scholarly journals A Note on the Reproducibility of Chaos Simulation

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 953
Author(s):  
Thalita E. Nazaré ◽  
Erivelton G. Nepomuceno ◽  
Samir A. M. Martins ◽  
Denis N. Butusov
Keyword(s):  
Experimental Data ◽  
Root Mean Square Error ◽  
Computer Simulations ◽  
Chaotic Systems ◽  
Mean Square ◽  
Finite Precision ◽  
Prediction Horizon ◽  
Code Sharing ◽  
Simulation Results

An evergreen scientific feature is the ability for scientific works to be reproduced. Since chaotic systems are so hard to understand analytically, numerical simulations assume a key role in their investigation. Such simulations have been considered as reproducible in many works. However, few studies have focused on the effects of the finite precision of computers on the simulation reproducibility of chaotic systems; moreover, code sharing and details on how to reproduce simulation results are not present in many investigations. In this work, a case study of reproducibility is presented in the simulation of a chaotic jerk circuit, using the software LTspice. We also employ the OSF platform to share the project associated with this paper. Tests performed with LTspice XVII on four different computers show the difficulties of simulation reproducibility by this software. We compare these results with experimental data using a normalised root mean square error in order to identify the computer with the highest prediction horizon. We also calculate the entropy of the signals to check differences among computer simulations and the practical experiment. The methodology developed is efficient in identifying the computer with better performance, which allows applying it to other cases in the literature. This investigation is fully described and available on the OSF platform.

The effects of CO2 database on a localized AquaCrop model construction based on the field experiment

2021 ◽  
Author(s):  
fawen li ◽  
chunya song ◽  
hua li
Keyword(s):  
Root Mean Square Error ◽  
Winter Wheat ◽  
Water Content ◽  
Soil Water ◽  
Soil Water Content ◽  
Mean Square Error ◽  
North China Plain ◽  
North China ◽  
Mean Square ◽  
Simulation Results

Abstract To examine whether the use of default CO2 database affected the simulation results, this paper built the AquaCrop models of winter wheat based on the measured CO2 database and the default CO2 database, respectively. The models were calibrated with data (2017–2018) and validated with the data (2018–2019) in the North China Plain. The residual coefficient method (CRM), root mean square error (RMSE), normalized root mean square error (NRMSE) and determination coefficient (R2) were used to test the model performance. The results showed that the accuracy of simulation under the two CO2 database were both good. Compared with the default CO2 database, the simulation accuracy under the measured CO2 database had higher accuracy. In order to verify the model further, the simulated values of evapotranspiration, soil water content and measured values were compared and analyzed. The results showed that there were some errors between the measured evapotranspiration and the values of simulation in the filling and waxing period of winter wheat. In general, the simulation values of evapotranspiration were consistent with the measured value at different irrigation levels. The simulated values ​​of the soil water content at the three levels of irrigation were all higher than the measured values, but the simulated results basically reflected the dynamic changes of soil water content throughout the growth period. The model adjustment value of WP*(the normalized water productivity) were a difference under the two CO2 databases, which is one of the reasons for the difference in the simulation results. The results show that in the absence of measured CO2 data, the default CO2 database can be used, which has little influence on the model construction, and the accuracy of the model constructed meets the actual demand. The research results can provide a basis for the establishment of crop models in North China Plain.

scholarly journals Wavefront Restoration Technology of Dynamic Non-Uniform Intensity Distribution Based on Extreme Learning Machine

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3877
Author(s):  
Haiqi Lin ◽  
Xing He ◽  
Shuai Wang ◽  
Ping Yang
Keyword(s):  
Root Mean Square Error ◽  
Extreme Learning Machine ◽  
Intensity Distribution ◽  
Near Field ◽  
Wavefront Sensor ◽  
Mean Square ◽  
Initial Value ◽  
Machine Method ◽  
Simulation Results ◽  
Learning Machine

Non-uniform intensity distribution of laser near-field beam results in the irregular shape of the spot in the wavefront sensor. The intensity of some sub-aperture spots may be too weak to be detected, and the accuracy of wavefront restoration is seriously affected. Therefore, an extreme learning machine method is proposed to realize high precision wavefront restoration under dynamic non-uniform intensity distribution. The simulation results show that this method has better accuracy of wavefront restoration than the classical modal algorithm under dynamic non-uniform intensity distribution. The root mean square error of the residual wavefront for the proposed method is only 2.9% of the initial value.

scholarly journals An Effective Method to Accurately Extract the Parameters of Single Diode Model of Solar Cells

Nanomaterials ◽  
2021 ◽  
Vol 11 (10) ◽  
pp. 2615
Author(s):  
Zhaoxu Song ◽  
Kun Fang ◽  
Xiaofang Sun ◽  
Ying Liang ◽  
Wei Lin ◽  
...  
Keyword(s):  
Experimental Data ◽  
Solar Cells ◽  
Root Mean Square Error ◽  
Iterative Method ◽  
Error Analysis ◽  
Accurate Method ◽  
Extraction Process ◽  
Model Parameters ◽  
Mean Square ◽  
Calculation Process

A non-iterative method is presented to accurately extract the five parameters of single diode model of solar cells in this paper. This method overcomes the problems of complexity and accuracy by simplifying the calculation process. Key parts of the equation are to be adjusted dynamically so that the desired five parameters can be obtained from the I–V curve. Then, the I-V and P-V characteristic curves of solar cells are used to compare the effectiveness of this method with other methods. Furthermore, the root mean square error analysis shows that this method is more applicable than other methods. Finally, the I-V and P-V characteristics simulated by using the extracted parameters in this method are compared and discussed with the experimental data of solar cells under different conditions. In fact, this extraction process can be regarded as an effective and accurate method to estimate solar cells’ single diode model parameters.

The drag of a compressible turbulent boundary layer on a smooth flat plate with and without heat transfer

1964 ◽  
Vol 18 (1) ◽  
pp. 117-143 ◽  
Author(s):  
D. B. Spalding ◽  
S. W. Chi
Keyword(s):  
Experimental Data ◽  
Root Mean Square Error ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Mixing Length ◽  
Mean Square ◽  
Temperature Ratio ◽  
Wide Range ◽  
Mixing Length Theory ◽  
Meansquare Error

The theoretical treatments given by earlier authors are classified, reviewed and where necessary extended; then the predictions of twenty of these theories are evaluated and compared with all available experimental data, the root-meansquare error being computed for each theory. The theory of van Driest-II gives the lowest root-mean-square error (11.0%).A new calculation procedure is developed from the postulate that a unique relation exists betweencfFcandRFRwherecfis the drag coefficient,Ris the Reynolds number, andFcandFRare functions of Mach number and temperature ratio alone. The experimental data are found to be too scanty for bothFcandFRto be deduced empirically, soFcis calculated by means of mixing-length theory andFRis found semi-empirically. Tables and charts of values ofFcandFRare presented for a wide range ofMGandTS/TG. When compared with all experimental data, the predictions of the new procedure give a root-mean-square error of 9.9%.

scholarly journals Drying Characteristics of Abelmoschus esculentus Thin Piece on Drying in a Fabricated Tunnel Dryer

2019 ◽  
pp. 1-5
Author(s):  
Dinesh Kumar ◽  
L. P. Singh ◽  
A. K. Singh
Keyword(s):  
Experimental Data ◽  
Root Mean Square Error ◽  
Abelmoschus Esculentus ◽  
Mean Bias Error ◽  
Bias Error ◽  
Drying Rate ◽  
Mean Square ◽  
Drying Time ◽  
Drying Characteristics ◽  
Tunnel Dryer

For the storage of crops, various drying processes are used. It should be synthesized on the basis of drying time, product quality such as colour texture and the taste of the product when uses. To study the drying characteristics of Abelmoschus esculentus (bhindi) thin piece was performed for a temperature range of 38°C and 88°C and velocity of air is fixed at 1.1 m/s in the fabricated tunnel. For the investigation of drying, characteristics experiment was performed, the result was found, the drying rate was falling. The sample studied at 38°C was much good in colour texture and aroma than sample studied at 58°C to 88°C. The experimental data were used on different models proposed, by equating the determination coefficient , Mean Bias Error (MBE), decreased  and Root Mean Square Error (RMSE) measured along with investigated moisture ratio.

scholarly journals Improving Quantitative Rainfall Prediction Using Ensemble Analogues in the Tropics: Case study of Uganda

2017 ◽  
Author(s):  
Isaac Mugume ◽  
Michel d. S. Mesquita ◽  
Yazidhi Bamutaze ◽  
Didier Ntwali ◽  
Charles Basalirwa ◽  
...  
Keyword(s):  
Root Mean Square Error ◽  
Ensemble Methods ◽  
Predictive Performance ◽  
Mean Square ◽  
New Approach ◽  
Rainfall Prediction ◽  
Ensemble Mean ◽  
Additional Improvement ◽  
The Tropics

Accurate and timely rainfall prediction enhances productivity and can aid proper planning in sectors such as agriculture, health, transport and water resources. This study is aimed at improving rainfall prediction using ensemble methods. It first assesses the performance of six convective schemes (Kain–Fritsch (KF); Betts–Miller–Janji´c (BMJ); Grell–Fretas (GF); Grell 3D ensemble (G3); New–Tiedke (NT) and Grell–Devenyi (GD)) using the root mean square error (RMSE) and mean error (ME) focusing on the March–May 2013 rainfall period over Uganda. 18 ensemble members are generated from the three best performing convective schemes (i.e. KF, GF & G3). The performance of three ensemble methods (i.e. ensemble mean (EM); ensemble mean analogue (EMA) and multi–member analogue ensemble (MAEM)) is also analyzed using the RMSE and ME. The EM presented a smaller RMSE compared to individual schemes (EM:10.02; KF:23.96; BMJ:26.04; GF:25.85; G3:24.07; NT:29.13 & GD:26.27) and a better bias (EM:-1.28; KF:-1.62; BMJ:-4.04; GF:-3.90; G3:-3.62; NT:-5.41 & GD:-4.07). The EMA and MAEM presented 13 out of 21 stations & 17 out of 21 stations respectively with smaller RMSE compared to EM thus demonstrating additional improvement in predictive performance. The MAEM is a new approach proposed and described in the study.

scholarly journals Addictive Games: Case Study on Multi-Armed Bandit Game

Information ◽  
2021 ◽  
Vol 12 (12) ◽  
pp. 521
Author(s):  
Xiaohan Kang ◽  
Hong Ri ◽  
Mohd Nor Akmal Khalid ◽  
Hiroyuki Iida
Keyword(s):  
Experimental Data ◽  
Ratio Schedule ◽  
Variable Ratio ◽  
Player Satisfaction ◽  
Simulation Results ◽  
The Difference ◽  
Skinner Box ◽  
Typical Test ◽  
Multiarmed Bandit

The attraction of games comes from the player being able to have fun in games. Gambling games that are based on the Variable-Ratio schedule in Skinner’s experiment are the most typical addictive games. It is necessary to clarify the reason why typical gambling games are simple but addictive. Also, the Multiarmed Bandit game is a typical test for Skinner Box design and is most popular in the gambling house, which is a good example to analyze. This article mainly focuses on expanding on the idea of the motion in mind model in the scene of Multiarmed Bandit games, quantifying the player’s psychological inclination by simulation experimental data. By relating with the quantification of player satisfaction and play comfort, the expectation’s feeling is discussed from the energy perspective. Two different energies are proposed: player-side (Er) and game-side energy (Ei). This provides the difference of player-side (Er) and game-side energy (Ei), denoted as Ed to show the player’s psychological gap. Ten settings of mass bandit were simulated. It was found that the setting of the best player confidence (Er) and entry difficulty (Ei) can balance player expectation. The simulation results show that when m=0.3,0.7, the player has the biggest psychological gap, which expresses that player will be motivated by not being reconciled. Moreover, addiction is likely to occur when m∈[0.5,0.7]. Such an approach can also help the developers and educators increase edutainment games’ efficiency and make the game more attractive.

Metaheuristic data fitting methods to estimate Weibull parameters for wind speed data: a case study of Hasan Polatkan Airport

2021 ◽  
pp. 1-33
Author(s):  
A. Kaba ◽  
A. E. Suzer
Keyword(s):  
Wind Speed ◽  
Numerical Methods ◽  
Root Mean Square Error ◽  
Objective Function ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Statistical Tests ◽  
Mean Square ◽  
Flight Delays

ABSTRACT Flight delays may be decreased in a predictable way if the Weibull wind speed parameters of a runway, which are an important aspect of safety during the take-off and landing phases of aircraft, can be determined. One aim of this work is to determine the wind profile of Hasan Polatkan Airport (HPA) as a case study. Numerical methods for Weibull parameter determination perform better when the average wind speed estimation is the main objective. In this paper, a novel objective function that minimises the root-mean-square error by employing the cumulative distribution function is proposed based on the genetic algorithm and particle swarm optimisation. The results are compared with well-known numerical methods, such as maximum-likelihood estimation, the empirical method, the graphical method and the equivalent energy method, as well as the available objective function. Various statistical tests in the literature are applied, such as R2, Root-Mean-Square Error (RMSE) and $\chi$ 2. In addition, the Mean Absolute Error (MAE) and total elapsed time calculated using the algorithms are compared. According to the results of the statistical tests, the proposed methods outperform others, achieving scores as high as 0.9789 and 0.9996 for the R2 test, as low as 0.0058 and 0.0057 for the RMSE test, 0.0036 and 0.0045 for the MAE test and 3.53 × 10−5 and 3.50 × 10−5 for the $\chi$ 2 test. In addition, the determination of the wind speed characteristics at HPA show that low wind speed characteristics and regimes throughout the year offer safer take-off and landing schedules for target aircraft. The principle aim of this paper is to help establish the correct orientation of new runways at HPA and maximise the capacity of the airport by minimising flight delays, which represent a significant impediment to air traffic flow.

scholarly journals Experimental Validation of Numerical Model for Bi-Tilt-Isolator

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Ming-Hsiang Shih ◽  
Wen-Pei Sung ◽  
Chia-Yu Ho
Keyword(s):  
Mathematical Model ◽  
Root Mean Square Error ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Friction Force ◽  
Polynomial Function ◽  
Mean Square ◽  
Test Results ◽  
Cubic Polynomial ◽  
Simulation Results

Bi-Tilt Isolator (BTI) is composed of bi-tilt beveled substrate and slider. The advantages of BTI are that the maximum upload seismic force of structure can be easily controlled and displacement of isolation layer will be reduced. Sliding force, friction force, and impulse force are caused in the slanting process of BTI, nonlinear behavior. A nonlinear mathematical model is derived based on the sliding upwards, sliding downwards, and transition stages. Then, BTI element of nonlinear analysis program, GENDYN, is developed by the fourth-order Runge-Kutta method, the discretized ordinary differential equation for three movement stages of BTI. Then, test set-up of superstructure installed with BTI is tested and recorded the real displacement and acceleration responses under conditions of full lubrication, mild lubrication, and without lubrication between interface of bi-tilt beveled substrate and slider with three various initial displacements. The comparison of simulation results and test results shows the following: (1) root mean square error is below 1.35% for WD40 sprayed, 0.47% for WD40 whipped, and 0.54% for without lubrication, respectively; (2) the maximum root mean square error for simulating with cubic polynomial function of friction is much less than those of constant friction except conditions of full lubrication, which are not affected by kinetic friction force; (3) application of cubic polynomial function for simulating friction of BTI with three different lubricated conditions can perform very fine simulation results, compared with the test results. This proposed mathematical model and BTI element of GENDYN program, using cubic polynomial function of friction, perform fine simulation capability to assess nonlinear isolation effect of structure installed with BTI.

scholarly journals Lyapunov-Based Controller for a Class of Stochastic Chaotic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Hossein Shokouhi-Nejad ◽  
Amir Rikhtehgar Ghiasi ◽  
Saeed Pezeshki
Keyword(s):  
Differential Equation ◽  
White Noise ◽  
Transient Response ◽  
Chaotic Systems ◽  
Direct Method ◽  
Control Law ◽  
Mean Square ◽  
Intrinsic Properties ◽  
General Control ◽  
Simulation Results

This study presents a general control law based on Lyapunov’s direct method for a group of well-known stochastic chaotic systems. Since real chaotic systems have undesired random-like behaviors which have also been deteriorated by environmental noise, chaotic systems are modeled by exciting a deterministic chaotic system with a white noise obtained from derivative of Wiener process which eventually generates an Ito differential equation. Proposed controller not only can asymptotically stabilize these systems in mean-square sense against their undesired intrinsic properties, but also exhibits good transient response. Simulation results highlight effectiveness and feasibility of proposed controller in outperforming stochastic chaotic systems.

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