Relative Error Of Model Research Articles

Set Pair Analysis Based on Phase Space Reconstruction Model and Its Application in Forecasting Extreme Temperature

In order to improve the precision of forecasting a time series, set pair analysis based on phase space reconstruction (SPA-PSR) model is established. In the new model, by using chaos analysis, we reconstruct the phase space with delay time and embedding dimension. Based on it, we rebuilt history sets and current sets in the SPA-PSR model. Two cases of forecasting extreme temperature in Mount Wutai and Datong are taken to examine the performance of SPA-PSR model. The results indicate that the mean relative error (MRE) of SPA-PSR model has decreased by 65.97%, 59.32%, and 7.79% in the case of Mount Wutai and 29.11%, 32.82%, and 9.03% in the case of Datong, respectively, compared with autoregression (AR) model, rank set pair analysis (R-SPA) model, and Back-Propagation (BP) neural network model. It gives a theoretical support for set pair analysis and improves precision of numerical forecasting.

粘弹性力学在高温铸造合金单向拉伸试验中的应用

给出了Kelvin链的应力–应变微分型本构关系。全面考虑初始条件，推导了Burgers四参量流体、Kelvin- Maxwell六参量模型在阶跃函数单向应力作用下的总应变通解。Burgers四参量流体、Kelvin-Maxwell六参量模型都可以近似地描述金属材料蠕变曲线的前两个阶段，但都不能反映第三个阶段。铸造Mar-M200合金蠕变曲线的计算表明，两种理论预测与实验测量的结果的一致性较好，特别是Kelvin-Maxwell六参量模型的最大相对误差仅为5.4765779%。 The stress-strain differential constitutive relation was given for Kelvin chain. On basis of all the initial conditions taken into account, the general solutions of total strain were derived for Burgers fluid with 4 parameters and Kelvin-Maxwell model with 6 ones under the step function uniaxial stress. Both Burgers fluid with 4 parameters and Kelvin-Maxwell model with 6 ones could approximately describe the former two stages of creep curve but not reflect the third stage. Numerical calculation for cast Mar-M200 alloy creep curve shows that two theories predictions are in good agreement with test measurement results, especially the maximum relative error of Kelvin-Maxwell model with 6 parameters is only 5.4765779%.

The Nitrogen Quantitative Model Based on Hyperspectral Image of Tomato Leaf

Based on hyperspectral image which integrates spectrum and image information, the tomato leaf nitrogen model is built. Tomato samples were soillessly cultured with different nitrogen content. The hyperspectral images of tomato leaves are gathered at different stages of tomato. Kjeldahl method determines nitrogen content of the corresponding tomato leaves. According to the hyperspectral information of leaf, the characteristic wave bands of tomato nitrogen are obtained in the method of stepwise regression. The images in the characteristic bands are processed and analyzed, and image features which have high correlation with nitrogen contents of tomato leaves are picked up. The PLS algorithm is used in three growth periods to build tomato nitrogen prediction model, The result of the predicted test shows that the forecast average relative error of PLS model may achieve 10%, and can satisfy the forecast request.

Application of Coupling Model of Projection Pursuit Partial Least-Square Regression Based on Real Coded Accelerating Genetic Algorithm in Land Use Change Forecasting

In study of Land Use Change forecasting, lots of methods have been developed ,such as Markov model、BP algorithm、Canonical correlation analysis, least-squares regression analysis ,but these methods have deficiency in decision and often inadequate in sample size. In response to these deficiencies，projection pursuit Partial Least-Square Regression based on real coded accelerating genetic algorithm model is developed to analyze and predict land use change in Yanji City. The computation results show that the relative error of Coupling Model of Partial Least-Square Regression Based on Projection Pursuit is smaller than traditional Partial Least-Square Regression model’s, and it has improved the prediction precision evidently.

A Research for Broadband Modeling Method of Electro-Absorption Modulator

This paper improves the broadband equivalent circuit model (ECM) modeling method of Electro-absorption Modulator. According to the principle of Circuit Partitioning Simplified, the series form of the original increased frequency impedance model is transformed into the parallel form. The result shows that the new method eliminates the process of the impedance type verification, will not introduce new nodes, and reduces the computation. After testing, the maximum relative error of this model to fit measurement data is only 0.693%. This method’s simulation results are consistent with the test data of ECM better in 0-8GHz frequency range.

Prediction model of DnBP degradation based on BP neural network in AAO system

A laboratory-scale anaerobic–anoxic–oxic (AAO) system was established to investigate the fate of DnBP. A removal kinetic model including sorption and biodegradation was formulated, and kinetic parameters were evaluated with batch experiments under anaerobic, anoxic, oxic conditions. However, it is highly complex and is difficult to confirm the kinetic parameters using conventional mathematical modeling. To correlate the experimental data with available models or some modified empirical equations, an artificial neural network model based on multilayered partial recurrent back propagation (BP) algorithm was applied for the biodegradation of DnBP from the water quality characteristic parameters. Compared to the kinetic model, the performance of the network for modeling DnBP is found to be more impressive. The results showed that the biggest relative error of BP network prediction model was 9.95%, while the kinetic model was 14.52%, which illustrates BP model predicting effluent DnBP more accurately than kinetic model forecasting.

Optimizing of SVM with Hybrid PSO and Genetic Algorithm in Power Load Forecasting

In this paper, we propose Hybrid Particle Swarm Optimization (HPSO) with genetic algorithm(GA) mutation to optimize the SVM forecasting model. In the process of doing so, we first use HPSO with genetic algorithm to make pretreatment of the data. PSO with GA model is a method for finding a solution of stochastic global optimizer based on swarm intelligence. Using the interaction of particles, PSOGA model searches the solution space intelligently, this will find out the best one and reduce the redundant information. The PSOGA-SVM method proposed in this paper is based on the global optimization of PSOGA and local accurate searching of SVM. And to prove the effectiveness of the model, single SVM algorithm and BP network was used to compare with the result of PSOGA-SVM. The results show that the model is effective and highly accurate in the forecasting of short-term power load than the other models. The root-mean-square relative error (RMSRE) of new model is only 1.82%, the SVM model and BP network is 2.43%, 4.10% separately.

Chemometrics-assisted spectrophotometry method for the determination of chemical oxygen demand in pulping effluent

A new method has been developed for the determination of chemical oxygen demand (COD) in pulping effluent using chemometrics-assisted spectrophotometry. Two calibration models were established by inducing UV-visible spectroscopy (model 1) and derivative spectroscopy (model 2), combined with the chemometrics software Smica-P. Correlation coefficients of the two models are 0.9954 (model 1) and 0.9963 (model 2) when COD of samples is in the range of 0 to 405mg/L. Sensitivities of the two models are 0.0061 (model 1) and 0.0056 (model 2) and method detection limits are 2.02-2.45mg/L (model 1) and 2.13-2.51mg/L (model 2). Validation experiment showed that the average standard deviation of model 2 was 1.11 and that of model 1 was 1.54. Similarly, average relative error of model 2 (4.25%) was lower than model 1 (5.00%), which indicated that the predictability of model 2 was better than that of model 1. Chemometrics-assisted spectrophotometry method did not need chemical reagents and digestion which were required in the conventional methods, and the testing time of the new method was significantly shorter than the conventional ones. The proposed method can be used to measure COD in pulping effluent as an environmentally friendly approach with satisfactory results.

Mathematical Model for Closed-Form Solution of Parameters of Cylinder Exhaust Port in Variable-Stroke Engine

A mathematical model for getting the closed-form solution of main parameters of cylinder exhaust port is present, based on a few known parameters of variable-stroke engine (VSE). Considering lack of parameters in the initial stage of design, empirical formula is applied to solve the initial specific time-area value of exhaust port, and the initial port timing angle is solved by using logarithmic alignment method, thereby height and width of the exhaust port can be solved, then the precise specific time-area value and port timing angle are solved by using the coefficient calculation method and logarithmic alignment method respectively, so that the relative errors between initial and precise values of specific time-area value and port timing angle are defined as the relative errors of the mathematical model. Application examples show that the relative errors of the model is less than 3%.

On non-linear sensitivity of marine biological models to parameter variations

Marine biological models are usually complex with many free parameters. Parameter prioritization (based on contribution to model output) is important for system management but difficult. A variance-based sensitivity analysis is developed in this paper using the Sobol’–Saltelli sensitivity indices, which measure the relative importance of each parameter (or group of parameters) and range these parameters along their contribution to output variability. To reduce the number of degrees of freedom, the model output is decomposed using the warping functions or irreversible predictability time. A simple three-component [nutrients, phytoplankton and zooplankton (NPZ)] model with 23 parameters for reproducing annual phytoplankton cycle of the Black Sea is taken as the example to show the usefulness and procedure of the sensitivity analysis. Single and total sensitivity indices showed strong sensitivity of the biological model to the light limitation of the phytoplankton growth. This agrees well with physical intuition. However, ranging model parameters along their contributions to model output variability does not follow exactly the physical intuition when model-related errors from large perturbations of the parameters are not small. For example, the model output becomes very sensitive to the nutrient stock parameterization for certain combinations of the light-related factors.

Modeling of Piezoelectric Actuator Based Nano-Positioning System Using Multi-Polynomial Regression with C<sup>1</sup> Continuity

For nano-positioning systems with piezoelectric actuators used for dynamic grinding control, sinusoidal command signals will used and will give additional problems compared with the commonly used step signals because of the hysteresis effects, which require a good modeling approach. The proposed approach of multiple polynomial regression with first order continuity gives a relative modeling error of 2.65%. The method reduces the error by 26.3-80.2% in comparison with the methods using the single, dual, and multiple polynomial regression with zero order continuity.

Multivariable PID Control Systems Design by Stable Partial Model Matching on Frequency Domain

In this paper, a tuning method of multivariable PID controllers based on partial model matching on frequency domain is proposed. Different from the previous methods which were considered by authors, in this case, determination of multivariable PID controller parameters is defined as a nonlinear optimization problem with inequality constraints. In this procedure, the objective function is constructed so as to minimize the relative frequency model error between the loop transfer function of the control system and that of reference model system at finite frequency points. Inequality constraints are introduced so as to guarantee the stability criteria of multivariable control system given in Rosenbrock's stability theorem. The effectiveness of the method is illustrated through a simulation of 2-input 2-output system.

Modelling of piezoelectric actuator based nano-positioning system under sinusoidal excitation using multi-polynomial regression

For nano-positioning systems with piezoelectric actuators used for dynamic active manufacturing precision control, sinusoidal input signals would be used and would give additional problems in comparison with the commonly used step signals due to the hysteresis effects, which require a good modelling approach. Using six polynomials with zero order continuity between them results in a relative model error of 3.6%, which represents a reduction from 44.5% to 73.1% in the error compared with the single and dual polynomial approaches.

DISTURBANCE REJECTION USING AN ILC ALGORITHM WITH ITERATION VARYING FILTERS

ABSTRACTAn Iterative Learning Control disturbance rejection approach is considered and it is shown that iteration variant learning filters can asymptotically give the controlled variable zero error and zero variance. Convergence is achieved with the assumption that the relative model error is less than one. The transient response of the suggested ILC algorithm is also discussed using a simulation example.

Feedforward Control under the Presence of Uncertainty*

In this paper, we study the effect of model errors on the performance of feedforward controllers. In accordance with the sensitivity function for feedback control, we define the feedforward sensitivities, Sff(feedforward from disturbance) and Sff,r (feedforward from set-point), as measures for the reduction in the output error obtained by the feedforward control. For “ideal” feedforward controllers based on the inverted nominal model, the feedforward sensitivities equal the relative model errors, which must thus remain less than 1 for feedforward control to have a positive (dampening) effect. For some common model error classes we provide rules for when the feedforward controller is effective, and we also design μ-optimal feedforward controllers.

Active Vibration Control of a Carrier in Warehouse Based on Partial Model Matching on Frequency Domain.

This paper is concerned with a design method of multivariable linear controller based on frequency domain analysis and its application to an active vibration control for a carrier in warehouse. The method is based on the tuning of multivariable linear controller parameters by achieving partial model matching so as to minimize performance functions with respect to the relative model error between the loop transfer function matrix of the control system and the reference model. The proposed method is exanmined and evaluated by both simulation and experiment using pilot-scale carrier model in warehouse.

An Experimental Evaluation of Adaptive PID Controller on Frequency Domain

Abstract This paper is concerned with a design method of adaptive PID controller based on frequency domain analysis. The method is based on the estimation of a nonparametric plant model in the frequency domain and the determination of the PID controller parameters by achieving partial model matching so as to minimize a performance function concerning to relative model error between the loop transfer function of the control system and the desired system. In this design method, the plant is represented only by a discrete set of points on the Nyquist curve of the plant. Therefore it is not necessary to estimate a full order parameterized plant model. The proposed method is evaluated experimentally by using a position control of mechanical pendulum system and the effectiveness of the method is confirmed through practical experiments.

A Parameter Tuning Method of Adaptive PID Controller on Frequency Domain.

This paper deals with a design method for a PID adaptive controller based on frequency domain analysis. The method is based on the estimation of a nonparametric process model in the frequency domain. The PID controller parameters are determined by achieving partial model matching so as to minimize a loss function concerning relative model errors between the loop transfer function of the control system and the reference model system. The process is represented only by a discrete set of points on the Nyquist curve of the process. Therefore, it is not necessary to estimate a full order parameterized process model to design a control system.

Tuning of a Multivariable PID Controller on Frequency Domain and Its Application.

We outline the design method of a multivariable PID controller based on frequency domain analysis. The method is based on the determination of multivariable PID controller parameters by achieving partial model matching so as to minimize performance functions with respect to the relative model error between the loop transfer function matrix of the control system and the reference model. The proposed method is evaluated experimentally using position control of a parallel pendulum system. The effectiveness of the method is confirmed through practical examination.

Inverse techniques in hyperthermia: a sensitivity study.

Numerical modeling methods and hyperthermia treatment temperature measurements have been used together to reconstruct steady-state tumor temperature distributions. However, model errors will exist which may in turn produce errors in the reconstructed temperature distributions. A series of computer experiments was conducted to study the sensitivity of reconstructed two-dimensional temperature distributions to perfusion distribution modeling errors. Temperature distributions were simulated using a finite element approximation of Pennes' bioheat transfer equation. Relevant variables such as tumor shape, perfusion distribution, and power deposition were modeled. An optimization method and the temperatures "measured" from the simulated temperature distributions were used to reconstruct the tumor temperature distribution. Using this procedure, the sensitivity of the reconstructed tumor temperature distribution to model-related errors, such as the perfusion function, was studied. It was found that: 1) if the problem is conduction dominated, large errors in the perfusion distribution produce only small errors in the reconstructed temperature distribution (maximum error < 1.0 degrees C), and 2) when the actual perfusion distribution contains a small random variation (+/- 15%) which is neglected by the model, the reconstructed temperature distribution will be in good agreement with the actual temperature distribution (maximum error < or = 0.3 degrees.