Multiple Nonlinear Regression Model Research Articles

Prediction of char production from slow pyrolysis of lignocellulosic biomass using multiple nonlinear regression and artificial neural network

Char produced from lignocellulosic biomass via slow pyrolysis have become one of the most feasible alternatives that can partially replace the utilisation of fossil fuels for energy production. In this study, the relationship between compositions of lignocellulosic biomass, operating conditions of slow pyrolysis, and characteristics of produced char have been analysed by using multiple nonlinear regression (MnLR) and artificial neural networks (ANN). Six input variables (temperature, solid residence time, production capacity, particle size, and fixed carbon and ash content) and five responses (char yield, and fixed carbon, volatile matter, ash content, HHV of produced char) were selected. A total of 57 literature references with 393–422 datasets were used to determine the correlation and coefficient of determination (R2) between the input variables and responses. High correlation results (>0.5) existed between pyrolysis temperature and char yield (-0.502) and volatile matter of produced char (-0.619), ash content of feedstock and fixed carbon (-0.685), ash content (0.871) and HHV (-0.571) of produced char. Whilst the quadratic model was selected for the regression model, then the model was further optimised by eliminating any terms with p-values greater than 0.05. The optimised MnLR model results showed a reasonable prediction ability of char yield (R2 = 0.5579), fixed carbon (R2 = 0.7763), volatile matter (R2 = 0.5709), ash (R2 = 0.8613), and HHV (R2 = 0.5728). ANN model optimisation was carried out as the results showed “trainbr” training algorithm, 10 neurons in the hidden layer, and “tansig” and “purelin” transfer function in hidden and output layers, respectively. The optimised ANN models had higher accuracy than MnLR models with the R2 greater than 0.75, including 0.785 for char yield, 0.855 for fixed carbon, 0.752 for volatile matter, 0.951 for ash and 0.784 for HHV, respectively. The trained models can be used to predict and optimise the char production from slow pyrolysis of biomass without expensive experiments.

Research on the Impact of Environmental Regulation on Enterprise Innovation from the Perspective of Official Communication

Many developing countries including China are implementing increasingly stringent environmental regulations to achieve sustainable development. However, we have limited understanding about whether environmental regulations promote enterprise innovation. To address this research gap, this study empirically analyzes the impact of environmental regulations which is represented by the China Environmental Protection Law (2015) on enterprise innovation and it explores the moderating effects of official communication on environmental regulations and corporate innovation. The Super-Slacks-Based Measure (Super-SBM) model and Multiple Nonlinear Regression model are used to analyze 34,074 samples in China’s A-share market during the 2015–2017 period. Our results show that, in general, a higher intensity of environmental regulations is more beneficial to incentivize enterprises to implement innovation. Meanwhile, there is an inverted U-type relationship between official communication and innovation of enterprises. Furthermore, at present, the average level of official communication in China is too high, which will weaken the role of environmental regulation in promoting enterprise innovation. Overall, this study can help us better understand the politics behind enterprise innovation in countries.

Multiple nonlinear regression model of cutting force for C/SiC composites by laser‐assisted micromachining

AbstractBased on the response surface methodology (RSM), laser‐assisted micromachining (LAMM) experiments of carbon fiber reinforced silicon carbide matrix(C/SiC) composites have been carried out to obtain the data of three‐direction cutting forces Fx, Fy, Fz, and result‐force F in the cutting process. A stepwise regression method is used to screen out the factors that significantly affected the cutting force, and hence a multivariate nonlinear mathematical regression model has been established. Through the analysis of variance and regression analysis, the R2 of the regression model is the cutting force Fx: 0.975, the cutting force Fy: 0.970, the cutting force Fz: 0.972, the resultant force F: 0.987, and the probability p > F‐values are all less than 0.001. The model analysis results show that the main effects and interactions of the three factors of laser power, cutting speed, and cutting depth significantly influence the cutting force. The main effect of the most considerable influence on the resultant F is cutting depth, followed by cutting speed and laser power, and the interactive effect is cutting speed and cutting depth. The experimental results show that the model prediction results are in good agreement with the experimental results.

Overall chilled water system energy consumption modeling and optimization

The emergence of increasingly affordable variable-speed drive technology has changed the approach used to control chilled water systems equipped with these drives. The purpose of this research was to develop an integrated chilled water modeling technique that can determine the optimal system setpoints and estimate the energy saving potential of chiller system. The chiller system equipped with Variable Frequency Drives (VFDs) on cooling tower fans and condenser water pumps. To accomplish the objective, physical component models of the centrifugal chiller, cooling tower and condenser water pump were established with the goal of incorporating the system’s condenser water flow rate and cooling tower fan speeds as optimization variables. Furthermore, a cooling load prediction algorithm was developed using a multiple non-linear regression model to approximate the building’s cooling load subject to a range of environmental conditions. The inputs and outputs of the individual component models were linked to estimate how adjusting the cooling tower fan and condenser water pump speed would influence the system’s comprehensive performance. The overall system model was then optimized using a generalized reduced gradient optimization algorithm to determine the potential energy savings through speed control with VFDs and to ascertain a control logic strategy for the building automation system to operate the heating and cooling system. A case-study was performed on a single chiller system at a museum and the model was calibrated according to logged data collected over four months. Results showed that for the system analyzed, the energy saving of optimizing the cooling tower fan system was found to be 12–15%, while the energy saving potential of optimizing the condenser water pump with the cooling tower fan was negligible. Additionally, comparing different cooling tower fan control strategies showed that a wet-bulb approach-based cooling tower control strategy was shown to have the highest correlation to the optimized fan speed with an R2 of 0.924.

Development of a local scour prediction model clustered by soil class

Abstract Several studies have been conducted to assess local scour formulas in order to select the most appropriate one. Confronted with the limits of the previous formulas, further studies have been performed to propose new local scour formulas. Generalizing a single scour formula, for all soil classes, seems approximate for such a complex phenomenon depending on several parameters and may eventually lead to considerable uncertainties in scour estimation. This study aims to propose several new scour formulas for different granulometric classes of the streambed by exploiting a large field database. The new scour formulas are based on multiple non-linear regression (MNLR) models. Supervised learning is used as an optimization tool to solve the hyper-parameters of each new equation by using the ‘Gradient Descent Algorithm’. The results show that the new formulas proposed in this study perform better than some other empirical formulas chosen for comparison. The results are presented as seven new formulas, as well as abacuses for the calculation of local scour by soil classes.

Application of an Artificial Neural Network and Multiple Nonlinear Regression to Estimate Container Ship Length Between Perpendiculars

Abstract Container ship length was estimated using artificial neural networks (ANN), as well as a random search based on Multiple Nonlinear Regression (MNLR). Two alternative equations were developed to estimate the length between perpendiculars based on container number and ship velocity using the aforementioned methods and an up-to-date container ship database. These equations could have practical applications during the preliminary design stage of a container ship. The application of heuristic techniques for the development of a MNLR model by variable and function randomisation leads to the automatic discovery of equation sets. It has been shown that an equation elaborated using this method, based on a random search, is more accurate and has a simpler mathematical form than an equation derived using ANN.

An estimation of motor yacht light displacement based on design parameters using computational intelligence techniques

The article presents equations for the estimation of steel motor yacht light displacement based on selected design parameters, such as length overall, draught and breadth. The data of 240 build steel motor yachts from 2000 to 2020 with lengths from 30 m to 86 m were used to develop these equations. The complex design equations based on all design parameters were developed through the use of computational intelligence techniques, such as random search and Artificial Neural Networks. The simple relationships based on only one input design parameter were developed using common linear and non-linear regression. The study showed that the random search method, which utilizes a Multiple Nonlinear Regression model, offers good results that are as accurate as those developed through the use of artificial neural networks. The developed equations may have practical application for the parametric design of yachts.

Public Debt Threshold in the Republic of North Macedonia

Research question: Is there a non-linear relationship between public debt and economic growth in North Macedonia, in the form of an inverted U-shape? Motivation: Government consumption plays an important role in the stability of the national economy, especially in periods of economic crisis. However, a rapidly growing public debt is a concerning issue nowadays, since it might jeopardize economic growth perspectives. Economic theory suggests that public debt has non-linear impact on economic growth in the form of an inverted U-shape. In other words, it is believed that after a certain threshold, the public debt will have deleterious impact on economic growth. Idea: Given that such threshold varies significantly across countries, the aim of this paper is to calculate the turning point of the public debt impact in the Republic of North Macedonia. Tools: For this purpose, we use non-linear multiple regression model for the real GDP growth rate as a dependent variable, general government public debt-to-GDP ratio (in nominal and squared terms) as a key independent variable, as well as several other controlling variables. Since theory also suggests reverse causality between economic growth and public debt, we use two different estimation techniques (Ordinary Least Squares and Generalized Method of Moments) to deal with potential endogeneity, and to cross-validate the results. Data: In this regard, we use annual data for the period 1998 – 2019, for 14 variables in total, obtained from several different data sources. Findings: Our results show that general government debt in the Republic of North Macedonia positively affects economic growth until it reaches around 30% of GDP, whereas further indebtedness after that turning point will most likely have a negative impact. Contribution: Given that current debt level is far above the estimated turning point, the need of urgent fiscal consolidation inevitably arises. This is especially important in the light of the ongoing COVID-19 crisis, which imposed the need for strong government intervention and pointed out the importance of the fiscal space for such matter.

Field study and regression modeling on soil water distribution with mulching and surface or subsurface drip irrigation systems

The soil water status was investigated under soil surface mulching techniques and two drip line depths from the soil surface (DL). These techniques were black plastic film (BPF), palm tree waste (PTW), and no mulching (NM) as the control treatment. The DL were 15 cm and 25 cm, with surface drip irrigation used as the control. The results indicated that both the BPF and PTW mulching enhanced the soil water retention capacity and there was about 6% water saving in subsurface drip irrigation, compared with NM. Furthermore, the water savings at a DL of 25 cm were lower (15-20 mm) than those at a DL of 15 cm (19-24 mm), whereas surface drip irrigation consumed more water. The distribution of soil water content (θv) for BPF and PTW were more useful than for NM. Hence, mulching the soil with PTW is recommended due to the lower costs and using a DL of 15 cm. The θv values were derived using multiple linear regression (MLR) and multiple nonlinear regression (MNLR) models. Multiple regression analysis revealed the superiority of the MLR over the MNLR model, which in the training and testing processes had coefficients of correlation of 0.86 and 0.88, root mean square errors of 0.37 and 0.35, and indices of agreement of 0.99 and 0.93, respectively, over the MNLR model. Moreover, DL and spacing from the drip line had a significant effect on the estimation of θv. Keywords: palm tree waste mulching, plastic film mulching, soil water distribution, regression models DOI: 10.25165/j.ijabe.20211402.5200 Citation: Mattar M A, Al-Othman A A, Elansary H O, Elfeky A M, Alshami A K. Field study and regression modeling on soil water distribution with mulching and surface or subsurface drip irrigation systems. Int J Agric & Biol Eng, 2021; 14(2): 142–150.

Optimized ANN model for predicting rock mass quality ahead of tunnel face using measure-while-drilling data

Rock mass quality assessment has a vital influence on the excavation of tunnels and caverns in rock mass. For this purpose, extensive field studies, including records of measure-while-drilling data and rock mass quality scores (RQS) from the observation reports of tunnel faces, have been conducted. In order to predict RQS, three optimized artificial neural network (ANN) models based on genetic algorithm (GA), particle swarm optimization (PSO), and imperialist competition algorithm (ICA) were developed. Six parameters of measure-while-drilling (MWD) data and their corresponding RQS constituted 1270 datasets, which were set as input and output of ANN, respectively. The traditional multiple linear regression (MLR), multiple nonlinear regression (MNR) statistical model, and ANN model were developed as comparative models. Comparison results reveal that PSO-ANN and ICA-ANN models are capable of predicting RQS with higher reliability than the MLR, MNR, ANN, and GA-ANN models. Results indicate that PSO-ANN and ICA-ANN models can be used to predict RQS; however, the PSO-ANN model has better performance.

Field study and regression modeling on soil water distribution with mulching and surface or subsurface drip irrigation systems

The soil water status was investigated under soil surface mulching techniques and two drip line depths from the soil surface (DL). These techniques were black plastic film (BPF), palm tree waste (PTW), and no mulching (NM) as the control treatment. The DL were 15 cm and 25 cm, with surface drip irrigation used as the control. The results indicated that both the BPF and PTW mulching enhanced the soil water retention capacity and there was about 6% water saving in subsurface drip irrigation, compared with NM. Furthermore, the water savings at a DL of 25 cm were lower (15-20 mm) than those at a DL of 15 cm (19-24 mm), whereas surface drip irrigation consumed more water. The distribution of soil water content (θv) for BPF and PTW were more useful than for NM. Hence, mulching the soil with PTW is recommended due to the lower costs and using a DL of 15 cm. The θv values were derived using multiple linear regression (MLR) and multiple nonlinear regression (MNLR) models. Multiple regression analysis revealed the superiority of the MLR over the MNLR model, which in the training and testing processes had coefficients of correlation of 0.86 and 0.88, root mean square errors of 0.37 and 0.35, and indices of agreement of 0.99 and 0.93, respectively, over the MNLR model. Moreover, DL and spacing from the drip line had a significant effect on the estimation of θv. Keywords: palm tree waste mulching, plastic film mulching, soil water distribution, regression models DOI: 10.25165/j.ijabe.20211402.5200 Citation: Mattar M A, Al-Othman A A, Elansary H O, Elfeky A M, Alshami A K. Field study and regression modeling on soil water distribution with mulching and surface or subsurface drip irrigation systems. Int J Agric & Biol Eng, 2021; 14(2): 142–150.

Estimating the Efforts of Mobile Application Development in the Planning Phase Using Nonlinear Regression Analysis

Abstract The authors consider the construction of a nonlinear multiple regression model, its confidence and prediction intervals to evaluate the efforts of mobile application development in the planning phase based on the multivariate normalizing transformation and outlier detection. The constructed model is compared to the linear regression model and nonlinear regression models based on the univariate transformations, such as the decimal logarithm, Box–Cox, and Johnson transformation. This model, in comparison with other regression models, has better prediction accuracy.

Quantitative Structure-activity Relationships; Studying the Toxicity of Metal Nanoparticles.

Metal nanomaterials are widely used in various fields, including targeted therapy and diagnosis. They are extensively used in targeted drug delivery and local treatments. However, the toxicity associated with these materials could lead to severe adverse health effects. In this study, we investigated the relationships between the toxicity and structures of metal nanoparticles by using theoretical calculations and quantitative structure-activity relationships. Twenty four physicochemical descriptors and toxicity data of 23 types of metal nanoparticles were selected as samples, and a multiple linear regression model was established to obtain a toxicity prediction equation with 5 descriptors with an R2 of 0.910. Structures of copper nanoparticles were designed based on the model, and the structure with low toxicity was searched. The multiple nonlinear regression model was used to further improve the prediction accuracy. The R2 values were 0.995 in the training set and 0.988 in the test set, which indicated that the prediction accuracy improved. Based on the result of multiple linear regression, we designed copper nanoparticles with low toxicity. The study confirmed that the quantitative structure-activity relationship was a reasonable method for predicting the toxicity and designing the structures with low toxicity of metal nanoparticles.

Plant components affect bacterial biofilms development by altering their cell surface physicochemical properties: a predictability study using Actinomyces naeslundii.

We hypothesized that the initial events leading to biofilm formation by bacteria, in general, are predominantly mediated by cell surface physicochemical interactions, and that natural products can impact the process by altering cell surface physicochemical properties. We exemplified this phenomenon using Actinomyces naeslundii as the model organism, and using tea products to modify its cell surface physicochemical properties. To test the hypothesis, a non-linear multiple regression model incorporating a normal distribution curve was constructed to explain the impact of tea extracts on the physiochemical processes of biofilm formation by A. naeslundii. The model utilized tea extract-induced changes in cell surface physicochemical properties as independent variables, and the corresponding biofilm formation as a dependent variable. Five different tea extracts were used to treat A. naeslundii, and their impact on the cell surface hydrophobicity, charge, auto-aggregation, attachment and biofilm formation on four different hard surfaces were measured and the data were used to construct the model. The established model was then tested in independent experiments involving other plant extracts and purified phytochemicals. Experimental results showed that the tea extracts significantly reduced cell surface hydrophobicity (by up to 21.3%), increased cell surface charge and auto-aggregation (by up to 4.5mV and 14.9%, respectively), inhibited attachment (by 0.6-2.5 log CFU cm-2) and affected biofilm formation (by up to 0.6 log CFU cm-2). The model indicated that both cell surface hydrophobicity and charge played an important role in bacterial auto-aggregation and attachment, and that the latter two phenomena significantly correlated with subsequent biofilm development. The accuracy of the model construct was approximately 64%. This modelling approach can be employed for other microbial colonization systems to predict biofilm formation, and to study the impact of cell surface physicochemical properties in biofilm development.

The Seychelles Child Development Study of methyl mercury from fish consumption: analysis of subscales from the Child Behaviour Checklist at age 107 months in the main cohort

Methyl mercury (MeHg) is neurotoxic and all fish contain at least trace amounts. Consequently, prenatal or fetal exposure occurs when pregnant women consume fish and children are exposed postnatally when they breastfeed or consume fish. However, the level of exposure at which toxicity occurs is presently unknown. Since behavioural endpoints can be sensitive indicators of toxic exposure, we administered the Child Behaviour Checklist (CBCL) to measure behaviour as part of a prospective, longitudinal, double blind study (n=779) of prenatal MeHg exposure, the Seychelles Child Development Study (SCDS). The CBCL Total T score was a primary endpoint at 66 and 107 month evaluations of the cohort and showed no association with prenatal or postnatal MeHg exposure. This paper reports the results of a secondary analysis of the CBCL subscales to see if specific aspects of behaviour might show associations. The SCDS main cohort was enrolled in 1989-90 and evaluated on five occasions through 107 months of age. The child's primary caregiver completed the CBCL at the 107 month evaluation. Prenatal exposure was determined by measuring total mercury (THg) in maternal hair growing during pregnancy and recent postnatal exposure by analysing the child's hair taken at the 107 month evaluation. Analysis included linear and nonlinear multiple regression models. For prenatal MeHg exposure, the Social Problems subscale was significantly associated and the Somatic Complaints subscale was marginally associated. Both were beneficial associations. For postnatal exposure the Thought Problems subscale was associated in an adverse direction. This secondary analysis identified a small number of subtle beneficial and adverse associations with prenatal and postnatal MeHg exposure for specific CBCL subscales. These analyses provide no evidence for an adverse effect of prenatal exposure. The adverse postnatal association is difficult to interpret because we measured only recent (about one month) exposure and no adjustment was made for the multiplicity of endpoints.

Study on the basic performance of basic magnesium sulfate cement concrete

The influence of multiple factors – namely, cement type, cement strength grade, cement content and water–binder ratio – on the basic performance, including the slump and early compressive strength, of basic magnesium sulfate (MgSO4) cement (BMSC) concrete was researched. In addition, multiple non-linear regression models of the basic performance of BMSC considering the raw materials and mix proportions were proposed. The results show that when the apparent density and water–binder ratios of BMSC were constant, the slump of BMSC increased and the early compressive strength decreased with the increase in the cement content. With the increase in the water–binder ratio, the slump of BMSC increased gradually and the early compressive strength decreased gradually. With the increase in the cement strength grade, the slump and early compressive strength values of BMSC all increased. The slump and standard cube compressive strengths of BMSC had a multiple non-linear power function relationship with the cement strength grade, cement content and water–binder ratio. When the cement content of BMSC was 530 kg/m3, the standard cube compressive strength grade of BMSC that was mixed with fly ash reached 82.7 MPa, and the standard cube compressive strength grade of BMSC that was mixed with slag reached 70.5 MPa.

Artificial Neural Network and a Nonlinear Regression Model for Predicting Electrical Pole Crash

This paper presents the investigation about a problem situation that Electric Distributor Companies are facing in Chile resulting from transit accidents. The number of vehicle crashes to power distribution poles and street lighting has grown. This situation causes discomfort to citizen and mainly to the neighbors due to power cuts and even on occasion , losses of human lives because of the accident that have occurred. Based on previous research, the accidents are not random nor chance dependent, but the majority of transit accident follow parameters or variables from the scenery where it occurs. In order to analyze the variables and the degree this variables affect the accidents, a model of Perceptron and Multipercetron Artificial Neural Networks and a Multiple Nonlinear Regression model are proposed. An empirical study was made; collecting data from a distributor company and from Chilean National Traffic Safety Commission, where the more frequent variables involved in accidents were determined to develop the mentioned models. These variables were investigated and also their influence on the occurrence of vehicle crashes to power distribution poles could be confirmed. With this data, the prediction of post crashes was developed, where through the application of the neural network and multiple nonlinear regression, revealed 95.7% of acceptable predictions. This study will bring benefits to power distribution companies considering a risk index in the streets, based on the number of crashes of poles per street; this will allow optimal decisions in future electrical distribution projects avoiding critical areas.

Prediction of Surface Roughness and Optimization of Cutting Parameters in CNC Turning of Rotational Features

This research presents a model for prediction surface roughness in terms of process parameters in turning aluminum alloy 1200. The geometry to be machined has four rotational features: straight, taper, convex and concave, while a design of experiments was created through the Taguchi L25 orthogonal array experiments in minitab17 three factors with five Levels depth of cut (0.04, 0.06, 0.08, 0.10 and 0.12) mm, spindle speed (1200, 1400, 1600, 1800 and 2000) r.p.m and feed rate (60, 70, 80, 90 and 100) mm/min. A multiple non-linear regression model has been used which is a set of statistical extrapolation processes to estimate the relationships input variables and output which the surface roughness which prediction outside the range of the data. According to the non-linear regression model, the optimum surface roughness can be obtained at 1800 rpm of spindle speed, feed-rate of 80 mm/min and depth of cut 0.04 mm then the best surface roughness comes out to be 0.04 μm at tapper feature at depth of cut 0.01 mm and same spindle speed and feed rate pervious which gives the error of 3.23% at evolution equation.

Theoretical investigation on QSAR of (2-Methyl-3-biphenylyl) methanol analogs as PD-L1 inhibitor

Cancer is one of the most serious issues in human life. Blocking programmed cell death protein 1 and programmed death ligand-1 (PD-L1) pathway is one of the great innovations in the last few years, a few numbers of inhibitors can be able to block it. (2-Methyl-3-biphenylyl) methanol derivative is one of them. Here, the quantitative structure-activity relationship (QSAR) established twenty (2-methyl-3-biphenylyl) methanol derivatives as the programmed death ligand-1 inhibitors. Density functional theory at the B3LPY/6-31+G(d,p) level was employed to study the chemical structure and properties of the chosen compounds. Highest occupied molecular orbital energy EHOMO, lowest unoccupied molecular orbital energy ELUMO, total energy ET, dipole moment DM, absolute hardness η, absolute electronegativity χ, softness S, electrophilicity ω, energy gap ΔE, etc., were observed and determined. Principal component analysis (PCA), multiple linear regression (MLR) and multiple non-linear regression (MNLR) analysis were carried out to establish the QSAR. The proposed quantitative models and interpreted outcomes of the compounds were based on statistical analysis. Statistical results of MLR and MNLR exhibited the coefficient R2 was 0.661 and 0.758, respectively. Leave-one-out cross-validation, rm2 metric, rm2 test, and “Golbraikh & Tropsha’s criteria” analyses were applied for the validation of MLR and MNLR, which indicate two models are statistically significant and well stable with data variation in the external validation towards PD-L1. The obtained results showed that the MNLR model predicts the bioactivity more accurately than MLR, and it may be helpful and supporting for evaluation of the biological activity of PD-L1 inhibitors.

The optimum of heat recovery - Determination of the optimal heat recovery based on a multiple non-linear regression model

This paper is intended to answer the question of whether there can be a clear optimum according thermal efficiency and the corresponding electric effort when using heat recovery systems (HRS) under specific framework conditions. Since the benefits and the associated effort can vary widely in individual cases due to the different framework conditions, the question arises whether it is sensible to define the HRS requirements based on individual criteria, rather than blanket, rigid statutory requirements as is done with EU Regulation 1253/2014. In order to be able to find a respective economic optimum of the heat recovery in individual cases on the basis of various framework conditions without an individual optimization, a polynomial equation based on the nonlinear multiple-regression analysis has to be developed to predict the relevant optimum easily and quickly on the base of multidimensional optimizations. Thus, the determination of an optimal heat recovery in any case can prevent that with a too small or too large heat recovery an economic potential is given away. This makes sense from a business as well as from a macroeconomic point of view, since the sum of the business (microeconomic) optima must lead to a macroeconomic optimum. The influence on the heat recovery is shown on the basis of the parameters outdoor air temperature, extract air temperature and operating time. As a result, both the optimal temperature efficiency of the heat recovery, and the therefore required optimal air velocity, as well as the corresponding optimal pressure drop or the represented SFP-value depending on the general framework conditions are highlighted on the basis of two load cases and two balance limits.