and Drainage Committee and Food and Agriculture Organization (FAO). On the other hand, the Hargreaves–Samani (HS) equation is an alternative method compared with the FAO-56 PM equation. In the present study, the original coefficient C of the HS equation is calibrated based on the FAO-56 PM equation for estimating the reference ET0 from 15 meteorological stations in central Iran (about 170,000 km2) under semiarid and arid conditions. After calibration, the new values for C are ranged from 0.0018 to 0.0037. The mean bias error (MBE), the root mean square error (RMSE), and the ratio of average estimations of ET0 (R) values for all stations are ranged from 0.12 to 5.38, −5.35 to 1.15 mm d−1 and 0.64 to 1.28 for the HS equation and from 0.12 to 2.48, −2.2 to 0.60 mm d−1, and 1.00 to 1.05 for the calibrated Hargreaves–Samani equation (CHS), respectively. Results indicate that the average RMSE and MBE values are decreased by 40% and 66%, respectively. Relationships for calibrating the C coefficient on the basis of annual average of daily temperature range (ΔT) and wind speed (V) are proposed, calibrated, and validated. Hence, the CHS equation can be used for ET0 estimates with acceptable accuracy instead of the FAO-56 PM method.

Motion Correction of Multi-b-value Diffusion-weighted Imaging in the Liver

Motion artifacts are a significant source of error in the acquisition and quantification of parameters from multi-b-value diffusion-weighted imaging (DWI). The objective of this article is to present a reliable method to reduce motion-related artifacts during free-breathing at higher b-values when signal levels are low. Twelve patients referred for magnetic resonance imaging of the liver underwent a clinical magnetic resonance imaging examination of the abdominal region that included DWI. Conventional single-shot spin-echo echo planar imaging acquisitions of the liver during free breathing were repeated in a "time-resolved" manner during a single acquisition to obtain data for multi-b-value analysis, alternating between low and high b-values. Image registration using a normalized mutual information similarity measure was used to correct for spatial misalignment of diffusion-weighted volumes caused by motion. Registration error was estimated indirectly by comparing the normalized root-mean-square error (NRMSE) values of data fitted to the biexponential intra-voxel incoherent motion model before and after motion correction. Regions of interest (ROIs) were selected in the liver close to the surface of the liver and close to internal structures such as large bile ducts and blood vessels. For the 12 patient datasets, the mean NRMSE value for the motion-corrected ROIs (0.38 ± 0.16) was significantly lower than the mean NRMSE values for the non-motion-corrected ROIs (0.41 ± 0.13) (P < .05). In cases where there was substantial respiratory motion during the acquisition, visual inspection verified that the algorithm markedly improved alignment of the liver contours between frames. The proposed method addresses motion-related artifacts to increase robustness in multi-b-value acquisitions.

Estimating Ambient Temperature for Malaysia Using Generalized Regression Neural Network

This paper presents a new method for predicting hourly ambient temperature series for Malaysia using generalized regression neural network (GRNN). MATLAB was used to develop the GRNN using the weather records for Malaysia. The developed model has five inputs and one output. The inputs of the proposed model are hour, day, month, sunshine ratio, and relative humidity, meanwhile ambient temperature is the output. To evaluate the accuracy of the GRNN, three statistical parameters, namely, the mean absolute percentage error (MAPE), mean bias error (MBE), and root mean square error (RMSE) are considered. The GRNN results give an accurate prediction of ambient temperatures for the selected testing months with average values of MAPE, MBE, and RMSE of 2.65%, 4.05%, and 0.347%, respectively. The advantage of the proposed method is that it is able to predict ambient temperature at sites where there is no ambient temperature-measuring instrument installed.

Assessment of Artificial Neural Networks for Hourly Solar Radiation Prediction

This paper presents an assessment for the artificial neural network (ANN) based approach for hourly solar radiation prediction. The Four ANNs topologies were used including a generalized (GRNN), a feed-forward backpropagation (FFNN), a cascade-forward backpropagation (CFNN), and an Elman backpropagation (ELMNN). The three statistical values used to evaluate the efficacy of the neural networks were mean absolute percentage error (MAPE), mean bias error (MBE) and root mean square error (RMSE). Prediction results show that the GRNN exceeds the other proposed methods. The average values of the MAPE, MBE and RMSE using GRNN were 4.9%, 0.29% and 5.75%, respectively. FFNN and CFNN efficacies were acceptable in general, but their predictive value was degraded in poor solar radiation conditions. The average values of the MAPE, MBE and RMSE using the FFNN were 23%, −.09% and 21.9%, respectively, while the average values of the MAPE, MBE and RMSE using CFNN were 22.5%, −19.15% and 21.9%, respectively. ELMNN fared the worst among the proposed methods in predicting hourly solar radiation with average MABE, MBE and RMSE values of 34.5%, −11.1% and 34.35%. The use of the GRNN to predict solar radiation in all climate conditions yielded results that were highly accurate and efficient.

Estimating turbulent fluxes through assimilation of geostationary operational environmental satellites data using ensemble Kalman filter

[1] In this study, a data assimilation scheme is developed on the basis of the ensemble Kalman filter algorithm and the common land model (CoLM); soil moisture and model parameters are simultaneously optimized to improve the estimates of turbulent fluxes. Land surface temperature (LST) is retrieved from geostationary operational environmental satellites (GOES) data, validated, and then assimilated into the model. The data assimilation results are validated at six observation sites in the United States that include grassland, cropland, and forestland cover types. Data assimilation results indicate that in addition to improvements in the prediction of turbulent fluxes, model uncertainties are also reduced as a result of the assimilation of GOES LST retrieval data. The average reductions in root mean square error (RMSE) values are 47.5 and 31.1 W m−2. The effects of simultaneous optimization of soil moisture and model parameters are compared with those resulting from separate optimization; simultaneous optimization is found to yield smaller RMSE values. Further, in this study, the effects of Moderate Resolution Imaging Spectroradiometer (MODIS) and GOES temporal resolution data on data assimilation results are studied. The assimilation results indicate that the average RMSE values for GOES temporal resolution data are smaller than that for MODIS temporal resolution data. During the assimilation time period, the soil moisture obtained from assimilation closely agrees with the observed values, and the four vegetation parameters show distinct seasonal variations. However, the lack of sufficient information makes it difficult to estimate the true value of these variables and parameters.

CSM‐IXIM: A New Maize Simulation Model for DSSAT Version 4.5

The CERES‐Maize model is the most widely used maize (Zea mays L.) model and is a recognized reference for comparing new developments in maize growth, development, and yield simulation. The objective of this study was to present and evaluate CSM‐IXIM, a new maize simulation model for DSSAT version 4.5. Code from CSM‐CERES‐Maize, the modular version of the model, was modified to include a number of model improvements. Model enhancements included the simulation of leaf area, C assimilation and partitioning, ear growth, kernel number, grain yield, and plant N acquisition and distribution. The addition of two genetic coefficients to simulate per‐leaf foliar surface produced 32% smaller root mean square error (RMSE) values estimating leaf area index than did CSM‐CERES. Grain yield and total shoot biomass were correctly simulated by both models. Carbon partitioning, however, showed differences. The CSM‐IXIM model simulated leaf mass more accurately, reducing the CSM‐CERES error by 44%, but overestimated stem mass, especially after stress, resulting in similar average RMSE values as CSM‐CERES. Excessive N uptake after fertilization events as simulated by CSM‐CERES was also corrected, reducing the error by 16%. The accuracy of N distribution to stems was improved by 68%. These improvements in CSM‐IXIM provided a stable basis for more precise simulation of maize canopy growth and yield and a framework for continuing future model developments.

Accuracy of volumetric flow rate measurements: an in vitro study using modern ultrasound scanners.

Volumetric flow measurement with Doppler ultrasound is useful in assessing blood flow as part of an evaluation of arteriovenous fistula maturity in patients undergoing hemodialysis. In this study, we assessed both accuracy and variability in volumetric flow measurements obtained using modern and commercially available ultrasound systems and an in vitro experimental setup. Volumetric flow measurements using duplex ultrasound were obtained by 3 users operating 5 different systems for randomized flow in the range of 100 to 1000 mL/min. Users performed 3 consecutive measurements at a given flow rate. Data were analyzed using statistical techniques to assess measurement accuracy and variability. Over the span of flow rates studied, the root mean square error (RMSE) for the 5 ultrasound systems ranged from 38.8 to 79.7, 36.8 to 52.0, 73.0 to 85.3, 26.7 to 44.6, and 43.9 to 93.5 mL/min. Corresponding average RMSE values were 60.3, 42.7, 81.1, 37.2, and 64.4 mL/min, respectively. A linear regression analysis of mean interobserver measurements revealed an excellent correlation for all ultrasound systems (r(2) > 99.1%). Assessment of intraobserver measurements revealed no statistically significant differences for any ultrasound system evaluated (P > .94). Comparison of interobserver measurements indicates no statistically significant differences between any of the 5 systems (P > .14). Modern ultrasound systems are reasonably accurate in blood flow measurement in an experimental setup mimicking clinically relevant blood flow ranges in a hemodialysis fistula. Users need adequate training and experience to perform multiple measurements and use appropriate techniques to minimize errors in flow measurement.

Experimental Evaluation of a Recursive Model Identification Technique for Type 1 Diabetes

A model-based controller for an artificial beta cell requires an accurate model of the glucose-insulin dynamics in type 1 diabetes subjects. To ensure the robustness of the controller for changing conditions (e.g., changes in insulin sensitivity due to illnesses, changes in exercise habits, or changes in stress levels), the model should be able to adapt to the new conditions by means of a recursive parameter estimation technique. Such an adaptive strategy will ensure that the most accurate model is used for the current conditions, and thus the most accurate model predictions are used in model-based control calculations. In a retrospective analysis, empirical dynamic autoregressive exogenous input (ARX) models were identified from glucose-insulin data for nine type 1 diabetes subjects in ambulatory conditions. Data sets consisted of continuous (5-minute) glucose concentration measurements obtained from a continuous glucose monitor, basal insulin infusion rates and times and amounts of insulin boluses obtained from the subjects' insulin pumps, and subject-reported estimates of the times and carbohydrate content of meals. Two identification techniques were investigated: nonrecursive, or batch methods, and recursive methods. Batch models were identified from a set of training data, whereas recursively identified models were updated at each sampling instant. Both types of models were used to make predictions of new test data. For the purpose of comparison, model predictions were compared to zero-order hold (ZOH) predictions, which were made by simply holding the current glucose value constant for p steps into the future, where p is the prediction horizon. Thus, the ZOH predictions are model free and provide a base case for the prediction metrics used to quantify the accuracy of the model predictions. In theory, recursive identification techniques are needed only when there are changing conditions in the subject that require model adaptation. Thus, the identification and validation techniques were performed with both "normal" data and data collected during conditions of reduced insulin sensitivity. The latter were achieved by having the subjects self-administer a medication, prednisone, for 3 consecutive days. The recursive models were allowed to adapt to this condition of reduced insulin sensitivity, while the batch models were only identified from normal data. Data from nine type 1 diabetes subjects in ambulatory conditions were analyzed; six of these subjects also participated in the prednisone portion of the study. For normal test data, the batch ARX models produced 30-, 45-, and 60-minute-ahead predictions that had average root mean square error (RMSE) values of 26, 34, and 40 mg/dl, respectively. For test data characterized by reduced insulin sensitivity, the batch ARX models produced 30-, 60-, and 90-minute-ahead predictions with average RMSE values of 27, 46, and 59 mg/dl, respectively; the recursive ARX models demonstrated similar performance with corresponding values of 27, 45, and 61 mg/dl, respectively. The identified ARX models (batch and recursive) produced more accurate predictions than the model-free ZOH predictions, but only marginally. For test data characterized by reduced insulin sensitivity, RMSE values for the predictions of the batch ARX models were 9, 5, and 5% more accurate than the ZOH predictions for prediction horizons of 30, 60, and 90 minutes, respectively. In terms of RMSE values, the 30-, 60-, and 90-minute predictions of the recursive models were more accurate than the ZOH predictions, by 10, 5, and 2%, respectively. In this experimental study, the recursively identified ARX models resulted in predictions of test data that were similar, but not superior, to the batch models. Even for the test data characteristic of reduced insulin sensitivity, the batch and recursive models demonstrated similar prediction accuracy. The predictions of the identified ARX models were only marginally more accurate than the model-free ZOH predictions. Given the simplicity of the ARX models and the computational ease with which they are identified, however, even modest improvements may justify the use of these models in a model-based controller for an artificial beta cell.

SU‐FF‐J‐108: Predicting Respiratory Waveform of 4D CT Patients Using Moving Least Square Method

Purpose: The purpose of this study was to predict patient respiratory waveform precisely and quickly using a Moving Least Square method. The external respiratory waveform may have a strong correlation with tumor motion in lung and upper abdomen. Prediction is important because tumor may move significantly during the finite time between monitored position change and beam adjustment. Method and Materials: An adaptive linear filter based on the Moving Least Square (MLS) algorithm was used to predict the respiratory waveform signals for six 4D CT patients. The respiratory waveform was acquired with a bellows system at a sampling frequency of 100 Hz or a sampling period of 10 ms. To predict one datum in the future (10 samples or 100 ms away), 10 s history data (1000 samples) were fed to the linear filter to calculate its coefficients with the MLS algorithm. The output of the linear filter was the predicted value. The predicted values were compared to the real data recorded. We also calculated the Root Mean Square Error (RMSE) of the prediction for each patient and normalized it with the average waveform amplitude. The accuracy of MLS method was compared with that of Wiener‐Hopf method in the normalized RMSE values. Results: For a 100 ms prediction interval, the average prediction RMSE for the 6 patients was 2.1%, with a standard derivation of 0.7%. The computation time for predicting one datum with MLS method was 0.5 ms, which is far less than the sampling period (10 ms). This MLS method shows smaller normalized RMSEs than the Wiener‐Hopf method for all 6 patients. Conclusion: The prediction of patient respiratory waveform using MLS method is both accurate and fast. Real time prediction of respiratory waveform and tumor motion is possible.

A comparison of four methods to map biomass from Landsat-TM and inventory data in western Newfoundland

Spatial measures of forest biomass are important to implement sustainable forest management, monitor global change, and model forest productivity. Several methods for estimating forest biomass by remote sensing have been developed, but their comparative advantages have not been evaluated for large areas in Canada. This study compares four methods to map forest biomass on an extended pilot region (20,000 km 2) located in western Newfoundland. The methods include: (i) Direct Radiometric Relationships (DRR), (ii) k-Nearest Neighbors ( k-NN), (iii) Land Cover Classification (LCC), and (iv) Biomass from Cluster Labeling Using Structure and Type (BioCLUST). The results of each method were evaluated using an independent set of ground survey plots and compared with a baseline biomass map generated from biomass tables applied to forest inventory stand maps. Considering the root mean square error (RMSE) assessed with the inventory plots, the DRR, k-NN, and BioCLUST methods provided similar results, with average RMSE values of 59, 59, and 58 t/ha, respectively. Bias values were lowest for the k-NN method followed by DRR, BioCLUST, and LCC (6, −8, 17, and 42 t/ha, respectively). Assessed with the baseline map, the BioCLUST method produced the lowest RMSE (41 t/ha) and bias (−4 t/ha) followed by the DRR and k-NN methods, with RMSE values of 47 and 54 t/ha and bias values of 9 and 23 t/ha, respectively. The method using biomass tables applied on the classified TM image (LCC) provided the greatest RMSE and bias, but may be suitable for applications that do not require a high level of precision. The BioCLUST and LCC methods provided practical advantages for the type of data sets available. Overall, the choice of a method rests on both the availability of data sets and the level of precision of the results required.