Maximum Average Relative Error Research Articles

Experimental study on shear mechanical properties of concrete joints under different unloading stress paths

In order to study the shear mechanical properties of rock joint under different unloading stress paths, the RDS-200 rock joint shear test system was used to carry out direct shear tests on concrete joint specimens with five different morphologies under the CNL path and different unloading stress paths. The unloading stress paths include unloading normal load and maintaining constant shear load (UNLCSL), unloading normal load and unloading shear load (UNLUSL), unloading normal load and increasing shear load (UNLISL). The results show that the peak shear strength, cohesion, internal friction angle, pre-peak shear stiffness and residual shear strength of concrete joints under CNL path increases with the increasing JRC and normal stress. Under the UNLCSL path, under the same initial shear stress τ1, instability normal stress σi decreases with the increasing JRC, and normal stress unloading amount Δσn increases with the increasing JRC. Under the same JRC, σi increases with the increase of τ1, and Δσn decreases with the increasing τ1. Under the same JRC and σi, τi is significantly smaller under the UNLCSL path than the CNL path. Under the same JRC, the cohesion under the UNLCSL path is less than the CNL path, and the internal friction angle is higher than that the CNL path. Under the same JRC and σi, τi is the largest under the path of CNL and UNLISL, followed by the UNLCSL path, and τi under the UNLUSL path is the smallest. Compared with the CNL path, the variation range of the specimen internal friction angle is within 3% while the average decrease percentage of the specimen cohesion reaches 37.6% under the UNLCSL path, UNLISL, and UNLUSL. Therefore, it can be inferred that the decrease in cohesion caused by normal unloading is the main reason for the decrease in joint instability shear strength. After introducing the correction coefficient k of cohesion to modify the Mohr-Coulomb criterion, the maximum average relative error after correction is only 3.5%, which is significantly improved compared with the maximum average relative error of 56.9% before correction. The research conclusions can provide some reference for the accurate estimation of shear bearing capacity of rock joints under different unloading stress paths, which is of great significance to the stability evaluation and disaster prevention of rock mass engineering.

Application of UVAS and TDLAS-based multi-combustion-parameter diagnosis using computerized tomography

Fossil fuel combustion is the main source of mechanical power and will be accompanied by the production of a large number of toxic and harmful substances, such as NO and CO. In this study, Computed Tomography-Tunable Diode Laser Absorption Spectroscopy (CT-TDLAS) and Computed Tomography-Ultraviolet Absorption Spectroscopy (CT-UVAS) were used to establish a multi-combustion-parameter diagnosis system. A corrected H2O absorption database was applied by the wavelength at 1388 nm and 1343 nm. The spectra at 2325 nm were used to establish the CO absorption database. NO absorption database at 214 nm/226 nm was established by UVAS. The nonlinear least squares with the polynomial fitting method was applied to CT reconstruction. A custom CT cell was designed to fix the fiber and probes of the CT-TDLAS and CT-UVAS, and its rationality was evaluated by the Sum of squared difference (SSD) and Zero-mean normalization cross-correlation (ZNCC) through the comparison between CFD simulation and CT reconstruction. In the experiment, the CT reconstruction of the temperature, H2O, and CO showed significant distribution profile differences between two premixed flames. The NO detection function was demonstrated by standard NO gas, and the maximum average relative error was 4.99 %. The results show that the multi-combustion-parameter diagnosis system can measure the temperature, H2O, CO, and NO distribution of the combustion flow field at high frequency. The multi-combustion-parameter diagnosis system will assist with research and diagnosis on controlling NO generation and promoting combustion efficiency.

Comparative Analysis of Ground-Based Solar Irradiance Measurements and Copernicus Satellite Observations

Solar irradiance data provided by the Copernicus program are crucial for several scientific, environmental, and energy management applications, but their validation by means of ground-based measurements may be necessary, especially if daily and hourly data resolutions are required. The validation process not only ensures that reliable information is available for solar energy resource planning, power plant performance assessment, and grid integration, but also contributes to the improvement of the Copernicus system itself. Ground-based stations offer site-specific data, allowing for comprehensive assessments of the system’s performance. This work presents a comparative statistical analysis of solar irradiance data provided by the Copernicus system and ground-based measurements on a seasonal basis at three specific Italian reference sites, showing a maximum average relative error of less than 7% for hourly horizontal global irradiance in the irradiance range defined by the IEC 61724-2.

An Ankle Joint Flexion and Extension Movement-Monitoring Device Based on Pressure Sensors.

Ankle joint flexion and extension movements play an important role in the rehabilitation training of patients who have been injured or bedridden for a long time before and after surgery. Accurately guiding patients to perform ankle flexion and extension movements can significantly reduce deep vein thromboembolism. Currently, most ankle rehabilitation devices focus on assisting patients with ankle flexion and extension movements, and there is a lack of devices for effectively monitoring these movements. In this study, we designed an ankle joint flexion and extension movement-monitoring device based on a pressure sensor. It was composed of an STM32 microcontroller, a pressure sensor, an HX711A/D conversion chip, and an ESP8266 WiFi communication module. The value of the force and the effective number of ankle joint flexion and extension movements were obtained. An experimental device was designed to verify the accuracy of the system. The maximum average error was 0.068 N; the maximum average relative error was 1.7%; the maximum mean-squared error was 0.00464 N. The results indicated that the monitoring device had a high accuracy and could effectively monitor the force of ankle flexion and extension movements, ultimately ensuring that the patient could effectively monitor and grasp the active ankle pump movement.

Interpreting coal component content in logging data by combining gray relational analysis and hybrid neural network

The coal component content is an important parameter during the coal resources exploration and exploitation. Previous logging curve regression and single neural network methods have the disadvantages of low accuracy and weak generalization ability in calculating coal component content. In this study, a gray relational analysis-hybrid neural network (GRA-HNN) method is developed by combining GRA and HNN to predict coal component content in logging data. First, the correlation degree between different conventional logging data and coal components is calculated using the GRA method, and logging curves with a correlation degree of ≥0.7 are selected as the input training data set. Then, a back propagation neural network, support vector machine neural network, and radial basis function neural network of different coal components are constructed based on the selected optimal input logging data, and the weighted average strategy is used to form an HNN prediction model. Finally, the GRA-HNN method is used to predict the coal component content of coalbed methane production wells in the Panji mining area. The application results indicate that the coal component content predicted by the GRA-HNN method has the highest accuracy compared with the logging curve regression method and its single neural network model, with a maximum average relative error of 13.4%. In addition, the accuracy of coal component content predicted by some single intelligent models is not always higher than the logging curve regression method, indicating that the neural network model is not necessarily suitable for all coal component content predictions. Our GRA-HNN method not only optimizes the prediction performance of a single neural network model by selecting effective input parameters but also comprehensively considers the prediction effect of several neural network models, which strengthens the generalization ability of neural network model and increases the log interpretation accuracy of coal component content.

Electromagnetic Displacement Sensor and Docking Method Based on Elliptic Integral Series Expansion

Automatic charging can improve the endurance of unmanned work platforms, but the docking accuracy limits its success rate and charging efficiency. In order to solve this problem, an accurate docking method based on elliptic integral series expansion is proposed. The relationship between load voltage and coil transverse offset distance is constructed by establishing a coil mutual inductance circuit, a coil center points transverse offset mutual inductance coefficient calculation model, and a triangular positioning geometry structure Numerical integration and elliptic integration series expansion are used to solve the exact correspondence between the coil mutual inductance coefficient and the coil transverse offset distance. Finally, the relationship between the load voltage and the lateral offset distance from the center of the coil is obtained. The method does not require the arrangement of additional sensors and coils, nor does it require extensive prior data collection for unique coil configurations. The system can be used for energy transmission and as a displacement sensor. It has been verified by COMSOL simulations that the maximum relative error in the coefficient of mutual inductance is 6.507% for the numerical integration method and 9.022% for the elliptic integration series expansion approach. After experimental verification, the maximum average relative error of the load voltage is 4.048% for the numerical integration method and 11.89% for the elliptic integration series expansion approach. This method achieved high accuracy positioning measurement with the error range at the centimeter level. The method contributes to the long-term application of unmanned operating platforms.

Numerical Analysis of Transient State Heat Transfer by Spectral Method Based on POD Reduced-Order Extrapolation Algorithm

In order to meet the requirements of high accuracy and fast algorithm for numerical heat transfer simulation, an iterative scheme of Proper Orthogonal Decomposition (for short, POD) dimension reduction based on the classical central difference Galerkin spectral method is proposed for solving two-dimensional transient heat conduction problems. The POD dimension reduction spectral method model is constructed by taking the calculation results of classical central difference Galerkin spectral method as sample data. The numerical algorithm characteristics of flow and heat transfer are studied by using a partial differential equation as a mathematical model, and the error estimation is given. Finally, different time intervals are used as parameters to simulate experiments. The results show that the POD method is applicable to transient nonlinear heat conduction problems, and the maximum average relative error of the reconstructed temperature field is 0.89675%. Moreover, the POD method not only has a high calculation accuracy, but also has an average calculation speed as high as 310.25 times that of the central difference Galerkin algorithm. It can be seen that under the condition that the error between the solution of POD dimension reduction extrapolation algorithm and the solution of classical central difference Galerkin spectrum method is small enough, the POD method can greatly reduce the calculation amount, shorten the running time, and ensure a high accuracy of the calculation results, thus verifying the effectiveness and feasibility of the algorithm.

An Integrated Interferometric Fiber Optic Sensor Using a 638 nm Semiconductor Laser for Air-Water Surface Velocity Measurements.

An integrated interferometric fiber optic velocimetry sensor has been proposed and demonstrated at the central wavelength of 638 nm. The sensor is based on the principle of two laser-beams' interference. The light signal scattered from the particles or vapor is demodulated to measure the water surface velocity and water vapor velocity. Three velocity measurement experiments are carried out to measure the velocity, and the experimental data shows that the velocity increases linearly in the range of 4 mm·s-1 to 100 mm·s-1, with a slope of linear fitting curve of 0.99777 and the R-Square of 1.00000. The velocity calculated from frequency shift fits well with the reference velocity. The maximum average relative error in the three velocity measurements is less than 2.5%. In addition, the maximum speed of 4.398 m·s-1 is confirmed in the rotating disk calibration experiment, which expands the sensor's velocity measurement range. To solve the problem that it is difficult to directly measure the velocity of small-scale water surface flow velocity, especially from the aspect of the low velocity of air-water surface, the interferometric fiber optic sensor can be applied to the measurement of water surface velocity and wind velocity on the water surface.

An Analytical Solution to Predict the Distribution of Streamwise Flow Velocity in an Ecological River with Submerged Vegetation

Aquatic submerged vegetation is widespread in rivers. The transverse distribution of flow velocity in rivers is altered because of the vegetation. Based on the vegetation coverage, the cross-section of the ecological channels can be divided into the non-vegetated area and the vegetated area. In the vegetated area, we defined two depth-averaged velocities, which included the water depth-averaged velocity, and the vegetation height-averaged velocity. In this study, we optimized the ratio of these two depth-averaged velocities, and used this velocity ratio in the Navier–Stokes equation to predict the lateral distribution of longitudinal velocity in the open channel that was partially covered by submerged vegetation. Based on the Navier–Stokes equations, the term “vegetation resistance” was introduced in the vegetated area. The equations for the transverse eddy viscosity coefficient ξ, friction coefficient f, drag force coefficient Cd, and porosity α were used for both the non-vegetated area and the vegetated area, and the range of the depth-averaged secondary flow coefficient was investigated. An analytical solution for predicting the transverse distribution of the water depth-averaged streamwise velocity was obtained in channels that were partially covered by submerged vegetation, which was experimentally verified in previous studies. Additionally, the improved ratio proposed here was compared to previous ratios from other studies. Our findings showed that the ratio in this study could perform velocity prediction more effectively in the partially covered vegetated channel, with a maximum average relative error of 4.77%. The improved ratio model reduced the number of parameters, which introduced the diameter of the vegetation, the amount of vegetation per unit area, and the flow depth. This theoretical ratio lays the foundation for analyzing the flow structure of submerged vegetation.

Computational procedure for simulating stall process of reciprocating compressors

This article presents in detail a computational procedure for simulating the stall process of reciprocating compressor. The focus of the work is the calculation of the compressor stall limits from the available torque curves of electrical motor. The procedure is composed by an algorithm to compute the compressor stall using a developed compressor simulation model. The compressor model considers the simulation of flow and mechanical interactions in the compressor components and was implemented in the GT-Power platform, a system simulation software. The compressor simulation results for steady state operation were compared with experimental data, indicating that the simulation model represented very well the overall compressor behavior, with a maximum relative error of 1.0% for the compressor global performance. The results for the compressor stall obtained by the proposed computational procedure agreed with the experimental stall tests, with a maximum average relative error of about 6.7%. The computed stall curve had similar trends in relation to experimental results. Performed parametric analyses considering statistical rank correlations indicated that the electric motor tension and motor temperature were the most influencing parameters on compressor stall. The obtained results show that the developed procedure could be an efficient tool for compressor design.

Machine learning based swift online capacity prediction of lithium-ion battery through whole cycle life

The machine learning (ML) based methods show great promise for the online battery capacity prediction. However, the feasibility and simplicity of indispensable feature extraction are both challenging to existing ML based methods, which restrict the implementation in electric vehicle usages. To reduce the computational burden and simultaneously enhance the accuracy of prediction results, this paper proposes a ML based approach for swift capacity prediction leveraging fractional charging voltage segments. A total number of 21 voltage feature segments (VFSs) are intercepted with different voltage ranges to analyze the influence of voltage intervals on the capacity prediction. Meanwhile, three advanced ML models including random forest regression (RFR), relevance vector machine (RVM) and Gaussian process regression (GPR) are meticulously designed to build a mapping function between the intercepted VFSs and battery capacity. The battery capacity prediction can be attained subsequently based on the established matched relationship using the VFS captured in real-time. The experimental and contrastive results show that the best model can accurately predict battery capacity through whole cycle life with the maximum average relative error of only 1.95%. This work emphasizes the application potential of combining straightforward and reliable feature with ML algorithms for online battery capacity prediction.

Predicting Indoor Temperature Distribution Based on Contribution Ratio of Indoor Climate (CRI) and Mobile Sensors

In practical building control, quickly obtaining detailed indoor temperature distribution is necessary for providing satisfying personal comfort and improving building energy efficiency. The aim of this study is to propose a fast prediction method for indoor temperature distribution without knowing the thermal boundary conditions in practical applications. In this method, the index of contribution ratio of indoor climate (CRI), which represents the independent contribution of each heat source to the temperature distribution, has been combined with the air temperature collected by one mobile sensor at the height of the working area. Based on a typical office model, the effectiveness of using mobile sensors was discussed, and the influence of its acquisition height and acquisition distance on the prediction accuracy was analyzed as well. The results showed that the proposed prediction method was effective. When the sensors fixed on the wall were used to predict the indoor temperature distribution, the maximum average relative error was 27.7%, whereas when the mobile sensor was used to replace the fixed sensors, the maximum average relative error was 4.8%. This indicates that using mobile sensors with flexible acquisition location can help promote both reliability and accuracy of temperature prediction. In the human activity area, data from a set of mobile sensors were used to predict the temperature distribution at four heights. The prediction accuracy was 2.1%, 2.1%, 2.3%, and 2.7%, respectively. However, the influence of acquisition distance of mobile sensors on prediction accuracy cannot be ignored. The distance should be large enough to disperse the distribution of the acquisition points. Due to the influence of airflow, some distance between the acquisition points and the room boundaries should be given.

Improving battery thermal behavior and consistency by optimizing structure and working parameter

• An electro-thermal model for an air-cooled pack is established. • Effect of temperature difference on the branch current distribution is included. • Effect of pack thermal behavior on its SOC difference is considered. • Prediction precision of the proposed model is validated. • Thermal behavior and consistency of pack are raised by optimizing structure and air speed. Improving battery consistency is the one of the main goals of battery management system (BMS). As its subsystem, the battery thermal management system (BTMS) should try to accomplish this aim. However, the traditional design of the BTMS considers only the battery temperature and temperature difference, and does not considers their influence on the battery consistency. This study establishes an electro-thermal model for an air-cooled pack. The coupled model can accurately predict the electrical and thermal behavior of the pack. At the pack level, the maximum prediction error of the terminal voltage is 0.58 V, and the maximum average relative error of temperature is only 1.73%. The coupled model is used to optimize the air channel and air speed. In order to improve consistency of the battery, the difference of state of charge (SOC) is added as the evaluation parameter in the optimization of the air channel and air velocity. The optimization process of the structure is divided into two phase and the dual DOEs (design of experiment) are applied. The DOE results are analyzed by the range and variance to select the structure with the best comprehensive performance. Compared with the original air channel and air velocity, the optimized air channel with the new air velocity reduces the maximum cell temperature and temperature difference by 2.67 °C and 1.11 °C respectively, makes the SOC difference falls from 0.37% to 0.29% in a discharging process, under the severest design condition. Moreover, the optimized pack is proved to have a better performance under other conditions.

Automatic extraction of building geometries based on centroid clustering and contour analysis on oblique images taken by unmanned aerial vehicles

ABSTRACT This paper introduces a method based on centroid clustering and contour analysis to extract area and height measurements on buildings from the 3D model generated by oblique images. The method comprises three steps: (1) extract the contour plane from the fused data of the digital surface model (DSM) and digital orthophoto map (DOM); (2) identify building contour clusters based on the number of centroids contained in each category determined by mean-shift centroid clustering; (3) remove the mis-identified contours in a given building contour cluster by a contour analysis and obtain the geometric information of the building using map algebra. The proposed approach was tested against four datasets. Compared with other results, the detection has effective completeness, correctness, quality, and higher geometric accuracy. The maximum average relative error of building height and area extraction is less than 8%. The method is fast for a large-scale collection of building attributes and improves the applicability of oblique photography in GIS.

Remote monitoring system for maize seeding parameters based on Android and wireless communication

Most traditional maize seeding parameter monitoring devices use wired data transmission. The problems include wiring troubles, short transmission distances. And human-computer interaction display terminals are unique and usually customized rather than universal. A remote monitoring system for maize seeding parameters based on Android and wireless communication was developed in this study. The system used a single-chip microcomputer as the main controller and an infrared photoelectric sensor to capture seed information. The Android terminal application was used to set and display the seeder’s seed parameter information and monitor it. The Air202 communication module enabled remote data transmission, while the Global Positioning System (GPS) monitored the speed of the planter. By establishing a message queue telemetry transmission (MQTT) cloud served as a data freight station, data reception, storage and forwarding can be performed. Seeding parameters can generate Excel spreadsheets in real-time for easy data processing and storage. In order to verify the reliability of the system, the seeding parameter monitoring comparison test and the multi-terminal remote monitoring test were designed. The results of the seeding parameter monitoring comparison test showed that the monitoring system of this study had higher monitoring accuracy. The maximum average relative error of seeding parameter monitoring was 0.4%, which had high monitoring accuracy. The multi-terminal remote monitoring test showed that the monitoring system of this research can adapt many types of Android terminals, realize the wireless connection, and realize remote synchronous monitoring at different distances. This study provides a reference for intelligent remote monitoring and intelligent agriculture on unmanned farms. Keywords: remote monitoring system, maize seeding parameters, Android and wireless communication, remote synchronous monitoring, intelligent agriculture DOI: 10.25165/j.ijabe.20201306.5485 Citation: Xie C J, Zhang D X, Yang L, Cui T, Zhong X J, Li Y H, et al. Remote monitoring system for maize seeding parameters based on Android and wireless communication. Int J Agric & Biol Eng, 2020; 13(6): 159–165.

Remote monitoring system for maize seeding parameters based on Android and wireless communication

Most traditional maize seeding parameter monitoring devices use wired data transmission. The problems include wiring troubles, short transmission distances. And human-computer interaction display terminals are unique and usually customized rather than universal. A remote monitoring system for maize seeding parameters based on Android and wireless communication was developed in this study. The system used a single-chip microcomputer as the main controller and an infrared photoelectric sensor to capture seed information. The Android terminal application was used to set and display the seeder’s seed parameter information and monitor it. The Air202 communication module enabled remote data transmission, while the Global Positioning System (GPS) monitored the speed of the planter. By establishing a message queue telemetry transmission (MQTT) cloud served as a data freight station, data reception, storage and forwarding can be performed. Seeding parameters can generate Excel spreadsheets in real-time for easy data processing and storage. In order to verify the reliability of the system, the seeding parameter monitoring comparison test and the multi-terminal remote monitoring test were designed. The results of the seeding parameter monitoring comparison test showed that the monitoring system of this study had higher monitoring accuracy. The maximum average relative error of seeding parameter monitoring was 0.4%, which had high monitoring accuracy. The multi-terminal remote monitoring test showed that the monitoring system of this research can adapt many types of Android terminals, realize the wireless connection, and realize remote synchronous monitoring at different distances. This study provides a reference for intelligent remote monitoring and intelligent agriculture on unmanned farms. Keywords: remote monitoring system, maize seeding parameters, Android and wireless communication, remote synchronous monitoring, intelligent agriculture DOI: 10.25165/j.ijabe.20201306.5485 Citation: Xie C J, Zhang D X, Yang L, Cui T, Zhong X J, Li Y H, et al. Remote monitoring system for maize seeding parameters based on Android and wireless communication. Int J Agric & Biol Eng, 2020; 13(6): 159–165.

Prediction of Aeration Performance for Inverted Umbrella Aerator Based on Dimensional Analysis

As core equipment of the wastewater treatment process in chemical enterprises, the inverted umbrella aerator has been well studied in the areas of structural design and performance improvement. However, the relations between two devices which are geometrically and dynamically similar are far from having been thoroughly researched. This paper aims at investigating the relationships between geometrically and dynamically similar aerators and establishing a general performance prediction model for them. Based on dimensional analysis, the effect of structure on aeration performance is formulated by dimensionless relational expressions using the experimental data of reduced-scale aerators (reduced-scale model), and thus the performance prediction mathematical model for other aerators with geometrical and dynamical similarities is established. The Froude number Fr is found to be the most important affecting parameter of the improved absorption number Y, which is the only dimensionless number characterizing aeration performance. Validation of the formulas is conducted through the comparison of predicted values and experimental data in two validation aerators whose scale differences to reduced-scale model are 33% and 66%, respectively. Finally, the maximum average relative error between predicted values and experimental data was 8.92%, which indicates that the formulas are reliable and applicable to the performance prediction of the scaled aerator through the data of its reduced-scale prototype.

Intelligent information-based construction in tunnel engineering based on the GA and CCGPR coupled algorithm

Based on the construction of the Beikou tunnel, a genetic algorithm (GA) and combined covariance Gaussian process regression (CCGPR) coupled algorithm (GA-CCGPR) were introduced for information-based construction in tunnel engineering. In the initial monitoring period, GA-CCGPR algorithm is used to execute displacement back analysis and predict displacement of surrounding rock; after entering the long-term monitoring period, GA-CCGPR algorithm for prediction of surrounding rock displacement is established by training with the measured displacement data directly. One GA and support vector regression (SVR) coupled algorithm (GA-SVR) is introduced in this study for comparison with the GA-CCGPR algorithm. The application results of the Beikou tunnel show that the maximum relative error and maximum average relative error of displacement prediction for 3 continuous excavation steps based on the GA-CCGPR algorithm are 14.13% and 11.26% in the stage of inversion prediction, respectively. Correspondingly, these two indexes of GA-SVR algorithm reach as high as 34.78% and 23.52%, respectively. The displacement prediction results of the surrounding rock indicate that the maximum relative error and maximum average relative error of the GA-CCGPR algorithm are only 10.64% and 3.59% in long-term monitoring period, respectively; however, these two indexes based on the GA-SVR algorithm are 46.3% and 6.18%, respectively. In addition, the computational time of the SVR algorithm is 3–4 times higher than that of the CCGPR algorithm in both the sample training and parameter identification in initial monitoring period. Similarly, the time required for the SVR algorithm to complete the sample training process is 3–4 times that of the CCGPR algorithm in long-term monitoring period. Finally, an optimization method for the preliminary support parameters was proposed based on the GA and CCGPR coupled algorithm presented in this paper to form a complete information-based construction method for tunnel engineering. With the advantages of fast processing, simple operation and high accuracy, this method can be widely used in tunnel engineering and similar applications.

Simulation of the Water Dynamics and Root Water Uptake of Winter Wheat in Irrigation at Different Soil Depths

Soil water content (SWC) distribution plays an important role in root water uptake (RWU) and crop yield. Reasonable deep irrigation can increase the yield of winter wheat. The soil water movement model of winter wheat was established by considering the root water uptake and the different soil depths of irrigation and using the source term of the soil water movement equation to simulate irrigation at different soil depths. For model verification, experiments on three treatments of winter wheat growth were conducted at irrigation soil depths of 0% (T1), 40% (T2), and 70% (T3) of the distribution depth of the winter wheat root system. The SWC calculated by the model is in accordance with the dynamic change trend of the measured SWC. The maximum absolute error of the model was 0.022 cm3/cm3. The maximum average relative error was 7.95%. The maximum root mean square error was 0.28 cm3/cm3. Therefore, the model has a high simulation accuracy and can be used to simulate the distribution and dynamic changes of SWC of winter wheat in irrigation at different soil depths. The experimental data showed that irrigation soil depth has a significant effect on the root distribution of winter wheat (p < 0.05), and deep irrigation can reduce the root length density (RLD) in the upper soil layers and increase the RLD in the deeper soil layers. The dynamic simulation of RWU and SWC showed that deep irrigation can increase the SWC and RWU in deep soil and decrease the SWC and RWU in upper soil. Consequently, deep irrigation can increase the transpiration of winter wheat, reduce evaporation and evapotranspiration, and increase the yield of winter wheat.

Simulation of the flow behavior of AZ91 magnesium alloys at high deformation temperatures using a piecewise function of constitutive equations

The hot deformation behavior of AZ91 magnesium alloy was studied using single-pass compression experiments within a temperature range of 473–623 K and strain rate of 0.001–1 s−1. The flow stress first increases to a peak value with the work hardening, and then decreases slowly during dynamic softening. New piecewise function models were proposed to describe the constitutive equations of AZ91 magnesium alloy of stress–strain curves. Meanwhile, new methods to obtain the material constants k, C1 and C2 were proposed to predict accurately the flow stress corresponding within the range of strain from peak values to end based on the phenomenological representation of stress–strain curves in the second stage. Furthermore, the strain-compensated Arrhenius equation model was also used to describe the constitutive equations of plastic stage. The results predicted by these models are in good agreement with the measured data in the second stage, and the maximum average relative error of the predicted results is less than 10%. The strain-compensated Arrhenius equation model shows good capability under certain conditions, but it has lower fitting precision and also needs consume much time to obtain more material constants compared with piecewise function models. The piecewise function models show higher precision; the average relative error of the predicted results is less than 3% when the stress–strain curves in the second stage are described as nonlinear functions. These proposed methods for obtaining material constants k, C1 and C2 are valid and the piecewise function models are significant for establishing constitutive equations of metal alloys in hot deformation processes.