Historical structure design method through data analysis and soft programming

Abstract The present study is focused on the method of designing historical structures through data analysis and soft programming. The current research aimed to find the design method of the old columns of the structure and compare it with modern design methods. The case study was Goharshad Mosque (1400 AC) located in Iran, Mashhad. A correlation matrix was created to find the relationship between structure parameters by data mining in Python. The results indicate that the modern design method was more reliable than the old method due to the safety factor, but some parameters such as loading calculation in the historical method and the modern method were the same with more than 70% similarity. But the results of the coefficient of determination show that the loading of the R2 results was more than 0.44 and the area of the columns was more than −0.5. The modern and old design has a big engineering gap. Finally, the current study shows the old structure design method and compares it with the new design method.


Introduction
Analyzing old structures is important for engineers to further their understanding in the field of engineering, in addition to helping improve the structure of future generations.Designing monuments are a big question for engineers.Currently, software engineers and developers have been able to solve complex questions by writing codes and programming.(Zucca et al., 2016) analyzed the historical building design against the recent 2009 (L'Aquila), 2012 (Emilia Romagna), and 2016 (Centro Italia).Their results show that the roof of the structure has to change to prevent more displacement.Moreover, their results show that this structure needs improvement against earthquakes (Ademovi ́c et al., 2022).investigated the rebuilding of the cultural-heritage residential masonry building after the 2020 Zagreb.They could strengthen the structure more in three levels and minimize the cracks.
Researchers are trying to increase the durability of the historical structure under earthquakes (Zucca et al., 2020).In this way, understanding the old and heritage design method is an essential issue to maintain the safety of the heritage structure.The design of the historical building is a big question for engineers.Currently, software engineering and developer solve complex questions by writing codes and programming.For example, data mining, Artificial intelligence (AI), and Machine Learning (ML) are the most famous programming methods in engineering, and technology (Zheng et al., 2022).
Data mining, ML, and AI can solve this complex question in less time, saving money (Agrawal, 2022;AlAlaween et al., 2022;Khorasani et al., 2022).Currently, many engineers have used data mining, ML, and Artificial Neural Networks (ANN) to predict the concrete mechanical properties and structure parameters (Akande et al., 2014;Erdal, 2013;Farooq et al., 2021;Khan et al., 2021;Peng et al., 2022;Yang et al., 2022).For example (Shahmansouri et al., 2022)., presented a new method to forecast compressive strength (f c ) of natural zeolitic concrete.In their current study, important variable was the curing period of concrete.More than 56 mixture designs were used.The Root Mean Square Errors (RMSE) was evaluated to find the accuracy of the prediction results.Their f c prediction results show that the RMSE was 1.6.The prediction results show high accuracy.
Some prediction methods such as Artificial Neural Networks (ANN) is established to find the f c of concrete (Akande et al., 2014;Akter et al., 2018;Fl ̈ory & Pottmann, 2010).For example (Chopra et al., 2016)., predicted the f c of concrete through ANNs.The ANN method was based on the curing period between 28-days, and 91-days.The Leveberg-Marquardt (LM) training function is applied through ANN to find the f c results.Their results indicated that forecasting f c was accurate.The Coefficient of Determination (R 2 ) result was more than 0.8.Using the curing periods as the main variable, is an advantage however, other parameters such as the qualities have been neglected in the ANN method.The programmer was not able to understand the quality of the mixture of materials, and the programmer have to add a new way to indicate the quality.Another negligence of the programming method was the lack of collecting data, the programming method was not able to collect all data about the concrete.(Topçu & Sarıdemir, 2007) used ANN, and Fuzzy Logic (FL) method to predict f c of concrete.In the current study, the predicted method was based on fly ash as a variable material.Their results shows that R 2 was more than 0.9 (Hematibahar et al., 2022).established the Logistic function to find the accurate compressive strength results.Their method was unrelated to the materials of concrete.(Hasanzadeh et al., 2022).used ML to find the mechanical properties of basalt fiber highperformance concrete (BFHPC).They used a new method to predict the mechanical properties through the relationship between mechanical properties, and different specimens of concrete.Their results showed that the ML technique is possible to predict mechanical properties with high accuracy.According to their results, the f c , tensile strength (f t ), and flexural strength (f f ) are predicted with R 2 more than 0.9.(Abd Elhamed et al., 2022).used machine learning to find the blast-induced structural response.They have improved a nonlinear program with Python to find the results.Their presented model reached high accuracy.
The current study is focused on the design of ancient building columns based on the Goharshad Mosque (1400 AC) located in Iran, Mashhad.The motivation of the current study was to compare modern structure and old structures and find the design model of old buildings.This study can solve the problem of old design structure via Machine Learning and Soft Learning through Python.

Materials and methods
This study analyzes the heritage mosque Goharshad as the case study.First, the design method of the columns has been calculated, and next, the old design method has been compared with the modern design method.The correlation matrix has been calculated to find the relationship between the parameters, and the design methods.Finally, the R 2 has been calculated to understand the differences between old and new designing methods.

Dome structure defection
The dome is one of the important elements of historical Iranian architecture, which takes many geometric shapes in its design.Recently, many researchers have been investigating the dome structure parameter (Hejazi et al., 2021) (Farshad, 1977).found the shape of brick masonry domes without bending anchor and tensile stress and calculated the meridian shape and thickness changes of such a dome and made a comparison between the theoretical dome without tension and the real historical Iranian brick masonry dome.
The dome structure can transfer the dead loading to the columns or walls.Figure 1 shows the Haruniyeh Dome (1200 A.C) located in Iran, Mashhad.This structure uses walls and columns to resist the dead load of the dome.The dead load of the dome is transferred to the ground and foundation through the columns.Figure 1(a) shows the interior of the structure and the columns that transfer the dead loads to the ground.Figure 1 This structure has been built with bricks and the most important part of this structure is the "dome".The special feature of this building is related to the fact that only walls are used in this building and not the columns to support the dome.The wall plays the role of columns in the current structure.
Sometimes the dome is supported by side domes and walls.For example, Figure 2 shows the Great Dome of Mehrabad (1100 A.C) located in Iran, Nishabur that uses six domes to support the main dome.Figure 2(a) shows the outside of the mosque and all six domes.Moreover, Figure 2(b) shows the inside of the dome and the support conditions.The concept of the current mosque is similar to the Haruniyeh Dome, but the current dome is made up of six domes and a middle dome, the engineers first built six domes to support the main dome and finally built the largest dome.
The concept of dome and columns are illustrated in Figure 3.The loading of the dome and mass are transferred through the shell form of the dome to the columns (see Figure 3(a).Figure 3(b) shows that the designer used more columns and walls rather than thick columns (Figure 3(c)).Figure 3 shows the loading conditions of the dome which transfer to the columns and walls.The idea of using walls instead of columns was due to the use of fewer columns and the distribution of the dome load throughout the wall structure.In this way, there is no need to use many columns.

Case study
Goharshad Mosque (1400 A.C) located in Iran, Mashhad has been chosen as the study in the current research (Figure 4) comprising of the dome (Figure 4a) and the Mosque (Figure 4b).The main idea of choosing the mosque was that the mosque was healthy after many years and that it has the ideal parameters for the present study.
The Goharshad Mosque details are illustrated in Figure 4.According to the probability plan, first, the columns have been built with bricks and Sarooj (special old Persian mortar) (Meddah et al., 2020).Second, the walls have been built and connected to the columns, from which the dome was built.

Ancient designing method
The old design method was the relationship between the dimensions of a brick, the load of the upper floors as dead loads, and finding the dimensions of the columns.Before coding the systems, the engineers first estimated the roof or dome estimated the amount of load and finally found the number of columns.They experimentally found the f c of a block and finally calculated the dimensions of the columns without safety factors.However, they used large support at the bottom of the column to connect to the foundations (Figure 6).These supports play the role of safety factors.For example, in Parse, buttresses connect columns to piers (Figure 6).
The mechanical properties and dimensions of the blocks played an important role in the design of an old structure, just like concrete in modern design.Bricks and blocks were important factors in the structure's resistance in a building.Figure 7 shows the bricks of the Goharshad Mosque.According to the ancient design algorithm, these methods were among the events that were obtained through computer programming (Figure 8).

Modern designing method
Following the ancient design, the new modern design is focused on the safety factor (see Eq. ( 1)) (McCormac & Nelson, 2005).
where φ is 0.65 for tied columns, f c is the compressive strength of concrete, A g is the area of the beam, A st is the area of rebar, f y is the tensile strength, and P n is the maximum axial loading.In Eq (1) many variables are affected by the area of the columns.The safety factors and the rebars are the most important parameters which reduce the area of columns.

Algorithm of study
In this research, the columns of Goharshad Mosque were calculated by programming.According to calculations, the designers first calculated the mass of the dome according to the mass of one brick and the accumulation of all bricks.In this part, the bricks of the dome are predicted about the roofs of the dome.Then they divided the mass of the dome into columns to find the area of the columns and finally found the area of the columns according to Raydan domes and dome bricks.In addition, the height of the building and other structural elements are also included in the planning (Figure 9).
Eq (1) is used to find the modern area and design of safety factors.After understanding the application of ancient and modern design, soft programming through Python programming software was applied to find the area of columns in modern and ancient ways.According to the Python software, first, several buildings were designed according to the ancient design, then they were planned according to the modern design and finally the results were analyzed.
Predicting column results through data mining to find the difference between modern and old calculations.The results can help us in the design and reliability of structures and formulas To scrutinize the quality of the model presented in this research, an indicator is taken into account including the coefficient of determination (R 2 ).The R 2 is a measure utilized in analysis to evaluate how well a model predicts future outcomes.It is achieved using Eq. ( 2) (Hasanzadeh et al., 2022): where y, ŷ, and � y are actual, predicted, and mean of the actual value, respectively.

Ancient and modern results
The ancient loading result for each column was 116 kN.This means that each column can resist 116 kN, and the supposed column dimension was 50 × 50 cm as the optimal dimensions of the columns.These results were obtained from soft programming when multiples of the area of the columns are divided by the height and mass of each brick in meters.
According to modern design, the maximum loading was more than 126 kN.The dimensions were 40 × 40 cm.The Goharshad columns' dimension was 50 × 70 cm.Figure 10 shows the correlation matrix of the parameters.It is obvious that the area of the old columns with the diameters of the dome does not meet the design value, but the area of the old columns has been more than 31% effective in the thickness of the dome.The area of the columns of the old design and the modern design was approximately 40% similar Ancient designers were able to measure the mass of the dome and data structure 70% similar to the modern designer.The diameter of the column and the thickness of the dome were 41% and 71% effective in calculating the mass load by the traditional method, respectively.While the effect of modern loading on the diameter of the dome was more than 70% and the thickness was more than 30%.The R 2 illustrated that the loading accuracy between old and new buildings was more than 0.44 and the Area of columns R 2 was more than −0.5.The results of R 2 show the differences between modern, and old structure designs.
More than 12 studies have been selected in this research.According to the results, sometimes modern designers use bigger areas for columns, and sometimes old designers used bigger columns.For example, the first number shows that the old designer used 0.9 m 2 while the modern designer used 0.25 m 2 as the column.However, number 4 shows that modern designers used more than 0.7 m 2 , and old designers used more than 0.12 m 2 for the same columns.The maximum error was more than 0.65 m 2 and the minimum error was less than 0.004 m 2 .According to Figure 12, the most effective parameter of the area of the old columns is related to the loading and thickness of the dome.While the effectiveness of the column area of the new design is related to the loading and the diameter of the dome (Figure 11).
The loading conditions are shown in Figure 12.The old loading is related to the thickness and diameter of the dome, respectively.While modern loading is affected by the diameter and thickness of the dome, respectively.Moreover, the loading parameters are related to different  factors.The old loading was predictional, however, the modern loading was close to experimental results.

Discussion
Many studies have investigated old and historical structures under different loading to understand the behavior of the building.Our study has been focused on the loading and the diameter of the dome and its structural properties.Loading is an important factor in the current study.For example, Charkhal is a historical building of Nepal built 105 years ago which has been studied for seismic reasons.This building was built with external walls and clay bricks.The large size of the room without any walls was a major problem.In this classification, the designer did not understand the loading potential and cannot predict the loading (Tiwari et al., 2020).The same problem has been raised for the ancient designer in our study.Figure 12 shows that the old designers were not able to fully understand the loading.
In another example, Timisoara is a city located in the western part of Romania that has the risk of earthquakes.In this city, there are many old structures.Many of these structures are made of wood (Onescu et al., 2022).analyzed that the old designer did not understand the importance of impact and cyclic loading and we also proved the same problem in the current study.Limit analysis of the designers was another problem that (Latifi et al., 2023).investigated.They have shown the reason for the cracks in the walls such as loading seismic loading, etc.This current study was able to find a way to prove that old designers were not able to predict the direct and perfect loading of a building and they used several ways to calculate the loading.In the current study, one way of loading and predicting old designers has been proved.According to this method, everything is related to the prediction of the mass of the domes, walls, and particles of structure.

Conclusions
The current study presented a new method to understand the historical designing method.In this article, the column design methods of ancient engineering types have been predicted by Python software.The Goharshad Mosque has been the base of the work.The main idea of the current study was to compare the old and modern study through Python software, and next compare the correlation matrix of both the old and new design.
The results show that the old design is related to the prediction of the weight of the bricks and the loading of the structure.According to the results, the loading of the old building was more than the prediction for the modern building.The current analysis is extended to other ancient and modern world works.According to the present study, the design of columns is shown and machine learning helps to understand the old design concept.The results illustrate that: (i) The correlation matrix has shown that the old loading and modern loading calculation have more than 73% similarity.Moreover, the results from the prediction show that the old loading prediction was more than the modern loading prediction.
(ii) There is a big gap between the old design method and the modern design method.Whereas, the old designers predicted the loading of the columns, domes, and structures more than the actual amount.
(iii) The modern loading design is focused on the diameter of the dome, while the old loading has been focused on the thickness of the dome.
(iv) Sometimes the area of the old design was more than the new design and sometimes the area of the modern design was bigger.
(v) The area of the columns area related to the thickness in the old design, and more related to the diameter in the modern design.
(vi) The current study is possible to extend the design of all structures such as the wall, beam, dome, etc. to find the structural behavior according to machine learning and modern design.
(b) illustrates the outside of the structure and dead load, and Figure 1(c) shows the structure of Haruniyeh Dome.
Figure 5(a) shows the whole structure of the mosque, and Figure 5(b) illustrates the plane details plans of the Goharshad Mosque.The Goharshad Mosque has more than eight columns and walls.

Figure
Figure 1.Haruniyeh Dome: a) the inside of the building, b) the outside, c) the structure of Haruniyeh Dome.

Figure
Figure 2. Great Dome of Mehrabad: a) the outside, b) the inside.

Figure 6 .
Figure 6.The support columns to join the foundation in Parse.

Figure 8 .
Figure 8.The algorithm of the ancient design.

Figure 9 .
Figure 9.The algorithm of the current study.

Figure 10 .
Figure 10.Correlation matrix of the current study.

Figure 11 .
Figure 11.Area of columns errors, modern and old designs.

Figure 12 .
Figure 12.Load of columns errors, modern and old designs.