scholarly journals Modeling and parameters estimation of a Spatial Predator-Prey distribution

2019 ◽  
Vol 2 (1) ◽  
Author(s):  
Denis Ndanguza ◽  
Jean Pierre Muhirwa ◽  
Anatholie Uwimana
Keyword(s):  
Stability Analysis ◽  
Synthetic Data ◽  
Simulated Data ◽  
Least Square Method ◽  
Parameters Estimation ◽  
Least Square ◽  
Coefficient Of Determination ◽  
Model Parameters ◽  
Predator Prey ◽  
Monte Carlo Algorithms

Predator prey interactions are important in ecology and most of time in the analysis, the two antagonists are assumed to be in a closed system. The aim of this study is to model the unclosed predator-prey system. The model is built and simulated data are computed by adding noise on deterministic solution. Therefore, model parameters are estimated using least square method. We compute the two critical points and the stability analysis is carried out and results show that the population is stable at one critical point and unstable at (0,0). The model fits the synthetic data with coefficient of determination R2 = 0.9693 equivalent to 96.93%. Using the residual analysis to test the validity of the model, it is shown that there is no pattern between residuals. To strengthen the validity of the model, the Markov Chain Monte Carlo algorithms are used as an alternative method in parameters estimation. Diagnostics prove the chains’ convergence which is the sign of an accurate model. As conclusion, the model is accurate and it can be applied to real data.Keywords: predator-prey, spatial distribution, parameters, Metropolis-Hastings algorithm, model diagnostic, stability analysis

scholarly journals Influence of Operating Parameters on Running-in Wear of EN-31 Steel

2016 ◽  
Vol 13 (1) ◽  
pp. 1-2
Author(s):  
M. Hanief ◽  
M. F. Wani
Keyword(s):  
Surface Roughness ◽  
Wear Rate ◽  
Least Square Method ◽  
Least Square ◽  
Coefficient Of Determination ◽  
Percentage Error ◽  
Model Parameters ◽  
Operating Parameters ◽  
Proposed Model ◽  
En 31

Abstract In this paper, effect of operating parameters (temperature, surface roughness and load) was investigated to determine the influence of each parameter on the wear rate. A mathematical model was developed to establish a functional relationship between the running-in wear rate and the operating parameters. The proposed model being non-linear, it was linearized by logarithmic transformation and the optimal values of model parameters were obtained by least square method. It was found that the surface roughness has significant effect on wear rate followed by load and temperature. The adequacy of the model was estimated by statistical methods (coefficient of determination (R2) and mean absolute percentage error (MAPE)) .

Examination of Correlation Between Arousal Level and Auditory Environmental Change Using Rock and Classic Music

2017 ◽  
Author(s):  
Kentaro Miyago ◽  
Kenyu Uehara ◽  
Takashi Saito
Keyword(s):  
Visual Cortex ◽  
Frontal Lobe ◽  
Traffic Accidents ◽  
Evaluation Method ◽  
Duffing Oscillator ◽  
Least Square Method ◽  
Arousal Level ◽  
Least Square ◽  
Model Parameters ◽  
Eeg Data

Recently, traffic accidents due to drowsy driving, operation mistake in the power plant by drowsiness and decrease arousal in employment during work have been attracted as problems. To avoid such an accident, arousal level could be quantitatively evaluated in real time. We suggested that the one of the parameters of Duffing oscillator parameters is related to the conventional arousal level using the EEG frequency component. However, in this examination, effects on the EEG from visual and active behavior were considered, but those from hearing also need to be investigated. In this paper, we performed the experiment in the musical environment using rock and classic music to investigate the model parameters for effect of the auditory stimulation, and acquired EEG data in Visual cortex and Frontal lobe. The acquired EEG data was used to identify the model parameters, which were identified solving the inverse problem by Least Square method. Results of investigating correlation between conventional arousal revel and model parameter shows a significant correlation in case of the auditory environmental situation. Moreover, Visual cortex is better than Frontal lobe as a measurement point in this evaluation method.

scholarly journals Online Parameter Identification and State of Charge Estimation of Battery Based on Multitimescale Adaptive Double Kalman Filter Algorithm

2020 ◽  
Vol 2020 ◽  
pp. 1-20
Author(s):  
Wenxian Duan ◽  
Chuanxue Song ◽  
Yuan Chen ◽  
Feng Xiao ◽  
Silun Peng ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Parameter Identification ◽  
Unscented Kalman Filter ◽  
Least Square Method ◽  
State Of Charge ◽  
Least Square ◽  
Accurate Estimation ◽  
Battery Life ◽  
Model Parameters ◽  
Simulation Results

An accurate state of charge (SOC) can provide effective judgment for the BMS, which is conducive for prolonging battery life and protecting the working state of the entire battery pack. In this study, the first-order RC battery model is used as the research object and two parameter identification methods based on the least square method (RLS) are analyzed and discussed in detail. The simulation results show that the model parameters identified under the Federal Urban Driving Schedule (HPPC) condition are not suitable for the Federal Urban Driving Schedule (FUDS) condition. The parameters of the model are not universal through the HPPC condition. A multitimescale prediction model is also proposed to estimate the SOC of the battery. That is, the extended Kalman filter (EKF) is adopted to update the model parameters and the adaptive unscented Kalman filter (AUKF) is used to predict the battery SOC. The experimental results at different temperatures show that the EKF-AUKF method is superior to other methods. The algorithm is simulated and verified under different initial SOC errors. In the whole FUDS operating condition, the RSME of the SOC is within 1%, and that of the voltage is within 0.01 V. It indicates that the proposed algorithm can obtain accurate estimation results and has strong robustness. Moreover, the simulation results after adding noise errors to the current and voltage values reveal that the algorithm can eliminate the sensor accuracy effect to a certain extent.

TWO-DIMENSIONAL DC RESISTIVITY MAPPING FOR SUBSURFACE INVESTIGATION USING SOFT COMPUTING APPROACHES

2015 ◽  
Vol 77 (17) ◽  
Author(s):  
Herman Wahid ◽  
Mohd. Hakimi Othman ◽  
Ruzairi Abdul Rahim
Keyword(s):  
Inverse Problem ◽  
Synthetic Data ◽  
Least Square Method ◽  
Least Square ◽  
Dc Resistivity ◽  
Two Dimensional ◽  
Actual Model ◽  
Subsurface Investigation ◽  
Artificial Neural Network Ann ◽  
Mlp Model

In geophysical subsurface surveys, difficulty to interpret measurement of data obtain from the equipment are risen. Data provided by the equipment did not indicate subsurface condition specifically and deviates from the expected standard due to numerous features. Generally, the data that obtained from the laws of physics computation is known as forward problem. And the process of obtaining the data from sets of measurements and reconstruct the model is known as inverse problem. Researchers have proposed multiple estimation techniques to cater the inverse problem and provide estimation that close to actual model. In this work, we investigate the feasibility of using artificial neural network (ANN) in solving two- dimensional (2-D) direct current (DC) resistivity mapping for subsurface investigation, in which the algorithms are based on the radial basis function (RBF) model and the multi-layer perceptron (MLP) model. Conventional approach of least square (LS) method is used as a benchmark and comparative study with the proposed algorithms. In order to train the proposed algorithms, several synthetic data are generated using RES2DMOD software based on hybrid Wenner-Schlumberger configurations. Results are compared between the proposed algorithms and least square method in term of its effectiveness and error variations to the actual values. It is discovered that the proposed algorithms have offered better performance in term minimum error difference to the actual model, as compared to least square method. Simulation results demonstrate that proposed algorithms can solve the inverse problem and it can be illustrated by means of the 2-D graphical mapping.

scholarly journals Grey power models based on optimization of initial condition and model parameters

2014 ◽  
Vol 4 (2) ◽  
pp. 370-382 ◽  
Author(s):  
Yunchol Jong ◽  
Sifeng Liu
Keyword(s):  
Least Square Method ◽  
Least Square ◽  
Model Parameters ◽  
Initial Condition ◽  
Content Type ◽  
Novel Approach ◽  
New Information ◽  
Power Models ◽  
Grey Verhulst Model ◽  
Verhulst Model

Purpose – The purpose of this paper is to propose a novel approach to improve prediction accuracy of grey power models including GM(1, 1) and grey Verhulst model. Design/methodology/approach – The modified new models are proposed by optimizing the initial condition and model parameters. The new initial condition consists of the first item and the last item of a sequence generated by applying the first-order accumulative generation operator on the sequence of raw data. Findings – It is shown that the newly modified grey power model is an extension of the previous optimized GM(1, 1) and grey Verhulst model. And the optimized initial condition reflected the principle of new information priority. Practical implications – The result of a numerical example indicates that the modified grey model presented in this paper with better prediction performance. Originality/value – The new initial condition are derived by weighted combination of the first item and the last item. The coefficients of weight obtained by the least square method.

The three‐parameter equation: An efficient tool to enhance the stack

Geophysics ◽  
1994 ◽  
Vol 59 (2) ◽  
pp. 297-308 ◽  
Author(s):  
Pierre D. Thore ◽  
Eric de Bazelaire ◽  
Marisha P. Rays
Keyword(s):  
Synthetic Data ◽  
Real Data ◽  
Least Square Method ◽  
Maximum Energy ◽  
Computational Effort ◽  
Velocity Estimation ◽  
Least Square ◽  
Waveform Data ◽  
Interval Velocity ◽  
Parameter Equation

We compare the three‐term equation to the normal moveout (NMO) equation for several synthetic data sets to analyze whether or not it is worth making the additional computational effort in the stacking process within various exploration contexts. In our evaluation we have selected two criteria: 1)The quality of the stacked image. 2) The reliability of the stacking parameters and their usefulness for further computation such as interval velocity estimation. We have simulated the stacking process very precisely, despite using only the traveltimes and not the full waveform data. The procedure searches for maximum coherency along the traveltime curve rather than a least‐square regression to it. This technique, which we call the Gaussian‐weighted least square, avoids most of the shortcomings of the least‐square method. The following are our conclusions: 1) The three term equation gives a better stack than the regular NMO. The increase in stacking energy can be more than 30 percent. 2)The calculation of interval velocities using a DIX formula rewritten for the three‐parameter equation is much more stable and accurate than the standard DIX formula. 3) The search for the three parameters is feasible in an efficient way since the shifted hyperbola requires only static corrections rather than dy namic ones. 4) Noise alters the parameters of the maximum energy stack in a way that depends on the noise type. The estimates obtained remain accurate enough for interval velocity estimation (where only two parameters are needed), but the use of the three parameters in direct inversion may be hazardous because of noise corruption. These conclusions should, however, be verified on real data examples.

Study on Detection of Epileptic Discharges Based on a Duffing Oscillator Model

2014 ◽  
Author(s):  
Takahiro Murakami ◽  
Yasumi Ukida ◽  
Masami Fujii ◽  
Michiyasu Suzuki ◽  
Takashi Saito
Keyword(s):  
Duffing Oscillator ◽  
Time History ◽  
Least Square Method ◽  
Least Square ◽  
Quantitative Detection ◽  
Model Parameters ◽  
Appearance Time ◽  
Epileptic Discharges ◽  
History Of ◽  
Electrocorticogram Ecog

In order to establish a quantitative detection method for appearance in epileptic discharges (EDs), we propose using the model parameters in a Duffing oscillator, which is a nonlinear mathematical model. Extracting four frequency bands of delta, theta, alpha and beta waves from the time history of the electrocorticogram (ECoG) obtained from rats with induced EDs, we applied a sweep window to the time history for each band. So as to fit the equation for the Duffing oscillator to the time history of the ECoG, we used the least square method to determine the model parameters expressing characteristics of ECoG. The Duffing oscillator has three kinds of vibrational parameters and four kinds of parameters about the amplitude for the driving force with two predominant frequencies contained in ECoG. In order to examine the appearance time of the EDs and the change of ECoG characteristics, we determined the model parameters for each sweep window. When epilepsy occurs, we found that the amount of the parameters related to “conservation”, “dissipation” and “input quantities” increases. On the other hand, the parameter value corresponding to nonlinearity tends to decrease. It is found that the proposed method by the model parameters of the Duffing oscillator can be used in quantitative detection for EDs.

Effect Factors Analysis of Flow Noise Generation from Perforated Duct Muffler Element

2011 ◽  
Vol 346 ◽  
pp. 204-209 ◽  
Author(s):  
Hai Jun Zhao ◽  
Zhao Xiang Deng
Keyword(s):  
Least Square Method ◽  
Least Square ◽  
Model Parameters ◽  
Noise Generation ◽  
Effect Factors ◽  
Expansion Chamber ◽  
Flow Noise ◽  
Factors Analysis ◽  
Structure Of Flow ◽  
Relationship Model

Flow noise regeneration from perforated tube muffler element was measured on the self-developing test bench, relationship model on total sound power of flow regeneration noise and structure parameters and work condition was established. Its model parameters were solved making use of hyper static least square method. Using the model effect factors of flow noise generation were discussed. Result shows that the reducing of the perforated diameter and the perforated part length is favor of the reduction of flow noise, and perforated ratio and expansion chamber diameter have less effect on flow noise. After analyzing spectrum structure of flow regeneration noise, it is displayed that with the increase of flow velocity projected peak value frequency has the trend of moving to middle and high, its intensity also becomes stronger, and sound energy in some the frequency accounts for about 60% of the total energy, Strophe number is the range of from 0.2 to 0.35.

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