Polynomial Distribution Research Articles

Gradual Replacement of Soybean Meal with Brewer’s Yeast in Fingerling Nile Tilapia (Oreochromis niloticus) Diet, Resulting in a Polynomial Growth Pattern, Independent of Whether Reared in a Biofloc or Clear-Water System

A 60-day feeding experiment was conducted to examine whether (i) soybean meal (SBM) protein in the diet of Nile tilapia (Oreochromis niloticus) can be replaced with protein from spent brewer’s yeast (SBY); (ii) co-rearing with biofloc alters fish growth, feed conversion and protein efficiency compared with rearing in clear water; and (iii) accumulated protein quantity and quality in biofloc acts as a possible feed source for the fish in periods of low feed intake. The fish were reared in either a bio-recirculating aquaculture system (Bio-RAS) or a clear-water RAS (Cw-RAS). In Bio-RAS, the mechanical and biological filters used in Cw-RAS were replaced with an open bioreactor that delivered heterotrophic-based biofloc to the rearing tanks and also acted as a sedimentation trap for effluent water before recirculating it back into the rearing unit. The fish were fed four iso-nitrogenous and iso-energetic diets (~28% crude protein, ~19 MJ kg−1 gross energy) in which SBM protein was replaced with increasing levels of SBY, with triplicate tanks per inclusion level. The results revealed that average fish growth was greater in a biofloc environment compared with clear water and also greater at higher inclusion levels of SBY. However, in both rearing environments, fish growth displayed a second-degree polynomial distribution with increasing SBY inclusion level, with a peak between 30% and 60% inclusion. Fish in the biofloc environment showed better feed conversion ratio and protein retention, likely through ingesting both given feed and biofloc. Biofloc contained a significant amount of accumulated protein with a high biological profile, thereby constituting a possible feed reserve for the fish. A conclusion underlined by the apparent improved feed conversion of Bio-RAS reared fish, where that ingestion of biofloc will reduce the need for external feed per unit growth.

Modelling and Parametric Study for Panel Flutter Problem using Functionally Graded Materials

Abstract In this paper we will demonstrate the possibility of weight optimization of panels under aero-thermal loading in hypersonic flow using functionally graded materials (FGM). The in-plane volume fraction of two constituents (Aluminium and Nickel) is modelled using polynomial distributions. Different material grading layouts are investigated, including cases with Nickel concentrated at corners, sides, midpoints and center. The solution of the problem utilized a higher order element with C1 continuity. The study covers the linear boundaries of the panel flutter problem as well as the non-linear post-buckling deflections. The results indicated Nickel placement strategies are shown to enhance dynamic pressure and vibration performance for a given mass reduction through optimal center and edge localization. Overall, the integrated modelling approach demonstrates the potential to systematically optimize stability, weight and integrity in hypersonic flow to optimize the weight of panels subject to aero-thermal loads.

Characteristics of surface ozone pollution and its correlations with meteorological factors: the case of Xiangtan.

Based on ozone (O3) monitoring data for Xiangtan and meteorological observation data for 2020-2022, we examined ozone pollution characteristics and the effects of meteorological factors on daily maximum 8-h average ozone (O3-8h) concentrations in Xiangtan. Thus, we observed significant increases as well as notable seasonal variations in O3-8h concentrations in Xiangtan during the period considered. The ozone and temperature change response slope (KO3-T) indicated that local emissions had no significant effect on O3-8h generation. Further, average O3-8h concentration and maximum temperature (Tmax) values showed a polynomial distribution. Specifically, at Tmax < 27 °C, it increased almost linearly with increasing temperature, and at Tmax between 27 and 37 °C, it showed an upward curvilinear trend as temperature increased, but at a much lower rate. Then, at Tmax > 37 °C, it decreased with increasing temperature. With respect to relative humidity (RH), the average O3-8h concentration primarily exceeded the standard value when RH varied in the range of 45-65%, which is the key humidity range for O3 pollution, and the inflection point for the correlation curve between O3-8h concentration and RH appeared at ~55%. Furthermore, at wind speeds (WSs) below 1.5 m∙s-1, O3-8h concentration increased rapidly, and at WSs in the 1.5-2 m∙s-1 range, it increased at a much faster rate. However, at WSs > 2 m∙s-1, it decreased slowly with increasing WS. O3-8h concentration also showed the tendency to exceed the standard value when the dominant wind directions in Xiangtan were easterly or southeasterly.

Land subsidence in Beijing: response to the joint influence of the South-to-North Water Diversion Project and ecological water replenishment, observed by satellite radar interferometry

ABSTRACT The South-to-North Water Diversion Project Middle Route (SNWD-MR) annually diverts hundreds of millions of cubic meters of water from the Danjiangkou Reservoir to Beijing, significantly impacting the regional groundwater cycle. To conserve water resources, the government has implemented ecological water replenishment (EWR) in some water systems. This study aimed to study the coupled process of groundwater dynamics and land subsidence (LS) in Yongding River (YDR) basin (Beijing section) following the implementation of the SNWD-MR and EWR. First, an Interferometric Synthetic Aperture Radar (InSAR) time series technique was used to detect spatial and temporal distributions of surface displacement between 2015 and 2020 based on satellite images from Sentinel-1A/B. The results indicated a predominant LS deceleration trend during the InSAR observation period. The area with subsidence velocity below 20 mm/yr decreased significantly by 18.6% after SNWD-MR and EWR (from 2016 to 2020). Then, groundwater level fluctuations during the InSAR observation period were analyzed using groundwater measurement well data. Over 60% of these wells showed a rebound in groundwater levels after the implementation of SNWD-MR and EWR. The polynomial distribution lag model (PDL) revealed the association between LS and groundwater level changes, depicting both short- and long-term lag effect. The results showed significant spatial and temporal heterogeneity on the short- and long-term response between groundwater level change and regional subsidence. In addition, we calculated the differential subsidence slope based on the InSAR-derived LS and analyzed its impact on the river slope after SNWD-MR and EWR. The results show that two sections with significant severe differential subsidence slope occur between 0 and 14,000 m and between 54,000 and 78,000 m along the YDR. The slope change caused by LS may reduce the conveyance capacity of surface canals, and more attention should be paid in those two sections. These findings have an important scientific significance for management strategy for LS control against the background of SNWD-MR and EWR.

Multi-Level Text Clustering in Subject Knowledge Library and its Visualization

The large-scale and complex data generated in the teaching field of business administration poses challenges for decision-makers and managers of companies, and how to effectively extract and manage the useful information contained in these data has become a problem to be solved. Currently available methods of subject knowledge library clustering and visualization struggle to handle the complexity and multi-hierarchies of such subject data effectively or meet users’ requirements for advanced semantic understanding and retrieval. In view of these matters, this study aims to probe deeper into the problem of multi-level text clustering in the subject knowledge library and its visualization. Firstly, an innovative strategy-based subject semantic representation method for knowledge libraries was proposed to better interpret and represent the semantic information of subject data. Secondly, a subject clustering model of the knowledge library was constructed based on an improved hierarchical Dirichlet polynomial distribution, enabling efficient and accurate clustering of subject data. Lastly, visualization technology was employed to display the cluster results, allowing users to gain a clear understanding of the internal relationships and structure of the subject data. The research findings of this study could provide valuable new tools and methods for solving the problem of subject knowledge library management and utilization, analyzing the subject data, and supporting decision-making. As a result, they hold both theoretical and practical significance.

The effects of prenatal PM2.5 oxidative potential exposure on feto-placental vascular resistance and fetal weight: A repeated-measures study

BackgroundFeto-placental hemodynamic deterioration is a critical contributing factor to fetal growth restriction. Whether PM2.5 oxidative potential (OP) affects feto-placental hemodynamics and what impact is on estimated fetal weight (EFW) have not been fully elucidated. We sought to evaluate the association of PM2.5 OP with EFW and to explore whether feto-placental vascular impedance hemodynamic change is a possible mediator in this association. MethodsA repeated-measures study was conducted involving sixty pregnant women with at least 26 weeks of follow-up during pregnancy in Guangzhou, China, from September 2017 to October 2018. Daily filter-based PM2.5 samples were prospectively collected from ground monitors, and estimates of OP for PM2.5 and its metallic (OPv-metal) and non-metallic constituents (OPv-nonmental) were determined by dithiothreitol assay. Ultrasound data of fetal growth and umbilical arterial resistance, including estimated fetal weight (EFW), pulsatility index, resistance index, and systolic-to-diastolic ratio, were also obtained during gestation. Generalized estimating equations and polynomial distribution lag models were applied to analyze the associations of maternal exposure to PM2.5 OP with EFW and umbilical artery indices. Causal mediation analysis was used to evaluate the mediating role of umbilical arterial resistance. ResultsPrenatal exposure to ambient PM2.5 OP was significantly inversely associated with EFW. The magnitudes of effects of OPv-nonmetal on EFW were larger than those of OPv-metal. Significant mediation for the relationship between PM2.5-related OP and EFW by increased impedance in the umbilical artery was observed, with the estimated percent mediated ranging from 31% to 61%. The estimated percent mediated for OPv-nonmetal was higher than those for OPv-metal. ConclusionsFindings suggest that increased impedance in the umbilical artery may be one of the potential mediators of the relationship between PM2.5 oxidative potential exposure and low fetal weight.

A three-dimensional wake model for wind turbines based on a polynomial distribution of wake velocity

Accurate and fast prediction of wake is essential for power generation prediction of wind farms. This paper proposes a three-dimensional wake model that considers the effect of wind shear and the mass loss caused by such shear. The model simplifies the wake velocity distribution by assuming a straightforward polynomial shape rather than a complex Gaussian distribution, which makes the model simpler and more intuitive. To be close to reality, it incorporates the anisotropic expansion of the wake boundary and provides expressions for crossflow and vertical wake expansion rates. By solely possessing information regarding the incoming wind conditions and wind turbine parameters, wake velocity at any position can be calculated in a fast way. This model's prediction accuracy is demonstrated by four cases including three experimental as well as large eddy simulation (LES) data. Compared to conventional Gaussian models, it can maintain a higher level of accuracy in all cases. The model is quite simple and offers high accuracy and low cost. It can be used in wind farm layout optimization and wake control.

Simulation of English part-of-speech classification based on artificial intelligence and additive logistic regression

English part-of-speech classification technology is a technology that can process text data, can effectively solve the problem of messy data in text information categories, make data structured and organized, and facilitate people to obtain effective information implicit in the text. This article transforms the original polynomial distribution into a generalized linear model and uses logistic regression algorithm for specific implementation. Moreover, the model proposed in this paper inherits the good explanatory characteristics of the decision tree, and it locally uses logistic regression to fit the data, which greatly improves the function space that logistic regression can fit. In addition, due to changes in the decision theory of logistic regression leaf nodes, the corresponding tree branch theory also needs to be changed accordingly. Finally, this paper designs experiments to study the performance of the model constructed in this paper. The research results show that the model constructed in this paper has high accuracy in the extraction and classification of English part-of-speech features.

Shape control of moderately thick piezoelectric beams

The present contribution focuses on shape control of thick beam-type structures. First the governing equations of a multi-layered beam are derived by taking advantage of the Timoshenko assumptions and the constitutive relations of piezoelectric materials. The deflection curves are explicitly given for a piezoelectric cantilever subjected to a polynomial distribution of the vertical load and the applied electric voltage. In order to find a solution for the optimal shape control voltage an objective function, which depends on the quadratic deflection curve over the beam length, is minimized. Finally several benchmark examples are given for thick beams and the outcome is compared to finite element results and previously derived shape control results from the scientific literature that hold for thin piezoelectric beams. The presented shape control method shows a better agreement with the numerical outcome than the analytical shape control results within the Bernoulli-Euler theory, but the desired voltage distribution only slightly differs from the outcome for thin beams. Furthermore it is found that for a given total thickness-to-length ratio piezoelectric bimorph structures may be more difficult to be perfectly controlled than three-layer beams with thin piezoelectric layers. This is due to higher order piezoelectric effects which are not considered by the present theory (e.g. the thickness deformation caused by the thickness piezoelectric coupling constant).

Polynomial Distributions and Transformations

Polynomials are common algebraic structures, which are often used to approximate functions, such as probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of systems rather than to assume polynomials for only approximating known or empirically estimated distributions. Polynomial distributions offer great modeling flexibility and mathematical tractability. However, unlike canonical distributions, polynomial functions may have non-negative values in the intervals of support for some parameter values; their parameter numbers are usually much larger than for canonical distributions, and the interval of support must be finite. Hence, polynomial distributions are defined here assuming three forms of a polynomial function. Transformations and approximations of distributions and histograms by polynomial distributions are also considered. The key properties of the polynomial distributions are derived in closed form. A piecewise polynomial distribution construction is devised to ensure that it is non-negative over the support interval. A goodness-of-fit measure is proposed to determine the best order of the approximating polynomial. Numerical examples include the estimation of parameters of the polynomial distributions and generating polynomially distributed samples.

Supply Sequence Modelling Using Hidden Markov Models

Logistics processes, their effective planning as well as proper management and effective implementation are of key importance in an enterprise. This article analyzes the process of supplying raw materials necessary for the implementation of production tasks. The specificity of the examined waste processing company requires the knowledge about the size of potential deliveries because the delivered waste must be properly managed and stored due to its toxicity to the natural environment. In the article, hidden Markov models were used to assess the level of supply. They are a statistical modeling tool used to analyze and predict the phenomena of a sequence of events. It is not always possible to provide sufficiently reliable information with the existing classical methods in this regard. Therefore, the article proposes modeling techniques with the help of stochastic processes. In hidden Markov models, the system is represented as a Markov process with states that are invisible to the observer but with a visible output (observation) that is a random state function. In the article, the distribution of outputs from the hidden states is defined by a polynomial distribution.

Effect of Solid Concentration and Particle Size on the Flotation Kinetics and Entrainment of Quartz and Hematite

Despite the importance of solid concentration in froth flotation, its effect on flotation kinetics and entrainment has rarely been studied. In this study, the flotation kinetics and entrainment in quartz and hematite single-mineral flotation systems as a function of the solid concentration and particle size were investigated using dodecylamine acetate as a collector. Kinetics modeling showed that the Gamma distribution achieved the best agreement with the experimental data, whereas the Classical and Klimpel models poorly fit the data (e.g., RMSE). The flotation rate constants (k) of both quartz and hematite at a higher solid concentration showed a concave shape, with the inflexion point at the middle-size range, whereas this trend altered at lower solid concentrations. Overall, quartz exhibited higher equilibrium recoveries (R∞) than hematite, which indicates its better overall rate constants. The degree of water recovery in both the quartz and hematite systems was higher at higher solid concentrations, but the hematite system exhibited higher water R∞ than the quartz system, meaning that the entrainment of gangue could be higher in direct hematite flotation than the reverse one. Therefore, a higher solid concentration is associated with better overall quartz recovery and can reduce hematite loss by entrainment during reverse flotation. An inverse relationship was identified between the solid concentration and particle size in terms of the ratio of water recovery to the concentrate. In the reverse flotation of iron ore, refraining from achieving equilibrium recovery could help limit entrainment, but this was not necessarily the case in direct flotation. No entrainment model or method other than the Warren and Ross model approximated the overall trends of flotation at the finest size range (−38 µm). However, extending the Warren method to polynomial distribution led to an improved fit with the experimental results. In addition to the solid concentration, particle density and size were revealed to be key to developing new entrainment models. Finally, after the fast recovery period (true flotation) was over, the slow recoveries were mainly driven by the slow-floating water fraction.

Field-measurement-based local wind field characteristics on bridge deck of truss girder bridges in a deep-cutting gorge bridge site area

Affected by many factors, the local wind environment on the bridge deck is complex and changeable, and it seriously threatens traffic safety. To accurately evaluate the wind field on the bridge deck, this paper develops a system to monitor the actual local wind environment and applies it to field measurement of the wind parameters at different positions of a complex truss girder bridge. The results show that the wind parameters on the bridge deck, including wind speed, gust factor, and turbulence intensity, are different from the bridge site due to the influence of the ancillary facilities. Also, the wind profile of the local wind field on the bridge deck is more in line with the polynomial distribution, which makes the equivalent height of the wind load much higher than the vehicle gravity. It should be noted that the measured power spectrum of the bridge deck is quite different from the wind spectrum applicable to the bridge site area, so it is not appropriate to use the wind spectrum of the bridge site area to carry out the analysis of the windmill bridge, and a more suitable wind spectrum for bridge deck wind field is proposed.

Analysis of Network Information Retrieval Method Based on Metadata Ontology

In order to solve the problem that people can accurately search for the network information they need, the research on network information retrieval methods becomes more important. This article is mainly about the research of network information retrieval methods based on metadata ontology calculations. This article constructs an LDA three-layer Bayesian model with a three-layer structure of document, topic, and single order. The three-layer structure obeys a random polynomial distribution and can be calculated the joint distribution probability of all variables in the LDA model greatly increases the calculation efficiency. Using a cross-modal information retrieval method, it can mine the common data features between different modal data and analyze the semantic correlation between different modal data, improve the accuracy of search, and solve the existence of different modal data. There is a gap in the expression semantics between heterogeneous and different modal data. The experimental results in this paper show that the text feature extraction of the network information retrieval method based on the metadata ontology calculation has a good performance in terms of accuracy, and the accuracy of the extraction and clustering results is as high as about 90%. The improved CCA algorithm used is better than the traditional CCA and the accuracy is improved by 23%, which is 12% higher than the LDA-CCA algorithm.

Experimental and modeling analysis of laminar flame speed over the pyrolytic gas from red pinewood

In combustion research, the laminar flame speed (SL) is an important basis for the study of fuel combustion and mechanism verification. A large number of studies have been done on various combustibles, mostly focusing on gas and liquid combustibles, but less on solid combustibles, and the SL of solid combustibles cannot be measured directly and effectively by conventional methods. This paper uses red pine wood as the object of study, analyses the pyrolysis gas components after high-temperature pyrolysis, and uses the Bunsen burner experimental system to study the SL of pyrolysis gas, and obtains the laminar flame speed (SL) of the gas-phase flame when burning red pine wood, which has certain guiding significance for the study of the laminar flame speed (SL) of solid combustibles. In this paper, firstly, the pyrolysis gas products of red pine wood were analyzed by TG-DSC as well as GC/MS, and it was found that the direct reaction was the most violent at 210°C–410 °C, and the reaction rate gradually levelled off after 410 °C. It was also found that the gas mainly consisted of H2, CO2, C2H4, CO, CH4, C2H6, C3H6 and C3H8, accounting for more than 98%, and with the pyrolysis Secondly, the laminar flame speed (SL) of the gas products was investigated using the Bunsen burner, and it was found that the laminar flame speed (SL) of the pyrolysis gases gradually increased with the increase of the pyrolysis temperature, with 15.7 cm-s−1, 32.94 cm-s−1 and 36.89 cm-s−1 for the pyrolysis gases at 350 °C, 450 °C and 550 °C, respectively Finally, numerical simulations were carried out to investigate the effects of initial temperature and altitude induced changes in air pressure and oxygen concentration on the laminar flame speed of the gas products, and it was found that the laminar flame speed of pyrolysis gases gradually increased with increasing initial temperature and decreased with increasing altitude. The effect of hydrocarbon gases on the SL-max of CH4 is essentially linear in the concentration range of 40%, while the effect of H2, CO and CO2 is essentially in the quadratic polynomial distribution.

Microstructural view of anatase to rutile phase transformation examined by in-situ high-temperature X-ray powder diffraction

The phase transformation of commercial TiO2 was investigated carefully by in-situ high-temperature X-ray powder diffraction. The diffractograms between 25 ​°C and 800 ​°C were employed to determine the composition, unit cell parameters, and microstructure. The phase transition initiated slowly at 400 ​°C due to the seeding effect of pre-existing rutile and accelerated above 600 ​°C. The unit cell volume of anatase exhibits a third-degree polynomial distribution similar to c-direction, where the volume increased before and decreased during the phase transition. In contrast, a and b unit cell parameters increased with temperature, following a second-degree polynomial distribution. The unit cell parameters and volume of rutile increased continually with temperature following a third-degree polynomial distribution. A slight difference in expansion rates before and during phase transformation reflects the formation and amalgamation of newly materialized rutile with pre-existing one. Both lattice strain and crystallite size of anatase increased before and decreased during the phase transition. The vigorous lattice vibration of the dominant anatase lattice is likely responsible for minor changes in the crystallite shape of pre-existing rutile, resulting in a nominal size decrease before phase transition. The materialization of newly formed rutile occurred under decreased lattice strain and increased crystallite size.

Modal gain characteristics of a two-section InGaAs/GaAs double quantum well passively mode-locked laser with asymmetric waveguide

Monolithic two-section InGaAs/GaAs double quantum well (DQW) passively mode-locked lasers (MLLs) with asymmetric waveguide, consisting of the layers of p-doped AlGaAs waveguide and no-doped InGaAsP waveguide, emitting at ~ 1.06 μm, with a fundamental repetition rate at ~ 19.56 GHz have been demonstrated. Modal gain characteristics, such as a gain bandwidth and a gain peak wavelength of the MLL, as a function of the saturable absorber (SA) bias voltage (Va) as well as the injection current of gain section (Ig), were investigated by the Hakki-Paoli method. With the increase of Va, the lasing wavelength and net modal gain peak of the MLL both exhibited red-shifts to longer wavelength significantly, while the modal gain bandwidth was narrowed. Both the net modal gain bandwidth and gain peak of the MLL followed a polynomial distribution versus the reverse bias at the absorber section. In addition, for the first time, it was found that Va had an obvious effect on the modal gain characteristics of the MLL.

A hyper-resolving polynomial aperture and its application in microscopy

BackgroundA hyper-resolving aperture composed of a polynomial distribution is suggested. The point spread function (PSF) is computed and compared with that corresponding to linear, quadratic, and circular apertures. In addition, the influence of the number of zones on the PSF is discussed. An application on confocal scanning laser microscope using Siemen’s star pattern as an object considering the polynomial apertures is given.ResultsWe have made polynomial apertures using MATLAB code, and we tested the resolution from the computation of the cut-off spatial frequency obtained from the computation of the point spread function.ConclusionsWe get compromised resolution and contrast for the polynomial apertures as compared with uniform circular apertures.

Short-duration exposure of 3-µm polystyrene microplastics affected morphology and physiology of watermilfoil (sp. roraima)

Microplastics are one of the most widely discussed environmental issues worldwide. Several studies have shown the effect of microplastic exposure on the marine environment; however, studies on freshwater systems are lacking. This study was conducted to investigate the effect of microplastics on hydroponically growing emergent freshwater macrophytes, watermilfoil (sp. roraima) under controlled environmental conditions. Plants were exposed to 0mg L-1 (control), 0.05mg L-1, 0.25mg L-1, 1.25mg L-1, and 6mg L-1 of 3-µm polystyrene microspheres for 7days. The oxidative stress, antioxidant response, pigmentations, Fv/Fm, and growth parameters in the above-water and below-water parts were analyzed separately. Microscopic observations were performed to confirm the tissue absorbance of the microplastics. Exposure to microplastics altered some parameters; however, growth was not affected. The effect of microplastics was not linear with the exposure concentration for most of the parameters and between 1.25 and 6mg L-1 concentrations. The response trends mostly followed the second-order polynomial distributions. Under the 1.25mg L-1 exposure, there were significant changes in root length, H2O2 content, catalase activity, anthocyanin content, and Fv/Fm. There were differences in parameters between the above-water and below-water parts, and the responses of the microplastics followed different trends. Microscopic observations confirmed the attachment of microplastic particles onto newly formed roots, except for older roots or shoot tissues.

Improved Energy Based Multi-Sensor Object Detection in Wireless Sensor Networks

Wireless Sensor Networks (WSNs) are spatially distributed to independent sensor networks that can sense physical characteristics such as temperature, sound, pressure, energy, and so on. WSNs have secure link to physical environment and robustness. Data Aggregation (DA) plays a key role in WSN, and it helps to minimize the Energy Consumption (EC). In order to have trustworthy DA with a rate of high aggregation for WSNs, the existing research works have focused on Data Routing for In-Network Aggregation (DRINA). Yet, there is no accomplishment of an effective balance between overhead and routing. But EC required during DA remained unsolved. The detection of objects belonging to the same event into specific regions by the Bayes Node is distributed through the Sensor Nodes (SNs). Multi-Sensor Data Synchronization Scheduling (MSDSS) framework is proposed for efficient DA at the sink in a heterogeneous sensor network. Secure and Energy-Efficient based In-Network Aggregation Sensor Data Routing (SEE-INASDR) is developed based on the Dynamic Routing (DR) structure with reliable data transmission in WSNs. Theoretical analysis and experimental results showed that in WSN, the proposed Bayes Node Energy Polynomial Distribution (BNEPD) technique reduced Energy Drain Rate (EDR) by 39% and reduced 33% of Communication Overhead (CO) using poly distribution algorithm. Similarly, the proposed MSDSS framework increased the Network Lifetime (NL) by 15%. This framework also increased 10.5% of Data Aggregation Routing (DAR). Finally, the SEE-INASDR framework significantly reduced EC by 51% using a Secure and Energy-Efficient Routing Protocol (SEERP).