Chatbots put to the test in math and logic problems: A preliminary comparison and assessment of ChatGPT-3.5, ChatGPT-4, and Google Bard

A comparison between three chatbots which are based on large language models, namely ChatGPT-3.5, ChatGPT-4 and Google Bard is presented, focusing on their ability to give correct answers to mathematics and logic problems. In particular, we check their ability to Understand the problem at hand; Apply appropriate algorithms or methods for its solution; and Generate a coherent response and a correct answer. We use 30 questions that are clear, without any ambiguities, fully described with plain text only, and have a unique, well defined correct answer. The questions are divided into two sets of 15 each. The questions of Set A are 15 "Original" problems that cannot be found online, while Set B contains 15 "Published" problems that one can find online, usually with their solution. Each question is posed three times to each chatbot. The answers are recorded and discussed, highlighting their strengths and weaknesses. It has been found that for straightforward arithmetic, algebraic expressions, or basic logic puzzles, chatbots may provide accurate solutions, although not in every attempt. However, for more complex mathematical problems or advanced logic tasks, their answers, although written in a usually "convincing" way, may not be reliable. Consistency is also an issue, as many times a chatbot will provide conflicting answers when given the same question more than once. A comparative quantitative evaluation of the three chatbots is made through scoring their final answers based on correctness. It was found that ChatGPT-4 outperforms ChatGPT-3.5 in both sets of questions. Bard comes third in the original questions of Set A, behind the other two chatbots, while it has the best performance (first place) in the published questions of Set B. This is probably because Bard has direct access to the internet, in contrast to ChatGPT chatbots which do not have any communication with the outside world

ANN-based surrogate model for predicting the lateral load capacity of RC shear walls

Reinforced concrete (RC) shear walls are often used as the main lateral-resisting component in the seismic design of buildings. They provide a large percentage of the lateral stiffness of the structure, and therefore, they may experience large shear stresses at some point under earthquake loading. Consequentially, to accurately predict their behavior, it is recommended to use detailed finite element (FE) modeling with appropriate non-linear constitutive models for concrete and steel. However, such types of simulations are challenging and could significantly increase the computational time required to obtain the analysis results. In this paper, we study the viability of creating an artificial neural-network-based surrogate model of the RC shear wall that is able to capture its nonlinear behavior and predict the results obtained with a detailed FE model, offering a much lower computational effort. For this purpose, we develop a detailed parametric non-linear FE model based on well-established practices and validated studies using the OpenSees finite element software framework. The FE model consists of multi-layer shell elements with the vertical and transverse reinforcement included as smeared rebar layers. The concrete layers implement a damage mechanism with smeared crack constitutive model, whereas the rebar layers consider a uniaxial plasticity material law. The parametric FE model is used to build a large database of RC walls of different sizes and characteristics, with their corresponding lateral load capacity that is obtained through the detailed non-linear pushover analysis. Finally, the obtained database is used to train and validate the ANN-surrogate model. The developed model is able to accurately predict the lateral load capacity of RC shear walls without the need of detailed FE modeling, thus drastically reducing the complexity and the computational time required for the numerical solution and providing a reliable and robust analysis alternative, with only small compromise of accuracy

Investigation of the Static Bending Response of FGM Sandwich Plates

In the present work, a displacement-based high-order shear deformation theory is introduced for the static response of functionally graded plates. The present theory is variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. By dividing the transverse displacement into the bending and shear parts and making further assumptions, the number of unknowns and equations of motion of the present theory is reduced a and hence makes them simple to use. The material properties of the plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of volume fractions of material constituents. The equilibrium equations of a functionally graded plate are given based on the higher order shear deformation theory. The numerical results presented in the paper are demonstrated by comparing the results with solutions derived from other higher-order models found in the literature and the present numerical results of Finite Element Analysis (FEA). In the numerical results, the effects of the grading materials, lay-up scheme and aspect ratio on the normal stress, shear stress and static deflections of the functionally graded sandwich plates are presented and discussed. It can be concluded that the proposed theory is accurate, elegant and simple in solving the problem of the bending behavior of functionally graded plates

Using artificial intelligence techniques for the accurate estimation of the ultimate pure bending of steel circular tubes

In this paper, the potential of building more accurate and robust models for the prediction of the ultimate pure bending capacity of steel circular tubes using artificial intelligence techniques is investigated. Therefore, a database consisting of 104 tests for fabricated and cold-formed steel circular tubes are collected from the open literature and used to train and validate the proposed data-driven approaches which include the Random Forest methodology in two variants: the original version in which the control parameters are manually updated, and an enhanced RF-PSO variant, where Particle Swarm Optimization is used for optimizing these parameters. The data set has four input parameters, namely the tube thickness, tube diameter, yield strength of steel and steel elasticity modulus, while the ultimate pure bending capacity is considered as the target output variable. The obtained results are compared to the real test values through various statistical indicators such as the root mean square error and the coefficient of determination. The results indicate that the proposed enhanced model can provide an accurate solution for modelling the complex behavior of steel circular tubes under pure bending conditions

Vulnerability assessment of cultural heritage structures

Cultural heritage (CH) assets are the legacy of a society that are inherited from the past generations and can give us lessons for contemporary construction. Not only the formally recognized CH assets but also the non-CH structures and infrastructure, and the interconnection between them are crucial to be considered in a vulnerability assessment tool for the sustainable reconstruction of historic areas. Since most CH assets were not designed based on robust design codes to resist natural hazards such as earthquakes, vulnerability assessment and preservation are pivotal tasks for the authorities. For this aim, Hyperion, an H2020 project (Grant agreement No 821054), was formed in order to take advantage of existing tools and services together with novel technologies to deliver an integrated vulnerability assessment platform for improving the resiliency of historic areas. Geometric documentation is the first and most important step toward the generation of digital twins of CH assets that can be facilitated using 3D laser scanners or drone imaging. Afterward, the finite element method is an accurate approach for developing the simulation-based digital twins of cultural heritage assets. For calibration of the models, the result of the operational modal analysis from the ambient vibration testing using accelerometers can be utilized. Structural analysis for the prediction of the structural behavior or near real-time analysis can be carried out on the calibrated models. However, the full finite element analysis needs a lot of computational effort, and to tackle this limitation, equivalent frame methods can be utilized

A Static and Free Vibration Analysis of Porous Functionally Graded Beams

In this work, the static and free vibration analysis of functionally graded (FG) porous beams is investigated using a new higher-order shear deformation model (HSD). The porosity that develops naturally during the fabrication of a material is arbitrary in nature. Therefore, in the present study, a variation is considered taking into account three distribution patterns, namely (i) even distribution, (ii) uneven distribution, and (iii) the logarithmic-uneven pattern. Furthermore, the impact of several micromechanical models on the bending and free vibration behavior of the beams was investigated. Different micromechanical models were used to examine the mechanical properties of functionally graded beams, the properties of which change continuously throughout the thickness following a power law. Using the HSD model, the equations of motion are obtained using Hamilton's principle. To obtain displacements, stresses, and frequencies, the Navier type solution method was employed, and the numerical results were compared to those published in the literature. The impact of porosity and volume fraction index, different micromechanical models, mode numbers, and geometry on the bending and natural frequencies of imperfect FG beams were investigated

Investigation of performance metrics in regression analysis and machine learning-based prediction models

Performance metrics (Evaluation metrics or error metrics) are crucial components of regression analysis and machine learning-based prediction models. A performance metric can be defined as a logical and mathematical construct designed to measure how close the predicted outcome is to the actual result. A variety of performance metrics have been described and proposed in the literature. Knowledge about the metrics' properties needs to be systematized to simplify their design and use. In this work, we examine various regression related metrics (14 in total) for continuous variables, including the most widely used ones, such as the (root) mean squared error, the mean absolute error, the Pearson correlation coefficient, and the coefficient of determination, among many others. We provide their mathematical formulations, as well as a discussion on their use, their characteristics, advantages, disadvantages, and limitations, through theoretical analysis and a detailed numerical example. The 10 unitless metrics are further investigated through a numerical analysis with Monte Carlo Simulation based on (i) random guessing and (ii) the addition of random noise with various noise ratios to the predicted values. Some of the metrics show a poor or inconsistent performance, while others exhibit good performance as evaluation measures of the 'goodness of fit'. We highlight the importance of the usage of the right metrics to obtain good predictions in machine learning and regression models in general

Bridge management through digital twin-based anomaly detection systems: A systematic review

Bridge infrastructure has great economic, social, and cultural value. Nevertheless, many of the infrastructural assets are in poor conservation condition as has been recently evidenced by the collapse of several bridges worldwide. The objective of this systematic review is to collect and synthesize state-of-the-art knowledge and information about how bridge information modeling, finite element modeling, and bridge health monitoring are combined and used in the creation of digital twins (DT) of bridges, and how these models could generate damage scenarios to be used by anomaly detection algorithms for damage detection on bridges, especially in bridges with cultural heritage value. A total of 76 relevant studies from 2017 up to 2022 have been taken into account in this review. The synthesis results show a consensus toward the future adoption of DT for bridge design, management, and operation among the scientific community and bridge practitioners. The main gaps identified are related to the lack of software interoperability, the required improvement of the performance of anomaly-detection algorithms, and the approach definition to be adopted for the integration of DT at the macro scale. Other potential developments are related to the implementation of Industry 5.0 concepts and ideas within DT frameworks

Optimum Design of Plane Trusses Using Mathematical and Metaheuristic Algorithms on a Spreadsheet

Mathematical optimization refers to the process of finding the values of variables that maximize or minimize a function. Structural optimization is the process of designing a structure in such a way as to minimize its weight or cost, while meeting a set of performance requirements, ensuring that it is robust, lightweight, and efficient. Two large categories of optimization algorithms are mathematical and metaheuristic algorithms. The ones of the first rely on mathematical principles, are deterministic and exact but may fail if the problem is too large or complex. The latter category, metaheuristics, represents algorithms that are used to find approximate solutions. They are high-level strategies that guide the search toward a good solution, rather than being a specific, deterministic algorithm. They are often used for problems where it is difficult or impractical to find the optimal solution using exact methods. Metaheuristics typically involve iteratively improving a solution through some type of search or exploration process. They make use of techniques from probability and statistics, such as randomization and stochastic optimization, to explore the search space and guide the search toward good solutions. Some examples include genetic algorithms, simulated annealing, differential evolution (DE), particle swarm optimization (PSO), and ant colony optimization. In this study, a mathematical optimizer and two metaheuristics (DE, PSO), are employed for the optimum structural design of plane truss structures aiming to minimize the weight of the structure under constraints on allowable displacements and stresses. A 10-bar plane truss is considered as the numerical example of the study. The constraints are checked by performing an analysis with matrix methods. All calculations are done on a spreadsheet. The results of the algorithms are compared to each other as well as to results from the literature in terms of convergence speed, number of function evaluations, and accuracy of the solution.The support of Qatar University is acknowledged, through the Student Grant entitled "Design Optimization of Truss Structures using Swarm Intelligence Methods" (QUST-2-CENG-2022-681)