Mathematical Model Using Soft Computing Techniques for Different Thermal Insulation Materials
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Abstract
The property of low thermal transmission of the small air gap between the constituents of combined material has been utilized to obtain energy-efficient wall sections. Ferro-cement is a highly versatile form of reinforced concrete made up of wire mesh, sand, water, and cement, which possesses unique qualities of strength and serviceability. The significant intention of the proposed technique is to frame a mathematical model with the aid of optimization techniques. Mathematical modeling is done by minimizing the cost and time consumed in the case of extension of the existing work. Mathematical modeling is utilized to predict the temperature of different walls such as reinforced cement concrete (RCC) wall, ferro-cement, combined RCC with ferro-cement, and combined ferro-cement wall. Different optimization algorithms such as social spider optimization (SSO) and genetic algorithm are utilized to find the optimal weights α and β of the mathematical modeling. All optimum results demonstrate that the attained error values between the output of the experimental values and the predicted values are closely equal to zero in the designed model. The proposed work is compared to the existing method, and from the results, the minimum error of 97.188% is determined by mathematical modeling in the SSO algorithm.
1 Introduction
Thermal insulation materials play an important role in achieving a building’s energy efficiency. Many kinds of thermal insulation materials for buildings are available. Among all, as environment-friendly and renewable materials, natural materials have numerous advantages over other materials and thus are the most promising for buildings [10]. Developing new types of thermal insulation materials has become a major trend in materials development. Among them, aerogel is one of the most promising new types of highly efficient thermal insulation materials [12]. Thermal insulation materials have an important role, and their use is a logical first step to reducing the energy required to keep a good interior temperature and therefore achieve energy efficiency [18]. The effective thermal resistivity of insulation materials decreases with temperature and increases with moisture content, and, consequently, increases the thermal losses of a building [20]. The thermal conductivity of insulation materials is greatly affected by their operating temperature and moisture content; however, limited information is available on the performance of insulation materials when subjected to actual climatic conditions [1]. Thermal transmittance can also be estimated through the ISO 6946 calculation method; however, several comparative studies demonstrated that the calculated U-values are usually lower than the measured ones [2]. The thermal properties of building materials such as clay used in construction are reported by many researchers in order to provide industrial designers with values based on high levels of confidence [4]. The widely used organic thermal insulation materials at present are flammable, and lots of hazards have been caused, especially when considering the fact that thermal insulation materials have side effects from the stage of their production until the end of their useful lifetime [26]. To achieve the highest possible thermal insulation resistance, new insulation materials and solutions with low thermal conductivity values have been and are being developed, in addition to using the current traditional insulation materials of ever-increasing thicknesses in the building envelopes [13]. The heat and moisture transport parameters were found generally to increase with temperature; however, within the limited temperature range characteristic of the climatic conditions of the temperate zone, their variations were not very dramatic, typically up to 20–30% [14]. To protect the ecological environment and reduce energy consumption of a building, a lot of attention is being paid to the development of environment-friendly and energy-efficient building materials [24]. The application of fiber-reinforced polymer (FRP) to the tension face of a concrete beam or slab has multiple benefits, including increased ultimate flexural strength capacity, increased post-cracking stiffness, as well as concrete crack control, whereby the bonding of FRP sheets to concrete beams results in finer and more evenly distributed cracks when compared to the cracks that develop in unstrengthened beams [8]. The use of FRP as an alternative reinforcement in concrete structures has emerged as an innovative solution owing to their non-corrosive and non-magnetic properties, making them ideal for severe environments and situations where magnetic transparency is required [15]. Fiber-reinforced concrete (FRC) is mostly applied in industrial pavements, pre-cast elements, and in tunneling. The application of FRC for retrofitting and seismic design purposes also has a particular interest [21]. Ferro-cement is a thin reinforced concrete composite typically consisting of cement mortar reinforced with closely spaced layers of continuous small-diameter wire mesh closely bonded together to create a stiff structural form [9]. The solution fibers (short)-mineral matrix could be an interesting alternative if the mechanical performances were not limited by a relatively small reinforcement ratio (usually <3–4% in volume), conditioned by the workability of the mortar, and the impossibility of controlling the fiber orientation [16]. The low level of technical skills required and the ready availability of materials make ferro-cement suitable for use in construction applications [25]. In addition, reducing emissions through insulation provides a cost-effective measure to combat climate change, reduces energy consumption and therefore reduces Europe’s dependence on foreign energy supplies, and creates value-added jobs in Europe [7]. The manufacture, transport, and installation in a building made of materials such as steel, concrete, and glass require a large quantity of energy, despite them representing a minimal part of the ultimate cost of the building as a whole [6].
2 Literature Review
In 2014, Tran and Kim [22] proposed the direct tensile behavior of high-performance fiber-reinforced cementation composites (HPFRCCs) at high strain rates between 10 and 40 s−1 by using a strain energy frame impact machine built by them. The influence of these three variables on the high strain rate effects on the direct tensile behavior of HPFRCCs was analyzed based on the test results. The enhancement was different according to the types of fiber, fiber volume content, and matrix strength: HPFRCCs with T-fibers produced higher impact resistance than H-fibers, and matrix strength was more influential than fiber contents for the high strain rate sensitivity. The rate sensitivity of HPFRCCs for all parameters decreased when the fiber volume content increased from 1% to 1.5%.
In 2014, Biddulph et al. [5] observed the thermal resistance as well as the effective thermal mass of a wall, with the help of heat flux and temperature measurements. The computation of heat loss requires the temperature of the air that is present in the interior and exterior to be subtracted against an estimate of the thermal transmittance (U-value) of the wall. Yet, in customary practices, these measurements span a period of 2 weeks in winter. The lumped thermal mass model and the Bayesian statistical analysis have worked in unison for yielding the estimation of the effective thermal mass as well as the U-value. The effect of weather on the U-values was properly examined with the smaller time scale, and the considerations related to thermal comfort were made available with the estimation of the effective thermal mass.
In 2013, Tran and Kim [23] proposed the process of measuring direct tensile stress versus the strain response of HPFRCCs at high strain rates between 10 and 40 s−1. The stress history of HPFRCC at high rates was estimated from two strain gauges attached to two sides of a transmitter bar, while the strain history was obtained by analyzing the sequential images recorded using a high-speed camera. The influence of gauge length on the measurement properties of HPFRCCs at higher strain rates was significant: both the tensile strength and strain capacity of HPFRCCs decreased as the gauge length of the HPFRCC specimen was increased.
In 2013, Rahman and Mundhada [19] put forth the design of reinforced cement concrete (RCC) along with its estimates, in addition to the pre-stressed concrete flat slabs, using a range of spans. The two kinds of flat slabs were designed using the MS Excel program. Programming in MS Excel allows the design of both types of flat slabs. A comparison between the outcomes of RCC and those of the pre-stressed concrete flat slabs was made. It was apparent from the results that the shorter spans have led to less expensive RCC, while the longer spans caused the pre-stressed concrete flat slab to be cheaper.
In 2012, Babu and Yerramala [3] expressed the potential features that are related to the largest feasible and high-capacity fly-ash roller-compacted concrete. The mixture was produced through the combination of 50–260 kg/m3 cement along with an enormous amount of fly ash that falls between 40% and 85% of the total cementation material in terms of mass. The duration spent for compacting was only 15–20 s. Then, the concretes were examined to identify properties such as split tensile strength, compressive strength and modulus of elasticity, rebound hammer number, and ultrasonic pulse velocity. Similar to the other concrete properties, the properties of this very high-volume RCC was also expressed in the form of compressive strength, and a comparison was made against the already available empirical equations of the usual concrete.
In 2011, Ozel [17] dealt with the performance of building walls, which were constructed of briquette, concrete, and autoclaved aerated concrete, thermally for both insulated as well as non-insulated structures. The insulation materials that were employed include extruded polystyrene and expanded polystyrene. The cooling and heating transmission loads are computed once a year through an implicit finite difference method that is subjected to stable periodic constraints. These loads serve as the inputs to an economic model, which incorporates the effect of the cost associated with the insulation material and the existing energy consumption rate nearly for a decade of the building’s life. With this setup, the optimum insulation thickness has been found. The following inferences were made from the results: (i) The optimal insulation thickness takes a value from 2 to 8.2 cm. (ii) The energy savings fall in the range of 2.78–102.16 $/m2. (iii) The payback periods change from 1.32 to 10.33 years. All these inferences were made based on five types of structure materials and two kinds of insulation materials. The degree-days approach was compared against the proposed methodology to prove its potential.
3 Proposed Methodology
The objective of the work was to predict the temperature of the different types of walls, which are the ferro-cement wall, RCC wall, and two types of cavity wall (combined RCC with ferro-cement and combined two ferro-cement walls) by utilizing mathematical modeling. The recognized inputs are the area of the wall, thickness, time, and testing temperature. The heat in the walls can be highly lowered with the use of thermally insulated construction materials. During real-time testing, the associated time period may be very large. However, the utilization of mathematical modeling with an optimization technique can bring about the reduction in the time interval to a great extent. In the preparation of the methodology, 80% of the dataset is employed for the training function and the remaining 20% of the dataset is utilized for the purpose of authenticating the scientific model. The mathematical modeling with optimization is successful by providing the optimal weights α and β. Several optimization techniques, such as social spider optimization (SSO) and genetic algorithm (GA), are effectively employed to ascertain the optimal weight of the system. The optimal values minimize the error and predict the temperature of the different walls. The proposed work improves the error accuracy compared to existing work. It is worth mentioning that the entire procedure is well implemented in the working platform of MATLAB 2014 software.
3.1 Mathematical Modeling
In mathematical modeling, the identified input and output datasets are employed to train the model for locating the optimal output equation of the innovative technique. At the outset, the arbitrary weights α and β are allocated in the network within a specific range. When the preparation of the dataset is complete, it is in the range of 80:20 for both training and testing purposes. In mathematical modeling, optimization methods are employed to evaluate the optimal weights α and β of the system for reducing the inaccuracy value of the model. Several optimization techniques are effectively employed to ascertain the optimal weight of the system in which the optimal weight is achieved in the SSO. The datasets are managed by the system for achieving the base slip by utilizing the weights α and β, which are modified for ascertaining the output of the input parameters. In mathematical modeling, which is generally dependent on various optimizations of weights, the identified inputs with the optimal weights are taken as per Eq. (2).
3.2 SSO
The SSO assumes that the entire search space is a communal web, where all the social spiders interact with each other. In the proposed approach, each solution within the search space represents a spider position in the communal web. Every spider receives a weight according to the fitness value of the solution that is symbolized by the social spider. The procedure for the SSO process is shown in the pseudo-code below.
Pseudo-code for SSO:
3.2.1 Initialization
Initialize the input parameters, such as weights α and β, which are defined as αi and βi , an initial solution of a spider, and i is a number of solutions, and also initialize the parameters. This process is known as the initialization process.
where Si defines an initial solution, iε [1, 2, …, 10] and jε [1, 2, …, 140], where the ith value is considered as the number of solution and the jth value is considered as the length of the solution.
Here, total input=4; hidden neuron (h)=20.
Based on Eq. (1), the attained solution length is 140 and the solution range lies between −10≤Sij ≤10. The input data are area thickness, testing temperature, and time. According to the initial solution, the wall temperature is evaluated.
3.2.2 Fitness Function
β is the weight of the input layer neuron, N is the number of information, and B is an input value. These values are essential to compute the basic performance:
where Bf is a basis function, βij is an input layer weight, and i is the number of inputs and j is the number of weights.
Evaluate the fitness value of each solution and then calculate the best solution values:
where Fi is a fitness function, α and β are weights, S is the input parameter, and h is the number of hidden neurons. The fitness value updates the new solution.
3.2.3 New Population Updation by Using the Following Procedure
The algorithm models two different search agents (spiders): males and females. Depending on gender, each individual is governed by a set of different evolutionary operators that mimic different cooperative behaviors that are commonly assumed within the colony. Considering N is the total number of n-dimensional colony members, define the number of male Nm and female Nf spiders in the entire population S:
where rand is a random number between [0, 1] and the floor (·) maps a real number to an integer number.
3.2.4 Weight Assignation
In the biological metaphor, the spider size is the characteristic that evaluates the individual capacity to perform better over its assigned tasks. Every individual (spider) receives a weight wi , which represents the solution quality that corresponds to spider i (irrespective of gender) of population S. To calculate the weight of every spider of S, Eq. (4) is used.
where F(si ) is the fitness value obtained by the evaluation of the spider position si with regard to the objective function F. The values worsts and bests are calculated with the following equation:
3.2.5 Fitness-Based Initialization of the Population
The algorithm begins by initializing the set S of N spider positions, where each spider position fi and mi is an n-dimensional vector containing the parameter values to be optimized. Such values are randomly and uniformly distributed between the pre-specified lower initial parameter bound
where i, j, and k are the parameters and individual indices, whereas zero signals the initial population. Hence fi ,j is the jth parameter of the ith female spider position.
3.2.6 Cooperative Operators
3.2.6.1 Female Cooperative Operator
Female spiders present an attraction or dislike over others irrespective of gender. For a particular female spider, such attraction or dislike is commonly developed over other spiders according to their vibrations, which are emitted over the communal web. As vibrations depend on the weight and distance of the members that had originated them, strong vibrations are produced either by big spiders or other neighboring members lying nearby the individual that is perceiving them. The first one involves the change in regard to the nearest member of i that holds a higher weight and produces the vibration Vibci . The second one considers the change regarding the best individual of the entire population S that produces the vibration Vibbi . The female vibrations Vibci and Vibbi are calculated by using Eq. (9):
The vibration Vibci is perceived by the individual i(si ) as a result of the information transmitted by the member c(sc ), which is an individual that has two important characteristics: it is the nearest member to i and it possesses a higher weight in comparison to i(wc >wi ). The vibration Vibbi is perceived by the individual i as a result of the information transmitted by the member b(sb ), with b being the individual holding the best weight that is the fitness of the entire population S, such that wb =maxk∈{1, 2, …, N}w(k).
If rm is smaller than the threshold PF, an attraction movement is generated; otherwise, a repulsion movement is produced. Therefore, such operator can be modeled as follows:
where α, β, δ and rand are random numbers between [0, 1], whereas k represents the iteration number. The individuals sc and sb represent the nearest members to i that hold a higher weight and the best individuals of the entire population S.
3.2.6.2 Male Cooperative Operator
Male members with a weight value above the median value within the male population are considered the dominant individuals D. In contrast, those under the median value are labeled as non-dominant ND males. In order to implement such computation, the male population
As the indices of the male population M in regard to the entire population S are increased by the number of female members Nf , the median weight is indexed by Nf+m . According to this, the change of positions for the male spider can be modeled as follows:
where the individual sf represents the nearest female individual to the male member i, whereas
By using this operator, two different behaviors are produced. First, the set D of particles is attracted to others in order to provoke mating. Such behavior allows incorporating diversity into the population. Second, the set ND of particles is attracted to the weighted mean of the male population M. This fact is used to partially control the search process according to the average performance of a subgroup of the population.
3.2.7 Mating Process
Mating in a social-spider colony is performed by dominant males and female members. Under such circumstances, when a dominant male mg spider (g∈D) locates a set Eg of female members within a specific range r (range of mating), it mates, forming a new brood snew, which is generated considering all the elements of the set Tg that, in turn, has been generated by the union Eg ∪mg . It is important to emphasize that if the set Eg is empty, the mating operation is canceled. The range r is defined as a radius that depends on the size of the search space. Randomly initialize the female
In the mating process, the weight of each involved spider (elements of Tg ) defines the probability of influence for each individual into the new brood. The spiders holding a heavier weight are more likely to influence the new product, while elements with lighter weight have a lower probability. The influence probability Psi of each member is assigned by the roulette method, which is defined as follows:
Once the new spider is formed, it is compared to the new spider candidate snew holding the worst spider swo of the colony, according to their weight values. If the new spider is better than the worst spider, the worst spider is replaced by the new one. Otherwise, the new spider is discarded and the population does not suffer changes. In the case of replacement, the new spider assumes the gender and index of the replaced spider. Such fact assures that the entire population S maintains the original rate between female and male members. These process finds the optimum hidden layer and neuron of the neural network process.
3.2.8 Optimal Solution
Based on the above-mentioned process, the optimal weights are attained and the optimal fitness, which is defined as Foptimal, is found. The optimal equation predicts the output temperature of the wall:
where α and β are weights in the range from −500 to 500, S is the input parameter, i is the number of inputs, j is the number of weights, and h is the number of hidden neurons. Then, the error value is found by using Eq. (8).
where ND is the number of the data, D is the desired value, and P is the predicted value, i=1, 2,…, n. By using this formula, the error value is obtained from the difference between the desired value and the predicted value.
4 Results and Discussion
In this study, parameters such as the thickness of the wall, applied temperature, area and time for the ferro-cement wall, RCC wall, combination of ferro-cement and RCC wall, and combination of two ferro-cement walls are analyzed. Mathematical modeling combined with SSO elegantly performs the fascinating function of finding the optimal solutions of α and β. Subsequently, the optimal solutions of the weights with input constraints are arrived at with the assistance of the amazing SSO process. The output is modified for the least error value by using the mathematical model. In other words, the differential error between real-time output and the attained output from the mathematical model is found to be nearly equal to zero [11]. With the result, the related output is evaluated by utilizing the temperature of the different walls.
4.1 Convergence Graph
Figure 1 successfully shows the average fitness graph for the thermal insulation material based on the iteration of the SSO and GA by altering the weights in the range of −500 to 500, and thus the error values are determined. The error graph is drawn with the iteration symbolized in the X-axis and fitness in the Y-axis.
Convergence Graph.
Figure 1 shows the convergence graph, which is plotted between the iteration and fitness estimations of the various strategies, such as SSO and GA. The minimum fitness value, i.e. the error value attained in the 100th iteration initial error value of the SSO and GA process, is 310, and the objective function of the algorithm minimizes the error values. The GA also reduces the fitness from 35 to 2 at below the 20th iteration and keeps it stable up to the 180th iteration, then reduces the fitness to 1 and keeps it constant up to the 60th iteration. In this, generally, SSO reduces the fitness level from 35 to 15 at the 1st iteration, then reduces the fitness to 10 at the 15th iteration and decreases the level of the error value. Through the graph, the SSO approach obviously specifies the ideal fitness value with competent results.
4.2 Error Values of Output Parameters in Different Algorithms
In this section, the number of data is varied and the error is calculated for some input data such as area, thickness, and testing temperature. The wall temperature error graph is shown in Figure 2.
Error Graphs for Different Wall Temperatures.
(A) Ferro-cement wall panel; (B) RCC wall panel; (C) combined ferro-cement and RCC wall panel; (D) combined two ferro-cement wall panels and (E) combined two RCC wall panels.
Figure 2 shows the temperature error values for the different walls of different testing data. Figure 2A shows the temperature error for the ferro-cement wall; the minimum error of the process is 0.013 for SSO in the initial testing data. Comparing this minimum error to the GA, the error difference is 96.45%. Also, the minimum error value of the ferro-cement wall of 0.14 is compared to other techniques, and the error difference is 86.93%. Figure 2B shows the RCC wall error value. This graph also compares the proposed method to the GA, and the difference is 85.63%. Figure 2C shows the cavity wall performance of temperature. When the original value is compared to that from the optimization techniques, the minimum error attained in the SSO process, the error nearby value, is 99.75%. Then, the next figure shows the cavity wall 2, which is the combined two ferro-cement wall panel temperature values. From the initial data for this wall, the maximum error value is 0.86, which, when compared to the proposed method, the error deviation is 88.6%. Figure 2E shows the temperature error value of the combined two RCC walls. For this wall, the maximum error value of the proposed method is 0.58 in testing data 5. The minimum error value of SSO is 0.001 in the third testing data. Comparing the SSO to the GA, the variation is 98.64% for the thermal insulation material.
4.3 Testing Results of Different Wall Panels
The mathematical modeling process consists of two divergent procedures such as the training and testing processes. In the training process, 80% of data are deftly used by duly modifying the weights and the remaining 20% are effectively employed in the testing process. Tables 1–5 show the experimental analysis results and forecasted temperature values based on the optimization technique.
Ferro-Cement Wall Panel.
| Input | Output (Temperature) | |||||
|---|---|---|---|---|---|---|
| Area | Thickness | Testing temperature | Time | Actual value | Predicted value | |
| SSO | GA | |||||
| 1 | 25 | 40 | 70 | 29 | 29.01 | 25.47 |
| 40 | 90 | 30.2 | 30.14 | 27.54 | ||
| 40 | 120 | 31.2 | 31.107 | 30.11 | ||
| 50 | 40 | 30 | 29.62 | 29.57 | ||
| 60 | 100 | 46 | 46.15 | 45.45 | ||
| 60 | 160 | 48 | 47.74 | 49.46 | ||
RCC Wall Panel.
| Input | Output (Temperature) | |||||
|---|---|---|---|---|---|---|
| Area | Thickness | Testing temperature | Time | Actual value | Predicted value | |
| SSO | GA | |||||
| 1 | 40 | 40 | 40 | 23 | 23.47 | 21.527 |
| 50 | 10 | 20.5 | 20.44 | 20.54 | ||
| 50 | 20 | 23 | 22.8 | 26.58 | ||
| 50 | 40 | 25 | 24.889 | 28.85 | ||
| 60 | 60 | 35 | 35.72 | 35.803 | ||
| 60 | 100 | 40 | 39.66 | 40.49 | ||
Combined Ferro-Cement Wall and RCC Wall Panels.
| Input | Output (Temperature) | |||||
|---|---|---|---|---|---|---|
| Area | Thickness | Testing temperature | Time | Actual value | Predicted value | |
| SSO | GA | |||||
| 1 | 90 | 40 | 160 | 24.5 | 24.44 | 25.62 |
| 40 | 180 | 25 | 24.63 | 27.73 | ||
| 50 | 90 | 24.8 | 24.53 | 22.52 | ||
| 50 | 110 | 25.1 | 25.15 | 23.91 | ||
| 60 | 60 | 24 | 23.24 | 23.09 | ||
| 60 | 130 | 29 | 28.38 | 25.04 | ||
Combined Two Ferro-Cement Wall Panels.
| Input | Output (Temperature) | |||||
|---|---|---|---|---|---|---|
| Area | Thickness | Testing temperature | Time | Actual value | Predicted value | |
| SSO | GA | |||||
| 1 | 120 | 40 | 90 | 27.6 | 27.73 | 26.51 |
| 50 | 130 | 33 | 32.39 | 32.35 | ||
| 60 | 50 | 30.7 | 30.04 | 33.91 | ||
| 60 | 60 | 32 | 32.24 | 34.33 | ||
| 60 | 70 | 33 | 33.17 | 35.87 | ||
| 60 | 150 | 43.3 | 43.75 | 44.32 | ||
Combined Two RCC Wall Panels.
| Input | Output (Temperature) | |||||
|---|---|---|---|---|---|---|
| Area | Thickness | Testing temperature | Time | Actual value | Predicted value | |
| SSO | GA | |||||
| 1 | 105 | 50 | 0 | 26 | 25.66 | 27.24 |
| 50 | 10 | 26 | 26.95 | 27.38 | ||
| 50 | 150 | 31 | 31.00 | 30.28 | ||
| 50 | 140 | 32.7 | 32.03 | 30.38 | ||
| 60 | 70 | 29.4 | 29.3 | 30.05 | ||
| 60 | 150 | 34.5 | 34.207 | 30.71 | ||
Tables 1–5 show the testing results of the mathematical modeling process for the thermal insulation material of the different walls. Ferro-cement, RCC wall, and different cavity wall temperatures are obtained based on the area, thickness, time, and testing temperature values. For the entire wall, the temperature nearby value is attained in the SSO process. The arithmetic model with the proposed optimization is compared to the other techniques, and the difference is 56.38% for the temperature, also the nearby value attained in the SSO. For all the drilling parameters, the predicted value of the AFSO process is 96.5%, near the experimental values.
4.4 Comparative Analysis
The graphs in Figure 3 successfully show the average fitness graphs for the different walls of the proposed method SSO and the existing process group search optimization (GSO) algorithm of least error value for the optimal equation with the optimal weights α and β.
Comparison Graph.
Figure 3 shows the different wall error temperature values for the proposed method (SSO technique) and the existing process (GSO). For the ferro-cement wall, the minimum error value is 0.999. In SSO, similar values are attained in all walls. The total difference of the proposed method and the existing method is 96.5% for all wall panels.
Figure 4 demonstrates the validation graph for five parameters, i.e. ferro-cement wall panel, reinforced wall panel, combined ferro-cement and RCC wall panel, combined two RCC wall panel, and combined two ferro-cement wall panel. The error value can be changed based on the wall panel types. The difference between every validation is 0.35%. The maximum value attained in validation 5 for the combined two RCC wall panel is in the range of nearly 1.
Validation Graph.
5 Conclusion
This paper elegantly explains the mathematical modeling technique called the SSO technique, which amazingly attains the accurate ideal values of the weights in the model. The multivariable optimization issues usher in the universal optimum solution and illustrate the adaptability to choose the design variables based on the weights. During the operation of the system, the output parameters are assessed with the datasets. The convincing results are observed to be nearly equal to the dataset minimum error value achieved in the optimization method. The minimum errors of mathematical modeling with the SSO process in the case of the ferro-cement wall, RCC wall, combined RCC with ferro-cement, combined two ferro-cement walls, and combined two RCC walls are 97.15%, 97.111%, 96.41%, 97.11%, and 98.15%, respectively. In the future, researchers can perform their platform with their own optimization techniques and execute the process better.
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Articles in the same Issue
- Frontmatter
- Precursor Selection for Sol–Gel Synthesis of Titanium Carbide Nanopowders by a New Cubic Fuzzy Multi-Attribute Group Decision-Making Model
- Modified and Optimized Method for Segmenting Pulmonary Parenchyma in CT Lung Images, Based on Fractional Calculus and Natural Selection
- PCI-PSO: Preference-Based Component Identification Using Particle Swarm Optimization
- Performance Evaluation of Modified Color Image Steganography Using Discrete Wavelet Transform
- Pythagorean Hesitant Fuzzy Hamacher Aggregation Operators in Multiple-Attribute Decision Making
- Mitral Regurgitation Severity Analysis Based on Features and Optimal HE (OHE) with Quantification using PISA Method
- Non-dominated Sorting Genetic Algorithms for a Multi-objective Resource Constraint Project Scheduling Problem
- Substation Equipment 3D Identification Based on KNN Classification of Subspace Feature Vector
- Mathematical Model Using Soft Computing Techniques for Different Thermal Insulation Materials
- Prediction Method of Railway Freight Volume Based on Genetic Algorithm Improved General Regression Neural Network
- Tree Physiology Optimization in Benchmark Function and Traveling Salesman Problem
- Design and Development of a Multiobjective Cost Function for Robust Video Watermarking Using Wavelet Transform
- Forecasting Air Quality Index Using an Ensemble of Artificial Neural Networks and Regression Models
- Particle Swarm Optimization-Enhanced Twin Support Vector Regression for Wind Speed Forecasting
