Time-delay nonlinear model based on interval grey number and its application

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This study explores the potential of utilizing weathered basalt waste, discarded from basalt stone quarrying, as a resource for producing efficient adsorbents to remove Fe (III) and Zn (II) from aqueous and real wastewater. Raw weathered basalt (RWB), and its calcined derivatives at 750 °C for 3 h (CWB-750) and at 950 °C for 1 h with activated carbon impregnation (CWB/AC-950), were prepared and characterized. Characterization using XRD, FTIR, SEM, and surface area analyzer revealed that calcination improved porosity and surface area with some privilege for CWB/AC-950. CWB/AC-950 revealed remarkable removal efficiency for Fe (III) at a pH value of 5, achieving 98.30%, closely matching that of RWB (98.00%), and outperforming CWB-750 (96.20%). In contrast, RWB exhibited the highest removal capacity for Zn (II) at a pH value of 6, with an efficiency of 55%, surpassing both CWB-750 and CWB/AC-950, which achieved approximately 36%. For both contaminants, Pseudo-2nd-order equation (R2 > 0.98) provided a superior fit, showcasing favorable sorption process by all the addressed materials. The Fe(III) sorption data for all the investigated materials were better described by the Freundlich (FL) model compared to the Langmuir (LM) model. Similarly, the Zn(II) sorption data for the calcined derivatives (CWB-750 and CWB/AC-950) were well-explained by the FL model. These findings are supported by the very high determination coefficients (R2 > 0.96) and significantly lower average relative error (ARE) values (8.66 and 13.69) compared to those obtained from the LM model (55.99 and 189.25, orderly). In contrast, for RWB, despite the very high R2 values (> 0.98) for both models, neither adequately captured the Zn(II) sorption behavior, as evidenced by the exceptionally high ARE values (52.67 and 161.19 for LM and FL, respectively). These findings are supported by the very high determination coefficients (R2 > 0.96) and significantly lower average relative error (ARE) values compared to those obtained from the LM model. In contrast, for RWB, despite the very high R2 values (> 0.98) for both models, neither adequately captured the Zn(II) sorption behavior, as evidenced by the exceptionally high ARE values (52.67 and 161.19 for LM and FL, respectively). The remediation mechanism of both Fe (III) and Zn (II) by all adsorbents was not exclusively governed by inter-particle diffusion. Eventually, these findings highlight the sustainable potential of repurposing RWB waste and its calcined derivatives for water remediation applications.

PurposeSmog seriously affects the ecological environment and poses a threat to public health. Therefore, smog control has become a key task in China, which requires reliable prediction.Design/methodology/approachThis paper establishes a novel time-lag GM(1,N) model based on interval grey number sequences. Firstly, calculating kernel and degree of greyness of the interval grey number sequence respectively. Then, establishing the time-lag GM(1,N) model of kernel and degree of greyness sequences respectively to obtain their values after determining the time-lag parameters of two models. Finally, the upper and lower bounds of interval grey number sequences are obtained by restoring the values of kernel and degree of greyness.FindingsIn order to verify the validity and practicability of the model, the monthly concentrations of PM2.5, SO2 and NO2 in Beijing during August 2017 to September 2018 are selected to establish the time-lag GM(1,3) model for kernel and degree of greyness sequences respectively. Compared with three existing models, the proposed model in this paper has better simulation accuracy. Therefore, the novel model is applied to forecast monthly PM2.5 concentration for October to December 2018 in Beijing and provides a reference basis for the government to formulate smog control policies.Practical implicationsThe proposed model can simulate and forecast system characteristic data with the time-lag effect more accurately, which shows that the time-lag GM(1,N) model proposed in this paper is practical and effective.Originality/valueBased on interval grey number sequences, the traditional GM(1,N) model neglects the time-lag effect of driving terms, hence this paper introduces the time-lag parameters into driving terms of the traditional GM(1,N) model and proposes a novel time-lag GM(1,N) model.

With the gradual extension of global coal mining to the deep, the problem of surface subsidence caused by repeated mining of multiple coal seams has attracted much attention. In this paper, the methods of theoretical analysis, numerical simulation and field monitoring are used to study the settlement model and settlement law under the condition of repeated mining of multiple coal seams, and the engineering application is carried out. Through theoretical analysis, it is concluded that there is a linear relationship between the amount of broken expansion of overlying rock mass, the buried depth of coal seam, the thickness of coal seam and the maximum subsidence value of surface. The opening size of surface subsidence basin in multi-coal seam mining is still linear with the mining depth of coal seam. Based on the probability integral method, fully considering the factors such as rock mass expansion and separation caused by repeated mining of unequal thickness and multiple coal seams, the prediction model of surface subsidence caused by repeated mining of multiple coal seams is constructed, and the calculation method and calculation formula of surface subsidence coefficient caused by repeated mining of multiple coal seams are given. The law of overlying strata and surface subsidence caused by repeated mining of multiple coal seams is analyzed by numerical simulation. The results show that the trend of surface subsidence is similar to that of repeated mining (second-layer coal) in multi-coal seam mining area. The subsidence curve is symmetrically distributed in the early stage of mining and asymmetrically distributed in the later stage. The maximum value of surface subsidence is located on the side of open-off cut. The numerical simulation results are highly similar to the calculation results of ' prediction model of surface subsidence caused by repeated mining of multi-coal seam '. The surface subsidence prediction model constructed in this paper is used to predict the coal mine site. The prediction results are compared with the field measurement results. The maximum relative error value of the working face tendency is 5.7%, and the average relative error value is 2.9%. Along the strike of the working face, the maximum relative error value is 6.7%, and the average relative error value is 5%. The overall prediction error is small, which verifies the rationality of the prediction model of the surface subsidence law of multi-coal seam repeated mining.

Discrete Linear sediment models were developed using sediment mobilized and direct sediment flow graphs of Chaukhutia watershed of the Ramganga reservoir catchment, India, and applied for sediment flow routing. The parameters of the models were estimated by Lagrangian method. The sediment graphs computed by these models compared with remarkable accuracy to the measured sediment graphs. The average values of integral square error, coefficient of efficiency and ratio of mean error to the mean observed output for four parameter sediment discharge model are 5.991 %, 97.183% and 0.0022 respectively. For three parameter sediment discharge model, the average value of relative error in estimated peak is 6.976%.

In the age of Big Data, we must do best to economically extract value from very large volumes of a wide variety of statistics. However, because of subjective and objective reasons, it is becoming increasing clear that much data is of poor quality, which has serious effects on the research results. With the analysis on the cause and process of the low quality data, this paper introduces the concept of gray system and proposes a data-gray-correction model, which could change the original data into gray interval number and reduce the influence from the former. Assessing the quality of data with classical econometric model and correcting the data by error correction model, then find the reasonable range of the real data and instead the crisp data by interval number, which contain much more information. An example is provided to illustrate the ecological civilization evaluation process under gray interval number.

Multiple attribute decision-making theory under uncertainty is an important part of decision making theory, in this paper, a grey multiple attribute decision-making approach is proposed to study multi-criteria decision-making problems under uncertainty in which criteria values are interval gray numbers. Using grey related analysis as a means to reflect uncertainty in multiple attribute models through interval numbers. According to related theory, a non-risk standard expected value decision-making matrix can be obtained. Though determining the ideal grey relation reference sequence and non-ideal grey relation reference sequence, we can calculate the distance-proximity and angle-proximity of each alternative, and then the best alternative can be obtained by optimal membership degree which is based on distance-proximity and angle-proximity. At last the numerical illustrations prove the new model to be effective and scientific.

Multivariate analysis helps to understand the relationships between dependent variables; this methodology has great potential in several areas of knowledge. The aim of this study was to adjust and compare the univariate and multivariate Gompertz and Logistic nonlinear models to describe the productive traits of sunn hemp (Crotalaria juncea L.). Two uniformity trials were performed, and the following productive traits were analyzed in 376 sunn hemp plants along 94 days of observations (four plants per day): the fresh mass of leaves (FML), the fresh mass of stem (FMS), and the fresh mass of the aerial parts (FMAP). The Gompertz and Logistic univariate models were adjusted for each productive trait. To adjust the multivariate models, the errors covariance matrix was calculated. The matrix (Cholesky factor) was obtained for each trait, and the multivariate Gompertz (GG) and Logistic (LL) nonlinear models were generated, together with the combination of both models (GL and LG). To define the best model, the residual standard deviation (RSD), the determination coefficient (R2), the Akaike information criterion (AIC), the mean absolute deviation (MAD), and the measures of intrinsic nonlinearity (INL) and parametric nonlinearity (PNL) were calculated. The nonlinear multivariate model LL was adequate and achieved satisfactory results to describe the productive traits of sunn hemp.

Fractional order time-delay multivariable discrete grey model for short-term online public opinion prediction

In this paper, we extend the traditional grey situation decision to the case of decision information serving as interval grey number, and provide multi-objective weight optimization model of multi-objective grey situation decision. Taking the deviation in different objectives among the effect measure of each situation, positive and negative ideal into consideration first, the optimization model is established, and the ideal objective weight of each situation also obtained. Then, a quadratic programming model is set up from the whole and objective integrated weight vector of grey situation decision acquired as well. We sort the situation of each event by the possibility degree of interval grey number and get the optimal situation, so that the traditional theory of grey situation decision is improved. The feasibility and efficiency of the model is finally tested and verified by an example.

As the process of LN <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> ’s phase transition and heat exchange with water in pressure-tight tank is complicated, the tank’s inner gas pressure is tough to be calculated by mathematical model or CFD simulation. Therefore by conducting orthogonal experimental design and its variance analysis, the first two significant influence factors of average pressurization rate of the pressurization process were determined, namely the mass of injected liquid nitrogen and the volume of compressed gas inside the pressure-tight tank. Then a RBF artificial neural network model was established, trained and tested for pressurization prediction by the orthogonal experimental data. The average value and standard deviation of relative prediction error for testing data set were 8.52% and 1.82%, respectively. Finally, the pressurization and free jumping experiments of the water jet thruster were performed. By applying the RBF neural network model, the average value and standard deviation of the relative prediction error were 8.93% and 2.33%, respectively. Thus the RBF neural network model can be taken as the theoretical pressurization prediction model and provide guidance for the robotic water jet thruster’s actual jump.

In order to predict hot deformation behavior of superalloy nimonic 80A, a back-propagational artificial neural network (BP-ANN) and strain-dependent Arrhenius-type model were established based on the experimental data from isothermal compression tests on a Gleeble-3500 thermo-mechanical simulator at temperatures ranging of 1050–1250 °C, strain rates ranging of 0.01–10.0 s−1. A comparison on a BP-ANN model and modified Arrhenius-type constitutive equation has been implemented in terms of statistical parameters, involving mean value of relative (μ), standard deviation (w), correlation coefficient (R) and average absolute relative error (AARE). The μ -value and w -value of the improved Arrhenius-type model are 3.0012% and 2.0533%, respectively, while their values of the BP-ANN model are 0.0714% and 0.2564%, respectively. Meanwhile, the R-value and ARRE-value for the improved Arrhenius-type model are 0.9899 and 3.06%, while their values for the BP-ANN model are 0.9998 and 1.20%. The results indicate that the BP-ANN model can accurately track the experimental data and show a good generalization capability to predict complex flow behavior. Then, a 3D continuous interaction space for temperature, strain rate, strain and stress was constructed based on the expanded data predicted by a well-trained BP-ANN model. The developed 3D continuous space for hot working parameters articulates the intrinsic relationships of superalloy nimonic 80A.

To obtain the load spectrum of the traction resistance of the three-point suspension device under tractor-plowing conditions, a load spectrum extrapolation method based on a genetic algorithm optimal threshold selection is proposed. This article first uses a pin force sensor to measure the plowing resistance of the tractor’s three-point suspension device under plowing conditions and preprocesses the collected load signal. Next, a genetic algorithm is introduced to select the threshold based on the Peak Over Threshold (POT) extremum extrapolation model. The Generalized Pareto Distribution (GPD) fits the extreme load distribution that exceeds the threshold range, generating new extreme points that follow the GPD distribution to replace the extreme points in the original data, achieving the extrapolation of the load spectrum. Finally, the loading spectrum that can be achieved on the test bench is obtained based on the miner fatigue theory and accelerated life theory. The results show that the upper threshold of the time-domain load data obtained by the genetic algorithm is 10.975 kN, and the grey correlation degree is 0.7249. The optimal lower threshold is 8.5455 kN, the grey correlation degree is 0.7722, and the fitting effect of the GPD distribution is good. The plowing operation was divided into five stages: plowing tool insertion, acceleration operation, constant speed operation, deceleration operation, and plowing tool extraction. A traction resistance loading spectrum that can be achieved on the test bench was developed. The load spectrum extrapolation method based on the genetic algorithm optimal threshold selection can improve the accuracy of threshold selection and achieve the extrapolation and reconstruction of the load spectrum. After processing the extrapolated load spectrum, it can be transformed into a load spectrum that can be recognized by the test bench.

The paper describes the study of the kinetics of filtration drying of barley brewer’s spent grain. The dependencies of the process at different parameters of the stationary layer and the heating agent are presented: different heights of the wet material H (40 mm, 80 mm, 120 mm, and 160 mm), different temperatures of the heating agent T (50 °C, 70 °C, 80 °C, and 90 °C), and the velocities of the heating agent through the stationary layer of material v0 (1.26 m/s, 1.55 m/s, 1.81 m/s, 2.31 m/s, and 2.82 m/s). The kinetic regularities of two drying periods were determined: the period of complete saturation of the heating agent with moisture and the period of partial saturation of the heating agent with moisture. The calculation dependencies describing the intensity of the filtration drying process in both periods are proposed. The equations for determining the drying time of barley brewer’s spent grain τI and τII during both periods are proposed. The absolute value of the maximum relative error of the experimental values of moisture content from the theoretically calculated ones is 19.83 %, and the average value of the relative error is 3.15 %, which is acceptable for practical design calculations of drying equipment.

This paper focuses on the effect of some water quality parameters of river water which helps in the calculation of water quality index (WQI) that culminates in the development of a regression model for prediction of WQI of the river system in India.The index was calculated by arithmetic index method using twelve various experimentally estimated water quality parameters such as potential hydrogen, chlorides, dissolved oxygen saturation, nitrates, sulphates, phosphates, total dissolved solids, biochemical oxygen demand, electrical conductivity, total hardness, turbidity and total coliform of the water at eight locations, for a 55 km stretch of Chalakkudy river November 2013 to December 2018.It was identified that total coliform is the major parameter contributing to the bad quality of water.Water quality regression model has been developed as a function of total coliform content.The performance of the model in predicting the WQI has been tested by comparing with the calculated WQI for the following year 2018.The regression model has been found to be good with an absolute average relative error and root mean square error values of 0.693 and 0.5 respectively.The results indicate that the basin is slowly getting into a serious drinking water crisis.