有限离散函数导数的几何和极限表现

通过引入最佳平均逼近直线 ,分别从几何直观和极限情形两个角度 ,研究了有限离散函数的导数概念的表现 .结果表明 ,在局部情况下 ,有限离散函数导数近似等于连续情形下的导数 .极限情况下 ,局部范围内一点处有限离散函数的导数就变成了常规情形下的导数 。

Application of nonlinear partial least square in catalyst modeling

The neural network partial least square (NNPLS) method was used to establish a robust reaction model for a multi-component catalyst of methane oxidative coupling. The details, including the learning algorithm, the number of hidden units of the inner network, activation function, initialization of the network weights and the principal components, are discussed. The results show that the structural organizations of inner neural network are 1-10-5-1, 1-8-4-1, 1-8-5-1, 1-7-4-1, 1-8-4-1, 1-8-6-1, respectively. The Levenberg-Marquardt method was used in the learning algorithm, and the central sigmoidal function is the activation function. Calculation results show that four principal components are convenient in the use of the multi-component catalyst modeling of methane oxidative coupling. Therefore a robust reaction model expressed by NNPLS succeeds in correlating the relations between elements in catalyst and catalytic reaction results. Compared with the direct network modeling, NNPLS model can be adjusted by experimental data and the calculation of the model is simpler and faster than that of the direct network model.

WEIGHTED LEAST SQUARE METHOD FOR S-N CURVE FITTING

An S-N curve fitting approach is proposed based on the weighted least square method, and the weights are inversely proportional to the length of mean confidence intervals of experimental data sets. The assumption coincides with the physical characteristics of the fatigue life scatter. Two examples demonstrate the method. It is shown that the method has better accuracy and reasonableness compared with the usual least square method.

Statistical evaluation of five failure criteria for intact salt rock

Five multiparameter empirical criteria were exclusively evaluated by comparing them with the strength data covering various stress conditions to find out which failure criterion best fits the test data and describes the mechanical behavior of the salt rock sequence (halite,bedded composite specimens and anhydrite interlayers).Full-scale comparison of all criteria for the three rock types was conducted based on five standard statistics calculated from least squares curve-fitting,which measures both the goodness of fitting and the quality of future prediction.The results indicate that all five nonlinear criteria with a basic power form are efficient in predicting the strength trend in the low tension area as well as in the high compression area of the soft rocks.The parameters obtained for the bedded rock salt are somewhat in the ones for the "pure" rocks and are even closer to those obtained for the halite.The generalized Hoek-Brown criterion is proven to perform best to two rock strength data followed by one for the Bieniawski empirical criterion,thus is the best candidate for the analysis of the salt rock.The Sheorey empirical criterion consistently achieves an intermediate performance for all the three rocks.It seems that the superiority of the poly-axial criteria (the Mogi 1967 criterion and the N-type criterion) over the former three triaxial criteria no longer exists when applied to the conventional triaxial strength data.Besides,the method of tension cut-off was proposed to solve the ambiguity problem of the two poly-axial criteria in the tension field in the plane of the major (σ1) andminor principal stress (σ3).

Local Partial Least Squares Based Online Soft Sensing Method for Multi-output Processes with Adaptive Process States Division

Local learning based soft sensing methods succeed in coping with time-varying characteristics of processes as well as nonlinearities in industrial plants. In this paper, a local partial least squares based soft sensing method for multi-output processes is proposed to accomplish process states division and local model adaptation,which are two key steps in development of local learning based soft sensors. An adaptive way of partitioning process states without redundancy is proposed based on F-test, where unique local time regions are extracted.Subsequently, a novel anti-over-fitting criterion is proposed for online local model adaptation which simultaneously considers the relationship between process variables and the information in labeled and unlabeled samples. Case study is carried out on two chemical processes and simulation results illustrate the superiorities of the proposed method from several aspects.

Short-term traffic flow online forecasting based on kernel adaptive filter

Considering that the prediction accuracy of the traditional traffic flow forecasting model is low,based on kernel adaptive filter(KAF)algorithm,kernel least mean square(KLMS)algorithm and fixed-budget kernel recursive least-square(FB-KRLS)algorithm are presented for online adaptive prediction.The computational complexity of the KLMS algorithm is low and does not require additional solution paradigm constraints,but its regularization process can solve the problem of regularization performance degradation in high-dimensional data processing.To reduce the computational complexity,the sparse criterion is introduced into the KLMS algorithm.To further improve forecasting accuracy,FB-KRLS algorithm is proposed.It is an online learning method with fixed memory budget,and it is capable of recursively learning a nonlinear mapping and changing over time.In contrast to a previous approximate linear dependence(ALD)based technique,the purpose of the presented algorithm is not to prune the oldest data point in every time instant but it aims to prune the least significant data point,thus suppressing the growth of kernel matrix.In order to verify the validity of the proposed methods,they are applied to one-step and multi-step predictions of traffic flow in Beijing.Under the same conditions,they are compared with online adaptive ALD-KRLS method and other kernel learning methods.Experimental results show that the proposed KAF algorithms can improve the prediction accuracy,and its online learning ability meets the actual requirements of traffic flow and contributes to real-time online forecasting of traffic flow.

Use of Horton Infiltration Model in Estimating Infiltration Characteristics of an Alfisol in the Northern Guinea Savanna of Nigeria

Field infiltration measurement is often a tedious task thus can be easily estimated from proposed infiltration models. The Horton equation is one of the popular models used in the characterization of field infiltration. In this study, the least square curve firing technique was employed to estimate the model parameters from fifteen field measured data and gave resultant mean regression coefficients （R2） value of 0.811. Furthermore, plotting the measured against the calculated infiltration rate for the first six （6） measurement points yielded R2 values close to unity in the regression curve indicating a marked relationship between the two. This indicates that the Horton infiltration model can be applied to estimate infiltration characteristics of soils in Samaru, Northern Guinea Savanna of Nigeria.

A study of particles penetration in sieving process on a linear vibration screen

This paper presented an investigation of particle collision and penetration using the discrete element method to understand the motion of particles and improve theoretical treatment in the sieving process. The process progressively was divided into looseness, stratification, collision, and penetration. Particle penetration has a direct effect on the screening performance. The penetration probability was defined, and the mathematical relationships between particle penetration and vibration parameters were established using the least squares method. To obtain the ideal penetration probability for materials the amplitude and frequency should preferably be near 3.0 mm and 25 Hz, respectively. The vibration direction angle has only a slight effect on penetration. The stage of the screening process from 0.1 to 0.7 s is the primary region for collision and penetration. This paper focused on the sieving process to more fully understand how particle collision and penetration influence the screening efficiency.

Genetic algorithm-based evaluation of spatial straightness error

A genetic algorithm(GA)-based approach is proposed to evaluate the straightness error of spatial lines. According to the mathematical definition of spatial straightness, a verification model is established for straightness error, and the fitness function of GA is then given and the implementation techniques of the proposed algorithm is discussed in detail. The implementation techniques include real number encoding,adaptive variable range choosing, roulette wheel and elitist combination selection strategies,heuristic crossover and single point mutation schemes etc.An applicatin example is quoted to validate the proposed algorithm. The computation result shows that the GA-based approach is a superior nonlinear parallel optimization method. The performance of the evolution population can be improved through genetic operations such as reproduction,crossover and mutation until the optimum goal of the minimum zone solution is obtained. The quality of the solution is better and the efficiency of computation is higher than other methods.

Straight line feature based image distortion correction

An image distortion correction method is proposed, which uses the straight line features. Many parallel lines of different direction from different images were extracted, and then were used to optimize the distortion parameters by nonlinear least square. The thought of step by step was added when the optimization method working. 3D world coordination is not need to know, and the method is easy to implement. The experiment result shows its high accuracy.

Effect of Topography and Accessibility on Vegetation Dynamic Pattern in Mountain-hill Region

Knowledge of both vegetation distribution pattern and phenology changes is very important.Their complicated relationship with elevation and accessibility were explored through a geographically weighted regression(GWR) framework in Fujian province,China.The 16-day time series of 250 m Moderate Resolution Imaging Spectroradiometer(MODIS) Enhanced Vegetation Index(EVI) dataset from 2000 to 2010 was applied.Wavelet transform method was adopted to decompose the original time series and construct the annual maximum EVI and amplitude of the annual phenological cycle(EVI).Candidate explaining factors included topographic conditions,accessibility variables and proportions of primary vegetation types.Results revealed very strong positive influence from parameters of elevation and accessibility to big rivers and negative effect from accessibility to resident on both maximum EVI and phenological magnitude through ordinary linear least square(OLS) regression analysis.GWR analysis revealed that spatially,the parameters of topography and accessibility had a very complex relationship with both maximum EVI and phenology magnitude,as a result of the various combinations of environmental factors,vegetation composition and also intensive anthropogenic impact.Apart from the continuously increasing trend of phenology magnitude with increasing altitude,the influence of topography and accessibility on maximum EVI and phenological magnitude generally decreased,even from strongly positive to negative,with increasing altitude or distance.Specially,the most rapid change of correlation coefficient between them was observed within a low elevation or close distance;less variation was discovered within a certain range of medium altitude or distance and their relationship might change above this range.Non-stationary approaches are needed to better characterize the complex vegetation dynamic pattern in Mountain-hill Region.

Parameter identification of inertially stabilized platforms using current command design

Accurate parameter identification is essential when designing controllers for inertially stabilized platforms （lSPs）. But traditional identification methods suffer from observation measurement noise and operating restrictions of ISPs. To address this issue, a novel identification method based on current command design and multilevel coordinate search （MCS） algorithm without any higher order measurement differentiations was proposed. The designed current commands were adopted to obtain parameter decoupled models with the platform operating under allowable conditions. MCS algorithm was employed to estimate the parameters based on parameter decoupled models. A comparison experiment between the proposed method and non-linear least square method was carried out and most of the relative errors of identified parameters obtained by the proposed method were below 10%. Simulation and experiment based on identified parameters were conducted. A velocity control structure was also developed with disturbance observer （DOB） for application in disturbance compensation control system of an ISR Experimental results show that the control scheme based on the identified parameters with DOB has the best disturbance rejection performance. It reduces the peak to peak value （PPV） of velocity error integral to 0.8 mrad which is much smaller than the value （10 mrad） obtained by the single velocity controller without DOB. Compared with the control scheme based on sweep model with DOB compensation, the proposed control scheme improves the PPV of velocity error integral by 1.625 times.

Slope displacement prediction based on morphological filtering

Combining mathematical morphology (MM),nonparametric and nonlinear model,a novel approach for predicting slope displacement was developed to improve the prediction accuracy.A parallel-composed morphological filter with multiple structure elements was designed to process measured displacement time series with adaptive multi-scale decoupling.Whereafter,functional-coefficient auto regressive (FAR) models were established for the random subsequences.Meanwhile,the trend subsequence was processed by least squares support vector machine (LSSVM) algorithm.Finally,extrapolation results obtained were superposed to get the ultimate prediction result.Case study and comparative analysis demonstrate that the presented method can optimize training samples and show a good nonlinear predicting performance with low risk of choosing wrong algorithms.Mean absolute percentage error (MAPE) and root mean square error (RMSE) of the MM-FAR&LSSVM predicting results are as low as 1.670% and 0.172 mm,respectively,which means that the prediction accuracy are improved significantly.

Phase Equilibrium of Isobutanol in Supercritical CO2

Vapor-liquid phase equilibrium data including composition,densities,molar volume and equilibrium constant of isobutanol in supercritical carbon dioxide from 313.2K to 353.2K were measured in a variable-volume visual cell.The properties of critical point were obtained by extrapolation.The results showed that critical temperature,critical pressure and critical compressibility factor of CO2-isobutanol system decreased with the increase of critical CO2 content.The phase equilibrium model was established by Peng-Robinson equation of state and van der Waals-2 mixing regulation,and model parameters were determined by optimization calculation of nonlinear least square method.The correlation between calculated values and the experimental data showed good agreement.

Unknown parameter’s variance-covariance propagation and calculation in generalized nonlinear least squares problem

The unknown parameter’s variance-covariance propagation and calculation in the generalized nonlinear least squares remain to be studied now, which didn’t appear in the internal and external referencing documents. The unknown parameter’s vari- ance-covariance propagation formula, considering the two-power terms, was concluded used to evaluate the accuracy of unknown parameter estimators in the generalized nonlinear least squares problem. It is a new variance-covariance formula and opens up a new way to evaluate the accuracy when processing data which have the multi-source, multi-dimensional, multi-type, multi-time-state, different accuracy and nonlinearity.

Crack detection using integrated signals from dynamic responses of girder bridges

An innovative approach for the identification of cracks from the dynamic responses of girder bridges was proposed.One of the key steps of the approach was to transform the dynamical responses into the equivalent static quantities by integrating the excitation and response signals over time.A sliding-window least-squares curve fitting technique was then utilized to fit a cubic curve for a short segment of the girder.The moment coefficient of the cubic curve can be used to detect the locations of multiple cracks along a girder bridge.To validate the proposed method,prismatic girder bridges with multiple cracks of various depths were analyzed.Sensitivity analysis was conducted on various effects of crack depth,moving window width,noise level,bridge discretization,and load condition.Numerical results demonstrate that the proposed method can accurately detect cracks in a simply-supported or continuous girder bridges,the five-point equally weighted algorithm is recommended for practical applications,the spacing of two discernable cracks is equal to the window length,and the identified results are insensitive to noise due to integration of the initial data.

A New Proposal to Adjust a Straight Line to a Normal Q-Q Plot

In this paper a new proposal of a straight line, the ＂modified Tukey＇s line＂, for fitting to a normal quantile-quantile Plot, or normal Q-Q plot, is presented. This probability plot allows us to determine whether a set of sample observations is distributed according to a normal distribution. For this, the sample quantiles are represented against the quantiles of a theoretical probability model, which in this case is the normal distribution. If the data set follows the above mentioned distribution, the plotted points will have a rectilinear configuration. To verify this, there are different alternatives for fitting a straight line to the plotted points. Among the straight lines which can be fitted to a Q-Q plot, in this paper, besides the proposed straight line, the following straight lines are considered： straight line that passes through the first and third quartiles, straight line that passes through the 10th and 90th percentiles, straight line fitted by the method of least squares, straight line with slope s and constant the average of the data set, Theil＇s line and Tukey＇s line. In addition, an example, in which there are represented the different straight lines considered and the proposed straight line on a normal Q-Q plot obtained for the same set of observations, is developed. In this example the existing differences among the straight lines are observed.

Multiple Excitation Wavelength Fluorescence Emission Spectra Technique for Discrimination of Phytoplankton

In vivo fluorescence methods are efficient tools for studying the distribution of phytoplankton in nature.Different algae species usually have different pigments with different ratios,which results in different fluorescence emission spectra.Based on multiple excitation wavelength fluorescence emission spectra,a discrimination technique is established in this study.The discrimination method,established by multivariate linear regression and weighted least-squares,was used to differentiate the samples cultured in the laboratory and collected from Jiaozhou Bay near Qingdao at the division level.The correctly discriminated samples were ≥ 86% for single algae samples,≥ 88% for simulatively mixed ones,≥ 91% for physically mixed ones and 100% for samples collected from Jiaozhou Bay.The result in this research is more definite for the physically mixed samples in the laboratory.The method described here can be employed to monitor the phytoplankton population in the marine environment.

Free Search Algorithm Based Estimation in WSN Location

This paper proposes a novel intelligent estimation algorithm in Wireless Sensor Network nodes location based on Free Search,which converts parameter estimation to on-line optimization of nonlinear function and estimates the coordinates of senor nodes using the Free Search optimization.Compared to the least-squares estimation algorithms,the localization accuracy has been increased significantly,which has been verified by the simulation results.

On-line least squares support vector machine algorithm in gas prediction

Traditional coal mine safety prediction methods are off-line and do not have dynamic prediction functions.The Support Vector Machine(SVM) is a new machine learning algorithm that has excellent properties.The least squares support vector machine(LS-SVM) algorithm is an improved algorithm of SVM.But the common LS-SVM algorithm,used directly in safety predictions,has some problems.We have first studied gas prediction problems and the basic theory of LS-SVM.Given these problems,we have investigated the affect of the time factor about safety prediction and present an on-line prediction algorithm,based on LS-SVM.Finally,given our observed data,we used the on-line algorithm to predict gas emissions and used other related algorithm to compare its performance.The simulation results have verified the validity of the new algorithm.