Modeling Problems Research Articles

Скінченно-елементна модель вертикального резервуара на жорсткій основі

This study addresses the problem of finite element modeling of a 20,000 m3 vertical steel tank subjected to static loads. The structure includes a cylindrical wall of total height 17,880 mm and diameter 39,900 mm. The shell thicknesses of the cylindrical wall are determined according to strength and buckling design standards. The geometric model is axisymmetric. The analysis involves the calculation of the stress and strain fields of the cylindrical wall and the contact zone between the flat bottom and the rigid foundation under various combinations of external loads, namely, excessive and hydrostatic pressures. The ANSYS Mechanical software is used for finite element analysis. Three-dimensional SOLID186 and SHELL281 elements are used for axisymmetric modeling of the shell structure in a three-dimensional formulation. To simulate the contact zone, CONTA174 and TARGE170 finite elements are used to model the moving contact surface of the bottom and the fixed surface of the rigid foundation, respectively. The model is verified by comparing the radial displacements calculated numerically and analytically. The discrepancy does not exceed 4%, thus evidencing the adequacy of the finite element model. The contact zone is analyzed for non-standard service conditions, such an excessive internal pressure in the tank (2.5 and 3 kPa compared to 2 kPa under normal conditions). The unilaterally constrained "bottom–foundation" contact zone model allows the bottom to detach from the foundation, thus leading to contact opening. A full detachment occurs under a certain combination of the excessive and the hydrostatic pressure. For certain liquid levels in the tank, the gap decreases, which may be due to a reduced effect of the excessive pressure. This is accompanied by the development of internal detachment caused by the increasing moment from the hydrostatic pressure. The internal detachment increases the bending moment at the wall–bottom junction, which, under certain conditions, may cause plastic deformations followed by the development of an emergency state.

Bridging Gaps: Pre-Service Mathematics Teachers’ Handling the Difficulties in Posing Real-World Mathematical Problems

Real-world mathematical problem (RWMP) solving and posing are important aspects of teaching and learning mathematical modelling, as well as developing a mathematization disposition for both teachers and students. Several researchers have explored blockages or difficulties in such modelling processes and in problem posing. However, prior research has identified difficulties that the pre-service mathematics teachers (PSMTs) encountered when they tried to pose a modelling problem by choosing the general topic themselves, as there is little known about possible obstacles that PSMTs can encounter when trying to pose a real-world problem relevant to a given mathematical topic. The current study explored the difficulties encountered by PSMTs in a RWMP-posing activity. The target group was 23 PSMTs with prior experience in mathematical modelling and mathematical problem posing. The findings showed that the PSMTs struggled with: (a) task organization, which involved selecting and understanding mathematical knowledge; (b) specialized content knowledge, which included a lack of real-world knowledge and difficulty in connecting mathematical concepts to real-world contexts; and (c) individual considerations of aptness, which encompassed authenticity, interest, complexity, language, and relevance to task organization. The PSMTs applied various strategies to complete the posing task, such as using problem-posing and solving heuristics, adapting existing problems, sharing and discussing with friends, and considering the perspective of a typical student. The implications of these findings should help in developing preparatory instructional practices for mathematics teachers.

Early fire detection technology based on improved transformers in aircraft cargo compartments

The implementation of early and accurate detection of aircraft cargo compartment fire is of great significance to ensure flight safety. The current airborne fire detection technology mostly relies on single-parameter smoke detection using infrared light. This often results in a high false alarm rate in complex air transportation environments. The traditional deep learning model struggles to effectively address the issue of long-term dependency in multivariate fire information. This paper proposes a multi-technology collaborative fire detection method based on an improved transformers model. Dual-wavelength optical sensors, flue gas analyzers, and other equipment are used to carry out multi-technology collaborative detection methods and characterize various feature dimensions of fire to improve detection accuracy. The improved Transformer model which integrates the self-attention mechanism and position encoding mechanism is applied to the problem of long-time series modeling of fire information from a global perspective, which effectively solves the problem of gradient disappearance and gradient explosion in traditional RNN (recurrent neural network) and CNN (convolutional neural network). Two different multi-head self-attention mechanisms are used to classify and model multivariate fire information, respectively, which solves the problem of confusing time series modeling and classification modeling in dealing with multivariate classification tasks by a single attention mechanism. Finally, the output results of the two models are fused through the gate mechanism. The research results show that, compared with the traditional single-feature detection technology, the multi-technology collaborative fire detection method can better capture fire information. Compared with the traditional deep learning model, the multivariate fire prediction model constructed by the improved Transformer can better detect fires, and the accuracy rate is 0.995.

Electrodynamic modeling of a four-channel antenna with an operating frequency band of octave

The actual problem of electrodynamic modeling of a four-channel antenna with an octave operating frequency range has been considered. The results of numerical electrodynamic modeling of a four-channel antenna have been presented. The considered antenna with an octave operating frequency range is a rectangular curtain comprising four independent non-equidistant channels. Numerical electrodynamic modeling of a four-channel antenna has been carried out in the ANSYS HFSS software package, with the convergence parameter DeltaS = 0.01. As a result of the simulation, the frequency characteristics of each channel have been obtained: VSWR, gain, reflection coefficient, directional pattern. The antenna provides a scanning angle as part of an ultra-wideband digital antenna array of at least ±30° in azimuth and from 0° to 60° in elevation. The gain of the antenna channels in the operating frequency range is not lower than 6 dB. According to the simulation results, the VSWR of each channel of the antenna in the operating frequency range does not exceed 2.55. To minimize the influence of mutual coupling of channels on the antenna characteristics, the distance from the phase centers of the curtain emitters to other elements of the ultra-wideband digital antenna array should be at least a wavelength in free space at the lower frequency of the operating frequency range. It has been shown that the considered four-channel antenna provides an octave operating frequency band and can be used as part of an ultra-wideband digital antenna array for direction finding of radiation sources.

Hybrid Model of Natural Time Series with Neural Network Component and Adaptive Nonlinear Scheme: Application for Anomaly Detection

It is often difficult to describe natural time series due to implicit dependences and correlated noise. During anomalous natural processes, anomalous features appear in data. They have a nonstationary structure and do not allow us to apply traditional methods for time series modeling. In order to solve these problems, new models, adequately describing natural data, are required. A new hybrid model of a time series (HMTS) with a nonstationary structure is proposed in this paper. The HMTS has regular and anomalous components. The HMTS regular component is determined on the basis of an autoencoder neural network. To describe the HMTS anomalous component, an adaptive nonlinear approximating scheme (ANAS) is used on a wavelet basis. HMTS is considered in this investigation for the problem of neutron monitor data modeling and anomaly detection. Anomalies in neutron monitor data indicate negative factors in space weather. The timely detection of these factors is critically important. This investigation showed that the developed HMTS adequately describes neutron monitor data and has satisfactory results from the point of view of numeric performance. The MSE model values are close to 0 and errors are white Gaussian noise. In order to optimize the estimate of the HMTS anomalous component, the likelihood ratio test was applied. Moreover, the wavelet basis, giving the least losses during ANAS construction, was determined. Statistical modeling results showed that HMTS provides a high accuracy of anomaly detection. When the signal/noise ratio is 1.3 and anomaly durations are more than 60 counts, the probability of their detection is close to 90%. This is a high rate in the problem domain under consideration and provides solution reliability of the problem of anomaly detection in neutron monitor data. Moreover, the processing of data from several neutron monitor stations showed the high sensitivity of the HMTS. This shows the possibility to minimize the number of engaged stations, maintaining anomaly detection accuracy compared to the global survey method widely used in this field. This result is important as the continuous operation of neutron monitor stations is not always provided. Thus, the results show that the developed HMTS has the potential to address the problem of anomaly detection in neutron monitor data even when the number of operating stations is small. The proposed HMTS can help us to decrease the risks of the negative impact of space weather anomalies on human health and modern infrastructure.

SCATTERING OF ELECTROMAGNETIC WAVES ON FLAT GRID TWO-PERIODIC STRUCTURES

Context. One of the scientific hypotheses for the creation of nonreciprocal optical metasurfaces is based on the use of a wave channel in which rays of the direct and reverse diffraction scenarios are realized on two-periodic flat structures with nonlinear elements. Such processes in the nanometer wavelength range of electronic devices require precise calculations of the interaction of waves and microstructures of devices. It is also important to describe the behavior of antenna devices in mobile communications. Expanding the wavelength range of stable communication is achieved by using prefractal structures in antenna devices in combination with periodic structuring. Similar modeling problems arise when electromagnetic waves penetrate materials with a crystalline structure (radio transparency).
 Objective. To test this hypothesis, it is necessary to carry out mathematical modeling of the process of scattering of electromagnetic waves by metasurfaces under conditions of excitation of several diffraction orders. It is known that among two-periodic flat lattices of different structures there are five types that fill the plane. These are the Bravais grilles. The problem of scattering of an incident monochromatic TE polarized wave on a metal screen with recesses in two-periodic structures filled with silicon was considered.
 Method. The paper builds mathematical models for the study of spatial-amplitude spectra of metasurfaces on Brave lattices and gives some results of their numerical study. The condition for determining the diffraction orders propagating over the grating is proposed. Scattered field amplitudes are from the solution of the boundary value problem for the Helmholtz equation in the COMSOL Multiphysics 5.4 package. Similar problem formulations are possible when studying the penetration of an electromagnetic field into a crystalline substance.
 Results. Obtained relations for diffraction orders of electromagnetic waves scattered by a diffraction grating. The existence of wavelengths incident on a two-periodic lattice for which there is no reflected wave is shown for different shapes (rectangular, square, hexagonal) of periodic elements in the center of which a depression filled with silicon was made. Distributions of reflection coefficients for different geometric sizes of colored elements and recesses are given. The characteristics of the electric field at resonant modes in the form of modulus isolines show the nature of the interaction of the field over the periodic lattice and the scatterersdepressions. At the resonant wavelengths of the incident waves, standing waves appear in the scatterers.
 Conclusions. A mathematical model of the set of diffraction orders propagating from a square and hexagonal lattice into halfspace is proposed z >= 0. It has been shown that flat periodic lattice with square or hexagonal periodicity elements and resonant scatterers in the form of cylindrical recesses filled with silicon can produce a non-mirrored scattered field in metal. The response of the lattices to changes in the wavelength of the incident field by the structure of diffraction orders of the scattered field and high sensitivity to the rotation of the incident plane were revealed. The two-periodic lattices have prospects for creating anti-reflective surfaces of various devices. Two-periodic lattices have prospects for creating anti-reflective surfaces for various devices, laser or sensor electronic devices, antennas in mobile communication elements, and radio transparency elements. They have more advanced manufacturing technologies in relation to spatial crystal structures.

A PROPOSAL FOR AN INNOVATIVE APPROACH TO EXTENDED MODELLING CYCLES INCORPORATING PROBLEM-POSING FROM A CREATIVITY PERSPECTIVE

Many studies have shown that mathematical modelling, creativity, and problem-posing activities are deeply related. However, there is a lack of research that poses mathematical modelling problems. Additionally,only few studies have conducted statistical analyses of the relationship between creativity in problem-posing and creativity in psychology. The purpose of this research is to conduct a survey to quantitatively evaluate creativity, and to propose a more effective modelling cycle based on the survey results. This study focuses on fluency a creativity factor that is measured by the number of problems posed by students. The survey results showed a moderate positive correlation between fluency in posing mathematical modelling problems and creativity in psychology (r = 0.44, p <0.01). Based on the results, an extended modelling cycle is proposed and discussed.

Meta Analysis Of Learning Models Problem Based Learning In Improving Critical Thinking Skills In Primary Schools

This study aims to analyze Problem-based Learning models intended to improve critical thinking skills in elementary school students. Problem-based learning models are learning processes where students are open minded, reflexive, active, reflective, and critical through real-world context activities. In this study the researchers used a meta-analysis method. First, the researcher formulated the research problem, then proceeded to review the existing relevant research for analysis. Data were collected by using a non-test technique by browsing electronic journals through Google Scholar and studying documentation in the library. Seven articles were found through Google Scholar and only one was found in the library. Based on the analysis of the results, the problem-based learning model can improve students' thinking ability from as little as 2.87% up to 33.56% with an average of 14.18%.

Математичне моделювання динамічних впливів на будівельні конструкції

The solution of the problem of mathematical modeling of dynamic influences on building structures is considered in general and in connection with important scientific and practical tasks. In modern conditions, special attention should be paid to the problems of taking into account dynamic influences, parameters of load-bearing structures of buildings that affect their structural reliability and safety. For many years, information about catastrophic destruction of buildings and structures has been appearing more often, which are the result not only of errors that arose during the construction of facilities, but also due to dynamic influences that arose during their operation. A buildable technical system will be used in advance with the technical parameters set, which is responsible for the control of the process of the preparation of structures, the installation of the equipment, during the operation and operation. The development will be carried out and the sporud will be constantly used to promote the development of future technologies, the development and the establishment of the future, as well as the development of dynamic developments in the future. In particular, it is important to understand the development of the engineering and geological minds of the spores, as they have known the front deformation of the non-essential axis of the runt foundations. Various methods are used for structural dynamics, such as modal analysis, response spectrum analysis, time analysis, and finite element analysis. These methods include mathematical modeling, numerical simulation, and computational methods to predict the behavior and response of a structure under dynamic load conditions. Knowing the frequency and form of the structure, it is possible to estimate the dynamic reaction of the design to the application. For the purpose of including the transfer of the world, the destruction of internal forces in the real parts of the construction. Analyses of the response to the additional assessment of the characteristics of the construction, the identification of critical areas and the re-conversion, which the project is able to meet the criteria.

A rumor propagation model in multilingual environment with time and state dependent impulsive control

In this paper we are interested in the problem of modeling, analysis and control of rumor spreading on online social networks. As the diversity of languages and the difference of user nodes in the network, a heterogeneous rumor spreading model with two language spreaders is proposed, and the impulsive isolation control strategy is considered. Firstly, the model with periodic impulsive isolation control and time-delay recovery rate is discussed. Based on the stability theory of impulsive differential equations, some conditions regarding the impulsive period and control gains are given for the rumor asymptotically disappearance and persistent existence. Secondly, a new type of event-triggered impulsive isolation control method is developed to address the tradeoff between restraining rumor and minimizing the cost of control, and some conditions are given to make the rumor disappear asymptotically. Furthermore, an improved event-triggered mechanism is established based on the fixed-time stability theory, which provides the conditions for the rumor to disappear within a fixed-time. Finally, some numerical simulations and an actual example are given to verify the rationality of the model and the effectiveness of the control methods.

Adaptable software tools for searching objects-analogues tasks 
 in NO-CODE concept

The paper is devoted to the problem of methodological and software support for the search of object analogues, performed when solving the problems of modelling and designing the development of oil and gas fields. The article shows that there is no single generally accepted methodology for searching analogues, existing methodologies differ in applied similarity criteria and search algorithms, are adapted to the search conditions, and are modernised. With the inconsistency of methods computer programs for searching analogues are created at a low level of abstraction, for a limited range of tasks, the existing developments are integrated with corporate databases and in general do not solve the problem of providing analysts with pro-software tools. As a solution we propose the development of programs for searching analogues in the concept of "no-code" (without programming) on the basis of analytical platforms. The "no-code" approach will allow analysts without involving programmers to create software tools for searching analogues, implementing their own variant methods. The article presents the authors' algorithm for express analysis of data at the initial stage of analogue search and the software tool that implements it, created "no code" on the basis of the Russian analytical platform Loginom.

Identification method of all-operating-point admittance model for wind farms considering frequency-coupling characteristics

Admittance identification is an effective tool to solve the issue of black-box admittance modeling in wind farms. However, due to the large operating range of wind farms, it is difficult to accurately identify the admittance model of wind farms under all operating conditions, which limits the research on wideband oscillation caused by the interaction between wind farms and the power grid. This paper analyses the characteristics of the frequency-coupling admittance for wind farms. It is found that the power-sharing ratio of wind turbine generators (WTGs) affects the admittance characteristic of the wind farm, which leads to a huge number of operating points for the wind farm. The all-operating-point (AOP) admittance model of wind farms considering frequency-coupling characteristics is hard to directly identify. Aiming for this problem, this paper proposes to first identify the AOP-admittance model for WTGs. Then, based on the operating points of each WTG and the network structure, the AOP-admittance model of the wind farm is obtained via the admittance aggregation and model reduction method. This proposed method solves the problem of black-box admittance modeling and addresses the problem of dimension disaster in admittance modeling for wind farms. The identified model of the wind farm can be used to accurately assess the stability of the wind power integration system under various operating conditions. Finally, the effectiveness of the proposed method is verified through the admittance measurement and stability analysis of the wind farm.

Experimental full waveform inversion for elastic material characterization with accurate transducer modeling

For quality assurance and in-service safety, sufficient characterization of the materials is essential during the development, manufacture, and processing of a material in any industrial setting. Evaluation of elastic coefficients, material microstructures, morphological features, and related mechanical properties are all part of the process of characterizing a material. Ultrasonic signals are sensitive to material properties such as wave speeds, attenuation, diffusion backscattering, microstructural variation, and elastic characteristics (e.g., elastic modulus, hardness, etc.). Ultrasonic computed tomography (USCT) is an emerging imaging method that can be implemented to obtain a quantitative estimation of material properties. In this study, a source estimation technique was initially proposed to obtain the source time function for accurate forward modeling by constructing a linear inverse problem for the unknown transducer modeling. Finally, a material characterization approach was proposed with accurate source estimation to extract wave speed distribution from an elastic material by employing a wave-based method, known as full waveform inversion (FWI). Systematic performance analysis of the proposed FWI model with accurate source estimation was assessed using experimental and synthetic data obtained from a 6061 aluminum sample. Overall, the proposed FWI technique has successfully reconstructed the wave speed distribution, exhibiting the potential of the proposed method of material characterization in various engineering applications.

Inducing Clusters Deep Kernel Gaussian Process for Longitudinal Data

We consider the problem of predictive modeling from irregularly and sparsely sampled longitudinal data with unknown, complex correlation structures and abrupt discontinuities. To address these challenges, we introduce a novel inducing clusters longitudinal deep kernel Gaussian Process (ICDKGP). ICDKGP approximates the data generating process by a zero-mean GP with a longitudinal deep kernel that models the unknown complex correlation structure in the data and a deterministic non-zero mean function to model the abrupt discontinuities. To improve the scalability and interpretability of ICDKGP, we introduce inducing clusters corresponding to centers of clusters in the training data. We formulate the training of ICDKGP as a constrained optimization problem and derive its evidence lower bound. We introduce a novel relaxation of the resulting problem which under rather mild assumptions yields a solution with error bounded relative to the original problem. We describe the results of extensive experiments demonstrating that ICDKGP substantially outperforms the state-of-the-art longitudinal methods on data with both smoothly and non-smoothly varying outcomes.

Imagine, Initialize, and Explore: An Effective Exploration Method in Multi-Agent Reinforcement Learning

Effective exploration is crucial to discovering optimal strategies for multi-agent reinforcement learning (MARL) in complex coordination tasks. Existing methods mainly utilize intrinsic rewards to enable committed exploration or use role-based learning for decomposing joint action spaces instead of directly conducting a collective search in the entire action-observation space. However, they often face challenges obtaining specific joint action sequences to reach successful states in long-horizon tasks. To address this limitation, we propose Imagine, Initialize, and Explore (IIE), a novel method that offers a promising solution for efficient multi-agent exploration in complex scenarios. IIE employs a transformer model to imagine how the agents reach a critical state that can influence each other's transition functions. Then, we initialize the environment at this state using a simulator before the exploration phase. We formulate the imagination as a sequence modeling problem, where the states, observations, prompts, actions, and rewards are predicted autoregressively. The prompt consists of timestep-to-go, return-to-go, influence value, and one-shot demonstration, specifying the desired state and trajectory as well as guiding the action generation. By initializing agents at the critical states, IIE significantly increases the likelihood of discovering potentially important under-explored regions. Despite its simplicity, empirical results demonstrate that our method outperforms multi-agent exploration baselines on the StarCraft Multi-Agent Challenge (SMAC) and SMACv2 environments. Particularly, IIE shows improved performance in the sparse-reward SMAC tasks and produces more effective curricula over the initialized states than other generative methods, such as CVAE-GAN and diffusion models.

Optimal control problem for mathematical modeling of Zika virus transmission using fractional order derivatives

This study delves into the dynamics of Zika virus transmission by employing a mathematical model to explain virus spread with fractional order derivatives. The population is divided into two groups: the human group and the ticks group to accurately explain the transmission routes of the virus. The objective of this research is to protect susceptible individuals from infection and curb the spread of this endemic disease. To achieve this, we have included two control measures: the first is a sensibilization program, and the second is treatment. We investigate the use of optimal control strategies and fractional derivative techniques under the Caputo method to reduce the number of exposed and infected individuals. By employing the Pontryagin maximum principle to analyze and characterize the optimal controls, the proposed method is further validated through numerical simulations. The outcome of this study highlights the importance of containing the rate of dynamic dissemination in preventing the Zika epidemic.

The Effect of Learning Models Problem Based Learning mediate Digital Flipbook Against Learning Outcomes Student Class XI on Acid-Base Material

Study This aim For know influence use of learning models Problem Based Learning assisted by Digital Flipbook media to results Study students and find out difference motivation Study students being studied with Digital Flipbook media using learning models Problem Based Learning on the material sour base class XI at SMA Negeri 1 Pancur Batu. Retrieval technique the sample used in the study This is random sampling that is method taking sample in a manner random . Design used is Quasi experimental non-equivalent type Control Group Design . Research sample is student class XI-MIA 3 and XI-MIA 4 totaling 60 people . Study This using test instruments as many as 20 items question choice double and 20 non- test instruments that is questionnaire motivation Study student . Hypothesis test using the side t test right with results study obtained mark tcount t table ie 26.51 1.70, meaning there is enhancement results Study chemistry students being studied with the PBL model assisted by Digital Flipbook media on the material sour base class XI received at level significance of 5%. Two- sided t test For see difference motivation Study chemistry students being studied with Digital Flipbook media using a learning model Problem Based Learning on the material sour base class XI which if sig α 0.05 states that Ha is accepted and H0 is rejected so that there is difference motivation Study student .Keywords : Digital Flipbook, PBL , Acid - Base, Learning Outcomes , Motivation Study .

Leveraging deep learning with progressive growing GAN and ensemble smoother with multiple data assimilation for inverse modeling

The incorporation of hard data in geostatistical modeling is crucial for enhancing the accuracy of interpolating or stochastically estimating subsurface spatial features. The hard data at specified points in the model domain serve as a guide in optimizing the unknown parameters to follow the patterns of the hard data. Recently, a novel approach to solving hydrogeologic/reservoir modeling problems has emerged by using deep generative models, specifically generative adversarial networks (GANs), to generate realistic and diverse images of channelized aquifers. This subsequently can be coupled with inverse models to solve parameter estimation problems. This study focused on using an improved GAN, called a progressive growing generative adversarial network (PGGAN), conditioned with hard data to perform parameter estimation of complex facies models by coupling an ensemble smoother with multiple data assimilation (ES-MDA). First, the PGGAN was trained to an image with 128 × 128 resolution. The trained PGGAN was used to generate hydraulic conductivity fields when fed an ensemble of latent variables and hard data. The ES-MDA then was used to update the latent variable with the help of hydraulic head data obtained from the groundwater model. The approach was tested on synthetic hydraulic conductivity data. Results show that this approach was able to perform efficient estimation of an unknown facies model domain. Additionally, the proposed method was applied to a different test case of a facies model exhibiting different statistical characteristics. The results were satisfactory, demonstrating that the method is not constrained to the particular hydraulic conductivity fields introduced in the generator’s training.

Regional 3D geological modeling along metro lines based on stacking ensemble model

This paper presents a regional 3D geological modeling method based on the stacking ensemble technique to overcome the challenges of sparse borehole data in large-scale linear underground projects. The proposed method transforms the 3D geological modeling problem into a stratigraphic property classification problem within a subsurface space grid cell framework. Borehole data is pre-processed and trained using stacking method with five different machine learning algorithms. The resulting modelled regional cells are then classified, forming a regional 3D grid geological model. A case study for an area of 324 km2 along Xuzhou metro lines is presented to demonstrate the effectiveness of the proposed model. The study shows an overall prediction accuracy of 85.4%. However, the accuracy for key stratigraphy layers influencing the construction risk, such as karst carve strata, is only 4.3% due to the limited borehole data. To address this issue, an oversampling technique based on the synthetic minority oversampling technique (SMOTE) algorithm is proposed. This technique effectively increases the number of sparse stratigraphic samples and significantly improves the prediction accuracy for karst caves to 65.4%. Additionally, this study analyzes the impact of sampling distance on model accuracy. It is found that a lower sampling interval results in higher prediction accuracy, but also increases computational resources and time costs. Therefore, in this study, an optimal sampling distance of 1 m is chosen to balance prediction accuracy and computation cost. Furthermore, the number of geological strata is found to have a negative effect on prediction accuracy. To mitigate this, it is recommended to merge less significant stratigraphy layers, reducing computation time. For key strata layers, such as karst caves, which have a significant impact on construction risk, further on-site sampling or oversampling using the SMOTE technique is recommended.

Using different digital tools in designing and solving mathematical modelling problems

While existing studies acknowledge the importance of using technology in the mathematical modelling process, questions about how to integrate digital tools into mathematical modelling are not still answered. This study aims to examine pre-service mathematics teachers’ designing and solving mathematical modelling problems by using different digital tools through the collaboration of two different courses in their education program. The GeoGebra-supported modelling cycle was adopted as the conceptual framework of the study. The case study was used to design the research. The participants of the study were three volunteer pre-service secondary mathematics teachers, who were able to use and integrate digital tools in mathematics education. The pre-service teachers were asked to design a mathematical modelling problem by integrating different digital tools as the final assignment in both courses. The designed mathematical modelling problem, the video records of pre-service teachers’ explanations including the designing and solving process, and the video records of the focus group interview were the data of the study. The results showed that the pre-service teachers were able to design and solve an effective and comprehensive mathematical modelling problem using technology by combining their skills that they had learnt through different courses. In particular, they were able to use different digital tools in both designing and solving a mathematical modelling problem. Their solution also led to the extension of the adopted framework by adding new technological actions into the modelling stages.