AI on How to reuse the solid waste from gutter sewerage using AI automation in something useful clearing out everything

Repurposing solid waste from gutter sewage into something useful using AI automation is a complex challenge that involves several steps and considerations:

1. Waste Collection and Separation: Develop automated systems, possibly using AI-based image recognition, to collect and separate different types of solid waste from gutter sewage, such as plastics, organic matter, and debris.

2. Waste Sorting and Processing: Use automated machinery and conveyor systems to sort and process the collected waste efficiently. AI algorithms can help identify recyclable materials and direct them to the appropriate processing lines.

3. Recycling and Repurposing: Investigate ways to recycle or repurpose the separated waste. For example, plastics could be recycled into new products, organic matter can be composted, and debris might be used for construction materials if feasible.

4. Water Treatment: Implement water treatment processes to purify the water from the sewage before it is released back into the environment. This is critical for environmental safety.

5. Energy Generation: Explore technologies like anaerobic digestion to convert organic waste into biogas, which can be used for energy generation.

6. Data Analytics: Use AI to gather and analyze data on waste composition, processing efficiency, and environmental impact. This data can inform continuous improvement efforts.

7. Environmental Impact Assessment: Assess the environmental impact of your system to ensure it meets sustainability goals and regulations.

8. Community Engagement: Involve the local community in waste management initiatives, including awareness campaigns and education on proper waste disposal practices.

9. Regulatory Compliance: Ensure compliance with local and national regulations related to waste management, water quality, and environmental protection.

10. Maintenance and Monitoring: Establish routine maintenance and monitoring procedures for the automated systems to ensure they operate effectively.

It's important to note that implementing such a system would require significant resources, including technology, infrastructure, and expertise in waste management, water treatment, and AI automation. Collaboration with local authorities and environmental organizations may also be necessary. Additionally, the specific approach would depend on the local context, available resources, and the types of waste in the gutter sewage.

How to use keechad.mud on road to useful things on the fly

Keechad, which means "mud" in Hindi, can be repurposed for various useful applications, especially in rural or construction settings. Here are some ways to use mud or keechad on roads for practical purposes:

1. Road Repair and Construction:

   • Mud and clay can be used as a base material for road construction, especially in rural areas. When properly compacted and graded, it can serve as a cost-effective road surface.

2. Brick Making:

   • Mud can be mixed with other materials to make adobe bricks or mud bricks, which are used in construction for walls, houses, or other structures.

3. Soil Improvement:

   • Mud can be used to amend soil quality in agricultural settings. It can improve soil structure and water retention, benefiting crop growth.

4. Natural Building Materials:

   • In eco-friendly construction, mud can be used to build earth houses or sustainable structures, reducing the environmental impact.

5. Art and Crafts:

   • Mud and clay can be used for pottery and crafting, creating decorative and functional items.

6. Traditional Medicine:

   • In some cultures, mud is used in traditional medicinal practices, such as mud baths or poultices for skin conditions.

7. Farming and Gardening:

   • Mud and clay can be used to create irrigation channels, line ponds, or as a component in making organic fertilizers.

8. Roadside Barriers:

   • In rural areas, mud barriers can be created to control soil erosion along roadsides.

9. Sculptures and Land Art:

   • Mud can be sculpted into various forms for artistic expression or land art installations.

When considering these applications, it's essential to assess the quality and composition of the mud or keechad, as well as any local regulations or environmental concerns. Properly managing the collection and use of mud is important to prevent adverse environmental impacts, such as soil erosion.

Additionally, while mud can be useful in many contexts, it's not suitable for all situations, and modern construction and road-building standards may require other materials for durability and safety. Always consider the specific needs and conditions of your project when repurposing mud or keechad.

p>Refining mud on the fly on roads typically involves using specialized construction equipment, often referred to as soil stabilizers or road reclamation machines. These machines are designed to improve the properties of the soil, including mud, for road construction and maintenance. Here are some popular machines for mud refining on roads:

1. Soil Stabilizers: These machines are equipped with rotary drums or milling heads that mix additives (such as cement, lime, or other stabilizing agents) with the existing soil or mud. They can operate on the road's surface to improve its load-bearing capacity and reduce the moisture content of mud.

2. Reclaimers: Reclaimers are heavy machinery used for road recycling and soil stabilization. They can mill and mix the existing road material, including mud or clay, with new materials to create a stable roadbed.

3. Graders: Motor graders are used to grade and level the road surface, including smoothing out muddy or uneven areas. They play a crucial role in road maintenance.

4. Compactors: Compactors, such as vibratory compactors or sheep's foot rollers, are used to compact and densify the roadbed, including mud or soil, to improve its load-bearing capacity.

5. Pavers: Asphalt pavers or concrete pavers are used to lay a new road surface over the stabilized or refined roadbed, covering any mud or soil.

6. Water Trucks: Water trucks are used to control dust and maintain moisture levels during construction. Proper moisture content is essential for road construction and soil stabilization.

7. Chemical Additive Spreaders: These machines are used to evenly distribute chemical stabilizers or binding agents, which can be mixed with mud to improve its properties.

8. Mud Mixing Trucks: In some cases, specialized mud mixing trucks can be used to blend mud with stabilizing agents or other materials to create a stable roadbed.

The choice of machine depends on various factors, including the condition of the road, the type of soil or mud, the desired road quality, and the available budget. Proper soil analysis and engineering expertise are critical when selecting and using these machines to ensure road stability and durability.

Machines to convert sludge and mud into useful resources on the fly

Converting sludge and mud into useful resources, such as energy or reusable materials, typically involves specialized equipment and processes. While some of these processes can be done relatively quickly, the term "on the fly" can vary depending on the scale and complexity of the operation. Here are some machines and processes used for converting sludge and mud into useful resources:

1. Anaerobic Digesters:

   • Anaerobic digestion is a biological process that breaks down organic materials, including sludge and mud, in the absence of oxygen. It produces biogas (methane), which can be used for energy production, and digestate, which can be used as a soil conditioner.

2. Thermal Dryers:

   • Thermal drying involves heating sludge or mud to remove moisture, resulting in dried solids that can be used as fuel, fertilizer, or construction materials. This process can be accelerated with specialized drying equipment.

3. Sludge Incinerators:

   • Incineration is a high-temperature process that combusts sludge, reducing it to ash and recovering energy in the form of heat. Incineration can be performed in specialized incinerators.

4. Decanter Centrifuges:

   • Decanter centrifuges are used to separate solids from liquids in sludge, dewatering the material and producing a drier, more manageable sludge cake.

5. Sludge Presses:

   • Sludge presses use mechanical pressure to dewater sludge and reduce its volume. The resulting sludge cake can be used for various applications.

6. Biomethane and Biogas Upgrading Systems:

   • Equipment for upgrading biogas (methane) produced from sludge digestion into biomethane, which can be used as a renewable natural gas.

7. Hydrothermal Carbonization (HTC):

   • HTC is a process that converts organic materials, including sludge, into hydrochar, a solid material with energy content and potential agricultural uses.

8. Composting Equipment:

   • For mud and organic-rich sludge, composting equipment can facilitate the conversion of organic matter into nutrient-rich compost suitable for soil improvement.

9. Electrokinetic Remediation:

   • In cases of contaminated mud or sludge, electrokinetic remediation can be used to remove heavy metals or other contaminants from the material.

10. Screw Presses and Filter Presses:

    • These machines are used for dewatering sludge and separating solids from liquids.

The choice of machine and process depends on factors such as the composition of the sludge or mud, the desired end product, and environmental regulations. Effective resource recovery from sludge and mud often requires a combination of equipment and expertise in waste management and environmental engineering.

The process of converting sludge into useful products through biological degradation involves various microorganisms, including bacteria and worms. Two common types of organisms used in this process are:

1. Bacteria (Microbial Biodegradation):

   • Anaerobic Bacteria: These bacteria thrive in environments devoid of oxygen and are commonly used in anaerobic digestion processes to break down organic matter in sludge, producing biogas (methane) as a byproduct. Methanogens are a type of anaerobic bacteria known for their role in this process.
   • Aerobic Bacteria: These bacteria require oxygen and can be used in aerobic digestion processes to break down organic materials in sludge. This process typically results in the production of stabilized sludge with reduced odors.

2. Worms (Vermiculture):

   • Earthworms, specifically red wigglers (Eisenia fetida), are commonly used in vermiculture, which is the process of using worms to break down organic waste, including sludge. Worms consume organic material and produce nutrient-rich worm castings, which can be used as a soil conditioner or fertilizer.

The choice of microorganisms depends on the specific characteristics of the sludge and the desired end product. For example, if the goal is to produce biogas for energy generation, anaerobic digestion with specialized bacteria is suitable. If the aim is to stabilize and reduce the volume of sludge for disposal or reuse in agriculture, both aerobic and anaerobic processes may be employed.

It's essential to design and manage the biological degradation process carefully, taking into consideration factors like temperature, pH, nutrient balance, and the presence of any contaminants or toxins in the sludge. Successful sludge conversion relies on maintaining favorable conditions for the microorganisms involved. Additionally, regulatory requirements and environmental considerations should be adhered to when using microbial or vermiculture-based methods for sludge treatment.

Article

Improving Soil Stability with Alum Sludge: An AI-Enabled

Approach for Accurate Prediction of California Bearing Ratio

Abolfazl Baghbani 1,*, Minh Duc Nguyen 2, Ali Alnedawi 3, Nick Milne 4, Thomas Baumgartl 5, and Hossam Abuel

Naga 6,*

1 School of Engineering, Deakin University, 3216 VIC, Australia; abaghbani@deakin.edu.au

2 School of Engineering, Deakin University, 3216 VIC, Australia; minhd@deakin.edu.au

3 Diwan Endowment, Investment Department, Baghdad, Iraq; alnedawi.ali.m@gmail.com

4 School of Engineering, Deakin University, 3216 VIC, Australia; n.milne@deakin.edu.au

5 Future Regions Research Centre, Federation University Australia, Churchill, Australia; t.baumgartl@federa-

tion.edu.au

6 Department of Civil Engineering, La Trobe University, 3086 VIC, Australia; h.aboel-naga@latrobe.edu.au

* Correspondence: AB: abaghbani@deakin.edu.au; HO: h.aboel-naga@latrobe.edu.au

Abstract: Alum sludge is a byproduct of water treatment plants and its use as a soil stabilizer has

gained increasing attention due to its economic and environmental benefits. Its application has been

shown to improve the strength and stability of soil, making it suitable for various engineering ap-

plications. However, to go beyond just measuring the effects of alum sludge as a soil stabilizer, this

paper explores the use of artificial intelligence (AI) methods to predict the California bearing ratio

(CBR) of soils stabilized with alum sludge. Three AI methods, including two black box methods

(artificial neural network and support vector machines) and one grey box method (genetic program-

ming), were used to predict CBR based on a database with nine input parameters. The results

showed that all three AI models were able to predict CBR with good accuracy, with coefficient of

determination (R2) values ranging from 0.94 to 0.99 and mean absolute error (MAE) values ranging

from 0.30 to 0.51. In a novel approach, the genetic programming method was used to produce an

equation to estimate CBR, which included seven inputs and accurately predicted CBR. The analysis

of sensitivity and importance of parameters showed that the number of hammer blows for compac-

tion was the most important parameter, while the parameters for maximum dry density of soil and

mixture were the least important. This study suggests that AI methods can effectively predict the

performance of alum sludge as a soil stabilizer, and the proposed equation using genetic program-

ming can be a useful tool for predicting CBR.

Keywords: Alum sludge; Soil stabilization; Artificial intelligence; California bearing ratio; Genetic

programming

1. Introduction

The alum sludge (also red mud or bauxite tailings) is a byproduct of the drinking

water treatment process alum [1]. In recent decades, several studies have examined the

use of alum sludge as a soil stabilizer [2]. As a soil stabilizer, alum sludge has the main

advantage of improving the soil's physical properties, such as strength and stability [3].

The reason for this is that alum sludge contains high levels of alum, which reacts with the

soil to form a solid and stable structure [4]. As a result of this reaction, soil density and

compaction increase and improving soil stability and reducing erosion sensitivity [4]. But

also, for pure aluminum sludge stability gained by adapted scheduling of bauxite tailings

is critical to warrant safe tailings deposition [5].

According to Nguyen et al. [4], alum sludge as a soil stabilizer reduces the soil's flex-

ibility and makes it less susceptible to deformation. This reduction in flexibility results in

improved soil structure and increased stability [4]. Also, in geotechnical side, Nguyen et

al. [4] showed that with increasing sludge to the soil, the undrained compression strength

Disclaimer/Publisher’s Note: The statements, opinions, and data contained in all publications are solely those of the individual author(s) and

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from any ideas, methods, instructions, or products referred to in the content.

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© 2023 by the author(s). Distributed under a Creative Commons CC BY license.

(UCS) of soil increased. In addition, several studies have demonstrated that alum sludge

can be an effective alternative to traditional soil stabilizing agents, such as cement and

lime [6-8].

Alum sludge as a soil stabilizer can have several environmental advantages [9]. The

first benefit is that it reduces the amount of waste produced by the alum production pro-

cess by recycling the sludge and reusing it for soil stabilization [9]. Furthermore, alum

sludge reduces the need for conventional soil stabilizers, which are often derived from

non-renewable sources and may emit large amounts of carbon dioxide [10]. In addition to

improving soil stability, alum sludge can also improve soil chemical properties [9]. Stud-

ies have shown that alum sludge can neutralize soil acidity and improve soil pH [11-12].

The importance of this is that soil acidity can inhibit plant growth and reduce crop yields

[11]. As a result, better water infiltration and retention occurs in the soil, which is essential

for the growth and development of plants. Additionally, improving soil permeability can

reduce soil erosion and contribute to improving soil health [13]. Alum sludge is cost-ef-

fective when used as a soil stabilizer compared to traditional soil stabilizers such as ce-

ment, coal and fly ash [14].

As a soil stabilizer, alum sludge has been shown to have varying efficiency depend-

ing on the type of soil and the conditions of its application. As an example, clay soils are

naturally active, so the use of alum sludge may greatly benefit them [15]. Similarly, the

effectiveness of alum sludge as a soil stabilizer can be affected by environmental factors

such as temperature, humidity, and rainfall [16]. Studies showed that it is important to

consider the specific soil and environmental conditions when using alum sludge as a soil

stabilizer [16-17].

In the history of studies, various factors have been identified as influencing the be-

havior of sludge. There are several parameters to consider, including soil and sludge den-

sity, specific gravity of soil, liquid limit and plasticity of soil, sludge content etc. The mul-

tiplicity of parameters and the non-linearity. It would be necessary to predict performance

using an equation with a large number of parameters that would require quantification,

which does not exist. In the last two decades, artificial intelligence (AI) methods have been

used to resolve this issue. Using artificial intelligence techniques, it is possible to deter-

mine the relationship between different parameters with a high degree of accuracy with-

out prior knowledge. Various topics in geotechnical engineering, such as slope stability

[18-20], tunnelling [21-23], pavement and road construction [24-25], soil cracking [26-28],

rock mechanics [29-30], soil dynamics [31-34] and soil stabilizers [35-37] have been ad-

dressed using artificial intelligence methods [38]. Nevertheless, only two studies have

used artificial intelligence to predict properties from mixing sludge with soil [39-40].

Aamir et al. [41] used a small database of 18 datasets to predict the CBR parameter using

artificial neural network (ANN). A high R2 of 0.99 was observed as well as a small RMSE

of 0.057. Similarly, Shah et al. [39] used a 21-sets database and artificial neural network

(ANN) method to predict the CBR of mixtures of sludge and soil. The results of the study

were very promising with a R2 of 0.97 and an RMSE of 0.58. However, the big gap is that

both studies used only one classic artificial intelligence method, ANN, and grey box meth-

ods were not employed. Grey box methods are those methods that have an output like a

tree or an equation. Also, the used databases were relatively small, which may limit the

range of values of the parameters.

In order to fill these gaps, this study uses two black-box AI methods, namely artificial

neural network (ANN) and super vector machines (SVM), as well as a grey-box AI

method, namely genetic programming (GP), in order to predict CBR. By using this ap-

proach, both black-box and grey-box models will be examined. The ANN method that is

currently used as standard will be compared with another black-box method, SVM. A

database of 27 CBR test results on a variety of soil types was used for this purpose. Ini-

tially, there are nine input parameters from laboratory tests, whose number are discussed

in detail. The sensitivity of the AI models as well as the importance of the input parame-

ters has been evaluated.

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2. Data-driven modeling

After analyzing the collected database, CBR was predicted using three artificial intel-

ligence methods, including artificial neural network (ANN), genetic programming (GP)

and support vector machine (SVM).

The use of AI algorithms for material characterization and design has been met with

skepticism due to concerns about the reliability of their complex models. The lack of trans-

parency and knowledge extraction processes in AI-based models is a major challenge.

Mathematical modeling techniques can be categorized as white-box, black-box, and grey-

box, depending on their level of transparency (Figure 4). While white-box models are

based on first principles and provide an explanation of the underlying physical relation-

ships of a system, black-box models do not provide any feasible structure of the model.

Grey-box models, on the other hand, identify the patterns between the data and provide

a mathematical structure of the model. ANN is a popular black-box modeling technique

widely used in engineering, but its weights and bias representation does not provide de-

tails about the derived relationships. GP is a newer grey-box modeling technique that uses

an evolutionary process to develop explicit prediction functions, making it more trans-

parent than other ML methods, especially black-box methods such as ANN and SVM. The

mathematical structures derived by GP can be used to gain important information about

the system performance.

Figure 4. Classification of the AI modelling techniques (Adapted from Giustolisi et al. [41] and

Zhang et al. [42]).

2.1. Support Vector Machine (SVM)

In supervised learning model (SVM) method, initially developed by Vapnik [43],

weights are calculated based on input data, known as training data, in order to learn the

governing function from a set of inputs. SVM selects a limited number of input sample

vectors, which are always a fraction of the total number of samples. These input vectors

are referred to as support vectors. Using these input vectors, parameter values of the

method for minimizing error are calculated. As a result, SVM requires much less data than

similar methods such as ANN, and as a result, it takes much less time and money.

The goal of this method is to find a classifier that separates the data and maximizes

the distance between these two classes. Figure 5 shows a plane cloud that separates two

sets of points.Physical knowledge

Interpretability of the models for user

Black box

Grey box

White box

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Figure 5. The hyperplane H that separates the two groups of points.

According to Figure 6, the closest points used alone to determine the hyperplane are

called support vectors. As is clear, there are many hypermaps that can divide samples into

two categories. The principle of SVM is to choose something that maximizes the minimum

distance between the hypermap and the training samples (that is, the distance between

the hypermap and the support vectors), this distance is called the margin.

Figure 6. Support vectors.

Kernel function, as an important part of SVM method, receives data as input and

transforms them into the required form. Various functions are provided for this purpose.

Some of these functions, including linear, nonlinear, polynomial, radial basis function

(RBF), and sigmoid, are given in equations 8 to 12. According to Equations 8 to 12, the

kernel function is a series of mathematical functions that provide a window for data ma-

nipulation. With the help of this transformation, a complex and non-linear level of deci-

sion-making becomes a linear equation, but in a larger number of dimensional spaces.

Polynomial kernel: 𝑘 = 𝑘(𝑥𝑖, 𝑥𝑗) = (𝑥𝑖. 𝑥𝑗 + 1)𝑑 (8)

Gaussian kernel: 𝑘 = 𝑘(𝑥𝑖, 𝑥𝑗) = 𝑒𝑥𝑝 (− ‖𝑥𝑖 − 𝑥𝑗‖2

2𝜎2 ) (9)

Radial basis function (RBF): 𝑘 = 𝑘(𝑥𝑖, 𝑥𝑗) = 𝑒𝑥𝑝 (−𝛾‖𝑥𝑖 − 𝑥𝑗‖2) (10)X

Y H

Support

Vectors

Support

Vectors

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Hyperbolic tangent kernel: 𝑘 = 𝑘(𝑥𝑖 , 𝑥𝑗 ) = 𝑡𝑎𝑛ℎ(𝑘′𝑥𝑖 . 𝑥𝑗 + 𝑐) (11)

Sigmoid kernel: 𝑘 = 𝑘(𝑥𝑖, 𝑥𝑗) = 𝑡𝑎𝑛ℎ(𝛼𝑥𝑇𝑦 + 𝑐) (12)

Where xi and xj are vectors in input space, γ and σ parameters define the distance

influence of a single sample, d is degree of polynomial, c ∈ R is the relative position to the

origin, κ’ is a real-valued positive type function/kernel, α, T and c are certain values.

In this study, two important functions, i.e., radial basis function (RBF) and Gaussian

kernel, which have been successful in past research, were evaluated along with two other

functions, i.e., Sigmoid kernel and Polynomial kernel functions.

2.2. Artificial Neural Network (ANN)

Artificial Neural Networks (ANNs) have a history that dates back to the mid-20th

century when the mathematical model for the perceptron was first introduced by Rosen-

blatt [44]. The development of the backpropagation algorithm in the 1980s by Rumelhart

et al. [45] improved the training of multi-layer ANNs and led to their widespread use in

various fields. Since then, ANNs have continued to evolve with the development of new

architectures and learning algorithms [46].

The Artificial Neural Network (ANN) is a machine learning model that is based on

the structure and function of the human brain [46]. Artificial neural networks are com-

posed of interconnected nodes or artificial neurons that process information and make

predictions in response to inputs. By combining the inputs and the weights assigned to

each connection, the interconnected nodes produce an output. There are a number of ap-

plications for artificial neural networks, including image classification, speech recogni-

tion, and natural language processing, among others. In the field of machine learning and

artificial intelligence, they have proven to be effective at solving complex problems.

Due to their ability to learn from data and make accurate predictions or classifications

based on that data, artificial neural networks (ANNs) have become one of the most pow-

erful tools in the field of machine learning and artificial intelligence [38]. As a result, they

simulate the structure and function of the human brain, which is composed of many neu-

rons connected by synapses.

Each node or artificial neuron in an ANN performs simple computations based on

the input it receives and the weights assigned to the connections [48]. One neuron's output

is then passed on as input to other neurons in the network, allowing the information to be

processed and transformed multiple times before it is finally produced. Feedforward re-

fers to this process of processing and transforming information through multiple layers

of neurons.

There are various types of artificial neural networks, each designed for a particular

task or application. The most popular types of ANNs include feedforward networks, re-

current networks, and convolutional neural networks [49]. An ANN can be used for a

variety of purposes, and each type has its own strengths and weaknesses.

As the most basic type of ANN, feedforward networks are used for simple tasks such

as binary classification and linear regression. On the other hand, recurrent networks are

used for sequences of data, such as speech or text, and are capable of capturing temporal

relationships. An image or video analysis can be performed using convolutional neural

networks, which are specifically designed to capture the spatial relations between pixels

in an image or video.

Artificial Neural Network (ANN) can be used to model complex relationships with

no established mathematical relationships [49]. The ANN method is consisting of artificial

neurons and is commonly used to fit nonlinear statistical data. For this purpose, ANN

identifies the relationships between input and output parameters based on the strength of

the connection between the two neurons, known as "weight". Next, the network seeks to

optimize the matrix of weights, which is achieved through practice and adjustment, which

is called the paradigm [51]. One of the strongest paradigms is the back-propagation

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paradigm. In this study, two back-propagation algorithms are used: (i) Levenberg-Mar-

quardt (LM) algorithm [52], and (ii) Bayesian Regularization (BR) [53] algorithm.

Input, hidden and output layers are 3 main components of ANN architecture. In this

study, for each algorithm, i.e., LM and BR, one, two, three, four and five hidden layers are

considered. Log-sig and tan-sig are transfer functions within each neuron. In this study, 5

different architectures of ANN, with 1 to 5 hidden layers, were modelled for each algo-

rithm. Furthermore, by trial and error, 45 neurons were considered for each hidden layer

and each network 3 times is re-trained.

2.3. Genetic programming (GP)

John Koza, a computer scientist and researcher at Stanford University, developed the

first genetic programming system in the early 1990s. Using this system, he evolved com-

puter programs capable of solving mathematical problems and controlling robots. Several

genetic programming frameworks and toolkits were developed as a result of this devel-

opment.

As a subfield of Artificial Intelligence and Evolutionary Computation, Genetic Pro-

gramming (GP) is a method for solving complex problems using a process inspired by

natural selection and genetics. In this approach, potential solutions are represented as

trees of operations (also known as computer programs) and then improved using genetic

algorithms.

The GP algorithm generates an initial population of computer programs at random

and evaluates their fitness in accordance with a problem-specific objective function.

Through genetic operators such as crossover and mutation, the best programs are selected

to produce the next generation. The process continues until a satisfactory solution is found

or a stopping criterion is met.

A wide range of problems can be solved using GP, including function approximation,

symbolic regression, and even game play. There are several strengths of GP, including its

ability to find complex solutions that are difficult or impossible to discover manually, as

well as its ability to handle high levels of uncertainty and noise in the data. It can, how-

ever, be computationally expensive and may have difficulty finding solutions in a reason-

able amount of time for very complex problems.

3. Database Collection and Processing

3.1. Experiment and data collection

The database was prepared based on the results of two studies [4, 40]. A 3D repre-

sentation of the collected database for CBR is shown in Figure 1. The existing database

considers nine input parameters, including liquid limit (LL) and plasticity index (PI) of

soil, the sludge content, compaction number of blows, optimum moisture content (OMC)

and maximum dry density (MDD) of soil and mixture and bulk modulus Gs of soil. CBR

is the only output.

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Figure 1. Database used for modelling based on the CBR.

Figure 2 shows the effect of different input parameters, such as compaction number

of blows, sludge content, maximum dry density and optimum water content, on CBR.

According to the results in Figure 2a, with an increase in the number of compression ham-

mer blows, CBRs increased dramatically as the number of compression hammers in-

creased. Figure 2b illustrates the effect of sludge content on CBR. It can be seen from Fig-

ure 2b that as the sludge content increased, CBR increased significantly at first. When the

sludge content reached around 8%, CBR began to decrease as the sludge percentage in-

creased. Figure 2c shows the effect of increasing the maximum dry density (MDD) of the

soil on the CBR of the soil. According to the results, it can be concluded that the CBR

increased as the maximum dry density of the soil increased. In addition, Figure 2d shows

the effect of optimum moisture content (OMC) on CBR. Results depict that CBR decreased

as optimum water content increased.CBR

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Figure 2. Effect of (a) compaction number of blows, (b) sludge content, (c) MDD and (d) OMC on

the CBR in collected database.

In order to provide a more detailed analysis of the database, Table 1 shows the sta-

tistical information including the minimum, maximum, mean and standard deviation.

Table 1. The statistical information of database.

Variable Observations Minimum Maximum Mean Std. deviation

CBR 27 0.900 16.700 6.856 4.013

LL-soil 27 26.120 55.000 46.391 12.660

PI-soil 27 8.830 34.000 26.239 11.399

% Sludge 27 0.000 100.000 11.667 20.438

Compaction-number of blows 27 10.000 65.000 31.667 19.513

OMC-soil 27 18.000 22.500 21.111 2.021

MDD-soil 27 1.560 1.725 1.596 0.048

OMC-mixture 27 18.000 41.500 21.315 4.545

MDD-mixture 27 1.060 1.746 1.577 0.146

Gs-soil 27 2.170 2.750 2.616 0.2430

2

4

6

8

10

12

14

16

18

0 20 40 60 80

CBR

Number of hammer blows for compaction(a)0

2

4

6

8

10

12

14

16

18

0 20 40 60 80 100

CBR

Sludge content (%)(b)0

2

4

6

8

10

12

14

16

18

1 1.2 1.4 1.6 1.8

CBR

Maximum dry density (g/cm3)(c)0

2

4

6

8

10

12

14

16

18

10 20 30 40 50

CBR

Optimum water content (%)(d)

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3.2. Preparation of the data for AI modelling

3.2.1. Normalization

In a database, each input or output variable has a specific unit. The data normaliza-

tion function can eliminate the weight of the units, reduce network errors, and increase

training speed by adjusting the data between zero and one. The linear normalization func-

tion utilized in this study is outlined below.

𝑋𝑛𝑜𝑟𝑚 = 𝑋 − 𝑋𝑚𝑖𝑛

𝑋𝑚𝑎𝑥 − 𝑋𝑚𝑖𝑛

(1)

The four terms in this equation are Xmax, Xmin, X, and Xnorm, which correspond to max-

imum, minimum, actual, and normalized values, respectively.

3.2.2. Testing and training databases

There are two types of databases required for the implementation of mathematical

models, namely training databases and testing databases. For all three mathematical mod-

els, training and testing were randomly divided. Figure 3 shows the main division of the

database, where 80% of the main database was used for training and 20% for testing.

A random database division resulted in two test and experiment databases that were

considered fixed and were used in all three mathematical models. Statistical parameters

are shown in Tables 2 and 3, respectively, for the training and test databases. The statistical

information, including the minimum, maximum, mean, and standard deviation, is very

similar for both databases. This issue can increase the accuracy of the network in predict-

ing the output.

Figure 3. Distribution of (a) training and (b) testing databases.CBR(a)CBR

(b)

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Table 2. The statistical information of training database.

Variable Observations Minimum Maximum Mean Std. deviation

CBR 21 0.900 16.700 6.883 4.379

LL-soil 21 26.120 55.000 45.252 13.046

PI-soil 21 8.830 34.000 25.220 11.731

% Sludge 21 0.000 100.000 13.095 22.784

Compaction-number of blows 21 10.000 65.000 30.000 18.841

OMC-soil 21 18.000 22.500 20.929 2.075

MDD-soil 21 1.560 1.725 1.600 0.054

OMC-mixture 21 18.000 41.500 21.357 5.094

MDD-mixture 21 1.060 1.746 1.573 0.161

Gs-soil 21 2.170 2.750 2.605 0.250

Table 3. The statistical information of testing database.

Variable Observations Minimum Maximum Mean Std. deviation

CBR 6 3.000 9.700 6.763 2.654

LL-soil 6 27.280 55.000 50.380 11.317

PI-soil 6 8.830 34.000 29.805 10.276

% Sludge 6 0.000 20.000 6.667 7.554

Compaction-number of blows 6 10.000 65.000 37.500 22.528

OMC-soil 6 18.000 22.500 21.750 1.837

MDD-soil 6 1.560 1.586 1.582 0.011

OMC-mixture 6 18.500 22.500 21.167 1.889

MDD-mixture 6 1.450 1.682 1.590 0.083

Gs-soil 6 2.170 2.750 2.653 0.237

3.2.3. Statistical parameters

The performance of a network can be evaluated through a variety of parameters such as

coefficient of determination (R2) and mean absolute error (MAE). Equations 2-7 show the

definitions of Mean Absolute Error (MAE), Mean Square Error (MSE), Root Mean Square

Error (RMSE), Mean Squared Logarithmic Error (MSLE), Root Mean Squared Logarithmic

Error (RMSLE), and Coefficient of Determination (R2).

𝑀𝐴𝐸 = ∑ (𝑋𝑚 − 𝑋𝑝)𝑁

𝑁 (2)

𝑀𝑆𝐸 = ∑ (𝑋𝑚 − 𝑋𝑝)2

𝑁

𝑁 (3)

𝑅𝑀𝑆𝐸 = √∑ (𝑋𝑚 − 𝑋𝑝)2

𝑁

𝑁 (4)

𝑀𝑆𝐿𝐸 = ∑ (log(𝑋𝑚 + 1) − log(𝑋𝑝 + 1))2

𝑁

𝑁 (5)

𝑅𝑀𝑆𝐿𝐸 = √∑ (log(𝑋𝑚 + 1) − log(𝑋𝑝 + 1))2

𝑁

𝑁 (6)

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𝑅2 = [ ∑ (𝑋𝑚 − 𝑋𝑚̅̅̅̅ )(𝑋𝑝 − 𝑋𝑝̅̅̅ )𝑁

𝑖=1

∑ (𝑋𝑚 − 𝑋𝑚̅̅̅̅ )2𝑁

𝑖=1 ∑ (𝑋𝑝 − 𝑋𝑝̅̅̅ )2𝑛

𝑖=1

]

2

(7)

Where N is the number of datasets, Xm and Xp are actual and predicted values, and

𝑋m̅̅̅̅ , 𝑋p̅̅̅ are the average of actual and predicted values, respectively. Ideally, the model

should have a R2 value of 1 and a MAE, MSE, RMSE, MSLE, RMSLE value of 0.

4. Results

4.1. Support Vector Machine (SVM)

In order to derive an optimal SVM model, multiple parameters were adjusted, and

the resulting model with the most favorable performance is delineated in this section. Ta-

ble 4 presents the specifications of the best Support Vector Machine (SVM) model derived

through parameter tuning. The model was constructed using the Sequential Minimal Op-

timization (SMO) algorithm with a penalty parameter of C = 2 and a tolerance value of

0.001. The epsilon parameter, which controls the width of the margin, was set to 0.5. The

input data was pre-processed using standardization to ensure that each feature had a

mean of zero and a standard deviation of one. The kernel function used in this model was

the radial basis function (RBF), which is a popular kernel function for SVMs due to its

flexibility in modeling complex, nonlinear relationships between input variables. The

gamma parameter of the RBF kernel was set to 0.5, which controls the smoothness of the

decision boundary. A lower value of gamma results in a smoother decision boundary,

while a higher value of gamma leads to a more complex boundary that can overfit the

data. Overall, these specifications provide a well-performing SVM model that can accu-

rately classify data while avoiding overfitting. These parameters can be used as a starting

point for future SVM modeling tasks or as a benchmark for comparing the performance

of other SVM models.

Table 4. The specifications of the best SVM.

SMO parameters Kernel parameters

C Tolerance Epsilon Pre processing Type of Kernel Gamma

2 0.001 0.5 Standardisation Radial basis function (RBF) 0.5

The predicted values of CBR against the values obtained from the test in the labora-

tory for the training and testing database are shown in Figure 7. The results show that the

SVM model has been able to predict CBR values with good accuracy.

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Figure 7. The results of the best SVM model to predict CBR value for (a) training and (b) testing

database.

Table 5 presents the performance metrics of an SVM used to predict California Bear-

ing Ratio (CBR) values for a mixture of Alum sludge and soil. Both training and testing

data sets were used to evaluate the performance of the SVM model.

The first performance metric is Mean Absolute Error (MAE), which measures the av-

erage absolute difference between the predicted and actual CBR values. In both the train-

ing and testing sets, the values are 0.497 and 0.512, respectively, indicating that the model

has an average error of approximately 0.5. A second performance metric is the Mean

Squared Error (MSE), which measures the average squared difference between the pre-

dicted and actual CBR values. Both the training and testing sets have values of 0.409 and

0.357, respectively, indicating that the model has a relatively low overall error in predict-

ing CBR values. The third performance metric is the Root Mean Squared Error (RMSE),

which is the square root of the Mean Square Error (MSE). Both the training and testing

sets have 0.640 and 0.598 values, respectively, indicating that the model has a relatively

low overall error in predicting CBR values. In addition to Mean Squared Log Error, the

fourth performance metric is Mean Squared Log Error (MSLE). MSLE measures the dif-

ference between the logarithm of the predicted CBR values and the logarithm of the actual

CBR values. For both the training and testing sets, the values are 0.017 and 0.011, respec-

tively, indicating that the model has a relatively low overall error when predicting CBR(a)(b)

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values. The fifth performance metric is the Root Mean Squared Log Error (RMSLE), which

is the square root of the MSLE. In both the training and testing sets, the values are 0.129

and 0.103 respectively, which indicates that the model has a relatively low overall error in

predicting CBR values on a logarithmic scale. The final performance metric is the R2,

which measures the amount of variance in the CBR values that can be explained by the

model. As can be seen from the values for the training and testing sets, the model has a

high degree of correlation between the predicted and actual CBR values. The results sug-

gest that the SVM model is capable of predicting CBR values for the mixture of Alum

sludge and soil, as indicated by the low error values and high R-squared values for both

training and testing.

Table 5. Results of SVM to predict CBR for mixture of Alum sludge and soil.

Performance metrics Training Database Testing Database

MAE 0.497 0.512

MSE 0.409 0.357

RMSE 0.640 0.598

MSLE 0.017 0.011

RMSLE 0.129 0.103

R² 0.978 0.939

4.2. Artificial neural network (ANN)

In this study, all artificial neural network (ANN) modeling was performed using

MATLAB (R2020a: The Math Works Inc., Natick, MA, USA). Table 6 displays the results

of the Bayesian regularization (BR) and Levenberg-Marquardt (LM) algorithms for all net-

works. The table contains the R2 and mean absolute error (MAE) values for both test and

training datasets. The results are based on the best-performing network among all 45 neu-

rons and three training repetitions, as determined by the highest R2 and lowest MAE val-

ues.

The findings indicate that the network with two hidden layers achieved the highest

performance for both the BR and LM algorithms. Moreover, the average accuracy of the

BR algorithm was superior to that of the LM algorithm.

Table 6. The results of ANN modelling.

The number of hidden layers R-Test R-Train MAE-Test MAE-Train

Bayesian Regulari-

zation

1H 0.943 0.955 0.563 0.598

2H 0.980 0.989 0.302 0.392

3H 0.972 0.977 0.405 0.431

4H 0.970 0.976 0.463 0.452

5H 0.963 0.971 0.490 0.523

Average 0.965 0.973 0.444 0.479

Levenberg-Mar-

quardt

1H 0.913 0.928 0.953 0.835

2H 0.956 0.969 0.512 0.463

3H 0.942 0.958 0.673 0.574

4H 0.933 0.951 0.753 0.682

5H 0.918 0.937 0.841 0.797

Average 0.932 0.948 0.746 0.670

Figure 8 depicts the comparison between the predicted values of the artificial neural

network (ANN) model and the actual values of laboratory experiments. The results

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indicate that the ANN model has exhibited a very high level of precision in predicting the

California Bearing Ratio (CBR) values for both the training and testing databases.

Figure 8. The results of the best ANN model to predict CBR value for (a) training and (b) testing

database.

Table 7 displays the best outcomes of utilizing the ANN modeling method to predict

the California Bearing Ratio (CBR) for the mixtures of alum sludge and soil. The perfor-

mance indicators of the ANN model are exhibited for both the training and testing da-

tasets. The ANN model yielded a Mean Absolute Error (MAE) of 0.392 and 0.303 for the

training and testing datasets, respectively. Similarly, the Mean Squared Error (MSE) val-

ues for the training and testing datasets were 0.200 and 0.116, correspondingly. Further-

more, the Root Mean Squared Error (RMSE) values obtained for the training and testing

datasets were 0.447 and 0.341, respectively. The ANN model's Mean Squared Log Error

(MSLE) values were 0.005 and 0.002 for the training and testing datasets, respectively,

while the Root Mean Squared Log Error (RMSLE) values were 0.074 and 0.046 for the

training and testing datasets, respectively. The ANN model yielded a high coefficient of

determination (R²) of 0.989 and 0.980 for the training and testing datasets, respectively,

implying that the model is highly precise in predicting the CBR values for a mixture of

alum sludge and soil.0

3

6

9

12

15

18

0 3 6 9 12 15 18

Actual CBR

Predicted CBR(a)(a)0

3

6

9

12

15

18

0 3 6 9 12 15 18

Actual CBR

Predicted CBR(b)

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Table 7. Results of ANN to predict CBR for mixture of Alum sludge and soil.

Performance metrics Training Database Testing Database

MAE 0.392 0.302

MSE 0.200 0.116

RMSE 0.447 0.341

MSLE 0.005 0.002

RMSLE 0.074 0.046

R² 0.989 0.980

One of the key determinants of the precision and complexity of an artificial intelli-

gence (AI) model is the number of neurons present in each hidden layer. To find the most

optimal number of neurons, the group of analyses is conducted. Figure 9a shows the ac-

curacy of the ANN model based on the number of neurons present in each hidden layer.

According to the results, the accuracy of the ANN model does not improve significantly

beyond a certain number of neurons which is 10 neurons. Therefore, it is essential to de-

termine the optimal number of neurons to achieve the best accuracy while minimizing the

complexity of the model. Figure 9b displays the model's error rate for each neuron. The

results show that the error rate remains almost constant after the 10th neuron. Thus, the

optimal number of neurons for the ANN model was determined to be 10. This information

is crucial for researchers and developers of AI models, as it allows them to minimize com-

plexity while achieving the best accuracy. By optimizing the number of neurons, the per-

formance of the AI model can be significantly enhanced.0.8

0.82

0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45

R²

Neuron number(a)

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Figure 9. (a) The accuracy (R2) and (b) error (MAE) of different neurons for training database in

ANN model.

4.3. Genetic programming (GP)

The genetics of programming involves applying evolutionary algorithms to generate

computer programs through the use of genetic operators such as crossover and mutation.

Important parameters that affect the effectiveness of genetic programming include popu-

lation size, mutation rate, and fitness evaluation function. In this study, after a series of

analyses, the best and most optimized GP model was selected based on its ability to pro-

duce high-quality programs for a given problem domain.

Figure 10 shows the projected values of CBR by the best GP model against the actual

values obtained in the experiments for both training and testing. According to the findings

presented in Figure 10, the best genetic programming (GP) model was capable of accu-

rately predicting the values of California Bearing Ratio (CBR) in the experiments, as indi-

cated by the close match between the model's projected values and the actual values ob-

tained. These results suggest that the GP model has a high level of accuracy in predicting

CBR values.

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Figure 10. The results of the best GP model to predict CBR value for (a) training and (b) testing

database.

A significant distinction between genetic programming (GP) and black box models

is that the GP produces an equation as an outcome, which can be directly utilized by the

reader. In this study, Equation 13 represents the GP model outcome for predicting Cali-

fornia Bearing Ratio (CBR) values. The reason for the length of this equation is that it in-

corporates seven distinct inputs, namely liquid limit, plasticity index, alum sludge con-

tent, number of compaction blows, optimum moisture content of soil and mixture, and Gs

of soil. It is worth noting that traditional methods are incapable of producing an equation

such as Equation 13, with the consideration of all seven influential inputs. Consequently,

this study represents the first successful attempt to formulate an equation for predicting

CBR numbers based on these seven important inputs. Also, it is important to notice that

the parameters in Equation 1 are normalized value and the readers should normalize their

values based on the Table 1 and then use them in Equation 13.

CBR=((((0.234+(((X2-0.339)-0.185)2))-((((X72)-X3)-((0.339-X5)3))*X6))*((X4+(((X52)*(0.339+X2))*((X3*X5)*(X1+0.339))))-((((X4+0.185)-X7)*((X6*X5)-

0.234))-((X53)-((0.2342)*(0.234+X1))))))) (13)

Where X1, X2, X3, X4 , X5 , X6 , X7 are LL, PI, AS content, number of compaction blows, OMC

of soil, OMC of mixture and Gs of soil.0

3

6

9

12

15

18

0 3 6 9 12 15 18

Actual CBR

Predicted CBR(a)0

3

6

9

12

15

18

0 3 6 9 12 15 18

Actual CBR

Predicted CBR(b)

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Table 9 presents the results of GP model to predict California Bearing Ratio (CBR) for

the mixtures of Alum sludge and soil. The GP model's performance was evaluated using

various performance metrics on both the training and testing datasets. The mean absolute

error (MAE) of the model on the training database was 0.459, indicating that, on average,

the model's predictions were off by 0.459 CBR units. The MAE on the testing database was

slightly higher at 0.475, indicating that the GP model's generalization ability was slightly

worse than its performance on the training database. The mean squared error (MSE) on

the training database was 0.358, indicating that the GP model's predictions had a higher

variance than its performance on the testing database (0.304). The root mean squared error

(RMSE) on the training database was 0.598, indicating that the GP model's predictions had

a higher magnitude of error than its performance on the testing database (0.552). The mean

squared logarithmic error (MSLE) on the training set was 0.010, and the corresponding

value on the testing set was slightly lower at 0.009, indicating that the GP model's predic-

tions were more accurate on the testing set. The root mean squared logarithmic error

(RMSLE) on the training set was 0.100, and the corresponding value on the testing set was

slightly lower at 0.097. Finally, the coefficient of determination (R²) was high for both the

training set (0.980) and the testing set (0.948), indicating that the model explained most of

the variance in the data and that it had a good fit to the data. In conclusion, the results

suggest that the GP model can be used to accurately predict CBR for a mixture of Alum

sludge and soil, and that it generalizes well to unseen data. However, the model's predic-

tions on the training set had a higher variance and magnitude of error compared to the

testing set.

Table 9. Results of GP to predict CBR for mixture of Alum sludge and soil.

Performance metrics Training Database Testing Database

MAE 0.459 0.475

MSE 0.358 0.304

RMSE 0.598 0.552

MSLE 0.010 0.009

RMSLE 0.100 0.097

R² 0.980 0.948

5. Discussion

5.1. Comparison of different models

Table 10 compares the results of three artificial intelligence (AI) models, namely arti-

ficial neural network (ANN), support vector machine (SVM), and genetic programming

(GP), to predict the California bearing ratio (CBR) using different performance metrics for

both the training and testing databases. The performance metrics used to evaluate the

models' performance include mean absolute error (MAE), mean squared error (MSE), root

mean squared error (RMSE), mean squared logarithmic error (MSLE), root mean squared

logarithmic error (RMSLE), and coefficient of determination (R²).

Also, Table 11 shows the ranking of different AI models. The SVM model was the

first AI model examined in this study and is known as a black box model. The ANN

method, another black box model, is subsequently employed to explore other black box

models' performance. The GP method is utilized to examine the grey box AI methods.

The results demonstrate that the SVM model exhibits the lowest accuracy for both

the training and test datasets, but still, it is a good performance. In contrast, the ANN

method performs significantly better and predicts CBR values with high accuracy, achiev-

ing R2 of 0.989 and 0.980 for the training and test databases, respectively. The GP method,

a grey box model, achieves slightly lower accuracy than the ANN method but still per-

forms well, with R2 of 0.98 and 0.948 for the training and testing databases, respectively.

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Notably, the GP method offers the benefit of producing an equation as output, which can

be used for other datasets.

The reason is that SVM and GP models are known to be better suited for problems

with a small number of inputs and a large number of data points, whereas ANN models

are better suited for problems with a large number of inputs and a small number of data

points. These findings contribute to a better understanding of the performance of different

AI models for predicting CBR, which may have implications for future research and prac-

tical applications in the field of civil engineering and transportation planning.

Table 10. Results of all three AI models to predict CBR for both training and testing databases.

Performance metrics Training Testing

SVM ANN GP SVM ANN GP

MAE 0.497 0.392 0.459 0.512 0.302 0.475

MSE 0.409 0.200 0.358 0.357 0.116 0.304

RMSE 0.640 0.447 0.598 0.598 0.341 0.552

MSLE 0.017 0.005 0.010 0.011 0.002 0.009

RMSLE 0.129 0.074 0.100 0.103 0.046 0.097

R² 0.978 0.989 0.980 0.939 0.980 0.948

Table 11. Overall rank analysis of different performance parameters for different machine learning techniques.

Performance

parameters

SVM ANN GP

TR TS TR TS TR TS

MAE 3 3 1 1 2 2

MSE 3 3 1 1 2 2

RMSE 3 3 1 1 2 2

MSLE 3 3 1 1 2 2

RMSLE 3 3 1 1 2 2

R² 3 3 1 1 2 2

Sub total 18 18 6 6 12 12

Total score 36 12 24

Overall rank 3 1 2

5.1 The variable importance of input parameters

Investigating the significance of input parameters is a crucial aspect of artificial intel-

ligence modelling. In this study, the impact of individual input parameters on network

error was examined by altering each parameter by 100%, while maintaining all other in-

puts at actual values. The resulting network errors were recorded for each alteration and

are presented in Figure 11 for each of the three AI models tested, namely Artificial Neural

Networks (ANN), Support Vector Machines (SVM), and Genetic Programming (GP).

Greater network error resulting from a given parameter alteration indicates that the net-

work exhibits increased sensitivity to that particular parameter. The variable importance

ranking was evaluated based on the input parameters, including Liquid limit of soil (LL-

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Soil), Plasticity index of soil (PI-Soil), Gs of soil, number of compaction blows (Compaction

Num. Hammer), optimum moisture content of soil (OMC-Soil), maximum dry density of

soil (OMC-Mixture), Optimum moisture content of mixture (OMC-mixture), maximum

dry density of mixture (MDD-Mixture), and sludge content (% Sludge). Table 12 summa-

rizes the ranking of inputs based on the different AI models.0

10

20

30

40

50

60

70

OMC-Mixture OMC-Soil MDD-Soil Gs-Soil % Sludge PI-Soil MDD-Mixture LL-Soil Compaction

Num. Hammer

Mean increase error

Variables(a)

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Figure 11. The importance of input parameters on the MAE of the best (a) SVM, (b) ANN and (c) GP model.

The results reveal that the SVM model ranked LL of soil as the most important input

parameter, followed by number of compactions blows and PI of soil. While MDD of soil

was the least important parameter. Also, ANN ranked number of compactions blows as

the most important input parameter, followed by PI and LL of soil. While MDD of mixture

was the least important parameter. GP ranked number of compactions blows as the most

important input parameter, followed by sludge content and LL of soil. For all three mod-

els, and according to Table 12, it can be concluded that parameters number of compactions

blows, and LL of soil are respectively the most important input parameters, while MDD

of soil and mixture are the least important.

The explanation for the variation in the importance ranking of input parameters

across AI models could be the differences in the underlying algorithms and architectures.

SVM is a kernel-based method that tries to find a hyperplane that maximally separates

data points. ANN is a feed-forward neural network with hidden layers, and it is trained

using a back-propagation algorithm. GP is an evolutionary algorithm that evolves a pop-

ulation of candidate solutions using genetic operators such as mutation and crossover.

Therefore, these algorithms have different ways of handling input parameters and con-

structing models.0

20

40

60

80

100

120

140

160

OMC-Mixture OMC-Soil MDD-Soil Gs-Soil % Sludge PI-Soil MDD-Mixture LL-Soil Compaction

Num. Hammer

Mean increase error

Variables(b)0

10

20

30

40

50

60

70

80

90

100

OMC-Mixture OMC-Soil MDD-Soil Gs-Soil % Sludge PI-Soil MDD-Mixture LL-Soil Compaction

Num. Hammer

Mean increase error

Variables(c)

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Another explanation for the variation in importance ranking could be the nature of

the input parameters themselves. Some parameters may have stronger correlations with

the target variable, which is CBR, in certain data sets or applications, while others may be

less relevant. Moreover, different input parameters may interact with each other in com-

plex ways, making it challenging to determine their individual contributions to the mod-

el's performance.

Table 12. The results of variable importance for all AI models.

Ranking Input parameters

LL-soil PI-Soil Gs-soil Compaction Num. Hammer OMC-Soil MDD-Soil OMC-Mixture MDD-Mixture % Sludge

SVM 1 3 4 2 7 9 8 6 5

ANN 3 2 5 1 7 8 6 9 4

GP 3 4 5 1 6 9 7 8 2

Total 7 9 14 4 20 26 21 23 11

Ranking 2 3 5 1 6 9 7 8 4

The California Bearing Ratio (CBR) is a measure of the soil's load-bearing capacity

and is widely used in geotechnical engineering to assess the suitability of soils for con-

struction. The CBR test involves measuring the resistance of a soil sample to penetration

by a standard plunger under controlled conditions of moisture and compaction. The stiff-

ness and load-bearing capacity of a soil depend on various factors, including its texture,

structure, moisture content, density, and compaction effort. The liquid limit of soil is an

important input parameter for predicting CBR because it reflects the soil's ability to resist

deformation and support loads. A soil with a high liquid limit is more plastic and less

stable, which results in lower CBR values. In contrast, a soil with a low liquid limit is more

rigid and stable, leading to higher CBR values. The number of compaction blows is an-

other critical input parameter for predicting CBR because it represents the compaction

effort applied to the soil during construction. The more compaction blows applied, the

higher the soil density and stiffness, which result in higher CBR values. Conversely, inad-

equate compaction effort leads to low soil density and stiffness, resulting in lower CBR

values.

Regarding the maximum dry density, it is an indicator of the soil's compactability

and weight. However, it does not directly relate to the soil's stiffness and load-bearing

capacity, which are the primary factors affecting CBR. Therefore, while it may affect CBR

values to some extent, its influence is relatively weak compared to other parameters such

as liquid limit and compaction effort.

5. Conclusions

The use of Alum sludge in geotechnical engineering has gained importance due to

its cost-effectiveness and environmental benefits, as it has been found to improve the

strength and stability of soils. CBR test is a crucial parameter in geotechnical engineering,

which measures the load-bearing capacity of soil. However, predicting the CBR of soil-

Alum sludge mixture can be challenging due to the large number of input variables. This

highlights the significance of utilizing artificial intelligence (AI) methods to overcome this

challenge, as this approach has not been widely used in this field.

This study aimed to address gaps in the literature by utilizing three different meth-

ods, including two black-box models (artificial neural network and support vector ma-

chine) and one grey-box model (genetic programming), to predict CBR of soil-Alum

sludge mixture. The study compared the performance of the different models using a da-

tabase of 27 CBR test results on various CBR of soil-Alum sludge mixtures and evaluated

Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 10 March 2023 doi:10.20944/preprints202303.0197.v1

the sensitivity and importance of the input parameters. The database consisted of nine

parameters, including liquid limit of soil, plasticity index of soil, specific gravity of soil,

number of compaction blows, optimum moisture content of soil, maximum dry density

of soil, optimum moisture content of mixture, maximum dry density of mixture, and

sludge content.

The results show that the SVM model had the lowest accuracy, while the ANN model

performed significantly better, achieving high accuracy with R2 of 0.989 and 0.980 for the

training and test databases, respectively. The GP method had slightly lower accuracy than

the ANN method but still performed well, with R2 of 0.98 and 0.948 for the training and

testing databases, respectively. The GP method has the advantage of producing an equa-

tion as output, which can be used for other datasets. Overall, the study provides valuable

insights into the performance of different AI models for predicting CBR and can be useful

for future research and practical applications.

The paper also showed the importance of determining the optimal number of neu-

rons to achieve the best accuracy while minimizing the complexity of the model. The re-

sults demonstrated that the accuracy of the ANN model did not improve significantly

beyond 10 neurons, indicating that this is the optimal number of neurons. This infor-

mation is crucial for researchers and developers of AI models, as it allows them to mini-

mize complexity while achieving the best accuracy.

The examination of parameter sensitivity and importance indicated that the number

of compaction hammer blows and the soil's liquid limit were the most significant param-

eters, while the maximum dry density parameters for soil and mixture were the least sig-

nificant. This can be attributed to the fact that liquid limit and the number of compaction

blows are crucial input parameters for CBR prediction, as they represent the soil's ability

to withstand deformation and support loads. On the other hand, maximum dry density

serves as an indicator of soil compactability and weight but has a weaker impact on CBR

compared to liquid limit and compaction effort. This information is important for engi-

neers and researchers to optimize their soil stabilization process.

Conflicts of Interest: The authors declare that they have no known competing financial interests or

personal relationships that could have appeared to influence the work reported in this paper.

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