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.

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.

A predictive functional control algorithm for multivariable systems with time delay

To improve the dynamic characteristics and the coupling capability, a new predictive functional control algorithm is proposed for strong coupling multivariable systems with time delay, which combines predictive functional control and decoupliug control. First, a decoupling control algorithm is proposed, in which first-order models with time delay are established by analyzing the amplitude-frequency and phase-frequency characteristics of the decoupled subject. Then, a controller is designed for the single-variable subjects after decoupling based on the principles of predictive functional control. The simulation results show that this proposed algorithm has less online computation time and faster tracking. It can provide a more effective control for complex multivariable systems.

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.

Neural Modeling of Multivariable Nonlinear Stochastic System. Variable Learning Rate Case

The objective of this paper is to develop a variable learning rate for neural modeling of multivariable nonlinear stochastic system. The corresponding parameter is obtained by gradient descent method optimization. The effectiveness of the suggested algorithm applied to the identification of behavior of two nonlinear stochastic systems is demonstrated by simulation experiments.

An Application of a Multivariable Self-Tuning Regulatorto the Control System of a Equipment Spare Parts

A discrete-dine control system model of equipment spare parts is proposed In this model,the stochastic demand, of the spare parts is described by the state equation disturbance. The controlpolicy of the system was deduced by means of the methods of a multivariable self-tuning regulatorand reduced-cud r state observer. An example was given in the end.

Weathering and accumulation of trace elements in the soils of the Porali Plain, Balochistan: repercussions in agriculture

This study is thefirst attempt to assess the nature of the soil,especially on the western side of the Porali Plain in Balochistan;a new emerging agriculture hub,using weathering and pollution indices supplemented by multi-variate analysis based on geochemical data.The outcomes of this study are expected to help farmers in soil manage-ment and selecting suitable crops for the region.Twenty-five soil samples were collected,mainly from the arable land of the Porali Plain.After drying and coning-quarter-ing,soil samples were analyzed for major and trace ele-ments using the XRF technique;sieving and hydrometric methods were employed for granulometric analysis.Esti-mated data were analyzed using Excel,SPSS,and Surfer software to calculate various indices,correlation matrix,and spatial distribution.The granulometric analysis showed that 76%of the samples belonged to loam types of soil,12%to sand type,and 8%to silt type.Weathering indices:CIA,CIW,PIA,PWI,WIP,CIX,and ICV were calculated to infer the level of alteration.These indices reflect mod-erate to intense weathering;supported by K_(2)O/AI_(2)O_(3),Rb/K_(2)O,Rb/Ti,and Rb/Sr ratios.Assessment of the geo-ac-cumulation and Nemerow Pollution indices pinpoint rela-tively high concentrations of Pb,Ni,and Cr concentration in the soils.The correlation matrix and Principal Compo-nent Analysis show that the soil in this study area is mainly derived from the weathering of igneous rocks of Bela Ophiolite(Cretaceous age)and Jurassic sedimentary rocks of Mor Range having SEDEX/MVT type mineralization.Weathering may result in the undesirable accumulation of certain trace elements which adversely affects crops.

Socioeconomic traits and the risk of Barrett’s esophagus and gastroesophageal reflux disease: A Mendelian randomization study

BACKGROUND Previous observational studies have shown that the prevalence of gastroesophageal reflux disease(GERD)and Barrett’s esophagus(BE)is associated with socioeconomic status.However,due to the methodological limitations of traditional observational studies,it is challenging to definitively establish causality.AIM To explore the causal relationship between the prevalence of these conditions and socioeconomic status using Mendelian randomization(MR).METHODS We initially screened single nucleotide polymorphisms(SNPs)to serve as proxies for eight socioeconomic status phenotypes for univariate MR analysis.The inverse variance weighted(IVW)method was used as the primary analytical method to estimate the causal relationship between the eight socioeconomic status phenotypes and the risk of GERD and BE.We then collected combinations of SNPs as composite proxies for the eight socioeconomic phenotypes to perform multivariate MR(MVMR)analyses based on the IVW MVMR model.Furthermore,a two-step MR mediation analysis was used to examine the potential mediation of the associations by body mass index,major depressive disorder(MDD),smoking,alcohol consumption,and sleep duration.RESULTS The study identified three socioeconomic statuses that had a significant impact on GERD.These included household income[odds ratio(OR):0.46;95% confidence interval(95%CI):0.31-0.70],education attainment(OR:0.23;95%CI:0.18-0.29),and the Townsend Deprivation Index at recruitment(OR:1.57;95%CI:1.04-2.37).These factors were found to independently and predominantly influence the genetic causal effect of GERD.Furthermore,the mediating effect of educational attainment on GERD was found to be mediated by MDD(proportion mediated:10.83%).Similarly,the effect of educational attainment on BE was mediated by MDD(proportion mediated:10.58%)and the number of cigarettes smoked per day(proportion mediated:3.50%).Additionally,the mediating effect of household income on GERD was observed to be mediated by sleep duration(proportion mediated:9.75%)CONCLUSION This MR study shed light on the link between socioeconomic status and GERD or BE,providing insights for the prevention of esophageal cancer and precancerous lesions.

Clinical outcome and prognostic factors of T4N0M0 colon cancer after R0 resection:A retrospective study

BACKGROUND Paradoxically,patients with T4N0M0(stage II,no lymph node metastasis)colon cancer have a worse prognosis than those with T2N1-2M0(stage III).However,no previous report has addressed this issue.AIM To screen prognostic risk factors for T4N0M0 colon cancer and construct a prognostic nomogram model for these patients.METHODS Two hundred patients with T4N0M0 colon cancer were treated at Tianjin Medical University General Hospital between January 2017 and December 2021,of which 112 patients were assigned to the training cohort,and the remaining 88 patients were assigned to the validation cohort.Differences between the training and validation groups were analyzed.The training cohort was subjected to multi-variate analysis to select prognostic risk factors for T4N0M0 colon cancer,followed by the construction of a nomogram model.RESULTS The 3-year overall survival(OS)rates were 86.2%and 74.4%for the training and validation cohorts,respectively.Enterostomy(P=0.000),T stage(P=0.001),right hemicolon(P=0.025),irregular review(P=0.040),and carbohydrate antigen 199(CA199)(P=0.011)were independent risk factors of OS in patients with T4N0M0 colon cancer.A nomogram model with good concordance and accuracy was constructed.CONCLUSION Enterostomy,T stage,right hemicolon,irregular review,and CA199 were independent risk factors for OS in patients with T4N0M0 colon cancer.The nomogram model exhibited good agreement and accuracy.

Characteristics and genesis of groundwater salinization in coastal areas of the Lower Reaches of Oujiang Basin

The coastal areas of the lower reaches of Oujiang River Basin are rich in groundwater resources.However,the unsustainable exploitation and utilization of groundwater have led to significant changes in the groundwater environment.Understanding the characteristics and genesis of groundwater salinization is crucial for preventing its deterioration and ensuring sustainable utilization.In this study,a comprehensive approach combining the ion ratio method,mineral saturation index method and multivariate statistical analysis was employed to investigate the hydrochemical characteristics and main controlling factors in the study area.The findings reveal that:(1)Groundwater samples in study area exhibit a neutral to slightly alkaline pH.The predominant chemical types of unconfined water are HCO_(3)-Ca·Na,HCO_(3)·Cl-Na·Ca and HCO_(3)·SO_(4)-Ca·Na,while confined water mainly exhibits Cl·HCO_(3)-Na and Cl-Na types.(2)Salinity coefficients indicate an increase in salinity from unconfined to confined water.TDS,Na^(+)and Cl^(–)concentrations show an increasing trend from mountainous to coastal areas in unconfined water,while confined water displays variability in TDS,Na^(+)and Cl^(–)concentrations.(3)Groundwater salinity is mainly influenced by water-rock interactions,including the dissolution of halite and gypsum,cation exchange,and seawater intrusion etc.Additionally,human activities and carbonate dissolution contribute to salinity in unconfined water.Seawater intrusion is identified as the primary factor leading to higher salinity in confined water compared to unconfined water,with increasing cation exchange and seawater interaction observed from unconfined to confined water.

R-Factor Analysis of Data Based on Population Models Comprising R- and Q-Factors Leads to Biased Loading Estimates

Effects of performing an R-factor analysis of observed variables based on population models comprising R- and Q-factors were investigated. Although R-factor analysis of data based on a population model comprising R- and Q-factors is possible, this may lead to model error. Accordingly, loading estimates resulting from R-factor analysis of sample data drawn from a population based on a combination of R- and Q-factors will be biased. It was shown in a simulation study that a large amount of Q-factor variance induces an increase in the variation of R-factor loading estimates beyond the chance level. Tests of the multivariate kurtosis of observed variables are proposed as an indicator of possible Q-factor variance in observed variables as a prerequisite for R-factor analysis.

Multivariable sales prediction for filling stations via GA improved BiLSTM

Accurate sales prediction in filling stations is the basis to fill in the refined oil in time and avoid the outof-stock as much as possible.Considering the defect of great“lag”in the general time series model,this paper summarizes the multiple factors that influence the oil sales and develops a multivariable long short-term memory(LSTM)neural network,with the hyper-parameters being improved by the genetic algorithm(GA).To further improve the prediction accuracy,the proposed LSTM neural network is generalized to bidirectional LSTM(Bi LSTM),in which the impact of future factors on present sales can be taken into account by backward training.Finally,different LSTM structures and genetic algorithm parameters are tested to discuss their impact on prediction accuracy.Results demonstrated that genetic algorithm improved Bi LSTM model is superior to extreme gradient boosting,ARIMA,and artificial neural network,having the highest accuracy of 89%.

MULTIVARIABLE MODEL REFERENCE ADAPTIVE CONTROL FOR A TURBOFAN ENGINE

A decentralized model reference adaptive control (MRAC) scheme is proposed and applied to design a multivariable control system of a dual-spool turbofan engine.Simulation studies show good static and dynamic performance of the system over the fullflight envelope. Simulation results also show the good effectiveness of reducing interactionin the multivariable system with significant coupling. The control system developed has awide frequency band to satisfy the strict engineering requirement and is practical for engineering applications.

Studies on Heavy Metal Pollution in Soil-Plant System:A Review

Heavy metal pollution in soil-plant system is of major environmental concern on a world scale and in China in particular with the rapid development of industry. The heavy metal pollution status in soil-plant system in China, the research progress on the bioavailability of heavy metals (affecting factors, extraction methods, free-ion activity model, adsorption model, multivariate regression model, Q-I relationship, and compound pollution), and soil remediation are reviewed in the paper. Future research and monitoring is also discussed.

Multivariable PI Type Generalized Predictive Control

This paper presents a multivariable generalized predictive controller with proportion and integration structure by modifying the quadratic criterion of the usual MGPC. The control performance has been improved greatly. The effectiveness of the controller is demonstrated by the simulation result.

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.

STRUCTURES OF SYSTEMS WITH EXPONENTIAL LIFE DISTRIBUTIONS

Structures of monotone systems and cold standby systems with exponen-tial life distributions and dependent components are studied. It is shown that a mono-tone system composed of components with multivariate HNBUE life distributions isessentially a series system composed of components with multivariate exponential lifedistributions. Also, it is proved that for cold standby systems composed of componentswith multivariate NBU life distributions, all but oue of the components are degenerateat zero while the remaining one is exponential. In addition, several equivalent char-acterizations of multivariate exponential distribution are provided in the multivariateHNBUE life distribution class which include many existing results as special cases.

Analysis of the Suitability of Surface Water for Irrigation Purposes: The Southwestern and Coastal River Systems in Ghana

Surface water basins all over the world are very crucial in irrigation industries. Irrigation schemes are particularly crucial in the agricultural economies due largely to the fact that global climate change has led to drastic changes in rainfall patterns. As a result, rain-fed agriculture alone is no more sustainable and irrigation schemes are being encouraged as poverty reduction/eradication strategies in the developing countries. This study was conducted to assess the overall controls on surface water resources in the coastal and south-western river basins in Ghana, and determine the suitability of these surface waters for irrigation activities. Multivariate statistical methods were applied to data on the physico-chemical parameters from the coastal and southwestern river basins. This study finds that the quality of surface water from these basins is controlled principally by leachate of chemicals from solid and mine wastes, the chemistry of rainfall, weathering of underlying silicate mineral-rich rocks and sediments, agricultural and domestic wastes. All the parameters are within the acceptable national concentration ranges for most domestic and industrial purposes. Sodium adsorption ratio (SAR) was used to assess the quality of water from the two basins for irrigation activities. The SAR values for all the months and years sampled are lower than 4 and the electrical conductivity values are equally low due to generally low ionic concentrations. When plotted on the Wilcox diagram, the data for all the months for the two years of the study, plot within the “excellent to good” category, suggesting that water from the area is of acceptable quality for irrigation activities.

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.

Comparison of attitude determination approaches using multiple Global Positioning System (GPS) antennas

GPS-based attitude system is an important research field, since it is a valuable technique for the attitude determination of platforms. There exist two classes approaches for attitude determination using the GPS. The one determines attitude via baseline estimates in two frames, the other one solves for attitude by incorporating the attitude parameters directly into the GPS measurements. However, comparisons between these two classes approaches have been unexplored. First of all, two algorithms are introduced in detail which on behalf of these two kinds of approaches. Then we present numerical simulations demonstrating the performance of our algorithms and provide a comparison evaluating.