A basic period prediction system for RC hillside structures

Abstract

A system for predicting the fundamental period for reinforced concrete buildings on slopes, consisting of: a data input module configured to retrieve building and soil parameters from datasets, including building height, field width, number of fields, slope angle, and soil conditions; a modal analysis module configured to perform a modal analysis of the input parameters using finite element analysis software and to generate results for different slope angles, soil conditions, and building configurations; a soil-structure interaction (SSI) module that includes a foundation modeling component that applies spring stiffness to column foundations based on Gazetas' formulas and simulates soil conditions categorized as stiff, medium or soft, thus incorporating soil-structure interaction effects; a regression and machine learning prediction module configured for developing predictive models using multiple linear regression, random forest, and XGBoost algorithms; and an output module configured to output the predicted basic period of the building based on the trained prediction models.

Description

FIELD OF THE INVENTION

[0001] The present disclosure relates to a fundamental period prediction system for reinforced concrete buildings on sloped terrain, particularly to a system that performs a simulation model to determine the effects of slope angle variations and soil-structure interaction (SSI) on the fundamental period of buildings in hilly regions. More specifically, the present invention relates to a system that performs fundamental period prediction that explains the seismic behavior of reinforced concrete (RC) buildings on sloped terrain. The present invention focuses on the critical influence of terrain slope and soil-structure interaction (SSI) on the fundamental period. BACKGROUND OF THE INVENTION

[0002] The fundamental period is a critical parameter in earthquake-resistant design because it influences the structure's response to earthquake forces. Current methods for estimating the fundamental period are predominantly based on height or number of stories and are primarily suitable for buildings on level ground. However, these traditional approaches do not adequately account for the complexities introduced by sloping terrain, leading to potentially inaccurate assessments of structures on slopes.

[0003] Reinforced concrete buildings on slopes present unique challenges due to their irregular structural configurations, which often result in uneven distribution of mass and stiffness. This structural irregularity makes buildings on slopes particularly vulnerable to seismic forces, as the uneven configuration affects their dynamic response. Current design codes such as the Egyptian Code, ASCE / SEI 7-16, and Eurocode 8 lack specific guidelines for calculating the fundamental period for buildings on sloping ground, leading to potential inaccuracies. The Indian Standard Code IS 1893:2016 proposes calculating the period based on the elevation from the highest ground point, resulting in overly conservative period estimates for slope structures.

[0004] Furthermore, the role of soil-structure interaction (SSI) is often underrepresented in standard analysis methods, despite SSI effects being critical for understanding the seismic behavior of buildings on challenging terrain. Recent inventions demonstrate that ignoring SSI and the unique factors associated with sloping terrain can lead to suboptimal designs that poorly predict structural behavior during seismic events.

[0005] To address these limitations, the present invention proposes a system for predicting the base period of reinforced concrete buildings on slopes, taking into account factors such as building height, span width, number of spans, slope angle, and soil conditions. By employing computational techniques, including modal analysis, multiple linear regression, and machine learning techniques, this invention provides a refined model that integrates both structural and site-specific variables, enabling more accurate period estimation compared to current code-based methods. SUMMARY OF THE INVENTION

[0006] The present disclosure relates to a system for predicting the foundation period for reinforced concrete buildings on slopes. The proposed system operates by simulating a linear Winkler foundation model to create the soil model, focusing on the influence of slope angle variations and load-bearing soil conditions on the building's foundation period. This invention proposes a system for developing models for reinforced concrete buildings on slopes with 3, 5, and 7 stories, featuring 4- or 5-bay configurations with 4-meter and 5-meter bay widths. These models consider variations in foundation slope angles of 0°, 10°, 20°, and 40° and consider different soil conditions, including stiff, medium, and soft soils, as well as fixed-base models.Through modal analysis, the system examines the base period of these configurations and finds that IS 1893:2016 underestimates this period by an average of 42.58%. Based on these findings, an alternative elevation-based calculation is proposed that uses the average elevation of the highest and lowest ground points for better accuracy. Furthermore, the system improves the base period estimate through multiple linear regression analyses, taking into account variables such as building height, field width, field number, slope angle, and soil type. This refined model achieves a mean square error (MSE) of 0.0088, significantly higher accuracy than IS 1893:2016, which has an MSE of 0.0171.

[0007] The present disclosure is intended to provide a system for predicting the foundation period for reinforced concrete buildings on slopes. The system comprises: a data input module configured to retrieve building and soil parameters from datasets, including building height, span width, number of spans, slope angle, and soil conditions; a modal analysis module configured to perform a modal analysis of the input parameters using finite element analysis software and generate results for different slope angles, soil conditions, and building configurations; a soil-structure interaction (SSI) module including a foundation modeling component that applies spring stiffness to column foundations based on Gazetas' formulas and simulates soil conditions categorized as stiff, medium, or soft, thereby incorporating soil-structure interaction effects;a regression and machine learning prediction module configured to develop prediction models using multiple linear regression, random forest, and XGBoost algorithms; and an output module configured to output the predicted base period of the building based on the trained prediction models.

[0008] In one embodiment, in the regression and machine learning module: The regression model quantifies the relationships between building geometry, slope angle, ground support condition, and base period, the random forest model aggregates predictions from multiple decision trees, and the XGBoost model sequentially builds decision trees to minimize prediction errors; In one embodiment, the modal analysis module is further configured to perform modal analysis on finite element models of 3-, 5-, and 7-story buildings with variable foundation slope angles and bay configurations.

[0009] In one embodiment, the soil-structure interaction (SSI) module includes six spring elements at each column foundation to account for six degrees of freedom, thus improving the simulation of soil flexibility on foundation stability under seismic loading.

[0010] In one embodiment, the regression and machine learning prediction module further comprises: a cross-validation component configured to evaluate the performance of the prediction models in terms of robustness and accuracy; and a regularization component in the XGBoost model to prevent overfitting by optimizing the regularization term during model training.

[0011] In one embodiment, the data input module is further configured to preprocess the input data by normalizing the building and ground parameters, thereby providing a consistent data representation across different building and ground configurations.

[0012] In one embodiment, the output module provides the predicted fundamental period in a user interface and displays a comparative graphical analysis between predicted results and conventional code-based predictions, providing insights into the accuracy improvements over IS 1893:2016 calculations.

[0013] In one embodiment, the regression and machine learning prediction module also uses the mean square error (MSE) metric to evaluate prediction accuracy, achieving an average MSE of 0.0088, indicating improved prediction performance compared to traditional computational methods.

[0014] An objective of the present disclosure is to provide a basic period prediction system for reinforced concrete buildings on slopes.

[0015] Another objective of the present disclosure is to develop a system that accurately predicts the fundamental vibration period of reinforced concrete (RC) buildings on slopes in sloping terrain.

[0016] Another objective of this disclosure is to improve the accuracy of the base period estimation by considering factors such as building height, field width, number of fields, slope angle, and soil conditions.

[0017] Another objective of the present disclosure is to evaluate the impact of different soil types and foundation slope angles on the base period, taking into account limitations in existing code standards such as IS 1893: 2016.

[0018] Another objective of this disclosure is to use multiple linear regression and machine learning models to refine the predictions of seismic behavior of reinforced concrete structures on slopes.

[0019] Another objective of this disclosure is to provide a more reliable alternative to elevation-based calculations, thereby reducing errors in estimating construction duration on sloped foundations.

[0020] To further clarify the advantages and features of the present disclosure, a more detailed description of the invention will be given with reference to specific embodiments thereof, which are illustrated in the accompanying drawings. It should be noted that these drawings represent only typical embodiments of the invention and are therefore not to be considered limiting its scope. The invention will be described and explained in additional detail and in greater detail with reference to the accompanying drawings. SHORT DESCRIPTION OF THE FIGURE

[0021] These and other features, aspects, and advantages of the present disclosure will be better understood when the following detailed description is read with reference to the accompanying drawings, in which like characters represent like parts throughout. Where: Fig. 1 shows a block diagram of a base period prediction system for reinforced concrete buildings on a slope according to an embodiment of the present disclosure.

[0022] Furthermore, those skilled in the art will appreciate that elements in the drawings are shown for convenience and may not necessarily be drawn to scale. For example, the flowcharts illustrate the method by key steps to enhance understanding of aspects of the present disclosure. Furthermore, with respect to device construction, one or more components of the device may have been represented in the drawings by conventional symbols, and the drawing may show only the specific details relevant to understanding embodiments of the present disclosure in order not to clutter the drawings with details that would be readily apparent to those skilled in the art who would benefit from the description herein. DETAILED DESCRIPTION:

[0023] To facilitate an understanding of the principles of the invention, reference will now be made to the embodiment illustrated in the drawings and described in specific language. It is to be understood, however, that no limitation on the scope of the invention is intended thereby, since such changes and further modifications of the illustrated system, and such further applications of the principles of the invention as illustrated therein, are contemplated as would normally occur to one skilled in the art to which the invention pertains.

[0024] It will be understood by one skilled in the art that the foregoing general description and the following detailed description are exemplary and explanatory of the invention and are not intended to be limiting thereof.

[0025] References in this specification to "one aspect," "another aspect," or similar language mean that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the present disclosure. Therefore, occurrences of the phrase "in one embodiment," "in another embodiment," and similar language throughout this specification may or may not all refer to the same embodiment.

[0026] The terms "comprises," "comprising," or other variations thereof are intended to cover non-exclusive inclusion, such that a process or method comprising a list of steps not only includes those steps, but may also include other steps not expressly listed or inherent in such process or method. Likewise, one or more devices or subsystems or elements or structures or components preceded by "comprises...a" does not preclude, without further limitation, the existence of other devices or other subsystems or other elements or other structures or other components or additional devices or additional subsystems or additional elements or additional structures or additional components.

[0027] Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. The system, methods, and examples provided herein are for illustrative purposes only and should not be considered limiting.

[0028] Embodiments of the present disclosure will be described in detail below with reference to the accompanying drawings.

[0029] The functional units described in this specification have been referred to as devices. A device may be implemented in programmable hardware devices such as processors, digital signal processors, central processing units, field-programmable gate arrays, programmable array logic, programmable logic devices, cloud processing systems, or the like. The devices may also be implemented in software for execution by various types of processors. An identified device may contain executable code and may, for example, comprise one or more physical or logical blocks of computer instructions, which may be organized, for example, as an object, procedure, function, or other construct.However, the executable file of an identified device need not be physically located together, but may comprise different instructions stored in different locations which, when logically linked together, constitute the device and fulfill the stated purpose of the device.

[0030] Indeed, executable code of a device or module may be a single instruction or multiple instructions, and may even be distributed across several different code segments, among different applications, and across multiple storage devices. Similarly, operational data may be identified and represented within the device and embodied in any suitable form and organized in any suitable type of data structure. The operational data may be captured as a single set of data or distributed across different locations, including different storage devices, and may exist, at least in part, as electronic signals in a system or network.

[0031] References in this specification to "a selected embodiment," "an embodiment," or "an embodiment" mean that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the disclosed subject matter. Therefore, the appearances of the phrases "a selected embodiment," "in an embodiment," or "in an embodiment" in various places in this specification do not necessarily refer to the same embodiment.

[0032] Furthermore, the described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided to provide a thorough understanding of embodiments of the disclosed subject matter. However, one of ordinary skill in the art will recognize that the disclosed subject matter may be practiced without one or more of the specific details, or with different methods, components, materials, etc. In other instances, well-known structures, materials, or operations are not shown or described in detail to avoid obscuring aspects of the disclosed subject matter.

[0033] According to the example embodiments, the disclosed computer programs or modules may be executed in many example ways, for example, as an application stored in the memory of a device or as a hosted application running on a server and communicating with the device application or browser using a variety of standard protocols such as TCP / IP, HTTP, XML, SOAP, REST, JSON, and other suitable protocols. The disclosed computer programs may be written in example programming languages ​​that execute from memory on the device or from a hosted server, for example, BASIC, COBOL, C, C++, Java, Pascal, or scripting languages ​​such as JavaScript, Python, Ruby, PHP, Perl, or other suitable programming languages.

[0034] Some of the disclosed embodiments comprise or otherwise involve data transmission over a network, such as communicating various inputs or files over the network. The network may comprise, for example, one or more of the following: the Internet, wide area networks (WANs), local area networks (LANs), analog or digital wired and wireless telephone networks (e.g., a PSTN, Integrated Services Digital Network (ISDN), a cellular network, and Digital Subscriber Line (xDSL)), radio, television, cable, satellite, and / or any other delivery or tunneling mechanism for transmitting data. The network may comprise multiple networks or subnetworks, each of which may comprise, for example, a wired or wireless data path. The network may comprise a circuit-switched voice network, a packet-switched data network, or any other network capable of transmitting electronic communications.For example, the network may include networks based on Internet Protocol (IP) or Asynchronous Transfer Mode (ATM), and may support voice using, for example, VoIP, Voice over ATM, or other comparable protocols used for voice data communications. In one implementation, the network includes a cellular network configured for the exchange of text or SMS messages.

[0035] Examples of the network include, but are not limited to, a Personal Area Network (PAN), a Storage Area Network (SAN), a Home Area Network (HAN), a Campus Area Network (CAN), a Local Area Network (LAN), a Wide Area Network (WAN), a Metropolitan Area Network (MAN), a Virtual Private Network (VPN), an Enterprise Private Network (EPN), the Internet, a Global Area Network (GAN), and so on.

[0036] Fig. 1 shows a block diagram of a base period prediction system (100) for reinforced concrete buildings on slopes according to an embodiment of the present disclosure.

[0037] With reference to Fig.1, the system (100) comprises a data input module (102) configured to retrieve building and soil parameters from data sets, including building height, bay width, number of bays, slope angle, and soil conditions; a modal analysis module (104) configured to perform a modal analysis of the input parameters using finite element analysis software and generate results for different slope angles, soil conditions, and building configurations; a soil-structure interaction (SSI) module (106) comprising a foundation modeling component (106a) that applies spring stiffness to column foundations based on Gazetas' formulas and simulates soil conditions categorized as stiff, medium, or soft, thereby incorporating soil-structure interaction effects;a regression and machine learning prediction module (108) configured to develop prediction models using multiple linear regression, random forest, and XGBoost algorithms; and an output module (110) configured to output the predicted base period of the building based on the trained prediction models.

[0038] In one embodiment, in the regression and machine learning module (108): The regression model (108a) quantifies relationships between building geometry, slope angle, ground support condition, and base period, the random forest model (108b) aggregates predictions from multiple decision trees, and the XGBoost model (108c) sequentially builds decision trees to minimize prediction errors.

[0039] In one embodiment, the modal analysis module (104) is further configured to perform modal analysis on finite element models of 3-story, 5-story, and 7-story buildings with variable foundation slope angles and bay configurations.

[0040] In one embodiment, the soil-structure interaction (SSI) module (106) includes six spring elements at each column foundation to account for six degrees of freedom and thus improve the simulation of soil flexibility on foundation stability under seismic loading.

[0041] In one embodiment, the regression and machine learning prediction module (108) further comprises: a cross-validation component (108d) configured to evaluate the performance of the prediction models in terms of robustness and accuracy; and a regularization component (108e) in the XGBoost model for preventing overfitting by optimizing the regularization term during model training.

[0042] In one embodiment, the data input module (102) is further configured to preprocess the input data by normalizing building and ground parameters, thereby providing a consistent data representation across different building and ground configurations.

[0043] In one embodiment, the output module (110) provides the predicted fundamental period in a user interface (110a) and displays a comparative graphical analysis between predicted results and conventional code-based predictions, providing insights into the accuracy improvements over IS 1893:2016 calculations.

[0044] In one embodiment, the regression and machine learning prediction module (108) further uses the mean square error (MSE) metric to evaluate prediction accuracy and achieves an average MSE of 0.0088, indicating improved prediction performance compared to conventional computational methods.

[0045] In one embodiment, the data input module (102), the modal analysis module (104), the soil-structure interaction (SSI) module (106), the regression and machine learning prediction module (108), and the output module (110) may be implemented in programmable hardware devices such as processors, digital signal processors, central processing units, field-programmable gate arrays, programmable array logic, programmable logic devices, cloud processing systems, or the like.

[0046] The present invention relates to a system for predicting the fundamental period for reinforced concrete buildings on slopes, taking into account the interaction between terrain slope and soil structure. The present invention aims to improve earthquake-resistant design practices for reinforced concrete (RC) buildings on slopes by developing a system for estimating their fundamental period. The proposed system first prepares a dataset, which is subsequently subjected to modal analysis and then used to perform soil-structure interaction (SSI) modeling. The system uses regression and machine learning models to predict the fundamental period. The system uses multiple linear regression and employs machine learning techniques such as random forest and XGBoost to improve the prediction accuracy.

[0047] The dataset used by the proposed system is derived from computer simulations of building models that consider key parameters such as building height, bay width, number of bays, slope angle, and soil conditions. The modal analysis module of the proposed system performs modal analysis of these models, which were created using symmetrical plans along the x- and y-axes. The models were divided into four groups: rigid support frames, and rigid support frames with stiff, medium, and soft support conditions. Variations in building height (9 m, 15 m, and 21 m), number of bays (4 and 5), bay width (4 m and 5 m), and slope angles (0°, 10°, 20°, 30°, and 40°) were considered, along with soil conditions ranging from stiff to medium to soft. A total of 229 models were created, with a standardized soil height of 3 meters. Additionally, the compressive strength of concrete and the yield strength of steel were set to 30 MPa and 40 MPa, respectively.500 MPa.

[0048] To simulate soil-structure interaction (SSI), the system considers three types of soil conditions: dense soil (DS), medium soil (MS), and soft soil (SS). The properties of these soil types are detailed in the dataset. To account for foundation flexibility, SSI was modeled using the spring stiffness at each column base, based on established Gazetas formulas for different soil conditions. The effects of SSI were simulated by assigning six springs to each column base, allowing for six degrees of freedom, which is a widely accepted approach for modeling soil-structure interaction effects.

[0049] The proposed system uses linear regression and machine learning to predict the base period. This allows the proposed system to quantify the relationships between building geometry, ground slope, soil properties, and construction period. The regression model considers parameters such as building height, number of bays, bay width, slope angle, and soil conditions to improve the accuracy of the period estimation. In addition to regression, machine learning techniques, specifically Random Forest and XGBoost, were used to refine the prediction accuracy. These machine learning techniques were selected for their ability to handle complex data and minimize prediction variance. The performance of the models was tested using cross-validation techniques to verify their robustness and precision.XGBoost is a sophisticated ensemble learning technique that improves prediction accuracy by sequentially constructing decision trees, with each tree correcting the errors of the previous one to minimize the overall loss. The model optimizes performance using gradient descent and regularization to avoid overfitting, making it both efficient and scalable. XGBoost is particularly effective at handling large datasets, missing data, and complex feature interactions, making it suitable for both classification and regression tasks. The Random Forest model is another ensemble learning technique that constructs multiple decision trees using random data subsets and features. Each tree is trained on a unique dataset sample, producing a diversity of predictions.For prediction, Random Forest aggregates the results of all trees, averages them for regression, or uses majority voting for classification. This aggregation reduces the risk of overfitting and improves generalization to new data. The randomness introduced by sampling features and data points improves the model's robustness to noise and allows it to capture complex relationships within the data. Due to its effectiveness and straightforward approach, Random Forest is widely used for classification and regression tasks.

[0050] The system's regression and machine learning module is also configured to perform regression analysis to explore the relationships between the dependent variable and the independent variables. The primary purpose of regression analysis is to model these relationships to enable prediction, interpretation, and trend detection. By estimating predictor coefficients, regression models provide insight into the impact of changes in independent variables on the target outcome. Linear regression is the simplest form, fitting a straight line to the data, while more advanced forms such as polynomial regression can capture nonlinear relationships, improving the model's flexibility and accuracy.

[0051] The present invention investigates the influence of structural and geometric parameters on the fundamental vibration period of reinforced concrete structures on sloping terrain using finite element analysis (FEA). This comprehensive analysis provides important insights that improve the understanding of seismic behavior, particularly in buildings on slopes.

[0052] Feature Relevance Analysis: Among the various parameters, building height emerges as the most important factor, contributing 45.8% to the model's prediction accuracy. This high contribution is consistent with earthquake design principles, where taller buildings have longer periods, making height a crucial factor in earthquake response. This is followed by slope angle and support conditions, contributing 25.3% and 24.6%, respectively. These results highlight the importance of considering slope geometry and foundation flexibility for an accurate fundamental period estimation. In comparison, span width and number of spans have minimal effects, contributing only 2.7% and 1.6%, respectively, highlighting that these structural design parameters are less critical for buildings on slopes.

[0053] Variations in base periods with building height and spans: For reinforced concrete buildings of different heights (9 m, 15 m, and 21 m) on sloping ground, it was observed that the number of spans has a significant influence on the base period for shorter buildings (9 m and 15 m), increasing the period by 11.4% and 9.3%, respectively. However, for 21 m tall buildings, changes in span width and number of spans have negligible effects, suggesting that at higher heights, other structural features influence the period more strongly.

[0054] Influence of slope angle: The slope angle exhibits a moderate negative correlation with the base period (-0.36), meaning that steeper slopes shorten the base period. A linear regression analysis shows a shortening of the period by 0.0042 units per degree increase in slope angle, with high statistical significance (p-value of 5.39×10-8). This result underscores the importance of considering slope in period calculations, as steeper slopes result in stiffer building behavior, which is crucial for the earthquake-resistant design of slope structures.

[0055] Influence of support conditions: The soil-structure interaction (SSI) analysis shows that with increasing soil flexibility, the base period also increases. The period increases by 8.80% on stiff soil, 29.03% on medium soil, and 47.17% on soft soil compared to a rigid foundation. These results indicate that buildings on softer soil have longer base periods and are more susceptible to seismic forces.

[0056] The proposed regression model for predicting the base period: The proposed regression model for predicting the base period, based on parameters such as building height, slope angle, and support conditions, achieves high accuracy. With an R-squared value of 0.928, an MAE of 0.0337, an RMSE of 0.0419, and a root mean square error (MSE) of 0.00176, the model offers a robust fit to actual data. Excluding the less effective variables "number of fields" and "field width" simplifies the model while maintaining high predictive power (R-squared value of 0.9108, MAE of 0.0374, and RMSE of 0.0467). This revised model focuses on important factors and ensures efficient and accurate period predictions.

[0057] Comparison of prediction models: When comparing three prediction models - Random Forest, XGBoost and linear regression - Random Forest performs best, achieving an RMSE of 0.0415, an MAE of 0.0346 and an R 2 -score of 0.9259. This comparison confirms that traditional and machine learning-based methods effectively predict the seismic period, with Random Forest leading in terms of accuracy.

[0058] Deviation analysis using IS 1893 standards: The proposed system exhibits better predictive performance compared to IS 1893:2002 and IS 1893:2016 standards. The 2002 standard consistently overestimates the period, while the 2016 standard underestimates it, with significant deviations, particularly for softer soils. The average underestimation by the 2016 standard under all conditions is 42.58%, and the overestimation by the 2002 standard is 14.56%. The proposed model, with an MSE of 0.0022, is in close agreement with the FEA results and highlights the need for a reassessment of existing standards for buildings on slopes.

[0059] Validation of the proposed model: Validation of the proposed regression model using different height measurement methods confirms that the model closely agrees with the FEA results, particularly when using a height measurement of 0.4747 (H+h), which yields an MSE of 0.0088. This method proves to be more accurate than the IS 1893:2002 and IS 1893:2016 methods, which yield higher MSE values ​​of 0.0235 and 0.0171, respectively.

[0060] Overall, the proposed system outperforms conventional elevation-based models by incorporating important structural and site-specific factors, thus improving the accuracy of fundamental period prediction for buildings on slopes. The results support a more advanced, multi-parameter approach that could refine earthquake design codes and make them more effective and reliable for diverse terrain and soil conditions.

[0061] The drawings and the foregoing description provide examples of embodiments. Those skilled in the art will recognize that one or more of the described elements may well be combined into a single functional element. Alternatively, certain elements may be separated into multiple functional elements. Elements from one embodiment may be added to another embodiment. For example, orders of the processes described herein may be changed and are not limited to the manner described herein. Furthermore, the actions of any flowchart need not be implemented in the order shown; nor do all actions necessarily need to be performed. Also, those actions that are not dependent on other actions may be performed in parallel with the other actions. The scope of the embodiments is in no way limited by these specific examples.Numerous variations, whether explicitly stated in the specification or not, such as differences in structure, dimensions, and use of materials, are possible. The scope of the embodiments is at least as broad as indicated in the following claims.

[0062] Advantages, other benefits, and solutions to problems have been described above with reference to specific embodiments. However, the advantages, benefits, solutions to problems, and any components that may cause an advantage or solution to occur or become more apparent are not to be construed as a critical, required, or essential feature or component of any or all of the claims. REFERENCES 100 A system for predicting the fundamental vibration period of RC buildings on a slope. 102 Data entry module 104 Modal Analysis Module 106 Soil-Structure Interaction (SSI) Module 106a Basic modeling component 108 Regression and Machine Learning Prediction Module 108a Regression model 108b Random Forest Model 108c XGBoost model 108d Cross-validation component 108e Regularization component 110 Output module 110a User Interface QUOTES CONTAINED IN THE DESCRIPTION

[0000] This list of documents submitted by the applicant was generated automatically and is included solely for the convenience of the reader. This list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions. Cited non-patent literature

[0000] Code standards such as IS 1893: 2016

[0017] IS 1893:2016 [0043, 0059] IS 1893 Standards

[0058] Comparison to the standards IS 1893:2002

[0058] IS 1893:2016 a

[0058] IS 1893:2002

[0059]

Claims

[1] A system for predicting the fundamental period for reinforced concrete buildings on slopes, consisting of: a data entry module configured to retrieve building and soil parameters from datasets, including building height, field width, number of fields, slope angle, and soil conditions; a modal analysis module configured to perform a modal analysis of the input parameters using finite element analysis software and to produce results for different slope angles, soil conditions and building configurations; a soil-structure interaction (SSI) module, which includes a foundation modeling component that applies spring stiffness to column foundations based on Gazetas formulas and simulates soil conditions categorized as stiff, medium, or soft, thus incorporating soil-structure interaction effects; a regression and machine learning prediction module configured to develop predictive models using multiple linear regression, random forest, and XGBoost algorithms; and an output module configured to output the predicted base period of the building based on the trained predictive models. [2] The system of claim 1, wherein in the regression and machine learning module: The regression model quantifies the relationships between building geometry, slope angle, soil bearing capacity and fundamental period. The Random Forest model aggregates predictions from multiple decision trees and The XGBoost model sequentially builds decision trees to minimize prediction errors. [3] The system of claim 1, wherein the modal analysis module is further configured to perform modal analysis on finite element models of 3-story, 5-story, and 7-story buildings with variable foundation slope angles and bay configurations. [4] The system of claim 1, wherein the soil-structure interaction (SSI) module includes six spring elements at each column foundation to account for six degrees of freedom and thus improve the simulation of soil flexibility on foundation stability under seismic loading. [5] The system of claim 1, wherein the regression and machine learning prediction module further comprises: a cross-validation component configured to evaluate the performance of the predictive models in terms of robustness and accuracy; and a regularization component in the XGBoost model to prevent overfitting by optimizing the regularization term during model training. [6] The system of claim 1, wherein the data input module is further configured to preprocess the input data by normalizing building and ground parameters to provide a consistent data representation across different building and ground configurations. [7] The system of claim 1, wherein the output module provides the predicted fundamental period in a user interface and displays a comparative graphical analysis between the predicted results and conventional code-based predictions, thereby providing insights into the accuracy improvements over IS 1893:2016 calculations. [8] The system of claim 1, wherein the regression and machine learning prediction module further uses the mean square error (MSE) metric to evaluate prediction accuracy and achieves an average MSE of 0.0088, indicating improved prediction performance compared to conventional computational methods.

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