Estimating tread width values for stair design appropriated to people’s comfort and safety needs with adaptive network-based fuzzy inference system

Abstract

In this study, it is aimed to develop an adaptive network-based fuzzy inference system (ANFIS) model that can estimate tread width values based on the physical characteristics of people and suitable for comfort and safety needs. The input values were obtained by measuring the height, step, and shoe sole lengths of the sample group of 200 people. For the tread width value to be used as output value, a prototype stair model in which different step sizes can be experienced was used. The tread width value obtained by using the test data in the developed ANFIS model was compared with the tread width value obtained from the experimental study. It has been concluded that the ANFIS model developed as a result of the comparison can be used as an efficient tool in estimating the value of stair tread width, which can meet people’s physical comfort needs.

Keywords

Stair design tread width adaptive network-based fuzzy inference system anthropometry decision making

Introduction

Different dimensional requirements are needed in the components of the stairs so that the stairs can be used safely and comfortably. In order to meet these dimensional requirements, certain formulas or standards are sought in many studies from the past to the present.^1,2,3 Formulas and standards aimed at increasing the quality of life of people cannot provide adequate safety and comfort conditions suitable for everyone. For example, when a work equipment is designed for 90% of the male population of the USA, 90% to the German; 80% to the French; 65% to Italian; 45% to Japan; 25% to Thai, it is seen that 10% is suitable for Vietnamese.⁴ In this direction, it is very important to determine the size of the steps suitable for each society’s own physical dimensions for the safe and comfortable use of the stairs. As a matter of fact, there are important deficiencies in terms of the belonging of the step dimensions used in Turkey and handled through various standards to the Turkish society. In the development of standards such as TS 12,576⁵ and TS 9111,⁶ which have an important place in terms of step dimensions, the use of stair standards belonging to societies such as Germany and America, which have significant anthropometric differences from Turkish society, and the similar dimensional values with these standards is a problem that should be addressed in terms of ergonomic design approach. Therefore, it is necessary to determine not a single ideal step dimension for all societies, but ideal step dimensions for each society that are specific, depending on the physical characteristics of people. Based on this need, in this study, it is aimed to create a step form suitable for the anthropometric dimensions of Turkish society. This study, which makes a difference to the stair design approaches with the use of artificial intelligence method, is aimed to be an inspiring study for different societies based on the step form-anthropometric relationship of Turkish society.

Background/Literature review

Stairs are defined as one of the building elements that provide the connection between planes with different heights and have their own design geometry and rules.⁷ Stairs, which have been the subject of many researches from the past to the present, consist of steps that are brought together in an orderly manner. According to Agyefi-Mensah et al.,⁸ steps, which are the basic functional unit of stair design and affect walking efficiency, are examined over two basic concepts: riser height and tread width (Figure 1).

Figure 1.

The structure of the stair form.

The successful realization of the need for stairs to reach high has been associated with ideal comfort and safety conditions in most studies.^9,10 According to Pauls,¹¹ the concepts of stair safety and comfort studied under three main headings have been discussed in various studies: stair form,^12,13 stair visibility,^14,15 and railing.^16,17 Johnson and Pauls, who also dealt with the energy spent during the ascend and descend stairs in addition to the concepts of comfort and safety, stated that these concepts have a decisive role in the preference of one stair over the other.¹² Unlike this study, Kim and Steinfeld stated that the interaction between the concepts of comfort, safety and satisfaction has an effect on stair use.¹⁸

As a matter of fact, the need for a detailed consideration of the human factor, which has an important place for the concept of satisfaction, arises. In this context, physical, sensory and cognitive characteristics of people who will be an obstacle to the use of stairs should be examined and solution-oriented designs should be made against these restrictions.¹⁰ The stair form, which is critical for safety and comfort adequacy, should consist of shapes and sizes that will facilitate walking.^12,13 In addition, it is important for the safety and comfort of the stairs that all the elements that make up the staircase (step, railing, landing, and head height limit) are clearly visible and perceptible.^14,15

The stairs are expected to meet the vertical circulation need with the least energy, in the shortest time and in the most physical comfortable way.¹² Despite the stated needs, stairs are sometimes tried to fit into a specific area based on design reasons and sometimes economic concerns. These stairs, where comfort and safety conditions are insufficient, cause problems that result in human, economic and social losses, such as falling, slipping, stumbling, missteps, and moments of temporary imbalance.^{13, 18, 19, 20, 21, 22, 23} According to Berger et al.,²⁴ accidents that are accepted as a potential risk inherent in stairs can result in simple injuries as well as loss of life. A survey conducted in the 1970s reported that 3,800 people were killed and more than 500,000 seriously injured in a year in the United States due to falling from a stair.¹⁴ Johnson²⁵ stated that there are deficiencies in the recording of these data and therefore the possibility of an increase in the number of cases. In a similar study, Topraklı²⁶ stated that there is a lack of reports of deaths and injuries caused by falls caused by stair accidents in Turkey. Although there is a lack of data on stair accidents, which are handled through the examples of America and Turkey, there is a need to review the stair design conditions in order to prevent possible accidents. According to Archea et al.¹⁴ and Templer,⁹ insufficiencies in comfort and safety conditions, which cause stairs to be seen as a source of obstacle, also cause higher energy use of stairs and related fatigue. Pauls²⁷ emphasized the importance of the size, design and use of stairs, which are an important factor in stair accidents. Therefore, in order to reduce these accidents, there is a need for a stair design that can meet the comfort and safety needs of people.

In the literature study, experimental studies to increase the comfort and safety features of the stairs come to the fore.^9,28,29,30 In literature, which was intended to determine optimal step sizes, Irvine et al. addressed people’s preferences for riser height and tread width.²⁹ According to the study, step sizes should be designed in accordance with the physical characteristics of people. Differently, in this study, which can be considered on the design of stairs related to the physical structure of the human body, Templer emphasized the importance of stair design based on various body dimensions and gait geometries of users.⁹ Agyefi-Mensah et al. states that the optimum stair dimensions can be supported by experimental study findings.⁸ At the same time, Sarı,⁷ Arslan and Erkan^,30 Sloan,³¹ and Pauls³² believe that experimental research on the physical properties of the human body will provide new data for the improvement of stair design.

According to Kaya and Özok,³³ the concept of design suitable for the physical characteristics of people, which is the focal point of the study, constitutes the first condition of the functionality of the living spaces, tools, and equipment used by people. According to Templer,³⁴ although most researchers consider stair design depending on the principles of function, aesthetics and durability of Vitruvius, the inadequacy of the design based on human body measurements associated with functionality stands out in these studies.

Stairs, which have a widespread use area, have been examined over various standards, different size values and various formulas in line with the changing human needs from the past to the present. Dimension values based on experiments, observations, and various calculations are given in Table 1.

Table 1.

Recommended stair tread width and riser height values.

Authors	Tread width (cm)	Riser height (cm)
Hodgson³⁵	27, 94	17, 78
Fitch et al.¹	27, 94–35, 56 cm	10,16–17, 78 cm
Vitruvius^2,3	46 cm–61 cm	23 cm–25, 5 cm
Sir Henry Wotton²	30, 5 cm–46 cm	At least 15 cm
Irvine et al²⁹	27, 9 cm or 30, 0 cm	18, 3 cm
Templer⁹	27, 94–35, 56 cm	10, 16–17, 78 cm

Chueca stated that different from the step dimensions given in Table 1, in cases where the tread width size is less than 24.99 cm, sufficient support cannot be provided for the foot, and in cases where the stair is more than 32 cm, the heels of the person using the stair can be attached to the edges of the steps.³⁶ Similarly, Allen¹⁶ and Templer²⁸ concluded that riser values higher than 18 cm may cause fatigue and values smaller than 10.16 cm may cause stumbling.

Unlike the studies in which dimensional value ranges came to the fore, François Blondel established a mathematical relationship between riser height, tread width, and step length, and formed the basis of the formulas that continue to be used today.^1,3 According to the results of Blondel’s personal observations:

2 R + T = 60, 96 cm

(1)

R: Riser Height, T: Tread with

This formula, defined as Blondel’s traditional step formula, was developed as a result of experimental studies conducted by Galper–Baldon Associates with a step length value of 66 cm, which forms one side of the equation.² In a similar study, Chueca³⁶ accepts the step length value as the range of 60.98–64.99 cm.

Although standards including ideal step sizes and formulas are claimed by different architects and organizations in today’s architectural practice, according to Pallasmaa,³⁷ these standards provide only an average physical comfort. According to Fitch et al.,¹ they should not be expressed by linear equations, since they have a restrictive and narrow adaptation range. According to Steinfeld and Maisel, stair design applications that should be as safe and usable as possible for healthy people of all ages and abilities fall behind the existing design knowledge.¹⁰ This situation raises the need for improvement by addressing step size suggestions and step formulas based on different factors, which are obtained through limited data and factors, which are insufficient in implementation and whose specificity to societies can be discussed. These deficiencies cause people to prefer vertical circulation tools such as escalators and elevators instead of using stairs. This situation highlights the lack of step size suggestions and step formulas, which have been dealt with limited data and factors in many studies in the past, were insufficient in practice and whose originality could be discussed for societies. Moreover, stair designs need to be improved by considering different factors and methods.³⁰

The step form suitable for comfort and safety conditions should be designed depending on various criteria, including factors related to the stair user and the environment. According to Kim and Steinfeld, physical characteristics of people and shoe features are among the factors belonging to the stair user.¹⁸ Different from current study, Arslan and Erkan stated that physical characteristics of people such as height, leg, knee, calf, thigh, foot /shoe length are factors that can be effective at the level of stair comfort.³⁰ In this study, which aims to determine the ideal step form, the height value is considered as a determining factor in stair design. According to Duyar³⁸ and Arslan and Erkan³⁰ although values such as leg, knee, calf and thigh length can be evaluated in a parallel effect to the height value, it is also important to determine their effects on the stair design as a separate parameter. The step length factor, which is considered among the factors belonging to the stair user, is related to the tread width and the riser height, as can be understood from the traditional step formula. Shoe characteristics, another factor that can be considered in this context, has an important effect especially on stair accidents, although it does not receive sufficient attention in the literature.³⁹ This effect is mostly seen in the problems of getting caught on the risers due to the high heel size and not finding sufficient footing area on the step surface due to the long shoe size.

Within the scope of the study, it is aimed to develop a model that can estimate the tread width values in accordance with the comfort and safety needs of people by using three different parameters such as height, step, and shoe sole lengths that affect the use of stairs. For this purpose, it is aimed to create a study based on different parameter relationships with an experimental database, unlike the step sizes obtained based on standards and formulas with restrictive and narrow adaptation range in the literature.

Case study: Data and methodology

Adaptive neuro fuzzy inference system

Artificial intelligence, which has recently found a wide field of research, gives a computer or machine abilities such as human thinking, inference, learning, and reasoning in order to model human intelligence. Adaptive Neuro Fuzzy Inference System (ANFIS) is a hybrid artificial intelligence method that combines the educational learning capability of artificial neural networks with the ease of providing expert knowledge of fuzzy logic inference systems (FIS) and flexible computing. Fuzzy logic has two important advantages over other traditional methods in the application of data analysis⁴⁰:

1. It reduces the difficulties in analyzing and modeling complex data.

2. Suitable for incorporating qualitative aspects of human experience into mapping rules that provide a way of capturing information.

ANFIS uses fuzzy logic’s ability to make decisions close to human logic by verbally expressing imprecise inputs and outputs together with the learning and information processing ability of artificial neural networks. Thus, by using the advantages of the two methods together, even in nonlinear problems, the system can produce results close to human logic by using the ability to learn through education.

The data-driven procedures used for the synthesis of ANFIS networks, which represent a useful neural network approach for solving function approximation problems, are based on the clustering of a training set of numerical examples of the unknown function to be approximated. ANFIS’s rule base includes fuzzy if-then rules of the Sugeno type, and ANFIS can create all possible rules within its own architecture. For a two-order structure with two input and one output variables, the rules are:

1. Rule 1: If x is A1 and y is B1 then f1 = p1x+q1y+r1

2. Rule 2: If x is A2 and y is B2 then f2 = p2x+q2y+r2

Where x and y inputs, A_i and B_i fuzzy sets, f_i fuzzy rules in accordance with the output p, q, and r express the parameters that occur in the training process. The learning algorithm of ANFIS is a hybrid algorithm because it uses the least squares method and the back propagation learning algorithm together. ANFIS network architecture consists of five layers, and nodes with different shapes in layers contain functions with different functions. Circle and square nodes are used in an adaptive network to indicate different adaptive abilities. Nodes shown as a square (adaptive node) have parameters, while nodes shown as a circle (fixed node) have no parameters.⁴¹

The ANFIS structure consists of five layers and the node functions of each layer in the ANFIS structure are as follows:

1. Layer (Fuzzyfing Layer): In this layer, the output of each node consists of the input values and membership degrees depending on the membership function of the fuzzy sets. For the output of nodes (O_1i) in this layer, it is calculated by equation (2) and equation (3).

O_{1 i} = μ A_{i} (x) i = 1,2

(2)

O_{1 i} = μ B_{i - 2} (x) i = 3,4

(3)

2. Layer (Implication Layer): In this layer, each node represents the rules created in the Sugeno fuzzy logic inference system. There are as many rules as the number of nodes. The output of the node shows the weight degrees of the rules, while the input values of the node show the membership function values of the variables in the premise of the rules. Cell outputs (O_2i) give the weight degrees (w_i) of the rules. The output of each rule node μ_i is the multiplication of the membership degrees from layer 1 (Equation 4).

O_{2 i} = w_{i} = μ A_{i} (x) . μ B_{i} (y) (i = 1, n)

(4)

3. Layer (Normalizing Layer): The inputs of the nodes contained in this layer show the weight degrees of the rules, while the outputs show the normalized weight degrees. The main purpose of this layer is to normalize the rule weights. The firing level of its normalized states is known as w_i and the calculation of w_i is shown in equation (5).

O_{3 i} = w_{i} = \frac{w_{i}}{w_{1} + w_{2} + \dots . + w_{n}} (i = 1, n)

(5)

4. Layer (Defuzzyfing Layer): The inputs of the nodes in this layer are associated with the node output results of the 3rd layer. The weighted result of the expressions found after the part of the rules in the node is calculated in this layer. Calculation of the defuzzification result values of each rule given in each node in the defuzzification layer is shown in equation (6).

O_{4 i} = w i \int i = w i . (p_{i} A + q_{i} B + r_{i}) (i = 1, n)

(6)

5. Layer (Combining Layer): The output of this layer, which is the last layer, consists of a single node. This layer is the output layer that has a node. The layer result is calculated with the sum of the output values of the nodes transmitted from the 4th layer to this layer. The calculation formula of the output value 05i is shown in equation (7).

O_{5 i} = \sum w i \int i = \frac{\sum w_{i .} \int i}{\sum w_{i}} (i = 1, n)

(7)

Development of ANFIS model for stair tread width

Initially, in order to develop the model, the height, step and shoe sole length of the people who will try the prototype stair were measured. People who tried prototype stair reported tread widths that they walked comfortably. The data obtained were divided into two groups as training and test data according to the Pareto principle. After the preparation of the data, fuzzy inference system was started to be created by using the MATLAB ANFIS editor. Different methods are used for fuzzy inference. But ANFIS only runs the Sugeno method. Sugeno method is a form of modification of Mamdani method. In this method, the operations to be applied to the input data are the same as the Mamdani method. The difference is that in the Sugeno method, the output variable is not a fuzzy set like in the Mamdani method, but a linear function or a constant value. Because ANFIS only operates Sugeno type models, the Sugeno method was used for the developed ANFIS model. Then, the parameters of the fuzzy inference system and the type and number of membership functions belonging to these parameters were determined. A fuzzy inference system was continued to be created by training data and finally created model rules. In line with the established rules, stair tread width estimation results were obtained. Finally, the accuracy of the model was tested using a data set that was not previously trained in the model (Figure 2).

Figure 2.

The stages of the model to be developed for stair tread width estimation.

Data used in the model

The study sample consisted of 240 (120 male–120 female) healthy individuals with an age range of 18–40 (average age = 21.67 standard deviation = ± 3.87) and had no previous orthopedic disorder.

Within the scope of the study, first, the values of height, step length and shoe sole length of the people constituting the sample were measured. In the measurement study, Lohman et al.⁴² and Pheasant’s⁴³ techniques and the practices and suggestions stated in the study of Güleç et al.⁴⁴ were taken into consideration. In the ongoing process, people who identified the necessary dimensional values were asked to experience the prototype stair model created and choose the tread width value in which they moved comfortably. The stair model was created by examining the tread width values that Templer³ considered within the scope of stair comfort and safety criteria. The study is based on the experience of each of the different tread width values given in Table 2 by keeping the riser height constant 17.8 cm in the prototype stair model created.

Table 2.

Tread width values used in the application phase.

Trial	Tread Widths (cm)
Trial 1	25.4
Trial 2	27.9
Trial 3	30.5
Trial 4	33
Trial 5	35.6
Trial 6	40

Forty data ANFIS model, which has the same input and output values from the data obtained within the scope of the study, was not used in the training and testing phase. 80% (160) of the data belonging to the remaining 200 people were used for training and 20% (40) for testing. Statistical information of the data used in the model is shown in Table 3.

Table 3.

Statistical analysis of data.

	Training Data				Testing Data
	Height	Step length	ShoeSole length	Tread Width	Height	Step length	ShoeSole length	Tread Width
Average (cm)	170.42	62.26	27.62	32	168.03	61.13	27.39	31.69
Standard Deviation	8.97	5.25	2.05	1.42	9.59	4.38	1.91	1.51
The Biggest (cm)	192	83	32	35.6	187	69	31.5	35.6
Smallest (cm)	154	50	23	27.9	154	51	24	27.9
The most	170	60	26–29	33	158	65–61	29	30.5
Hydrangea	170	62	28	33	166.5	61	27.25	30.5
Total (cm)	27,267	9961	4418.5	5120.2	6721	2445	1095.5	1267.5
Number	160	160	160	160	40	40	40	40

Development of the model

Within the scope of the study, the stair tread width was estimated using ANFIS, based on the parameters of the person’s height, step length, and shoe sole length. Accordingly, ANFIS model has been developed using Süleyman Demirel University in MATLAB2019b (SDU-student version) software. The basic structure of the neural fuzzy inference system to be established for stair tread width estimation is shown in Figure 3.

Figure 3.

The basic structure of the adaptive network-based fuzzy inference system model.

After determining the parameters, it is necessary to decide the number and type of membership function for each input. Some model experiments were conducted during the determination of the number and type of membership function. In order to determine the number and type of membership function, training data were trained with 1000 epochs. Root Mean Square Error (RMSE) equation was used to calculate the errors in the developed ANFIS models. Statistical error results regarding the developed model experiments are shown in Table 4 for both training and test data.

Table 4.

Comparison of training and testing data results of adaptive network-based fuzzy inference system models developed.

		Root Mean Square Error (RMSE)
		Membership function (MF) type
ANFIS Models		Trimf	Trapmf	Gbellmf	Gaussmf	Gauss2mf	Pimf	Dsigmf	Psigmf
3 3 3	Training Data	0.937	0.968	0.727	0.868	0.891	0.932	0.944	0.864
	Testing Data	0.765	0.683	0.590	0.610	0.757	0.672	0.692	0.673
	Total	1.702	1.651	1.317	1.478	1.648	1.604	1.636	1.536
4 4 4	Training Data	0.892	0.982	0.470	0.666	0.838	0.937	0.567	0.548
	Testing Data	0.750	0.855	0.745	0.651	0.749	0.839	1.014	1.126
	Total	1.643	1.838	1.214	1.317	1.587	1.776	1.581	1.674
5 5 5	Training Data	0.516	0.598	0.130	0.315	0.347	0.403	0.202	0.198
	Testing Data	0.977	0.752	0.707	0.861	4.717	0.657	0.459	0.490
	Total	1.492	1.349	0.837	1.176	5.063	1.060	0.661	0.688
6 6 6	Training Data	0.360	0.504	0.060	0.367	0.460	0.515	0.205	0.091
	Testing Data	0.946	1.752	1.128	1.282	0.589	2.196	0.984	1.132
	Total	1.306	2.255	1.188	1.649	1.049	2.711	1.190	1.223
7 7 7	Training Data	0.136	0.412	0.029	0.074	0.091	0.390	0.007	0.007
	Testing Data	1.058	12.232	1.691	3.713	5.973	12.802	4.927	4.932
	Total	1.194	12.643	1.720	3.787	6.064	13.192	4.934	4.939

As shown in Table 4, the total minimum error rate in all data was observed as a result of 3-input 5-subset ANFIS calculations. Therefore, a network structure with five membership functions has been determined for each input (Figure 4).

Figure 4.

adaptive network-based fuzzy inference system Model Structure.

As shown in Table 4, the membership function type that gives the lowest error value has been determined as dsigmf (Sigmodial Membership Function). The subsets and membership functions defined in the model developed with the least error rate after the experiments are shown in Figure 5.

Figure 5.

The subsets and membership functions defined in the model.

The definition or value of the parameters belonging to the model developed after the experiments are shown in Table 5.

Table 5.

Model parameters.

Model parameters	Description/Value
Fuzzy Inference system	ANFIS (Sugeno tipi)
Number of layers	5
Epochs	1000
Membership function (MF) type	Dsigmf
Number of membership functions	5 5 5
Output function	Constant
Number of nodes	286
Number of linear parameters	125
Number of nonlinear parameters	60
Total number of parameters	185
Number of training data pairs	160
The number of fuzzy rules	125
Optimization Algorithm	hybrid
And method	prod
Or method	probor
Defuzzification	wtaver
Range of influence	0.5
Squash factor	1.25
Accept ratio	0.5
Reject ratio	0.15

Training the model

Supervised learning model is used for ANFIS training. The learning process was carried out with the help of a hybrid network, which is a combination of the least squares method and the back propagation method. First of all, training of ANFIS is carried out with the training data set to solve the problem. While learning the relationships between variables in the ANFIS model, training errors are expected to decrease depending on the number of iterations and to be fixed after a certain iteration. The learning process continues until the estimation error is minimized. Thus, the decreasing graphic of the training errors in the training of the model is an indication that the network is being trained. The difference between the output obtained during the training and the actual output gives the error (Figure 6).

Figure 6.

Training Error Graph.

The number of training epochs is 1000 and there is an error of 0.202 in the output of the neural network. In the training data set, the ratio of the actual values and the estimated values overlap was compared. While the data shown with “*” show the values estimated by the ANFIS model using the training inputs, the data shown with the “o” sign are the actual output values (Figure 7).

Figure 7.

Results of training of adaptive network-based fuzzy inference system.

After the training stage, the efficiency of the developed model was measured with the test data not used in the training of the model. The average error in testing the model is 0.459. In the test data set, the ratio of the actual values and the estimated values coincided was compared. While the data shown with “*” show the values estimated by the ANFIS model using test inputs, the data shown with the “.” mark are the actual output values (Figure 8).

Figure 8.

Results of testing of adaptive network-based fuzzy inference system.

The ANFIS model determines the variable intervals and fuzzy rules of the model whose training has been completed. The rule editor automatically creates the rules based on the input and output variables defined in the fuzzy inference system. In this model, ANFIS has created 125 (5 * 5 * 5) rules for three inputs and five membership functions for each input.

Limitations

The research sample was limited to 240 people in the 18–40 age range. Dimensional differences due to the shoe models of the participants were ignored, only the sole length of the shoes was focused on. The prototype stair model used in the experimental stage of this study, which is limited by the stair climbing movement, allows six different tread width values to be experienced.

Results

As a result of the ANFIS model with five sub-clusters with three inputs, the scatter diagram of the estimated values for both the training data and the test data and the values obtained from the data obtained from these graphs and the estimated stair tread width values, 45° a line is shown in Figure 9.

Figure 9.

Comparison of the adaptive network-based fuzzy inference system and target data for a training set and a testing set.

Discussion

While there are stair standards with distinct dimensional differences for spaces with different usage characteristics such as public spaces or residences in any country, it is a striking negative situation that the standards used in different countries contain similar dimensional values. Arslan (2019)’s⁴⁵ comparison of the Planned Areas Zoning Bylaws,⁴⁶ Istanbul Municipality Zoning Bylaws⁴⁷ and Ankara Municipality Zoning Bylaws⁴⁸ standards used in Turkey with the Americans with Disabilities Act (ADA),⁴⁹ Deutsches Institut für Normung (DIN18065),⁵⁰ British Standards (BS5395-1),⁵¹ and Building Officials Code Administrators (BOCA)⁵² standards of different countries is an example that supports this situation. In the study, ADA⁴⁹ with a max pier height of 18 cm and a step width of min 28 cm and DIN 18,065⁵⁰ with a max pier height of 19 cm and a step width of min 26 cm standards have similar dimensional values with Planned Areas Zoning Bylaws,⁴⁶ which has a maximum pier height of 18 cm and a step width of min 27 cm.

When the sources used in the creation of TS 12,576⁵ and TS 9111⁶ standards, which are used within the scope of stair design in Turkish society, are examined, it is seen that the standards of German and American society, which have different anthropometric structures, were used to develop these standards. At this point, the production of standards containing similar step sizes for Turkish, German and American societies with different anthropometric structures is considered as a negative situation and is claim as another finding emphasizing the importance of the study.

Based on the negative situations mentioned, it is clearly seen that the Turkish stair standards need to be reconsidered based on the anthropometric dimensions specific to Turkish society. In this direction, the tread width values specific to the Turkish society have been produced with the prediction model created. With the obtained tread width values, it is expected to design stairs that people can use comfortably and safely. With these values, it is necessary to improve the tread width values used by the Turkish society in the current situation.

Conclusions

In this study, which aims to create a model that will estimate the tread width values that will meet the physical comfort needs of people in accordance with various dimensional values of the human body, an ANFIS-based model has been developed using height, step and shoe sole lengths. With this developed model, tread width values can be obtained depending on different parameters that can meet the comfort and safety needs of people, unlike the standards and formulas with restrictive and narrow adaptation range in the literature. Tread width values estimated by using the test data not used in the training of the developed ANFIS model and the tread width values selected by the people participating in the experimental study were compared. As a result of the comparison, the coefficient of determination (R²) was found to be 0.9105. This has shown that the ANFIS approach can be used as an efficient tool to estimate the stair tread width that can meet the comfort needs of people.

This study, which has common aims with the studies in the literature in terms of reaching the ideal step sizes and having an experimental base, allows to create stair design criteria suitable for the body dimensions of the people rather than the stair standards with restrictive and narrow adaptation range and various step formulas, unlike the pioneering studies. In this way, new combinations of steps with different sizes required by different body sizes needed in daily life can be resolved quickly.

Better results can be obtained by adding different input parameters to the developed model, which will be obtained as a result of experimental studies, and training this model with more data. In a similar approach, by adding different parameters (such as knee height, weight and shoulder width) a model can be developed for the estimation of the riser height value. Thanks to the developed models, it will be possible to create step forms specific to societies whose body measurement values are known. Thus, stair designs suitable for people’s comfort and safety conditions can be realized. With the step form obtained, it is expected that accidents such as stumbling due to high riser dimensions encountered in daily life and stumbling due to not finding sufficient footing area are expected to decrease.

Footnotes

Acknowledgements

We thank all the subjects who helped us by voluntarily participating our study.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Fadime Diker

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