non linear regression

In this research, firstly, the importance of accurate calculation of satellite speed losses and the factors affecting them were discussed. The input data of 15 satellite launchers built by different countries around the world with variations in the number of stages, orbital height and payload mass were collected and by means of accurate path simulation software, their optimal turn angle program was extracted as well as speed losses due to earth's gravity, propulsion and the drag is calculated and presented. In the following, by using the non-linear regression method, three analytical relations with acceptable error have been extracted and introduced to estimate speed losses, which can replace the use of route simulation code in the conceptual design phase of carriers. These relationships have been evaluated by the information of two satellites outside the statistical data used in the regression, including Safir and Epsilon, and the accuracy of the algorithm has been confirmed with a maximum error of 12% and an average error of less than 6%.

Particulate matters (PM) with an aerodynamic diameter less than 10 microns will cause serious damages to human health. Moreover, their presence can have a critical impact on climate change, global warming, and earth radiance budget. Therefore, obtaining precise information about their concentration and spatial distribution is crucial for public health and environmental studies. High concentration of PM10 can be named as a major environmental and public health problems especially for industrial and populated cities around the world. Thus, policymakers and environmental organizations have decided to establish pollution station to measure various pollutants including PM10. Obviously, it is not possible to establish many pollution stations based on economic justifications so, an only limited number of these instruments are located in every city. However these instruments can measure and record the PM10 concentration with high precision, they only provide sparse point observations. In this case, remote sensing data can be utilized to fill this gap and solve the existing discontinuity problem. Generally, two kinds of remote sensing data which have a good representation of existing pollutant in the atmosphere can be used for this purpose. Aerosol optical depth (AOD) and aerosol contributions to apparent reflectance (ACR) are two of these data. ACR images can be simply calculated from each satellite image consisting of Red and SWIR (2.1 µm) bands. This could be achieved by estimating the surface reflectance (SR) of the Red band from the top of atmosphere reflectance (TOAR) of the SWIR band. Then, the difference of SR and TOAR of the Red band can be a representation of the amount of atmosphere reflectance related to existing pollutants. In this study, we have used ACR images instead of AOD data to estimate PM10 concentrations and produce PM10 pollution maps for Tehran city in Iran based on three reasons. First, they have better spatial resolution and second, they are spatially continuous in contrast to AOD data which include much gaps in the study area due to dark target limitations for AOD value retrieval. Lastly, an aerosol robotic network (AERONET) station is not located in this area which is required to evaluate the precision of retrieved AOD values. MODIS level-1B images named MOD02HKM for 8 days in 2017 with corresponding ground measurements of PM10 concentrations from 14 pollution stations have been utilized in this area. Four different regression model including linear, exponential, logarithmic, and power regressions are employed to estimate PM10 concentrations and produce pollution map. Three criteria of R square, the correlation between estimated and observed (measured) PM10 concentrations, and root mean square error (RMSE) are employed to investigate the performance of four regression models. Based on the R square criterion, the linear regression model with 0.5912 performs better than exponential, logarithmic and power regressions with 0.5826, 0.5808, and 0.5782 R square values respectively. Since we have observed different performance from four regression model based on three evaluation criterion, we have applied a ranking method based on the evaluation criterion to determine the best regression model. Based on the ranking, we recognize that the exponential regression model performs better than linear, logarithmic and power regressions.

The use of different synthetic dyes in textile industries has increased in recent decay, resulting in the release of dye-containing industrial effluents into natural aquatic ecosystem. Since most of dyes are usually very recalcitrant to microbial degradation, therefore dye removal from effluent is a main concern in many studies. Different process was used for the treatment of dye effluent. In the last few years, studies were focused on advanced oxidation process (AOPs) methods such as UV-ZnO, UV-H2O2, UV-O3 and UV-TiO2. Photocatalytic process such as UV-ZnO is an efficient method that treats non-degradable wastewater by active radicals. The photocatalysis needs a photo-reactor that contacts reactant, products and light. In recent years, different types of photo-reactors have been used for wastewater treatment. In some reactors, nano-photocatalysts are utilized in slurry form, and the other particles are coated on bed. In Photocatalytic reactors with fixed bed, nano-photocatalysts are immobilized on bed and do not need the separation unit, but the main disadvantage of this photo-reactors is the low mass transfer rate between wastewater and nano-photocatalysts. Consequently, Different optimal photo-reactors were developed for increasing mass transfer rate. In this study, a novel photocatalytic cascade disc reactor coated with ZnO nano-photocatalysts was applied and in order to increase mass transfer rate artificial roughness were created on the surface of disks. Applying artificial roughness changes mass transfer rate by providing vertical mixing, creating secondary currents and increasing the Reynolds number. This photo-reactor has a number of advantages that include eliminating the need for catalyst separation units as the catalyst is immobilized, creating the flow mixing by non-mechanical method, increasing the transport of oxygen from the gas phase to the photocatalyst surface by providing the flow cascade pattern. The photo-reactor was used in order to remove Reactive Yellow 81 (RY81) dye from textile industry effluent, by means of UV-ZnO process. RY81 is a reactive dye composed of 10 Benzene rings and two –N=N azo bonds. The effect of different operational parameters such as initial Concentration of dye, pH, Catalyst surface loading and flow rate in removal efficiency was investigated, and the optimal value of those parameters were 50 mg/L, 8, 40 gr/m2 and 80 cc/s, respectively. A rate equation for the removal of RY81 was obtained by mathematical kinetic modeling. The Langmuir-Hinshelwood kinetic model is one of the most common kinetic models that are used for studying the kinetics of heterogeneous photo-catalysis. The results of reaction kinetic modeling indicate the conformity of removal kinetics with Langmuir-Hinshelwood model, and the constants kL-H and Kads were obtained 7.17 mg L-1 hr-1, 0.122 mg-1 L, respectively.
One way of inserting various operational parameters to a rate equation is regression analysis. Therefore, in this study, nonlinear regression model was developed for prediction pseudo- first order rate constant as a function of initial concentration of dye, pH, catalyst surface loading and flow rate. This equation could properly predict (R2=0.95) the removal rate constant of RY81 removal in the photocatalytic cascade disk reactor under different operational conditions and a good consistency was observed between the calculated results and experimental findings.