what is experimental research design according to authors

Experimental Research Design — 6 mistakes you should never make!

Since school days’ students perform scientific experiments that provide results that define and prove the laws and theorems in science. These experiments are laid on a strong foundation of experimental research designs.

An experimental research design helps researchers execute their research objectives with more clarity and transparency.

In this article, we will not only discuss the key aspects of experimental research designs but also the issues to avoid and problems to resolve while designing your research study.

Table of Contents

What Is Experimental Research Design?

Experimental research design is a framework of protocols and procedures created to conduct experimental research with a scientific approach using two sets of variables. Herein, the first set of variables acts as a constant, used to measure the differences of the second set. The best example of experimental research methods is quantitative research .

Experimental research helps a researcher gather the necessary data for making better research decisions and determining the facts of a research study.

When Can a Researcher Conduct Experimental Research?

A researcher can conduct experimental research in the following situations —

• When time is an important factor in establishing a relationship between the cause and effect.
• When there is an invariable or never-changing behavior between the cause and effect.
• Finally, when the researcher wishes to understand the importance of the cause and effect.

Importance of Experimental Research Design

To publish significant results, choosing a quality research design forms the foundation to build the research study. Moreover, effective research design helps establish quality decision-making procedures, structures the research to lead to easier data analysis, and addresses the main research question. Therefore, it is essential to cater undivided attention and time to create an experimental research design before beginning the practical experiment.

By creating a research design, a researcher is also giving oneself time to organize the research, set up relevant boundaries for the study, and increase the reliability of the results. Through all these efforts, one could also avoid inconclusive results. If any part of the research design is flawed, it will reflect on the quality of the results derived.

Types of Experimental Research Designs

Based on the methods used to collect data in experimental studies, the experimental research designs are of three primary types:

1. Pre-experimental Research Design

A research study could conduct pre-experimental research design when a group or many groups are under observation after implementing factors of cause and effect of the research. The pre-experimental design will help researchers understand whether further investigation is necessary for the groups under observation.

Pre-experimental research is of three types —

• One-shot Case Study Research Design
• One-group Pretest-posttest Research Design
• Static-group Comparison

2. True Experimental Research Design

A true experimental research design relies on statistical analysis to prove or disprove a researcher’s hypothesis. It is one of the most accurate forms of research because it provides specific scientific evidence. Furthermore, out of all the types of experimental designs, only a true experimental design can establish a cause-effect relationship within a group. However, in a true experiment, a researcher must satisfy these three factors —

• There is a control group that is not subjected to changes and an experimental group that will experience the changed variables
• A variable that can be manipulated by the researcher
• Random distribution of the variables

This type of experimental research is commonly observed in the physical sciences.

3. Quasi-experimental Research Design

The word “Quasi” means similarity. A quasi-experimental design is similar to a true experimental design. However, the difference between the two is the assignment of the control group. In this research design, an independent variable is manipulated, but the participants of a group are not randomly assigned. This type of research design is used in field settings where random assignment is either irrelevant or not required.

The classification of the research subjects, conditions, or groups determines the type of research design to be used.

Advantages of Experimental Research

Experimental research allows you to test your idea in a controlled environment before taking the research to clinical trials. Moreover, it provides the best method to test your theory because of the following advantages:

• Researchers have firm control over variables to obtain results.
• The subject does not impact the effectiveness of experimental research. Anyone can implement it for research purposes.
• The results are specific.
• Post results analysis, research findings from the same dataset can be repurposed for similar research ideas.
• Researchers can identify the cause and effect of the hypothesis and further analyze this relationship to determine in-depth ideas.
• Experimental research makes an ideal starting point. The collected data could be used as a foundation to build new research ideas for further studies.

6 Mistakes to Avoid While Designing Your Research

There is no order to this list, and any one of these issues can seriously compromise the quality of your research. You could refer to the list as a checklist of what to avoid while designing your research.

1. Invalid Theoretical Framework

Usually, researchers miss out on checking if their hypothesis is logical to be tested. If your research design does not have basic assumptions or postulates, then it is fundamentally flawed and you need to rework on your research framework.

2. Inadequate Literature Study

Without a comprehensive research literature review , it is difficult to identify and fill the knowledge and information gaps. Furthermore, you need to clearly state how your research will contribute to the research field, either by adding value to the pertinent literature or challenging previous findings and assumptions.

3. Insufficient or Incorrect Statistical Analysis

Statistical results are one of the most trusted scientific evidence. The ultimate goal of a research experiment is to gain valid and sustainable evidence. Therefore, incorrect statistical analysis could affect the quality of any quantitative research.

4. Undefined Research Problem

This is one of the most basic aspects of research design. The research problem statement must be clear and to do that, you must set the framework for the development of research questions that address the core problems.

5. Research Limitations

Every study has some type of limitations . You should anticipate and incorporate those limitations into your conclusion, as well as the basic research design. Include a statement in your manuscript about any perceived limitations, and how you considered them while designing your experiment and drawing the conclusion.

6. Ethical Implications

The most important yet less talked about topic is the ethical issue. Your research design must include ways to minimize any risk for your participants and also address the research problem or question at hand. If you cannot manage the ethical norms along with your research study, your research objectives and validity could be questioned.

Experimental Research Design Example

In an experimental design, a researcher gathers plant samples and then randomly assigns half the samples to photosynthesize in sunlight and the other half to be kept in a dark box without sunlight, while controlling all the other variables (nutrients, water, soil, etc.)

By comparing their outcomes in biochemical tests, the researcher can confirm that the changes in the plants were due to the sunlight and not the other variables.

Experimental research is often the final form of a study conducted in the research process which is considered to provide conclusive and specific results. But it is not meant for every research. It involves a lot of resources, time, and money and is not easy to conduct, unless a foundation of research is built. Yet it is widely used in research institutes and commercial industries, for its most conclusive results in the scientific approach.

Have you worked on research designs? How was your experience creating an experimental design? What difficulties did you face? Do write to us or comment below and share your insights on experimental research designs!

Frequently Asked Questions

Randomization is important in an experimental research because it ensures unbiased results of the experiment. It also measures the cause-effect relationship on a particular group of interest.

Experimental research design lay the foundation of a research and structures the research to establish quality decision making process.

There are 3 types of experimental research designs. These are pre-experimental research design, true experimental research design, and quasi experimental research design.

The difference between an experimental and a quasi-experimental design are: 1. The assignment of the control group in quasi experimental research is non-random, unlike true experimental design, which is randomly assigned. 2. Experimental research group always has a control group; on the other hand, it may not be always present in quasi experimental research.

Experimental research establishes a cause-effect relationship by testing a theory or hypothesis using experimental groups or control variables. In contrast, descriptive research describes a study or a topic by defining the variables under it and answering the questions related to the same.

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Home » Experimental Design – Types, Methods, Guide

Experimental Design – Types, Methods, Guide

Table of Contents

Experimental Design

Experimental design is a process of planning and conducting scientific experiments to investigate a hypothesis or research question. It involves carefully designing an experiment that can test the hypothesis, and controlling for other variables that may influence the results.

Experimental design typically includes identifying the variables that will be manipulated or measured, defining the sample or population to be studied, selecting an appropriate method of sampling, choosing a method for data collection and analysis, and determining the appropriate statistical tests to use.

Types of Experimental Design

Here are the different types of experimental design:

Completely Randomized Design

In this design, participants are randomly assigned to one of two or more groups, and each group is exposed to a different treatment or condition.

Randomized Block Design

This design involves dividing participants into blocks based on a specific characteristic, such as age or gender, and then randomly assigning participants within each block to one of two or more treatment groups.

Factorial Design

In a factorial design, participants are randomly assigned to one of several groups, each of which receives a different combination of two or more independent variables.

Repeated Measures Design

In this design, each participant is exposed to all of the different treatments or conditions, either in a random order or in a predetermined order.

Crossover Design

This design involves randomly assigning participants to one of two or more treatment groups, with each group receiving one treatment during the first phase of the study and then switching to a different treatment during the second phase.

Split-plot Design

In this design, the researcher manipulates one or more variables at different levels and uses a randomized block design to control for other variables.

Nested Design

This design involves grouping participants within larger units, such as schools or households, and then randomly assigning these units to different treatment groups.

Laboratory Experiment

Laboratory experiments are conducted under controlled conditions, which allows for greater precision and accuracy. However, because laboratory conditions are not always representative of real-world conditions, the results of these experiments may not be generalizable to the population at large.

Field Experiment

Field experiments are conducted in naturalistic settings and allow for more realistic observations. However, because field experiments are not as controlled as laboratory experiments, they may be subject to more sources of error.

Experimental Design Methods

Experimental design methods refer to the techniques and procedures used to design and conduct experiments in scientific research. Here are some common experimental design methods:

Randomization

This involves randomly assigning participants to different groups or treatments to ensure that any observed differences between groups are due to the treatment and not to other factors.

Control Group

The use of a control group is an important experimental design method that involves having a group of participants that do not receive the treatment or intervention being studied. The control group is used as a baseline to compare the effects of the treatment group.

Blinding involves keeping participants, researchers, or both unaware of which treatment group participants are in, in order to reduce the risk of bias in the results.

Counterbalancing

This involves systematically varying the order in which participants receive treatments or interventions in order to control for order effects.

Replication

Replication involves conducting the same experiment with different samples or under different conditions to increase the reliability and validity of the results.

This experimental design method involves manipulating multiple independent variables simultaneously to investigate their combined effects on the dependent variable.

This involves dividing participants into subgroups or blocks based on specific characteristics, such as age or gender, in order to reduce the risk of confounding variables.

Data Collection Method

Experimental design data collection methods are techniques and procedures used to collect data in experimental research. Here are some common experimental design data collection methods:

Direct Observation

This method involves observing and recording the behavior or phenomenon of interest in real time. It may involve the use of structured or unstructured observation, and may be conducted in a laboratory or naturalistic setting.

Self-report Measures

Self-report measures involve asking participants to report their thoughts, feelings, or behaviors using questionnaires, surveys, or interviews. These measures may be administered in person or online.

Behavioral Measures

Behavioral measures involve measuring participants’ behavior directly, such as through reaction time tasks or performance tests. These measures may be administered using specialized equipment or software.

Physiological Measures

Physiological measures involve measuring participants’ physiological responses, such as heart rate, blood pressure, or brain activity, using specialized equipment. These measures may be invasive or non-invasive, and may be administered in a laboratory or clinical setting.

Archival Data

Archival data involves using existing records or data, such as medical records, administrative records, or historical documents, as a source of information. These data may be collected from public or private sources.

Computerized Measures

Computerized measures involve using software or computer programs to collect data on participants’ behavior or responses. These measures may include reaction time tasks, cognitive tests, or other types of computer-based assessments.

Video Recording

Video recording involves recording participants’ behavior or interactions using cameras or other recording equipment. This method can be used to capture detailed information about participants’ behavior or to analyze social interactions.

Data Analysis Method

Experimental design data analysis methods refer to the statistical techniques and procedures used to analyze data collected in experimental research. Here are some common experimental design data analysis methods:

Descriptive Statistics

Descriptive statistics are used to summarize and describe the data collected in the study. This includes measures such as mean, median, mode, range, and standard deviation.

Inferential Statistics

Inferential statistics are used to make inferences or generalizations about a larger population based on the data collected in the study. This includes hypothesis testing and estimation.

Analysis of Variance (ANOVA)

ANOVA is a statistical technique used to compare means across two or more groups in order to determine whether there are significant differences between the groups. There are several types of ANOVA, including one-way ANOVA, two-way ANOVA, and repeated measures ANOVA.

Regression Analysis

Regression analysis is used to model the relationship between two or more variables in order to determine the strength and direction of the relationship. There are several types of regression analysis, including linear regression, logistic regression, and multiple regression.

Factor Analysis

Factor analysis is used to identify underlying factors or dimensions in a set of variables. This can be used to reduce the complexity of the data and identify patterns in the data.

Structural Equation Modeling (SEM)

SEM is a statistical technique used to model complex relationships between variables. It can be used to test complex theories and models of causality.

Cluster Analysis

Cluster analysis is used to group similar cases or observations together based on similarities or differences in their characteristics.

Time Series Analysis

Time series analysis is used to analyze data collected over time in order to identify trends, patterns, or changes in the data.

Multilevel Modeling

Multilevel modeling is used to analyze data that is nested within multiple levels, such as students nested within schools or employees nested within companies.

Applications of Experimental Design 

Experimental design is a versatile research methodology that can be applied in many fields. Here are some applications of experimental design:

• Medical Research: Experimental design is commonly used to test new treatments or medications for various medical conditions. This includes clinical trials to evaluate the safety and effectiveness of new drugs or medical devices.
• Agriculture : Experimental design is used to test new crop varieties, fertilizers, and other agricultural practices. This includes randomized field trials to evaluate the effects of different treatments on crop yield, quality, and pest resistance.
• Environmental science: Experimental design is used to study the effects of environmental factors, such as pollution or climate change, on ecosystems and wildlife. This includes controlled experiments to study the effects of pollutants on plant growth or animal behavior.
• Psychology : Experimental design is used to study human behavior and cognitive processes. This includes experiments to test the effects of different interventions, such as therapy or medication, on mental health outcomes.
• Engineering : Experimental design is used to test new materials, designs, and manufacturing processes in engineering applications. This includes laboratory experiments to test the strength and durability of new materials, or field experiments to test the performance of new technologies.
• Education : Experimental design is used to evaluate the effectiveness of teaching methods, educational interventions, and programs. This includes randomized controlled trials to compare different teaching methods or evaluate the impact of educational programs on student outcomes.
• Marketing : Experimental design is used to test the effectiveness of marketing campaigns, pricing strategies, and product designs. This includes experiments to test the impact of different marketing messages or pricing schemes on consumer behavior.

Examples of Experimental Design 

Here are some examples of experimental design in different fields:

• Example in Medical research : A study that investigates the effectiveness of a new drug treatment for a particular condition. Patients are randomly assigned to either a treatment group or a control group, with the treatment group receiving the new drug and the control group receiving a placebo. The outcomes, such as improvement in symptoms or side effects, are measured and compared between the two groups.
• Example in Education research: A study that examines the impact of a new teaching method on student learning outcomes. Students are randomly assigned to either a group that receives the new teaching method or a group that receives the traditional teaching method. Student achievement is measured before and after the intervention, and the results are compared between the two groups.
• Example in Environmental science: A study that tests the effectiveness of a new method for reducing pollution in a river. Two sections of the river are selected, with one section treated with the new method and the other section left untreated. The water quality is measured before and after the intervention, and the results are compared between the two sections.
• Example in Marketing research: A study that investigates the impact of a new advertising campaign on consumer behavior. Participants are randomly assigned to either a group that is exposed to the new campaign or a group that is not. Their behavior, such as purchasing or product awareness, is measured and compared between the two groups.
• Example in Social psychology: A study that examines the effect of a new social intervention on reducing prejudice towards a marginalized group. Participants are randomly assigned to either a group that receives the intervention or a control group that does not. Their attitudes and behavior towards the marginalized group are measured before and after the intervention, and the results are compared between the two groups.

When to use Experimental Research Design 

Experimental research design should be used when a researcher wants to establish a cause-and-effect relationship between variables. It is particularly useful when studying the impact of an intervention or treatment on a particular outcome.

Here are some situations where experimental research design may be appropriate:

• When studying the effects of a new drug or medical treatment: Experimental research design is commonly used in medical research to test the effectiveness and safety of new drugs or medical treatments. By randomly assigning patients to treatment and control groups, researchers can determine whether the treatment is effective in improving health outcomes.
• When evaluating the effectiveness of an educational intervention: An experimental research design can be used to evaluate the impact of a new teaching method or educational program on student learning outcomes. By randomly assigning students to treatment and control groups, researchers can determine whether the intervention is effective in improving academic performance.
• When testing the effectiveness of a marketing campaign: An experimental research design can be used to test the effectiveness of different marketing messages or strategies. By randomly assigning participants to treatment and control groups, researchers can determine whether the marketing campaign is effective in changing consumer behavior.
• When studying the effects of an environmental intervention: Experimental research design can be used to study the impact of environmental interventions, such as pollution reduction programs or conservation efforts. By randomly assigning locations or areas to treatment and control groups, researchers can determine whether the intervention is effective in improving environmental outcomes.
• When testing the effects of a new technology: An experimental research design can be used to test the effectiveness and safety of new technologies or engineering designs. By randomly assigning participants or locations to treatment and control groups, researchers can determine whether the new technology is effective in achieving its intended purpose.

How to Conduct Experimental Research

Here are the steps to conduct Experimental Research:

• Identify a Research Question : Start by identifying a research question that you want to answer through the experiment. The question should be clear, specific, and testable.
• Develop a Hypothesis: Based on your research question, develop a hypothesis that predicts the relationship between the independent and dependent variables. The hypothesis should be clear and testable.
• Design the Experiment : Determine the type of experimental design you will use, such as a between-subjects design or a within-subjects design. Also, decide on the experimental conditions, such as the number of independent variables, the levels of the independent variable, and the dependent variable to be measured.
• Select Participants: Select the participants who will take part in the experiment. They should be representative of the population you are interested in studying.
• Randomly Assign Participants to Groups: If you are using a between-subjects design, randomly assign participants to groups to control for individual differences.
• Conduct the Experiment : Conduct the experiment by manipulating the independent variable(s) and measuring the dependent variable(s) across the different conditions.
• Analyze the Data: Analyze the data using appropriate statistical methods to determine if there is a significant effect of the independent variable(s) on the dependent variable(s).
• Draw Conclusions: Based on the data analysis, draw conclusions about the relationship between the independent and dependent variables. If the results support the hypothesis, then it is accepted. If the results do not support the hypothesis, then it is rejected.
• Communicate the Results: Finally, communicate the results of the experiment through a research report or presentation. Include the purpose of the study, the methods used, the results obtained, and the conclusions drawn.

Purpose of Experimental Design 

The purpose of experimental design is to control and manipulate one or more independent variables to determine their effect on a dependent variable. Experimental design allows researchers to systematically investigate causal relationships between variables, and to establish cause-and-effect relationships between the independent and dependent variables. Through experimental design, researchers can test hypotheses and make inferences about the population from which the sample was drawn.

Experimental design provides a structured approach to designing and conducting experiments, ensuring that the results are reliable and valid. By carefully controlling for extraneous variables that may affect the outcome of the study, experimental design allows researchers to isolate the effect of the independent variable(s) on the dependent variable(s), and to minimize the influence of other factors that may confound the results.

Experimental design also allows researchers to generalize their findings to the larger population from which the sample was drawn. By randomly selecting participants and using statistical techniques to analyze the data, researchers can make inferences about the larger population with a high degree of confidence.

Overall, the purpose of experimental design is to provide a rigorous, systematic, and scientific method for testing hypotheses and establishing cause-and-effect relationships between variables. Experimental design is a powerful tool for advancing scientific knowledge and informing evidence-based practice in various fields, including psychology, biology, medicine, engineering, and social sciences.

Advantages of Experimental Design 

Experimental design offers several advantages in research. Here are some of the main advantages:

• Control over extraneous variables: Experimental design allows researchers to control for extraneous variables that may affect the outcome of the study. By manipulating the independent variable and holding all other variables constant, researchers can isolate the effect of the independent variable on the dependent variable.
• Establishing causality: Experimental design allows researchers to establish causality by manipulating the independent variable and observing its effect on the dependent variable. This allows researchers to determine whether changes in the independent variable cause changes in the dependent variable.
• Replication : Experimental design allows researchers to replicate their experiments to ensure that the findings are consistent and reliable. Replication is important for establishing the validity and generalizability of the findings.
• Random assignment: Experimental design often involves randomly assigning participants to conditions. This helps to ensure that individual differences between participants are evenly distributed across conditions, which increases the internal validity of the study.
• Precision : Experimental design allows researchers to measure variables with precision, which can increase the accuracy and reliability of the data.
• Generalizability : If the study is well-designed, experimental design can increase the generalizability of the findings. By controlling for extraneous variables and using random assignment, researchers can increase the likelihood that the findings will apply to other populations and contexts.

Limitations of Experimental Design

Experimental design has some limitations that researchers should be aware of. Here are some of the main limitations:

• Artificiality : Experimental design often involves creating artificial situations that may not reflect real-world situations. This can limit the external validity of the findings, or the extent to which the findings can be generalized to real-world settings.
• Ethical concerns: Some experimental designs may raise ethical concerns, particularly if they involve manipulating variables that could cause harm to participants or if they involve deception.
• Participant bias : Participants in experimental studies may modify their behavior in response to the experiment, which can lead to participant bias.
• Limited generalizability: The conditions of the experiment may not reflect the complexities of real-world situations. As a result, the findings may not be applicable to all populations and contexts.
• Cost and time : Experimental design can be expensive and time-consuming, particularly if the experiment requires specialized equipment or if the sample size is large.
• Researcher bias : Researchers may unintentionally bias the results of the experiment if they have expectations or preferences for certain outcomes.
• Lack of feasibility : Experimental design may not be feasible in some cases, particularly if the research question involves variables that cannot be manipulated or controlled.

About the author

Muhammad Hassan

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• Open access
• Published: 07 May 2024

Multicriteria optimization of the composition, thermodynamic and strength properties of fly-ash as an additive in metakaolin-based geopolymer composites

• Van Su Le 1 ,
• Artem Sharko 1 ,
• Oleksandr Sharko 2 ,
• Dmitry Stepanchikov 3 ,
• Katarzyna Ewa Buczkowska 4 &
• Petr Louda 5  

Scientific Reports volume  14 , Article number:  10434 ( 2024 ) Cite this article

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• Engineering
• Environmental impact
• Environmental sciences
• Materials science

This paper presents the construction of intelligent systems for selecting the optimum concentration of geopolymer matrix components based on ranking optimality criteria. A peculiarity of the methodology is replacing discrete time intervals with a sequence of states. Markov chains represent a synthetic property accumulating heterogeneous factors. The computational basis for the calculations was the digitization of experimental data on the strength properties of fly ashes collected from thermal power plants in the Czech Republic and used as additives in geopolymers. A database and a conceptual model of priority ranking have been developed, that are suitable for determining the structure of relations of the main factors. Computational results are presented by studying geopolymer matrix structure formation kinetics under changing component concentrations in real- time. Multicriteria optimization results for fly-ash as an additive on metakaolin-based geopolymer composites show that the optimal composition of the geopolymer matrix within the selected variation range includes 100 g metakaolin, 90 g potassium activator, 8 g silica fume, 2 g basalt fibers and 50 g fly ash by ratio weight. This ratio gives the best mechanical, thermal, and technological properties.

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Introduction.

As high-strength materials, geopolymers are increasingly recognized for their competitive properties with Portland cement, the predominant construction material 1 , 2 . A critical concern is the substantial environmental impact of Portland cement production, releasing 0.8 tons of CO 2 into the atmosphere per ton of cement produced, with global cement plants emitting a staggering 1.5 billion tons of CO 2 annually 3 , 4 , 5 . Geopolymers offer a promising solution by utilizing secondary raw materials such as blast furnace slag and fly ash from thermal power plants, thereby demonstrating eco-friendliness 6 , 7 , 8 . High belite cement 9 and supersulfated cement 10 are known for their reduced carbon footprint compared to traditional Portland cement, while geopolymers are also considered low-carbon alternatives. By comparing these different types of low-carbon cement, researchers and engineers can evaluate their performance, environmental impact, and suitability for various applications, helping to advance sustainable construction practices.

Worldwide, intensive research is dedicated to identifying the optimal formulation of geopolymer mixtures that meet specific thermal and mechanical property requirements 11 , 12 , 13 . In such weakly structured systems, numerous factors interconnect, forming a complex web of relationships influenced by both internal and external conditions. However, multiparameter optimization poses significant computational challenges, given the unknown analytical expressions for their boundary values in most practical cases 14 .

The stochastic process of determining the ideal geopolymer composition, guided primarily by expert input without rigorous mathematical processing, involves a series of random experimental measurements governed by optimality criteria. The choice of optimal composition relies heavily on intuitive expert judgment. This process takes on a Markovian character as subsequent decisions become independent of previous ones. The initial probability distribution defines the current state of the experimental input information. Moreover, the selection of the initial step in constructing an intelligent system for optimal geopolymer composition relies on evaluating and adjusting the probabilities associated with key physical and mechanical characteristics, leading to a shift in the reference point. This process continues iteratively, creating a Markov chain with a unique stationary distribution of states after a certain number of transitions 15 .

Some research has focused on activators for geopolymers derived from biomass ash waste, reducing environmental burdens 16 , while other studies have analyzed the suitability of geopolymer composites for withstanding alternating loads 17 , 18 . Additionally, modeling geopolymers based on pore size distribution and considering particle aggregation into clusters for nanostructure nucleation has been explored 19 . Water sorption in geopolymers has been studied through simulation using the Monte Carlo method and Markov chains 20 . Innovations extend to creating intelligent systems for civil infrastructure repairs, maintenance optimization, and evaluating the optimum content of calcium-rich fly ash in metakaolin-based geopolymers 21 , 22 , 23 .

Furthermore, criteria for calculating the durability of geopolymer bridges reinforced with carbon fiber have been developed 24 , 25 , 26 . The selection criteria for construction materials based on fly ash for optimizing geopolymer compositions have been delineated as part of broader efforts to reduce greenhouse gas emissions 27 , 28 .

This work's uniqueness lies in its quantitative analysis of alternating loads on a large scale and the associated challenges of choosing optimal solutions when considering multiple optimality criteria. The practical application of Markov chains extends to economic development prediction 29 , 30 , 31 , 32 , 33 , monitoring lymphatic drainage systems 32 , and studying the COVID-19 pandemic 34 . Additionally, information-entropy models underpin management decisions amidst uncertainty and risk 31 .

In recent studies, the mechanical properties of foamed geopolymers at high temperatures have been assessed, along with the optimization of fly ash parameters in geopolymers 16 , 18 . Notably, innovative systems have been proposed for studying organizational and technical objects autonomously 21 , modeling technological development 23 , and employing probabilistic models for optimal system trajectory estimation 22 , 24 .

Given that practical problems often involve multiple criteria for selecting optimal alternatives, the emerging theme in these studies is the use of multicriteria optimization methods to guide decision-making. This approach aims to balance evaluations of different criteria, fostering the transition from subjective to objective optimal solutions. In practice, determining the ideal geopolymer composition involves a process of random expert input, often lacking rigorous mathematical processing, and therefore introducing elements of randomness. Consequently, achieving the desired outcome can be highly dependent on expert qualifications. The primary objective worldwide remains the quest for the optimal formulation of geopolymer mixtures that satisfy specific thermal and mechanical property requirements. This work's focus is squarely on the precision of optimization. The proposed model introduces an innovative approach by integrating multicriteria optimization and Markov chains. The role of Markov chains in the model is to establish the weight coefficients for criteria combinations, enhancing the accuracy and reliability of assessments for geopolymer formulation optimization. The central task of this study was to identify an optimal geopolymer composition that maximizes compressive strength, bending strength, impact toughness, and thermal conductivity while minimizing density and thermal conductivity. In contrast to conventional approaches, this research avoids generalizing or specifying geopolymer composition solely by empirically varying physical and mechanical properties. It tackles the challenge of obtaining an optimal geopolymer formulation while accounting for a multitude of varying properties.

The process of determining optimal geopolymer compositions, observed in these studies, involves a series of randomly selected experimental measurements. In addition to intuition, the selection process retains elements of randomness due to the expertise of the individuals involved. This paper suggests incorporating Markov chains and multicriteria optimization as a more structured and systematic approach to address this limitation. As a result of the model's comprehensive use of multicriteria optimization and Markov chains, the weighting coefficients for criteria combinations are determined by Markov chains. Combining physical and mechanical properties improves the accuracy and reliability of assessments in geopolymer formulation optimization. In addition to examining the physical properties of various geopolymer compositions, this study also aimed to develop a methodology for determining the optimal geopolymer composition based on diverse prioritizations of optimization parameters. To achieve this, samples covering a broad range of physical and mechanical properties were prepared, allowing a deeper understanding of the interrelationships within geopolymer compositions. Under different conditions, this approach allows the prediction of various states of geopolymers, providing valuable insights and practical recommendations.

Materials, methods, technology, and equipment

The materials employed in this study encompass metakaolin, an activator, carbon fiber, silica fume, and various types of fly ash. The inorganic two-component aluminosilicate binder, commercially designated as Bausik LK and produced by České lupkové závody, a.s. in the Czech Republic, is a metakaolin-based material with a density (ρ = 1220 kg/m 3 ) and a chemical composition consisting of 40.10 wt.% Al 2 O 3 , 54.10 wt.% SiO 2 , 0.80 wt.% K 2 O, 1.10 wt.% Fe 2 O 3 , 1.80 wt.% TiO 2 , 0.18 wt.% MgO, 0.13 wt.% CaO, 2.20 wt.% LOI. The grain size distribution is characterized by D50 = 3 μm and D90 = 10 μm. Activated by an aqueous alkaline activator, this binder is renowned for its commendable adhesion, chemical resistance, and ability to withstand extreme temperatures. Typically, a mixing ratio of 5 parts metakaolin to 4 parts activator is employed. Additionally, silica fume sourced from Kema Morava rehabilitation center a.s. in the Republic of Slovenia is incorporated into the mortar. This silica fume exhibits a density (ρ = 350 kg/m 3 ) and a chemical composition comprising 90 wt.% SiO 2 , 1 wt.% Al 2 O 3 , 0.8 wt.% CaO, 1.5 wt.% MgO, 0.5 wt.% Na 2 O. The average grain size is 100 μm. Recycled carbon fibers with a density (ρ = 1800 kg/m 3 ) and a chemical composition of > 95 wt.% C, with an average length of 6 mm, are employed as reinforcing fibers. These chopped fibers are particularly well-suited for the production of dry and molding mortars. The geopolymer production process involves the incorporation of fly ashes labelled as FA1-7 (refer to Table 1 and 2 ) obtained from thermal power plants in the Czech Republic. These fly ashes, characterized by densities of 625.89, 645.53, 669.08, 667.89, 702.92, 692.05, and 623.23 kg/m 3 , respectively, are utilized in the production process. The chemical compositions of the raw materials were analyzed using X-ray fluorescence (BRUKER S8 Tiger instrument, BRUKER, Karlsruhe, Germany) and scanning electron microscopy (SEM Carl Zeiss Ultra Plus). The findings are presented in Table 1 . These materials have been comprehensively elucidated in the research paper titled "Multicriteria Assessment for Determining the Optimal Proportion of Calcium-Rich Fly Ash in Metakaolin-Based Geopolymers".

The preparation of the geopolymer mix entailed a sequential process. Initially, cement-based metakaolin and an alkaline potassium activator were combined in a proportion of 5:4, as prescribed by the manufacturer, and subjected to thorough mixing for three minutes. Subsequently, the inclusion of silica fume, fly ash, and fibers into the geopolymer mortar followed, with the mixing process extended to a duration of five minutes. These procedures collectively influenced the characteristics of the freshly prepared geomortar. The resultant mixture was then cast into molds, and a protective layer of polyethylene film was applied to mitigate shrinkage during the curing process. Subsequently, the specimen was allowed to undergo curing at ambient room temperature for 28 days, in preparation for subsequent testing and analysis. The ratios and types of the constituent materials used in all mixtures are presented in Table 2 .

The input information for the physical and mechanical properties of different concentrations of fly ash in the composition of geopolymer mixtures included tests for bending, compression, impact strength, and measurement of density and thermal conductivity.

The apparent density was estimated by dividing the mass of the sample by its apparent volume. The samples have dimensions of 30 by 30 by 150 mm 3 . Bending and compression tests were carried out on an Instron (Model 4202) Universal Testing Machine with a 10 kN load cell traverse speed of 2.5 mm/min according to the UNI EN 1015–11:2019 standard 35 . The compressive strength tests were carried out on the same specimens as the bending tests, and their geometric dimensions were 30 by 30 by 30 mm 3 (Fig.  1 ). The Charpy impact strength was determined using a PIT-C Series Pendulum Impact Testing Machine on samples measuring 20 by 19 by 60 mm 3 by the ISO 148–1:2016 test method 36 (Fig.  2 ). The setup for stress tests is depicted in Figs.  1 and 2 . Using test samples with dimensions of 300 by 300 by 30 mm 3 , the thermal conductivity was investigated using the NETZSCH HFM 446 instrument.

Stress testing setup: ( a ) Instron model 4202 testing machine, ( b ) bending testing setup, ( c ) compression testing setup.

Charpy impact test setup: ( a ) universal testing machine, ( b ) specimen testing setup.

The determination of priorities and preferences in multicriteria optimization is based on the fact that there exists a function U, whose domain of definition is determined by the preference criteria A and B, with A being preferable to B.

If A = B, then there is a state of indifference

At the same time, the presented calculation scheme provides only the ranking of criteria, not their numerical values. The simultaneous optimization of two or more conflicting target functions in a given domain of definition is multicriteria. A multiattribute preference function with three target functions can be represented as follows.

In Eq. ( 3 ) there are three target functions and three constants, i.e. we have a definition of the best priority on the admissible set of optimality criteria.

Markov chains are a method of modeling random events that represent a discrete sequence of phases, each of which is located at discrete points in the state space.

Applied to the research problem, they are a tool of the theory of random processes consisting of a sequence of states. This is interpreted as the sum of several probabilities of some event K, depending on the occurrence of state I, where event K = m + 1, I = m, i.e. event K differs from I by 1.

where r is the matrix rank.

The probability distribution in a Markov chain depends only on transitions from the current state to the next state. Therefore, a Markov chain is represented as a sequence of states n  ∈  N. Mathematically it looks like this.

where at each moment the process takes such values in the discrete set E that

where \({\forall }\) is the quantum of generality:

Let us denote all possible states of the system as S 1 , S 2 , … S n , then

The transition probabilities from one state to another are represented as square matrices.

When passing from one row to the next in the transition probability matrix, an induced stationary distribution over the rows appears. Let us denote by Pi0(0) the probability of starting the process from the state Si. Pij0(0) is the probability that as a result of the process, the state will change from Si to Sj. Pij is the probability that the result of the calculation will be Si

Multiplying the line describing the probability distribution at a certain stage of determining the composition of geopolymer matrices corresponding to optimal mechanical properties by the transition probability matrix, we obtain the probability distribution at the next stage.

Thus, Markov chains combine a priori assumptions and experimental data to obtain the a posteriori distribution of the parameter of interest.

When establishing criteria for assessing the strength of geopolymers, it is necessary to select such benchmarks that cover the conditions of realization of the objective as much as possible. For the successful selection of alternatives for geopolymer formulation, it is necessary that all variants of work are compatible with each other, i.e. they could be comparable in terms of the factors of geopolymer structure. To compare the alternatives, a score is assigned to each of them and the final evaluation is performed by prioritizing them on a ranking scale.

The synthesis of ideas on multicriteria optimization of geopolymer composition is based on the use of efficiency algorithms included in the definition of the evaluation functional F = {f jk }, and computations are performed to find the optimal solution x 0   ∈  X according to the chosen criterion.

In expanded form, this procedure will be characterized by a matrix, elements f jk which are quantitative estimates of the quantity x k   ∈  X corresponding to experimental values y k   ∈  Y.

An evaluation functional F has positive ingredient F  + if the decision is based on the condition that xmax k   ∈   X { f jk }. In this case.

The negative ingredient is based on the condition of achieving a x mink   ∈   X { f jk }. In this case.

The value of generalized estimates characterizes the degree of approximation to the goal.

Both the averaging function and the maximin function can be used as generalizing functions.

Optimization of geopolymer mixture composition consists of finding a solution, at which the values of target functions would be acceptable for the task.

Decision-making criteria for selecting the optimal formulation of geopolymer mixtures to ensure maximum mechanical properties can be considered as preference operations on the set of alternatives, providing an interactive solution to optimization problems. The optimization criteria are not extreme, but some compromise values correspond to the main objective of the optimization.

The range of variation of the resulting characteristics of strength and physical–mechanical properties is determined by setting the extrema of the boundaries of the target values of the criteria.

In simple terms, the optimization of a geopolymer mixture aims to improve its physical properties, such as density and strength (flexural, compressive, and impact), by using a scalar function that gives a linear ranking of the results. This is achieved by reducing the density and converting vector estimates to scalar ones, as the target orientations and dimensions are different. The scalar functions based on the extreme values of the mixture.

The procedure of determining the optimal geopolymer composition based on the analysis of physical–mechanical and strength parameters begins with the construction of the efficiency matrix, which looks as follows 23 .

where q1…qi is the fly ash content in the geopolymer mixture, Π1…Πj is the physical–mechanical and strength parameters of geopolymer, i is the line number, j is the column number.

The relative deviation δy ij jth attribute from the optimal value is determined as follows.

As parameters it is necessary to choose the best values of the analyzed parameters from the point of view of the problem to be solved—it can be maximum or minimum from the experimental sample. In such an approach, formula ( 15 ) will translate dimensional values into a ratio within the scale (0, 1). However, with such a choice of parameters cj will necessarily be observed coinciding with the value of cj corresponding elements of matrix (Eq. 14 ), which will lead to δyij = 0. When using additive convolution (Eq. 16 ), this leads to the dropping of the corresponding attribute from the overall evaluation of the object, and when using multiplicative convolution (Eqs. 17 , 18 ) to its nullification. The obvious way to exclude such situations is to extend the upper (for maximum) or lower (for minimum) limit of each feature c j in the same percentage ratio. Below the maximum (minimum) values of each of the analyzed parameters, c j was increased (decreased) by 1%.

To select the optimal combination of the composition of fly ash components and to ensure maximum strength properties at minimum density and thermal conductivity of the geopolymer mixture, it is necessary to take into account more than one criterion. Therefore, it is necessary to reconcile such multidirectional criteria.

The following generalized multicriteria utility functions were used in the theoretical analysis 23 , 37 .

Additive convolution:

where ω j is the weight coefficient of the jth attribute.

Stepwise multiplicative convolution:

Additional multiplicative convolution:

The fly ash composition having a minimum value of functions (Eqs. 16 – 18 ) is considered to be the best.

Wald criterion (minimum maximum):

Laplace criterion (minimum minimum):

Since obtaining the thermal and physical–mechanical properties of geopolymers by changing their formulations does not have a constant time reference, we will use the steps that characterize the successive approximation of the approach states to the achievement of the intended goal as the time. In this case, time is replaced by the step number with a hierarchy of discretization intervals as an argument. This is an undoubted novelty and innovation in solving the problems of the process of constructing an intelligent system of optimality criteria.

The points of innovation in the presented methodology are as follows:

Replacement of expert evaluation in the selection of multidirectional geopolymer strength orientations by mathematical justification;

construction of a conceptual model of the selective choice of geopolymer formulation using Markov chains and multicriteria optimization;

rank-based approach to optimization criteria;

replacement of time references by discretization intervals;

scalability and adaptation to loadings through scaling;

scalarization of vector estimates.

Conditional probabilities of optimality criteria are presented in Table 3 .

The construction of Table 3 begins with filling in its first row based on expert judgments and a priori knowledge about the subject area. The formalization of the presented knowledge in the form of Table 3 parameters is implemented using logical inference and evolution of iteration steps.

Results and discussion

When compiling the matrix of transition probabilities, the values of parameters of the conditional probability of current and subsequent states of strength properties of geopolymers when changing the composition and technology of their manufacture are determined from expert assessments by studying the basic phenomenological assumptions reflected in the mechanisms of structure change through relative magnitudes.

Compressive strength, which determines the maximum weight a building material can bear, is manifested in changes in properties such as deformability under increasing pressure, elasticity level depending on the number of pores in the mortar, spreading or creep, shrinkage, swelling, frost resistance, and resistance to chemical influences.

The bending strength depends on the irregularity of shrinkage, modes, and types of curing, and conditions of processes in air or water.

Impact toughness is determined by the work at impact, which is manifested by the initial height of the pendulum before impact and the height of the pendulum after impact. This characteristic is related to compressive and bending strengths through the mechanism of structure formation. However, the quantitative parameters of such a relationship require certain conditions to be met and are therefore expressed in our work through probabilistic parameters.

A separate parameter affecting the complex strength characteristics is density, which determines the structure of the geopolymer mixture. The interaction between the density and strength characteristics of geopolymer concrete is weakly structured. It is pro.

Thermal conductivity as a thermophysical characteristic of geopolymers, in addition to its main purpose, is associated with correlations with the linear stretching coefficient and direction of stretching, linear shrinkage, impact toughness, and thermal resistance. Functional relationships between these events have not been established due to a lack of information or the complexity of these relationships. The structure of geopolymers has gas-filled pores that open at high temperatures.

The presented aspects of the strength and thermophysical properties of geopolymers and their interrelationships through the mechanisms of structure formation were taken as a basis for the construction of the transition probability matrix.

Difficulties arising in the ranking of multicriteria optimization criteria show that experience and intuition are not always the keys to a successful solution.

A useful tool for these purposes is simulation modeling, which allows for the purposeful generation of decision-making options, meaningful selection of structures, and programming of points of interest.

The priority of the arrangement of conditional probabilities of strength properties was determined based on experimental assessments of the role of this parameter in the mechanism of geopolymer structure formation, taking into account that the sum of conditional probabilities in the row of the matrix is equal to one. The columns of the conditional probability matrix, characterize the number of iterations and transitions of the system during its evolutionary transformations and should not be summed.

In this case, it is envisaged to set the weighting coefficients in the form of the probability distribution for all admissible values of Markov chains. This approach allows us to take into account the a priori distribution overall output parameters and to calculate the posterior distribution by the generated assumptions.

Each state of the parameters characterizing the information situation of determining the thermophysical and physical–mechanical properties of geopolymers at a given formulation of their production is assigned a certain probability recorded in the form of a line of the matrix of states. The matrix of intensities or transitions of the system describes the wandering of the system through its states. In the process of analyzing the state matrix, all possible states of the parameters are renumbered with their probabilities, i.e., we deal with a set of probability values between iterations. These iterations are performed for different geopolymer strength parameters.

The initial state vector in Table 3 can be written in the form:

The transition probability matrix has the following form:

Multiplying the initial state vector P(0) by the transition probability matrix T, we obtain the probability distribution at the first decision stage P(1). According to the method of calculating Markov chains, this probability will be equal to:

Multiplying the state vector P(1) by the transition probability matrix T, we obtain the probability distribution for the next stage of decision-making P(2). The probability P(2) that, being in state S 1 of the information system, the decision will move to state S o , characterized by parameter ν 2 , is equal to:

Multiplying the state vector P(2), characterized by the parameter ν 2 , by the transition probability matrix T, we obtain the probability distribution of the next decision step P(3).

The transition probability of the system from state S3 to state S4 is determined by multiplying P(3) by the transition probability matrix.

It follows from the theory of Markov chains that the shorter the cycle length, the more accurate analyses can be performed. As seen, starting from the third step, the probabilities came to a stationary state in which the probability values correspond to the weight coefficients of the parameters for optimizing the strength properties:

Compressive strength 0.313

Bending strength 0.234

Impact strength 0.162

Density 0.147

Thermal conductivity 0.144

The analysis of step-by-step calculations of conditional probabilities shows that the ranking should start with the compressive strength characteristics, the next strength criterion will be bending resistance, and then impact toughness, density, and thermal conductivity. The best values of the analyzed strength parameters from the point of view of the problem to be solved should be selected as reference points—these can be maximum, minimum, or intermediate values from the experimental sample.

In this case, the method of selection by ordering the objects according to the model is used. In this case, a transition from vector to scalar estimations of objects is necessary. The functions used in solving multicriteria problems play the role of convolution of the vector argument.

To perform scalar optimization, additional knowledge about the properties of generalizing functions, scales of features, and their weight coefficients is needed. Since such knowledge is expert knowledge, the ordering of objects in n-dimensional space cannot be unambiguous. Therefore, it is important to study the influence of the properties of generalization functions and weighting coefficients on the optimization results. The physical and mechanical characteristics of the samples are presented in Table 4 .

Relative deviations calculated by the formula ( 15 ) δy ij physical and mechanical characteristics of geopolymers from the optimal value, as well as the values of convolutions (Eqs. 16 – 18 ) and criteria (Eqs. 19 – 21 ), are presented in Table 4 . The calculations were based on the relative change of measured values from their optimal values for the number of samples under study. The maximum and minimum deviation values were calculated for each sample and additive, multiplicative and additional multiplicative convolutions were determined for each sample.

The calculations were performed under the assumption that all criteria have different importance defined above with the help of Markov chains.

For the conclusion regarding the optimal geopolymer composition, it is necessary to take into account the coincidences of different generalization functions and the degree of adequacy of each generalization function to the problem being solved. The analysis of the results presented in Table 5 shows that additive convolution, additional multiplicative convolution, and the Laplace criterion unambiguously point to sample No.6, which corresponds to group FA2 at a fly ash content of 50 g, and the Wald criterion gives close to this result.

Thus, most of the criterion methods used in this work give practically the same results and allow us to conclude: that the best is the geopolymer composition from the FA2 group with fly ash content of 0.5–0.75 max.

The formalization of the main measures to determine the optimal composition of geopolymer matrices based on Markov chains and multicriteria analysis is presented in Fig.  3 .

Conceptual model for selecting geopolymer formulations.

The novelty of the presented conceptual model is the computer support of the geopolymer formulation selection process. The peculiarity of the presented model is that it considers multidirectional criteria in the process of structure formation with a constant share of uncertainty and risk present in this process.

The main stages of determining the optimal components of the geopolymer matrix for noise-protective panels according to the presented conceptual model work with quantitative information, mathematical calculations, storage and exchange of information, and interpretation of results. The sequence of models underlying the methodology includes Markov chains for determining the ranking of criteria, multicriteria optimization models, algorithms, and techniques of their hybrid implementation.

The modeling of changes in the strength properties of geopolymers as parameters of target functions has shown the advantage of evaluating the digitalization of technologies for their production in the analysis of geopolymer properties, where the qualitative side of loosely structured problems is solved using Markov chains, whereas, for quantitative conclusions about the optimal composition of geopolymers, criterion methods are used.

Multicriteria optimization involves the simultaneous optimization of multiple conflicting target functions within a defined domain. When analyzing the impact of ingredient composition changes on the physical properties of geopolymers, the ability to graph these changes becomes increasingly challenging as the number of properties under consideration grows. While graphical representation works for two properties, it evolves into a volumetric representation for three properties. However, beyond this point, with five properties involved, such as density, compression resistance, shear resistance, impact viscosity, and thermal conductivity, visual representation loses its effectiveness. This complexity makes it impossible to identify optimal geopolymer formulations solely through trend analysis.

The multicriteria optimization problem revolves around finding a vector of target variables that adheres to specified constraints, primarily driven by experimental data. In this context, optimization seeks a solution in which the target function values align with the task requirements. It is essential to note that discussing the need for additional experimental studies to validate the proposed model is irrelevant here. This is because the strength and other geopolymer properties obtained in this model do not represent fixed values but rather a representation of the feature space defined by the criteria used. Therefore, the focus lies on ranking these criteria, with the first criterion holding the highest priority in this study.

The integration of modeling, prediction, and optimization in geopolymer formulation replaces expert judgment with mathematical reasoning when selecting diverse geopolymer strength parameters. The presented conceptual model for selectively determining geopolymer formulations through experimental data and their processing via multicriteria optimization methods serves as a methodological tool to enhance the accuracy of geopolymer matrix composition estimations.

Conclusions

The choice of the optimal formulation of geopolymers is explained by the peculiarities of the methodology used, based on the processing of the available experimental material with discrete changes in properties, the values of which correspond to the data presented in the form of characteristics of the samples under study. When issuing conclusions on the optimization of properties of the used experimental sample, the result is presented in the form of a sample number with properties known in advance.

The use of the multicriteria approach in the presence of several optimality criteria allows us to make adequate decisions on the composition of the geopolymer mixture, which simultaneously provides maximization of the technological and mechanical properties of fly ash used as additives in the composition of geopolymer composites. Increasing the efficiency of such solutions is achieved through the use of hidden opportunities associated with the adaptation of preference selection of factors determining the thermodynamic and strength properties of the mixture and the synthesis of procedures for their selection in the analytical hierarchy of preferences.

Structural compositions and their manifestations can be characterized by independent thermal and physical–mechanical properties, which cover the full range of geopolymer strength manifestations. Markov chains in the system of multicriteria optimization represent a synthetic apparatus accumulating heterogeneous factors of exogenous and endogenous nature. Each state of parameters characterizing the information situation of physical and mechanical property determination at a given formulation of their obtaining is assigned a certain probability of transition matrix. The rows of this matrix contain the states in which the system is currently located, while the columns contain the states to which the Markov chain can transition. This allows us to observe how the Markov chain converges to a stationary distribution and to calculate the weighting coefficients of multicriteria optimization.

Since the task of the research was to select from the whole variety of analyzed experimental data those that correspond to differently directed reference points, maximum values of compressive strength, bending strength, and impact toughness with minimum density and thermal conductivity, which are the means of achieving the goal with the help of the proposed innovative methodology of processing the results, its experimental confirmation is the identification of the available information on the composition and manufacturing technology of geopolymers. Combining subjective and objective elements of selection, and calculations based on the results of experiments, the proposed method of information processing allows for increasing the accuracy of determining the optimum composition of geopolymers that maximize their strength properties.

scalarization of vector estimates

Multicriteria optimization results for fly-ash as an additive on metakaolin-based geopolymer composites show that the optimal composition of the geopolymer matrix within the selected variation range includes 100 g metakaolin, 90 g potassium activator, 8 g silica fume, 2 g basalt fibers and 50 g fly ash by ratio weight. This ratio gives the best mechanical, thermal, and technological properties.

Data availability

All data generated and analyzed during the study are available from the corresponding author upon reasonable request.

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Acknowledgements

This investigation was supported by the project “Development of geopolymer composites as a material for protection of hazardous wrecks and other critical underwater structures against corrosion”, project number TH80020007. The support was obtained through the Financial Support Technology Agency of the Czech Republic (TACR) within the Epsilon Program in the Call 2021 M-ERA.Net3..

This research was funded by the Faculty of Mechanical Engineering at the University of Kalisz, under grant number PIN: 618-188-02-48.

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Kherson State Maritime Academy, Ushakov Ave., Kherson, 73000, Ukraine

Oleksandr Sharko

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Dmitry Stepanchikov

Department of Material Science, Faculty of Mechanical Engineering, Technical University of Liberec, Liberec, Czech Republic

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Van Su Le: Methodology, Investigation, Writing the draft manuscript, Editing Artem Sharko: Investigation, Writing the draft manuscript Oleksandr Sharko: Conceptualization, Investigation, Writing the draft manuscript Dmitry Stepanchikov: Formal Analysis Katarzyna Ewa Buczkowska: Methodology Petr Louda: Conceptualization. All authors have read and agreed to the published version of the manuscript.

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Le, V.S., Sharko, A., Sharko, O. et al. Multicriteria optimization of the composition, thermodynamic and strength properties of fly-ash as an additive in metakaolin-based geopolymer composites. Sci Rep 14 , 10434 (2024). https://doi.org/10.1038/s41598-024-61123-1

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Experimental Research Design

• First Online: 10 November 2021

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• Stefan Hunziker 3 &
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This chapter addresses the peculiarities, characteristics, and major fallacies of experimental research designs. Experiments have a long and important history in the social, natural, and medicinal sciences. Unfortunately, in business and management this looks differently. This is astounding, as experiments are suitable for analyzing cause-and-effect relationships. A true experiment is a brilliant method for finding out if one element really causes other elements. Also, researchers find relevant information on how to write an experimental research design paper and learn about typical methodologies used for this research design. The chapter closes with referring to overlapping and adjacent research designs.

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Hunziker, S., Blankenagel, M. (2021). Experimental Research Design. In: Research Design in Business and Management. Springer Gabler, Wiesbaden. https://doi.org/10.1007/978-3-658-34357-6_12

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