HIGHER-ORDER MULTIVARIABLE EULER'S POLYNOMIALAND HIGHER-ORDER MULTIVARIABLEBERNOULLI'S POLYNOMIAL

In this paper, the definitons of both higher-order multivariable Euler's numbersand polynomial. higher-order multivariable Bernoulli's numbers and polynomial aregiven and some of their important properties are expounded. As a result, themathematical relationship between higher-order multivariable Euler's polynomial(numbers) and higher-order higher -order Bernoulli's polynomial (numbers) are thusobtained.

PSEUDO-DIVISION ALGORITHM FOR MATRIX MULTIVARIABLE POLYNOMIAL AND ITS APPLICATION

Pseudo-division algorithm for matrix multivariable polynomial are given, thereby with the view of differential algebra, the sufficient and necessary conditions for transforming a class of partial differential equations into infinite dimensional Hamiltonianian system and its concrete form are obtained. Then by combining this method with Wu's method, a new method of constructing general solution of a class of mechanical equations is got, which several examples show very effective.

A New Method for Constructing the Inversion of Multivariable Linear Systems

A new algorithm for constructing an inverse of a multivariable linear system is presented. This algorithm makes the constructing an inverse of the higher order matrices into searching for the equivalent normal form of the lower order matrices. Consequently, the calculation is more simple efficient and programmed than previous methods. Another result of the paper is that the lower reduced inverse system is obtained, by selecting special bases of the observable space of the original systems, it reveals the effect of the observability of the original systems on the order of the inverse systems.

AN ALGEBRAIC METHOD FOR POLE PLACEMENT IN MULTIVARIABLE SYSTEMS

This paper considers the pole placement in multivariable systems involving known delays by using dynamic controllers subject to multirate sampling. The controller parameterizations are calculated from algebraic equations which are solved by using the Kronecker product of matrices. It is pointed out that the sampling periods can be selected in a convenient way for the solvability of such equations under rather weak conditions provided that the continuous plant is spectrally controllable. Some overview about the use of nonuniform sampling is also given in order to improve the system's performance.

Incremental multivariable predictive functional control and its application in a gas fractionation unit

The control of gas fractionation unit(GFU) in petroleum industry is very difficult due to multivariable characteristics and a large time delay.PID controllers are still applied in most industry processes.However,the traditional PID control has been proven not sufficient and capable for this particular petro-chemical process.In this work,an incremental multivariable predictive functional control(IMPFC) algorithm was proposed with less online computation,great precision and fast response.An incremental transfer function matrix model was set up through the step-response data,and predictive outputs were deduced with the theory of single-value optimization.The results show that the method can optimize the incremental control variable and reject the constraint of the incremental control variable with the positional predictive functional control algorithm,and thereby making the control variable smoother.The predictive output error and future set-point were approximated by a polynomial,which can overcome the problem under the model mismatch and make the predictive outputs track the reference trajectory.Then,the design of incremental multivariable predictive functional control was studied.Simulation and application results show that the proposed control strategy is effective and feasible to improve control performance and robustness of process.

A method for real power transfer allocation using multivariable regression analysis

A multivariable regression(MVR) approach is proposed to identify the real power transfer between generators and loads.Based on solved load flow results,it first uses modified nodal equation method(MNE) to determine real power contribution from each generator to loads.Then,the results of MNE method and load flow information are utilized to determine suitable regression coefficients using MVR model to estimate the power transfer.The 25-bus equivalent system of south Malaysia is utilized as a test system to illustrate the effectiveness of the MVR output compared to that of the MNE method.The error of the estimate of MVR method ranges from 0.001 4 to 0.007 9.Furthermore,when compared to MNE method,MVR method computes generator contribution to loads within 26.40 ms whereas the MNE method takes 360 ms for the calculation of same real power transfer allocation.Therefore,MVR method is more suitable for real time power transfer allocation.

Multiobjective optimization and multivariable control of the beer fermentation process with the use of evolutionary algorithms

This paper describes empirical research on the model, optimization and supervisory control of beer fermentation.Conditions in the laboratory were made as similar as possible to brewery industry conditions. Since mathematical models that consider realistic industrial conditions were not available, a new mathematical model design involving industrial conditions was first developed. Batch fermentations are multiobjective dynamic processes that must be guided along optimal paths to obtain good results.The paper describes a direct way to apply a Pareto set approach with multiobjective evolutionary algorithms (MOEAs).Successful finding of optimal ways to drive these processes were reported.Once obtained, the mathematical fermentation model was used to optimize the fermentation process by using an intelligent control based on certain rules.

ANALYSIS OF BENDING, VIBRATION AND STABILITY FOR THIN PLATE ON ELASTIC FOUNDATION BY THE MULTIVARIABLE SPLINE ELEMENT METHOD

In this paper, the bicubic splines in product form are used to construct the multi-field functions for bending moments, twisting moment and transverse displacement of the plate on elastic foundation. The multivariable spline element equations are derived, based on the mixed variational principle. The analysis and calculations of bending, vibration and stability of the plates on elastic foundation are presented in the paper. Because the field functions of plate on elastic foundation are assumed independently, the precision of the field variables of bending moments and displacement is high.

Medium-Term Electric Load Forecasting Using Multivariable Linear and Non-Linear Regression

Medium-term forecasting is an important category of electric load forecasting that covers a time span of up to one year ahead. It suits outage and maintenance planning, as well as load switching operation. We propose a new methodol-ogy that uses hourly daily loads to predict the next year hourly loads, and hence predict the peak loads expected to be reached in the next coming year. The technique is based on implementing multivariable regression on previous year's hourly loads. Three regression models are investigated in this research: the linear, the polynomial, and the exponential power. The proposed models are applied to real loads of the Jordanian power system. Results obtained using the pro-posed methods showed that their performance is close and they outperform results obtained using the widely used ex-ponential regression technique. Moreover, peak load prediction has about 90% accuracy using the proposed method-ology. The methods are generic and simple and can be implemented to hourly loads of any power system. No extra in-formation other than the hourly loads is required.

Recent developments on applications of sequential loop closing and diagonal dominance control schemes to industrial multivariable system

With a focus on an industrial multivariable system, two subsystems including the flow and the level outputs are analysed and controlled, which have applicability in both real and academic environments. In such a case, at first, each subsystem is distinctively represented by its model, since the outcomes point out that the chosen models have the same behavior as corresponding ones. Then, the industrial multivariable system and its presentation are achieved in line with the integration of these subsystems, since the interaction between them can not actually be ignored. To analyze the interaction presented, the Gershgorin bands need to be acquired, where the results are used to modify the system parameters to appropriate values. Subsequently, in the view of modeling results, the control concept in two different techniques including sequential loop closing control(SLCC) scheme and diagonal dominance control(DDC) schemes is proposed to implement on the system through the Profibus network, as long as the OPC(OLE for process control) server is utilized to communicate between the control schemes presented and the multivariable system. The real test scenarios are carried out and the corresponding outcomes in their present forms are acquired. In the same way, the proposed control schemes results are compared with each other, where the real consequences verify the validity of them in the field of the presented industrial multivariable system control.

Design of decoupling Smith control for multivariable system with time delays

In order to solve the decoupling control problem of multivariable system with time delays,a new decoupling Smith control method for multivariable system with time delays was proposed. Firstly,the decoupler based on the adjoint matrix of the multivariable system model with time delays was introduced,and the decoupled models were reduced to first-order plus time delay models by analyzing the amplitude-frequency and phase-frequency characteristics. Secondly,according to the closed-loop characteristic equation of Smith predictor structure,proportion integration (PI) controllers were designed following the principle of pole assignment for Butterworth filter. Finally,using small-gain theorem and Nyquist stability criterion,sufficient and necessary conditions for robust stability were analyzed with multiplicative uncertainties,which could be encountered frequently in practice. The result shows that the method proposed has superiority for response speed and load disturbance rejection performance.

Data-driven and physical-based identification of partial differential equations for multivariable system

Data-driven partial differential equation identification is a potential breakthrough to solve the lack of physical equations in complex dynamic systems.However,existing equation identification methods still cannot effectively identify equations from multivariable complex systems.In this work,we combine physical constraints such as dimension and direction of equation with data-driven method,and successfully identify the Navier-Stocks equations from the flow field data of Karman vortex street.This method provides an effective approach to identify partial differential equations of multivariable complex systems.

Observer-based multivariable fixed-time formation control of mobile robots

This paper proposes a multivariable fixed-time leaderfollower formation control method for a group of nonholonomic mobile robots, which has the ability to estimate multiple uncertainties. Firstly, based on the state space model of the leader-follower formation, a multivariable fixed-time formation kinematics controller is designed. Secondly, to overcome uncertainties existing in the nonholonomic mobile robot system, such as load change,friction, external disturbance, a multivariable fixed-time torque controller based on the fixed-time disturbance observer at the dynamic level is designed. The designed torque controller is cascaded with the formation controller and finally realizes accurate estimation of the uncertain part of the system, the follower tracking of reference velocity and the desired formation of the leader and the follower in a fixed-time. The fixed-time upper bound is completely determined by the controller parameters, which is independent of the initial state of the system. The multivariable fixed-time control theory and the Lyapunov method are adopted to ensure the system stability.Finally, the effectiveness of the proposed algorithm is verified by the experimental simulation.

Choice of operative method for pancreaticojejunostomy and a multivariable study of pancreatic leakage in pancreaticoduodenectomy

BACKGROUND As one of the major abdominal operations,pancreaticoduodenectomy(PD)involves many organs.The operation is complex,and the scope of the operation is large,which can cause significant trauma in patients.The operation has a high rate of complications.Pancreatic leakage is the main complication after PD.When pancreatic leakage occurs after PD,it can often lead to abdominal bleeding and infection,threatening the lives of patients.One study found that pancreatic leakage was affected by many factors including the choice of pancreaticojejunostomy method which can be well controlled.AIM To investigate the choice of operative methods for pancreaticojejunostomy and to conduct a multivariate study of pancreatic leakage in PD.METHODS A total of 420 patients undergoing PD in our hospital from January 2014 to March 2019 were enrolled and divided into group A(n=198)and group B(n=222)according to the pancreatointestinal anastomosis method adopted during the operation.Duct-to-mucosa pancreatojejunostomy was performed in group A and bundled pancreaticojejunostomy was performed in group B.The operation time,intraoperative blood loss,and pancreatic leakage of the two groups were assessed.The occurrence of pancreatic leakage after the operation in different patients was analyzed.RESULTS The differences in operative time and intraoperative bleeding between groups A and B were not significant(P>0.05).In group A,the time of pancreatojejunostomy was 26.03±4.40 min and pancreatic duct diameter was 3.90±1.10 mm.These measurements were significantly higher than those in group B(P<0.05).The differences in the occurrence of pancreatic leakage,abdominal infection,abdominal hemorrhage and gastric retention between group A and group B were not significant(P>0.05).The rates of pancreatic leakage in patients with preoperative albumin<30 g/L,preoperative jaundice time≥8 wk,and pancreatic duct diameter<3 mm,were 23.33%,33.96%,and 19.01%,respectively.These were significantly higher than those in patients with preoperative albumin≥30 g/L,preoperative jaundice time<8 wk,and pancreatic duct diameter≥3 cm(P<0.05).Logistic regression analysis showed that preoperative albumin<30 g/L,preoperative jaundice time≥8 wk,and pancreatic duct diameter<3 mm were risk factors for pancreatic leakage after PD(odds ratio=2.038,2.416 and 2.670,P<0.05).CONCLUSION The pancreatointestinal anastomosis method during PD has no significant effect on the occurrence of pancreatic leakage.The main risk factors for pancreatic leakage include preoperative albumin,preoperative jaundice time,and pancreatic duct diameter.

A closed-loop particle swarm optimizer for multivariable process controller design

Design of general multivariable process controllers is an attractive and practical alternative to optimizing design by evolutionary algorithms (EAs) since it can be formulated as an optimization problem. A closed-loop particle swarm optimization (CLPSO) algorithm is proposed by mapping PSO elements into the closed-loop system based on control theories. At each time step, a proportional integral (PI) controller is used to calculate an updated inertia weight for each particle in swarms from its last fitness. With this modification, limitations caused by a uniform inertia weight for the whole population are avoided, and the particles have enough diversity. After the effectiveness, efficiency and robustness are tested by benchmark functions, CLPSO is applied to design a multivariable proportional-integral-derivative (PID) controller for a solvent dehydration tower in a chemical plant and has improved its performances.

Fractional derivative multivariable grey model for nonstationary sequence and its application

Most of the existing multivariable grey models are based on the 1-order derivative and 1-order accumulation, which makes the parameters unable to be adjusted according to the data characteristics of the actual problems. The results about fractional derivative multivariable grey models are very few at present. In this paper, a multivariable Caputo fractional derivative grey model with convolution integral CFGMC(q, N) is proposed. First, the Caputo fractional difference is used to discretize the model, and the least square method is used to solve the parameters. The orders of accumulations and differential equations are determined by using particle swarm optimization(PSO). Then, the analytical solution of the model is obtained by using the Laplace transform, and the convergence and divergence of series in analytical solutions are also discussed. Finally, the CFGMC(q, N) model is used to predict the municipal solid waste(MSW). Compared with other competition models, the model has the best prediction effect. This study enriches the model form of the multivariable grey model, expands the scope of application, and provides a new idea for the development of fractional derivative grey model.

Modelling of Energy Storage Photonic Medium by Wavelength-Based Multivariable Second-Order Differential Equation

Wavelength-dependent mathematical modelling of the differential energy change of a photon has been performed inside a proposed hypothetical optical medium.The existence of this medium demands certain mathematical constraints,which have been derived in detail.Using reverse modelling,a medium satisfying the derived conditions is proven to store energy as the photon propagates from the entry to exit point.A single photon with a given intensity is considered in the analysis and hypothesized to possess a definite non-zero probability of maintaining its energy and velocity functions analytic inside the proposed optical medium,despite scattering,absorption,fluorescence,heat generation,and other nonlinear mechanisms.The energy and velocity functions are thus singly and doubly differentiable with respect to wavelength.The solution of the resulting second-order differential equation in two variables proves that energy storage or energy flotation occurs inside a medium with a refractive index satisfying the described mathematical constraints.The minimum-value-normalized refractive index profiles of the modelled optical medium for transformed wavelengths both inside the medium and for vacuum have been derived.Mathematical proofs,design equations,and detailed numerical analyses are presented in the paper.

THE MULTIVARIABLE NYQUIST PREDICTIVE CONTROL AND ITS APPLICATION

This paper firstly presents an algorithm of multivariable Nyquist predictivecontrol.Also,its relevant closed-feedback frame is proposed,by which the stability of thesystem can be immediately tested and the calculation of the algorithm is very convenient.Finally,the simulation of the predictive control algorithm to design a multivariable tem-perature control system for a 200MW thermal power unit is illustrated.The results of thesimulation show that the control system has good control performance.

A matrix Padé-type-Routh model reduction method for multivariable linear systems

In the present paper, the formulae for matrix Padé-type approximation were improved. The mixed model reduction method of matrix Padé-type-Routh for the multivariable linear systems was presented. A well-known example was given to illustrate that the mixed method is efficient.

Research on Dynamic Forecast of Flowering Period Based on Multivariable LSTM and Ensemble Learning Classification Task

The flowering forecast provides recommendations for orchard cleaning, pest control, field management and fertilization, which can help increase tree vigor and resistance. Flowering forecast is not only an important part of the construction of agro-meteorological index system, but also an important part of the meteorological service system. In this paper, by analyzing local meteorological data and phenological data of “Red Fuji” apples in Fen County, Linfen City, Shanxi Province, with the help of machine learning and neural networks, we proposed a method based on the combination of time series forecasting and classification forecasting is proposed to complete the dynamic forecasting model of local flowering in Ji County. Then, we evaluated the effectiveness of the model based on the number of error days and the number of days in advance. The implementation shows that the proposed multivariable LSTM network has a good effect on the prediction of meteorological factors. The model loss is less than 0.2. In the two-category task of flowering judgment, the idea of combining strategies in ensemble learning improves the effect of flowering judgment, and its AUC value increases from 0.81 and 0.80 of single model RF and AdaBoost to 0.82. The proposed model has high applicability and accuracy for flowering forecast. At the same time, the model solves the problem of rounding decimals in the prediction of flowering dates by the regression method.