This paper proposes a method combining blue the Haar wavelet and the least square to solve the multi-dimensional stochastic Ito-Volterra integral equation.This approach is to transform stochastic integral equations in...This paper proposes a method combining blue the Haar wavelet and the least square to solve the multi-dimensional stochastic Ito-Volterra integral equation.This approach is to transform stochastic integral equations into a system of algebraic equations.Meanwhile,the error analysis is proven.Finally,the effectiveness of the approach is verified by two numerical examples.展开更多
To improve the measurement and evaluation of form error of an elliptic section, an evaluation method based on least squares fitting is investigated to analyze the form and profile errors of an ellipse using coordinate...To improve the measurement and evaluation of form error of an elliptic section, an evaluation method based on least squares fitting is investigated to analyze the form and profile errors of an ellipse using coordinate data. Two error indicators for defining ellipticity are discussed, namely the form error and the profile error, and the difference between both is considered as the main parameter for evaluating machining quality of surface and profile. Because the form error and the profile error rely on different evaluation benchmarks, the major axis and the foci rather than the centre of an ellipse are used as the evaluation benchmarks and can accurately evaluate a tolerance range with the separated form error and profile error of workpiece. Additionally, an evaluation program based on the LS model is developed to extract the form error and the profile error of the elliptic section, which is well suited for separating the two errors by a standard program. Finally, the evaluation method about the form and profile errors of the ellipse is applied to the measurement of skirt line of the piston, and results indicate the effectiveness of the evaluation. This approach provides the new evaluation indicators for the measurement of form and profile errors of ellipse, which is found to have better accuracy and can thus be used to solve the difficult of the measurement and evaluation of the piston in industrial production.展开更多
Current research in broken rotor bar(BRB) fault detection in induction motors is primarily focused on a high-frequency resolution analysis of the stator current.Compared with a discrete Fourier transformation, the par...Current research in broken rotor bar(BRB) fault detection in induction motors is primarily focused on a high-frequency resolution analysis of the stator current.Compared with a discrete Fourier transformation, the parametric spectrum estimation technique has a higher frequency accuracy and resolution. However, the existing detection methods based on parametric spectrum estimation cannot realize online detection, owing to the large computational cost. To improve the efficiency of BRB fault detection,a new detection method based on the min-norm algorithm and least square estimation is proposed in this paper. First, the stator current is filtered using a band-pass filter and divided into short overlapped data windows. The min-norm algorithm is then applied to determine the frequencies of the fundamental and fault characteristic components with each overlapped data window. Next, based on the frequency values obtained, a model of the fault current signal is constructed. Subsequently, a linear least squares problem solved through singular value decomposition is designed to estimate the amplitudes and phases of the related components. Finally,the proposed method is applied to a simulated current and an actual motor,the results of which indicate that, not only parametric spectrum estimation technique.展开更多
Kalman filter is commonly used in data filtering and parameters estimation of nonlinear system,such as projectile's trajectory estimation and control.While there is a drawback that the prior error covariance matri...Kalman filter is commonly used in data filtering and parameters estimation of nonlinear system,such as projectile's trajectory estimation and control.While there is a drawback that the prior error covariance matrix and filter parameters are difficult to be determined,which may result in filtering divergence.As to the problem that the accuracy of state estimation for nonlinear ballistic model strongly depends on its mathematical model,we improve the weighted least squares method(WLSM)with minimum model error principle.Invariant embedding method is adopted to solve the cost function including the model error.With the knowledge of measurement data and measurement error covariance matrix,we use gradient descent algorithm to determine the weighting matrix of model error.The uncertainty and linearization error of model are recursively estimated by the proposed method,thus achieving an online filtering estimation of the observations.Simulation results indicate that the proposed recursive estimation algorithm is insensitive to initial conditions and of good robustness.展开更多
The development of prediction supports is a critical step in information systems engineering in this era defined by the knowledge economy, the hub of which is big data. Currently, the lack of a predictive model, wheth...The development of prediction supports is a critical step in information systems engineering in this era defined by the knowledge economy, the hub of which is big data. Currently, the lack of a predictive model, whether qualitative or quantitative, depending on a company’s areas of intervention can handicap or weaken its competitive capacities, endangering its survival. In terms of quantitative prediction, depending on the efficacy criteria, a variety of methods and/or tools are available. The multiple linear regression method is one of the methods used for this purpose. A linear regression model is a regression model of an explained variable on one or more explanatory variables in which the function that links the explanatory variables to the explained variable has linear parameters. The purpose of this work is to demonstrate how to use multiple linear regressions, which is one aspect of decisional mathematics. The use of multiple linear regressions on random data, which can be replaced by real data collected by or from organizations, provides decision makers with reliable data knowledge. As a result, machine learning methods can provide decision makers with relevant and trustworthy data. The main goal of this article is therefore to define the objective function on which the influencing factors for its optimization will be defined using the linear regression method.展开更多
Based on the model structure of the influence coefficient method analyzed in depth by matrix theory,it is explained the reason why the unreasonable and instable correction masses with bigger MSE are obtained by LS inf...Based on the model structure of the influence coefficient method analyzed in depth by matrix theory,it is explained the reason why the unreasonable and instable correction masses with bigger MSE are obtained by LS influence coefficient method when there are correlation planes in the dynamic balancing.It also presened the new ridge regression method for solving correction masses according to the Tikhonov regularization theory,and described the reason why the ridge regression can eliminate the disadvantage of the LS method. Applying this new method to dynamic balancing of gas turbine, it is found that this method is superior to the LS method when influence coefficient matrix is ill-conditioned,the minimal correction masses and residual vibration are obtained in the dynamic balancing of rotors.展开更多
Geometric error is the main factor affecting the machining accuracy of hybrid machine tools.Kinematic calibration is an effective way to improve the geometric accuracy of hybrid machine tools.The necessity to measure ...Geometric error is the main factor affecting the machining accuracy of hybrid machine tools.Kinematic calibration is an effective way to improve the geometric accuracy of hybrid machine tools.The necessity to measure both position and orientation at each pose,as well as the instability of identification in case of incomplete measurements,severely affects the application of traditional calibration methods.In this study,a kinematic calibration method with high measurement efficiency and robust identification is proposed to improve the kinematic accuracy of a five-axis hybrid machine tool.First,the configuration is introduced,and an error model is derived.Further,by investigating the mechanism error characteristics,a measurement scheme that only requires tool centre point position error measurement and one alignment operation is proposed.Subsequently,by analysing the effects of unmeasured degrees of freedom(DOFs)on other DOFs,an improved nonlinear least squares method based on virtual measurement values is proposed to achieve stable parameter identification in case of incomplete measurement,without introducing additional parameters.Finally,the proposed calibration method is verified through simulations and experiments.The proposed method can efficiently accomplish the kinematic calibration of the hybrid machine tool.The accuracy of the hybrid machine tool is significantly improved after calibration,satisfying actual aerospace machining requirements.展开更多
We propose a new least squares finite element method to solve the Stokes problem with two sequential steps.The approximation spaces are constructed by the patch reconstruction with one unknown per element.For the firs...We propose a new least squares finite element method to solve the Stokes problem with two sequential steps.The approximation spaces are constructed by the patch reconstruction with one unknown per element.For the first step,we reconstruct an approximation space consisting of piecewise curl-free polynomials with zero trace.By this space,we minimize a least squares functional to obtain the numerical approximations to the gradient of the velocity and the pressure.In the second step,we minimize another least squares functional to give the solution to the velocity in the reconstructed piecewise divergence-free space.We derive error estimates for all unknowns under both L 2 norms and energy norms.Numerical results in two dimensions and three dimensions verify the convergence rates and demonstrate the great flexibility of our method.展开更多
This paper gives a class of descent methods for nonlinar least squares solu-tion. A class of updating formulae is obtained by using generalized inverse matrices.These formulae generate an approximation to the second p...This paper gives a class of descent methods for nonlinar least squares solu-tion. A class of updating formulae is obtained by using generalized inverse matrices.These formulae generate an approximation to the second part of the Hessian ma-trix of the objective function, and are updated in such a way that the resultingapproximation to the whole Hessian matrix is the convex class of Broyden-like up-dating formulae. It is proved that the proposed updating formulae are invarantunder linear transformation and that the class of factorized quasi-Newton methodsare locally and superlinearly convergent. Numerical results are presented and showthat the proposed methods are promising.展开更多
The training algorithm of classical twin support vector regression (TSVR) can be attributed to the solution of a pair of quadratic programming problems (QPPs) with inequality constraints in the dual space.However,this...The training algorithm of classical twin support vector regression (TSVR) can be attributed to the solution of a pair of quadratic programming problems (QPPs) with inequality constraints in the dual space.However,this solution is affected by time and memory constraints when dealing with large datasets.In this paper,we present a least squares version for TSVR in the primal space,termed primal least squares TSVR (PLSTSVR).By introducing the least squares method,the inequality constraints of TSVR are transformed into equality constraints.Furthermore,we attempt to directly solve the two QPPs with equality constraints in the primal space instead of the dual space;thus,we need only to solve two systems of linear equations instead of two QPPs.Experimental results on artificial and benchmark datasets show that PLSTSVR has comparable accuracy to TSVR but with considerably less computational time.We further investigate its validity in predicting the opening price of stock.展开更多
Based on the theory of planned behavior( TPB),Taking 399 livestock and poultry farms and households in Shandong Province as samples,risk cognitive variables were introduced. Besides,with the aid of the structural equa...Based on the theory of planned behavior( TPB),Taking 399 livestock and poultry farms and households in Shandong Province as samples,risk cognitive variables were introduced. Besides,with the aid of the structural equation model( SEM) and partial least squares method( PLS),through an empirical analysis on antibiotic prophylactic behavior of livestock and poultry breeding farms and households in the context of " antibiotic free" production,the response mechanism of " antibiotic free" production was explored. Results indicated that the use of antibiotic prophylaxis by livestock and poultry farms and households is still very common. In the observation samples,61. 4% clearly expressed they would use antibiotic prophylaxis; the understanding of hazard of improper antibiotic prophylaxis was inadequate,only 32. 3% breeding households believed that the overuse of antibiotic prophylaxis is the main reason leading to excessive drug residue in animal products. This study was in line with the process of deduction of TPB. The breeding households' reduction of antibiotic prophylaxis is influenced by their intentions,while the intention is influenced by the attitude,subjective norms and perceptual behavior control; different risks have different influences,but most risks have greater influence on perceptual behavior control,because the perceptual behavior control determines whether breeding households have the ability of implementing the corresponding behavior.展开更多
The Moon's physical librations have been extensively studied, and elaborate researches have been developed for the purpose of deriving accurate modes of free librations. Our motivation comes from the Planetary and...The Moon's physical librations have been extensively studied, and elaborate researches have been developed for the purpose of deriving accurate modes of free librations. Our motivation comes from the Planetary and Lunar Ephemeris DE430 by JPL/NASA, which was created in April 2013,and is reported to be the most accurate lunar ephemeris today using the data from Gravity Recovery and Interior Laboratory(GRAIL). Therefore, the residuals after fitting the model have reduced owing to improvement in the libration models, and the free librations embedded in the Euler angles have also improved. We use Fourier analysis to extract the approximate frequencies from DE430 and then a quadratic interpolation method is used to determine higher accuracy frequencies. With the frequencies,the linear least-squares fitting method is employed to fit the lunar physical librations to DE430. From this analysis we identified the three modes of free physical librations, and estimated the amplitudes as 1.471′′in longitude, 0.025′′in latitude and 8.19′′× 3.31′′for the wobble, with the respective periods of1056.16, 8806.9 and 27262.99 d. Since the free librations damp with time, they require recent excitation or a continuous stimulating mechanism in order to sustain.展开更多
Goal of this experiment is basically measuring the velocity of light. As usual we will measure two-way velocity of light (from A to B and back). In contrast to the similar experiments we will not assume that speeds of...Goal of this experiment is basically measuring the velocity of light. As usual we will measure two-way velocity of light (from A to B and back). In contrast to the similar experiments we will not assume that speeds of light from A to B and from B to A are equal. To achieve this we will take into account Earth’s movement through the space, rotation around its axis and apply “least squares method for cosine function”, which will be explained in Section 9. Assuming that direction East-West is already known, one clock, a source of light and a mirror, is all equipment we need for this experiment.展开更多
The classical autoregressive(AR)model has been widely applied to predict future data usingmpast observations over five decades.As the classical AR model required m unknown parameters,this paper implements the AR model...The classical autoregressive(AR)model has been widely applied to predict future data usingmpast observations over five decades.As the classical AR model required m unknown parameters,this paper implements the AR model by reducing m parameters to two parameters to obtain a new model with an optimal delay called as the m-delay AR model.We derive the m-delay AR formula for approximating two unknown parameters based on the least squares method and develop an algorithm to determine optimal delay based on a brute-force technique.The performance of them-delay AR model was tested by comparing with the classical AR model.The results,obtained from Monte Carlo simulation using the monthly mean minimum temperature in PerthWestern Australia from the Bureau of Meteorology,are no significant difference compared to those obtained from the classical AR model.This confirms that the m-delay AR model is an effective model for time series analysis.展开更多
We propose a numerical method to solve the Monge-Ampère equation which admits a classical convex solution.The Monge-Ampère equation is reformulated into an equivalent first-order system.We adopt a novel reco...We propose a numerical method to solve the Monge-Ampère equation which admits a classical convex solution.The Monge-Ampère equation is reformulated into an equivalent first-order system.We adopt a novel reconstructed discontinuous approximation space which consists of piecewise irrotational polynomials.This space allows us to solve the first-order system in two sequential steps.In the first step,we solve a nonlinear system to obtain the approximation to the gradient.A Newton iteration is adopted to handle the nonlinearity of the system.The approximation to the primitive variable is obtained from the approximate gradient by a trivial least squares finite element method in the second step.Numerical examples in both two and three dimensions are presented to show an optimal convergence rate in accuracy.It is interesting to observe that the approximation solution is piecewise convex.Particularly,with the reconstructed approximation space,the proposed method numerically demonstrates a remarkable robustness.The convergence of the Newton iteration does not rely on the initial values.The dependence of the convergence on the penalty parameter in the discretization is also negligible,in comparison to the classical discontinuous approximation space.展开更多
Unmanned aerial vehicle(UAV)chemical application is widely used for crop protection,and spraying pattern is one of the most important factors that influence the chemical control efficacy.A method for UAV spraying patt...Unmanned aerial vehicle(UAV)chemical application is widely used for crop protection,and spraying pattern is one of the most important factors that influence the chemical control efficacy.A method for UAV spraying pattern measurement with partial least squares(PLS)model based spectrum analysis was proposed in this study to measure the UAV spraying pattern more accurately.The method involved the steps of fluorescent tracer solution spray and its droplets collection,the spectrum on paper strip acquiring,spectrum processing and analysis,PLS modeling.In order to verify the applicability of the method and obtain the parameters of the PLS model,UAV spraying experiments were performed in the field.Then Fluorescent tracer solution was sprayed and its droplets are collected by paper strip,and the original spectrum on paper strip obtained by a spectrometer was processed by the Savitzky-Golay and standard normalized variable(SNV)method.The prediction model of coverage rate selected as the droplet deposition parameter to measure the UAV spraying pattern,was established by using PLS method.To verify the superiority of the PLS model,a traditional linear regression(LR)model of coverage rate was established simultaneously.The results demonstrate that the method with PLS model based spectrum analysis can measure the UAV spraying pattern effectively,and PLS model has a better performance of RV2=0.94 and RMSEP=0.9446 than that of the LR model.展开更多
Prediction of power generation of a wind turbine is crucial,which calls for accurate and reliable models.In this work,six different models have been developed based on wind power equation,concept of power curve,respon...Prediction of power generation of a wind turbine is crucial,which calls for accurate and reliable models.In this work,six different models have been developed based on wind power equation,concept of power curve,response surface methodology(RSM)and artificial neural network(ANN),and the results have been compared.To develop the models based on the concept of power curve,the manufacturer’s power curve,and to develop RSM as well as ANN models,the data collected from supervisory control and data acquisition(SCADA)of a 1.5 MW turbine have been used.In addition to wind speed,the air density,blade pitch angle,rotor speed and wind direction have been considered as input variables for RSM and ANN models.Proper selection of input variables and capability of ANN to map input-output relationships have resulted in an accurate model for wind power prediction in comparison to other methods.展开更多
When one solves differential equations by a spectral method,it is often convenient to shift from Chebyshev polynomials Tn(x) with coefficients anto modified basis functions that incorporate the boundary conditions.For...When one solves differential equations by a spectral method,it is often convenient to shift from Chebyshev polynomials Tn(x) with coefficients anto modified basis functions that incorporate the boundary conditions.For homogeneous Dirichlet boundary conditions,u(±1)=0,popular choices include the "Chebyshev difference basis" ζn(x)≡Tn+2(x)-Tn(x) with coefficients here denoted by bnand the "quadratic factor basis" Qn(x)≡(1-x2)Tn(x) with coefficients cn.If u(x) is weakly singular at the boundary,then the coefficients andecrease proportionally to O(A(n)/nκ) for some positive constant κ,where A(n) is a logarithm or a constant.We prove that the Chebyshev difference coefficients bndecrease more slowly by a factor of 1/n while the quadratic factor coefficients cndecrease more slowly still as O(A(n)/nκ-2).The error for the unconstrained Chebyshev series,truncated at degree n=N,is O(|A(N)|/Nκ) in the interior,but is worse by one power of N in narrow boundary layers near each of the endpoints.Despite having nearly identical error norms in interpolation,the error in the Chebyshev basis is concentrated in boundary layers near both endpoints,whereas the error in the quadratic factor and difference basis sets is nearly uniformly oscillating over the entire interval in x.Meanwhile,for Chebyshev polynomials,the values of their derivatives at the endpoints are O(n2),but only O(n) for the difference basis.Furthermore,we give the asymptotic coefficients and rigorous error estimates of the approximations in these three bases,solved by the least squares method.We also find an interesting fact that on the face of it,the aliasing error is regarded as a bad thing;actually,the error norm associated with the downward curving spectral coefficients decreases even faster than the error norm of infinite truncation.But the premise is under the same basis,and when involving different bases,it may not be established yet.展开更多
Wheat is a major grain crop in China.Water is one of the most important factors which influence the lifecycle and yield of wheat.It is of great significance to study the water content at the key stages of wheat growth...Wheat is a major grain crop in China.Water is one of the most important factors which influence the lifecycle and yield of wheat.It is of great significance to study the water content at the key stages of wheat growth in order to make irrigation decision to raise its yield.As Terahertz(THz)spectroscopy is a brand new sensing technology and sensitive to water absorption,the relationship between terahertz spectra and water content in winter wheat leaf was investigated and a preliminary result was presented in this paper.Forty winter wheat leaves samples with diverse range of water content(42.8%-72.5%)were collected.The Terahertz time domain spectra(THz-TDS)were first obtained and then transformed into Frequency-domain amplitude with the Fast Fourier Transformation(FFT)method.The absorption and refractive index spectra were then calculated.The spectra were linearly fitted to obtain the slope and intercept used for building a calibration model.The partial least squares(PLS)method and linear regression were employed to establish models to determine leaf water content in the winter wheat.The predicted correlation coefficient and the root mean square error of the optimal model established with the Frequency-domain amplitude parameter at 0.3 THz by linear regression were 0.812%and 4.4%,respectively.The results showed that terahertz spectroscopy performed well in water content prediction and could be an effective and potential method for leaf water content measurement in winter wheat.展开更多
Three uncertain parameters(peak ground acceleration,soil density,and soil modulus of elasticity)have been studied with regard to their effects on the stability and damage of a circular tunnel during an earthquake.A ti...Three uncertain parameters(peak ground acceleration,soil density,and soil modulus of elasticity)have been studied with regard to their effects on the stability and damage of a circular tunnel during an earthquake.A time history of an actual earthquake in the literature with modification has been adopted in the numerical simulation and analysis of the tunnel responses.Meta-models have been constructed based on an experimental method with quadratic and interaction terms using matlab codes in order to predict the compressive damage,tensile damage,and the overall displacement of the tunnel.The results of the meta-models predicted a highly reasonable response of the tunnel with regard to the maximum principal stresses in the tunnel lining and predicted a remarkable response of the tunnel with respect to the overall displacement of the tunnel.Moreover,the peak ground acceleration was observed to exert the highest effect on the overall displacement of the tunnel,compared to the soil density and soil modulus of elasticity.Furthermore,the metamodels revealed the inverse relationship between the soil modulus of elasticity and the compressive and tensile damages of the tunnel lining.The meta-models exhibited high efficiency of representation of the behavior of the structural system during earthquakes.展开更多
基金Supported by the NSF of Hubei Province(2022CFD042)。
文摘This paper proposes a method combining blue the Haar wavelet and the least square to solve the multi-dimensional stochastic Ito-Volterra integral equation.This approach is to transform stochastic integral equations into a system of algebraic equations.Meanwhile,the error analysis is proven.Finally,the effectiveness of the approach is verified by two numerical examples.
基金Supported by National Natural Science Foundation of China(Grant No.51575438)
文摘To improve the measurement and evaluation of form error of an elliptic section, an evaluation method based on least squares fitting is investigated to analyze the form and profile errors of an ellipse using coordinate data. Two error indicators for defining ellipticity are discussed, namely the form error and the profile error, and the difference between both is considered as the main parameter for evaluating machining quality of surface and profile. Because the form error and the profile error rely on different evaluation benchmarks, the major axis and the foci rather than the centre of an ellipse are used as the evaluation benchmarks and can accurately evaluate a tolerance range with the separated form error and profile error of workpiece. Additionally, an evaluation program based on the LS model is developed to extract the form error and the profile error of the elliptic section, which is well suited for separating the two errors by a standard program. Finally, the evaluation method about the form and profile errors of the ellipse is applied to the measurement of skirt line of the piston, and results indicate the effectiveness of the evaluation. This approach provides the new evaluation indicators for the measurement of form and profile errors of ellipse, which is found to have better accuracy and can thus be used to solve the difficult of the measurement and evaluation of the piston in industrial production.
基金Supported by National Natural Science Foundation of China(Grant No.51607180)
文摘Current research in broken rotor bar(BRB) fault detection in induction motors is primarily focused on a high-frequency resolution analysis of the stator current.Compared with a discrete Fourier transformation, the parametric spectrum estimation technique has a higher frequency accuracy and resolution. However, the existing detection methods based on parametric spectrum estimation cannot realize online detection, owing to the large computational cost. To improve the efficiency of BRB fault detection,a new detection method based on the min-norm algorithm and least square estimation is proposed in this paper. First, the stator current is filtered using a band-pass filter and divided into short overlapped data windows. The min-norm algorithm is then applied to determine the frequencies of the fundamental and fault characteristic components with each overlapped data window. Next, based on the frequency values obtained, a model of the fault current signal is constructed. Subsequently, a linear least squares problem solved through singular value decomposition is designed to estimate the amplitudes and phases of the related components. Finally,the proposed method is applied to a simulated current and an actual motor,the results of which indicate that, not only parametric spectrum estimation technique.
基金This work is supported by Postgraduate Research&Practice Innovation Program of Jiangsu Province(KYCX18_0467)Jiangsu Province,China.During the revision of this paper,the author is supported by China Scholarship Council(No.201906840021)China to continue some research related to data processing.
文摘Kalman filter is commonly used in data filtering and parameters estimation of nonlinear system,such as projectile's trajectory estimation and control.While there is a drawback that the prior error covariance matrix and filter parameters are difficult to be determined,which may result in filtering divergence.As to the problem that the accuracy of state estimation for nonlinear ballistic model strongly depends on its mathematical model,we improve the weighted least squares method(WLSM)with minimum model error principle.Invariant embedding method is adopted to solve the cost function including the model error.With the knowledge of measurement data and measurement error covariance matrix,we use gradient descent algorithm to determine the weighting matrix of model error.The uncertainty and linearization error of model are recursively estimated by the proposed method,thus achieving an online filtering estimation of the observations.Simulation results indicate that the proposed recursive estimation algorithm is insensitive to initial conditions and of good robustness.
文摘The development of prediction supports is a critical step in information systems engineering in this era defined by the knowledge economy, the hub of which is big data. Currently, the lack of a predictive model, whether qualitative or quantitative, depending on a company’s areas of intervention can handicap or weaken its competitive capacities, endangering its survival. In terms of quantitative prediction, depending on the efficacy criteria, a variety of methods and/or tools are available. The multiple linear regression method is one of the methods used for this purpose. A linear regression model is a regression model of an explained variable on one or more explanatory variables in which the function that links the explanatory variables to the explained variable has linear parameters. The purpose of this work is to demonstrate how to use multiple linear regressions, which is one aspect of decisional mathematics. The use of multiple linear regressions on random data, which can be replaced by real data collected by or from organizations, provides decision makers with reliable data knowledge. As a result, machine learning methods can provide decision makers with relevant and trustworthy data. The main goal of this article is therefore to define the objective function on which the influencing factors for its optimization will be defined using the linear regression method.
文摘Based on the model structure of the influence coefficient method analyzed in depth by matrix theory,it is explained the reason why the unreasonable and instable correction masses with bigger MSE are obtained by LS influence coefficient method when there are correlation planes in the dynamic balancing.It also presened the new ridge regression method for solving correction masses according to the Tikhonov regularization theory,and described the reason why the ridge regression can eliminate the disadvantage of the LS method. Applying this new method to dynamic balancing of gas turbine, it is found that this method is superior to the LS method when influence coefficient matrix is ill-conditioned,the minimal correction masses and residual vibration are obtained in the dynamic balancing of rotors.
基金supported by the National Natural Science Foundation of China(Nos.52275442 and 51975319)。
文摘Geometric error is the main factor affecting the machining accuracy of hybrid machine tools.Kinematic calibration is an effective way to improve the geometric accuracy of hybrid machine tools.The necessity to measure both position and orientation at each pose,as well as the instability of identification in case of incomplete measurements,severely affects the application of traditional calibration methods.In this study,a kinematic calibration method with high measurement efficiency and robust identification is proposed to improve the kinematic accuracy of a five-axis hybrid machine tool.First,the configuration is introduced,and an error model is derived.Further,by investigating the mechanism error characteristics,a measurement scheme that only requires tool centre point position error measurement and one alignment operation is proposed.Subsequently,by analysing the effects of unmeasured degrees of freedom(DOFs)on other DOFs,an improved nonlinear least squares method based on virtual measurement values is proposed to achieve stable parameter identification in case of incomplete measurement,without introducing additional parameters.Finally,the proposed calibration method is verified through simulations and experiments.The proposed method can efficiently accomplish the kinematic calibration of the hybrid machine tool.The accuracy of the hybrid machine tool is significantly improved after calibration,satisfying actual aerospace machining requirements.
基金supported by the Science Challenge Project(No.TZ2016002)the National Natural Science Foundation in China(No.11971041 and 11421101).
文摘We propose a new least squares finite element method to solve the Stokes problem with two sequential steps.The approximation spaces are constructed by the patch reconstruction with one unknown per element.For the first step,we reconstruct an approximation space consisting of piecewise curl-free polynomials with zero trace.By this space,we minimize a least squares functional to obtain the numerical approximations to the gradient of the velocity and the pressure.In the second step,we minimize another least squares functional to give the solution to the velocity in the reconstructed piecewise divergence-free space.We derive error estimates for all unknowns under both L 2 norms and energy norms.Numerical results in two dimensions and three dimensions verify the convergence rates and demonstrate the great flexibility of our method.
文摘This paper gives a class of descent methods for nonlinar least squares solu-tion. A class of updating formulae is obtained by using generalized inverse matrices.These formulae generate an approximation to the second part of the Hessian ma-trix of the objective function, and are updated in such a way that the resultingapproximation to the whole Hessian matrix is the convex class of Broyden-like up-dating formulae. It is proved that the proposed updating formulae are invarantunder linear transformation and that the class of factorized quasi-Newton methodsare locally and superlinearly convergent. Numerical results are presented and showthat the proposed methods are promising.
基金supported by the National Basic Research Program (973) of China(No.2013CB329502)the National Natural Science Foundation of China(No.61379101)the Fundamental Research Funds for the Central Universities,China(No.2012LWB39)
文摘The training algorithm of classical twin support vector regression (TSVR) can be attributed to the solution of a pair of quadratic programming problems (QPPs) with inequality constraints in the dual space.However,this solution is affected by time and memory constraints when dealing with large datasets.In this paper,we present a least squares version for TSVR in the primal space,termed primal least squares TSVR (PLSTSVR).By introducing the least squares method,the inequality constraints of TSVR are transformed into equality constraints.Furthermore,we attempt to directly solve the two QPPs with equality constraints in the primal space instead of the dual space;thus,we need only to solve two systems of linear equations instead of two QPPs.Experimental results on artificial and benchmark datasets show that PLSTSVR has comparable accuracy to TSVR but with considerably less computational time.We further investigate its validity in predicting the opening price of stock.
文摘Based on the theory of planned behavior( TPB),Taking 399 livestock and poultry farms and households in Shandong Province as samples,risk cognitive variables were introduced. Besides,with the aid of the structural equation model( SEM) and partial least squares method( PLS),through an empirical analysis on antibiotic prophylactic behavior of livestock and poultry breeding farms and households in the context of " antibiotic free" production,the response mechanism of " antibiotic free" production was explored. Results indicated that the use of antibiotic prophylaxis by livestock and poultry farms and households is still very common. In the observation samples,61. 4% clearly expressed they would use antibiotic prophylaxis; the understanding of hazard of improper antibiotic prophylaxis was inadequate,only 32. 3% breeding households believed that the overuse of antibiotic prophylaxis is the main reason leading to excessive drug residue in animal products. This study was in line with the process of deduction of TPB. The breeding households' reduction of antibiotic prophylaxis is influenced by their intentions,while the intention is influenced by the attitude,subjective norms and perceptual behavior control; different risks have different influences,but most risks have greater influence on perceptual behavior control,because the perceptual behavior control determines whether breeding households have the ability of implementing the corresponding behavior.
基金supported by the National Natural Science Foundation of China(Grant No.41590851)the Major State Basic Research Development Program of China(2015CB857101)
文摘The Moon's physical librations have been extensively studied, and elaborate researches have been developed for the purpose of deriving accurate modes of free librations. Our motivation comes from the Planetary and Lunar Ephemeris DE430 by JPL/NASA, which was created in April 2013,and is reported to be the most accurate lunar ephemeris today using the data from Gravity Recovery and Interior Laboratory(GRAIL). Therefore, the residuals after fitting the model have reduced owing to improvement in the libration models, and the free librations embedded in the Euler angles have also improved. We use Fourier analysis to extract the approximate frequencies from DE430 and then a quadratic interpolation method is used to determine higher accuracy frequencies. With the frequencies,the linear least-squares fitting method is employed to fit the lunar physical librations to DE430. From this analysis we identified the three modes of free physical librations, and estimated the amplitudes as 1.471′′in longitude, 0.025′′in latitude and 8.19′′× 3.31′′for the wobble, with the respective periods of1056.16, 8806.9 and 27262.99 d. Since the free librations damp with time, they require recent excitation or a continuous stimulating mechanism in order to sustain.
文摘Goal of this experiment is basically measuring the velocity of light. As usual we will measure two-way velocity of light (from A to B and back). In contrast to the similar experiments we will not assume that speeds of light from A to B and from B to A are equal. To achieve this we will take into account Earth’s movement through the space, rotation around its axis and apply “least squares method for cosine function”, which will be explained in Section 9. Assuming that direction East-West is already known, one clock, a source of light and a mirror, is all equipment we need for this experiment.
文摘The classical autoregressive(AR)model has been widely applied to predict future data usingmpast observations over five decades.As the classical AR model required m unknown parameters,this paper implements the AR model by reducing m parameters to two parameters to obtain a new model with an optimal delay called as the m-delay AR model.We derive the m-delay AR formula for approximating two unknown parameters based on the least squares method and develop an algorithm to determine optimal delay based on a brute-force technique.The performance of them-delay AR model was tested by comparing with the classical AR model.The results,obtained from Monte Carlo simulation using the monthly mean minimum temperature in PerthWestern Australia from the Bureau of Meteorology,are no significant difference compared to those obtained from the classical AR model.This confirms that the m-delay AR model is an effective model for time series analysis.
基金This research was supported by the National Natural Science Foundation in China(Nos.12201442,and 11971041).
文摘We propose a numerical method to solve the Monge-Ampère equation which admits a classical convex solution.The Monge-Ampère equation is reformulated into an equivalent first-order system.We adopt a novel reconstructed discontinuous approximation space which consists of piecewise irrotational polynomials.This space allows us to solve the first-order system in two sequential steps.In the first step,we solve a nonlinear system to obtain the approximation to the gradient.A Newton iteration is adopted to handle the nonlinearity of the system.The approximation to the primitive variable is obtained from the approximate gradient by a trivial least squares finite element method in the second step.Numerical examples in both two and three dimensions are presented to show an optimal convergence rate in accuracy.It is interesting to observe that the approximation solution is piecewise convex.Particularly,with the reconstructed approximation space,the proposed method numerically demonstrates a remarkable robustness.The convergence of the Newton iteration does not rely on the initial values.The dependence of the convergence on the penalty parameter in the discretization is also negligible,in comparison to the classical discontinuous approximation space.
基金This study was supported by Zhang Ruirui's Beijing Nova Program(No.Z181100006218029)National Natural Science Foundation of China(31601228)+1 种基金BAAFS'Innovation Ability Construction Program 2018(No.KJCX20180424)National Key R&D Program of China(2016YFD0200701-2).
文摘Unmanned aerial vehicle(UAV)chemical application is widely used for crop protection,and spraying pattern is one of the most important factors that influence the chemical control efficacy.A method for UAV spraying pattern measurement with partial least squares(PLS)model based spectrum analysis was proposed in this study to measure the UAV spraying pattern more accurately.The method involved the steps of fluorescent tracer solution spray and its droplets collection,the spectrum on paper strip acquiring,spectrum processing and analysis,PLS modeling.In order to verify the applicability of the method and obtain the parameters of the PLS model,UAV spraying experiments were performed in the field.Then Fluorescent tracer solution was sprayed and its droplets are collected by paper strip,and the original spectrum on paper strip obtained by a spectrometer was processed by the Savitzky-Golay and standard normalized variable(SNV)method.The prediction model of coverage rate selected as the droplet deposition parameter to measure the UAV spraying pattern,was established by using PLS method.To verify the superiority of the PLS model,a traditional linear regression(LR)model of coverage rate was established simultaneously.The results demonstrate that the method with PLS model based spectrum analysis can measure the UAV spraying pattern effectively,and PLS model has a better performance of RV2=0.94 and RMSEP=0.9446 than that of the LR model.
文摘Prediction of power generation of a wind turbine is crucial,which calls for accurate and reliable models.In this work,six different models have been developed based on wind power equation,concept of power curve,response surface methodology(RSM)and artificial neural network(ANN),and the results have been compared.To develop the models based on the concept of power curve,the manufacturer’s power curve,and to develop RSM as well as ANN models,the data collected from supervisory control and data acquisition(SCADA)of a 1.5 MW turbine have been used.In addition to wind speed,the air density,blade pitch angle,rotor speed and wind direction have been considered as input variables for RSM and ANN models.Proper selection of input variables and capability of ANN to map input-output relationships have resulted in an accurate model for wind power prediction in comparison to other methods.
基金supported by National Science Foundation of USA (Grant No. DMS1521158)National Natural Science Foundation of China (Grant No. 12101229)+1 种基金the Hunan Provincial Natural Science Foundation of China (Grant No. 2021JJ40331)the Chinese Scholarship Council (Grant Nos. 201606060017 and 202106720024)。
文摘When one solves differential equations by a spectral method,it is often convenient to shift from Chebyshev polynomials Tn(x) with coefficients anto modified basis functions that incorporate the boundary conditions.For homogeneous Dirichlet boundary conditions,u(±1)=0,popular choices include the "Chebyshev difference basis" ζn(x)≡Tn+2(x)-Tn(x) with coefficients here denoted by bnand the "quadratic factor basis" Qn(x)≡(1-x2)Tn(x) with coefficients cn.If u(x) is weakly singular at the boundary,then the coefficients andecrease proportionally to O(A(n)/nκ) for some positive constant κ,where A(n) is a logarithm or a constant.We prove that the Chebyshev difference coefficients bndecrease more slowly by a factor of 1/n while the quadratic factor coefficients cndecrease more slowly still as O(A(n)/nκ-2).The error for the unconstrained Chebyshev series,truncated at degree n=N,is O(|A(N)|/Nκ) in the interior,but is worse by one power of N in narrow boundary layers near each of the endpoints.Despite having nearly identical error norms in interpolation,the error in the Chebyshev basis is concentrated in boundary layers near both endpoints,whereas the error in the quadratic factor and difference basis sets is nearly uniformly oscillating over the entire interval in x.Meanwhile,for Chebyshev polynomials,the values of their derivatives at the endpoints are O(n2),but only O(n) for the difference basis.Furthermore,we give the asymptotic coefficients and rigorous error estimates of the approximations in these three bases,solved by the least squares method.We also find an interesting fact that on the face of it,the aliasing error is regarded as a bad thing;actually,the error norm associated with the downward curving spectral coefficients decreases even faster than the error norm of infinite truncation.But the premise is under the same basis,and when involving different bases,it may not be established yet.
基金This work was supported in part by the National Key Research and Development Project Fund Project(Grant No.2016YFD0702002)Beijing Academy of Agriculture and Forestry Innovation team Project(Grant No.JNKYT201604)+1 种基金Construction Project of Scientific Research and Innovation Platform of Beijing Academy of Agricultural and Forestry Sciences for 2018(Grant No.PT2018-23)Beijing Academy of Agriculture and Forestry International Cooperation Fund(Grant No.GJHZ2017-7).
文摘Wheat is a major grain crop in China.Water is one of the most important factors which influence the lifecycle and yield of wheat.It is of great significance to study the water content at the key stages of wheat growth in order to make irrigation decision to raise its yield.As Terahertz(THz)spectroscopy is a brand new sensing technology and sensitive to water absorption,the relationship between terahertz spectra and water content in winter wheat leaf was investigated and a preliminary result was presented in this paper.Forty winter wheat leaves samples with diverse range of water content(42.8%-72.5%)were collected.The Terahertz time domain spectra(THz-TDS)were first obtained and then transformed into Frequency-domain amplitude with the Fast Fourier Transformation(FFT)method.The absorption and refractive index spectra were then calculated.The spectra were linearly fitted to obtain the slope and intercept used for building a calibration model.The partial least squares(PLS)method and linear regression were employed to establish models to determine leaf water content in the winter wheat.The predicted correlation coefficient and the root mean square error of the optimal model established with the Frequency-domain amplitude parameter at 0.3 THz by linear regression were 0.812%and 4.4%,respectively.The results showed that terahertz spectroscopy performed well in water content prediction and could be an effective and potential method for leaf water content measurement in winter wheat.
文摘Three uncertain parameters(peak ground acceleration,soil density,and soil modulus of elasticity)have been studied with regard to their effects on the stability and damage of a circular tunnel during an earthquake.A time history of an actual earthquake in the literature with modification has been adopted in the numerical simulation and analysis of the tunnel responses.Meta-models have been constructed based on an experimental method with quadratic and interaction terms using matlab codes in order to predict the compressive damage,tensile damage,and the overall displacement of the tunnel.The results of the meta-models predicted a highly reasonable response of the tunnel with regard to the maximum principal stresses in the tunnel lining and predicted a remarkable response of the tunnel with respect to the overall displacement of the tunnel.Moreover,the peak ground acceleration was observed to exert the highest effect on the overall displacement of the tunnel,compared to the soil density and soil modulus of elasticity.Furthermore,the metamodels revealed the inverse relationship between the soil modulus of elasticity and the compressive and tensile damages of the tunnel lining.The meta-models exhibited high efficiency of representation of the behavior of the structural system during earthquakes.
