Proposed Analysis Method Research Articles

Determination of Optical and Structural Parameters of Thin Films with Differently Rough Boundaries

The optical characterization of non-absorbing, homogeneous, isotropic polymer-like thin films with correlated, differently rough boundaries is essential in optimizing their performance in various applications. A central aim of this study is to derive the general formulae necessary for the characterization of such films. The applicability of this theory is illustrated through the characterization of a polymer-like thin film deposited by plasma-enhanced chemical vapor deposition onto a silicon substrate with a randomly rough surface, focusing on the analysis of its rough boundaries over a wide range of spatial frequencies. The method is based on processing experimental data obtained using variable-angle spectroscopic ellipsometry and spectroscopic reflectometry. The transition layer is considered at the lower boundary of the polymer-like thin film. The spectral dependencies of the optical constants of the polymer-like thin film and the transition layer are determined using the Campi–Coriasso dispersion model. The reflectance data are processed using a combination of Rayleigh–Rice theory and scalar diffraction theory in the near-infrared and visible spectral ranges, while scalar diffraction theory is used for the processing of reflectance data within the ultraviolet range. Rayleigh–Rice theory alone is sufficient for the processing of the ellipsometric data across the entire spectral range. We accurately determine the thicknesses of the polymer-like thin film and the transition layer, as well as the roughness parameters of both boundaries, with the root mean square (rms) values cross-validated using atomic force microscopy. Notably, the rms values derived from optical measurements and atomic force microscopy show excellent agreement. These findings confirm the reliability of the optical method for the detailed characterization of thin films with differently rough boundaries, supporting the applicability of the proposed method in high-precision film analysis.

An augmented integral method for probability distribution evaluation of performance functions

The paper proposes an efficient augmented integral method for probability distribution evaluation of performance functions. In the proposed method, the performance function is augmented by adding an auxiliary random variable, whose probability density function (PDF) and cumulative distribution function (CDF) are formulated as the integrations of the original performance function with respect to basic random variables. The optimal auxiliary random variable is determined to provide an accurate estimation of the integrations by investigating the geometric properties of integrands and a distribution parameter optimization approach based on moment analysis. According to the convolution formula, the relationship between the PDFs of the augmented performance function and the original performance function is clarified. Then, the PDF of the original performance function is calculated by solving an unconstrained optimization problem that is established using the convolution formula. Finally, three numerical examples are investigated to demonstrate the efficiency and accuracy of the proposed method for structural reliability analysis. The results indicate that the proposed method can evaluate the probability distribution of performance functions accurately and efficiently, even when the performance functions are strongly nonlinear and implicit.

An Analysis and Optimization of Distortion Effect Caused by Pupil Decentering in Optical Gun Scope

During the use of optical gun scopes, slight movements between the human eye and the instrument can cause the pupil to offset from the optical axis, resulting in a dynamic distortion effect. This affects the accuracy and stability of aiming. Based on the mechanism, this study established parameters of the centroid’s deviation of image spots for marginal field points under pupil decentering and centering conditions and their differences to quantitatively evaluate the distortion. These evaluation parameters were obtained by performing a double integral calculation of the ray aberration distribution function over the entire designed exit pupil. Based on this evaluation method, three optical design strategies for reducing the distortion were proposed: optimizing ray aberrations, optimizing centroid shift of image spots, and utilizing vignetting effects. An optimization process was established by combining increasing vignetting and suppressing centroid shift. For a gun scope with significant distortion, the distortion effect was significantly weakened by increasing the vignetting factor and optimizing the centroid shift of image spots. This proved the effectiveness of the proposed analysis, evaluation, and optimization design methods.

Robust and stochastic sparse subspace clustering

Sparse subspace clustering (SSC) has been widely employed in machine learning and pattern recognition, but it still faces scalability challenges when dealing with large-scale datasets. Recently, stochastic SSC (SSSC) has emerged as an effective solution by leveraging the dropout technique. However, SSSC cannot robustly handle noise, especially non-Gaussian noise, leading to unsatisfactory clustering performance. To address the above issues, we propose a novel robust and stochastic method called stochastic sparse subspace clustering with the Huber function (S3CH). The key idea is to introduce the Huber surrogate to measure the loss of the stochastic self-expression framework, thus S3CH inherits the advantage of the stochastic framework for large-scale problems while mitigating sensitivity to non-Gaussian noise. In algorithms, an efficient proximal alternating minimization (PAM)-based optimization scheme is developed. In theory, the convergence of the generated sequence is rigorously proved. Extensive numerical experiments on synthetic and six real datasets validate the advantages of the proposed method in clustering accuracy, noise robustness, parameter sensitivity, post-hoc analysis, and model stability.

FROM ENERGY INTENSITY TO SUSTAINABILITY: AN ANALYSIS OF TRENDS IN THE ALUMINIUM INDUSTRY

The article analyses trends in the aluminium industry from the point of view of sustainable development and energy efficiency. The significant impact of industrial enterprises on the environment is discussed, particularly, the high level of greenhouse gas emissions caused by energy consumption in aluminium smelting. Possibilities of reducing the negative impact due to the use of renewable energy sources, such as hydropower, as well as the implementation of energy-efficient practices, have been identified. A taxonomic analysis was used to assess the sustainable development of aluminium enterprises due to its advantage in identifying problems and directions for production improvement. The proposed method of analysis is based on the system of factors that influence the development of the industry and correspond to the concept of sustainable development. Based on the available data of the International Aluminium Institute (IAI), the analysis was carried out using the following factors: economic (volume of production, energy intensity of primary aluminium smelting, total energy consumption of production, labour productivity, impact of energy intensity on emissions), environmental (emissions of greenhouse gases and energy consumption of aluminium smelting using different energy sources), social (million hours reported worked, lost time accident rate, restricted work/medical treatment accident rate). Approbation of the proposed methodology on the example of international statistical data makes it possible to determine the biggest gaps in ensuring the sustainable development of aluminium industry production, including the use of various energy sources. Based on the results of the analysis, it was found that none of the factors used in monitoring the activities of aluminium producers reach the reference values. In the block of economic factors, the taxonomic indicator varies between 0.18 and 0.38 (the worst efficiency is observed in terms of total production volumes). Environmental factors have taxonomic values in the range of 0.07–0.36 (the largest reserves exist in ensuring the efficiency of energy consumption using hydropower, as well as reducing greenhouse gas emissions in the process of primary aluminium production). Among the social factors, the biggest problems are labour safety and lost working hours; as a result, the taxonomic indicator for this block is in the range of 0.04 - 0.33. The obtained results indicate the need for constant improvements in the production of aluminium, which is one of the main producers of greenhouse gases due to the high energy intensity of production. The proposed approach for conducting an analysis can be improved depending on the available statistical data and the goals of the analysis. In any case, it is valuable for obtaining information on the most critical areas in supporting the sustainable development of the industry.

Cancer subtype identification by multi-omics clustering based on interpretable feature and latent subspace learning

In recent years, multi-omics clustering has become a powerful tool in cancer research, offering a comprehensive perspective on the diverse molecular characteristics inherent to various cancer subtypes. However, most existing multi-omics clustering methods directly integrate heterogeneous features from different omics, which may struggle to deal with the noise or redundancy of multi-omics data and lead to poor clustering results. Therefore, we propose a novel multi-omics clustering method to extract interpretable and discriminative features from various omics before data integration. The clinical information is used to supervise the process of feature extraction based on SHAP (SHapley Additive exPlanation) values. Singular value decomposition (SVD) is then applied to integrate the extracted features of different omics by constructing a latent subspace. Finally, we utilize shared nearest neighbor-based spectral clustering on the latent representation to obtain the clustering result. The proposed method is evaluated on several cancer datasets across three levels of omics, in comparison to several state-of-the-art multi-omics clustering methods. The comparison results demonstrate the superior performance of the proposed method in multi-omics data analysis for cancer subtyping. Additionally, experiments reveal the efficacy of utilizing clinical information based on SHAP values for feature extraction, enhancing the performance of clustering analyses. Moreover, enrichment analysis of the identified gene signatures in different subtypes is also performed to further demonstrate the effectiveness of the proposed method.Availability: The proposed method can be freely accessible at https://github.com/Tianyi-Shi-Tsukuba/Multi-omics-clustering-based-on-SHAP. Data will be made available on request.

An energy and information analysis method of logic gates based on stochastic thermodynamics.

To reduce the energy consumption of logic gates in digital circuits, the size of transistors approaches the mesoscopic scale, e.g. sub-7 nanometers. However, existing energy consumption analysis methods exhibit various deviation for logic gates when the nonequilibrium information processing of mesoscopic scale transistors with ultra-low voltages is analyzed. Based on the stochastic thermodynamics theory, an information energy ratio method is proposed for the energy consumption estimation of XOR gates composed of mesoscopic scale transistors. The proposed method provides a new insight to quantify the transformation between the information capacity and energy consumption for XOR gates and extending to other logic gates. Utilizing the proposed analysis method, the supply voltage of the parity check circuit can be optimized by numerical simulations without expensive and complex practical measurements. The information energy ratio is the first analytical method to quantify the energy and information transformation of logic gates at the mesoscopic scale.

Transverse seismic analysis method of underground interchange prefabricated utility tunnel

The rapid development of underground utility tunnels has led to the formation of a large number of interchange utility tunnels. Due to significant differences in the lateral resisting stiffness in orthogonal directions, coupled with the close relationship between soil deformation and the depth of the utility tunnel, the seismic response mechanism of the interchange utility tunnel is complex. This paper proposes a method for transverse seismic analysis of the underground interchange utility tunnel based on the response displacement method. A load-structure analysis model of a certain underground cross-type interchange utility tunnel is first established. Then, the different conditions corresponding to maximum relative deformation between layers of the interchange node are discussed, and the proposed method is validated via the time-history analysis method. Based on the proposed analysis method in this paper, seismic response analysis is performed on the interchange utility tunnel considering the condition of vertical incidence of three different input seismic waves. Discussions are conducted in terms of internal forces, inter-story displacement angles, and damage responses under seismic excitations in different principal axis directions. The results show that under major earthquakes, the maximum inter-story displacement angle of the interchange node exceeds the standard limit by up to approximately 184 %, while the tensile damage can reach up to 0.985, significantly surpassing the tensile damage limit. Accordingly, the interchange node is the weakest part of the interchange utility tunnel. There exists deformation inconsistency between the interchange node and standard segments due to significant stiffness differences, with the influence range of the interchange node on internal forces, inter-story displacement angles, joint deformations and damage of the utility tunnel is approximately 7, 6, 8, and 6 prefabricated standard segments, respectively. Since the maximum relative deformation between layers of the interchange node does not occur simultaneously, for double-layered and multi-layered interchange utility tunnels, it is necessary to comprehensively consider the maximum inter-story displacement angle between each layer to determine their most unfavorable condition. The analytical method and related research conclusions presented in this paper can provide references for the transverse seismic design of interchange utility tunnels.

New global exponential stability conditions for nonlinear delayed differential systems with three kinds of time-varying delays

For a class of nonlinear differential systems with heterogeneous time-varying delays, including distributed, leakage and transmission time-varying delays, a novel global exponential stability (GES) analysis method was developed. Based on the GES definition, some sufficient conditions and rigorous convergence analysis of nonlinear delayed differential systems are presented directly, which ensure all states to be globally exponentially convergent. The proposed analysis method not only avoids the construction of the Lyapunov–Krasovskii functional, but also uses some simple integral reduction techniques to determine the global exponential convergence rate. Furthermore, the main advantages and low calculation complexity are demonstrated through a theoretical comparison. Finally, three numerical examples are provided to verify the effectiveness of the theoretical results.

Resistance Analysis of Crack Propagation in Concrete Subjected to Hydraulic Pressure.

The KR resistance curve for hydraulic crack propagation in a concrete beam was determined and discussed. A semi-analytical method was introduced to calculate the hydraulic crack propagation in concrete. A series of concrete beams with various hydraulic pressures and initial crack depths were tested, and the hydraulic crack propagation in these beams was calculated. The calculated P-CMOD curves were first verified, and then the calculated KR resistance curve for hydraulic crack propagation was determined. Based on the test results and calculation results, the following conclusions can be drawn: The proposed analysis method can accurately predict the hydraulic crack propagation process in concrete. The KR resistance to hydraulic crack propagation in concrete decreases with the increase in hydraulic pressure but is less influenced by the initial crack depth of the test beams. In addition, the concrete beams collapse immediately under hydraulic fracturing once the KIw curve reaches the KR resistance curve. This indicates that the failure of concrete structures under hydraulic fracturing occurs immediately once the driving force of crack propagation, dominated by the hydraulic pressure in the crack, becomes significant.

Renewable energy sharing based on the effect of energy supply from energy transportation and storage side on building load demand

Abstract To lower environmental-based operation costs, many literatures studied the relationship between the energy generation side (EGS) and building load (BL) demand side based on solar-based integrated energy systems (SIESs), without directly considering the effect of energy from energy transportation and storage side (ETSS) on BL demand, which may result in waste of solar energy extracted. To enhance energy utilization, this study proposed an analysis method that renewable energy source shares among different buildings was investigated based on the supply relationship between energy from the ETSS side and BL demand side. ETSS included an electric boiler/chiller (EB/C), double-effect absorption heat pump (AHP) and tank. According to the energy sources from ETSS and building loads for a hotel, a residence and a hospital on a heating/cooling day. The proposed analysis method was used to develop the potential of available renewable energy through energy sharing from the perspective of the energy consumption differences of the three buildings. The results presented that the potential of renewable energy utilization was further developed by reasonably operating the use and storage of energy sources from ETSS based on the optimization between energy sources from EGS and building loads. Energy source shares among different buildings with different energy consumption characteristics enhanced energy efficiency according to reasonably change the useable time of energy sources from tanks. When a building required a large number of energy sources, the buildings with low energy consumption directly shared renewable energy without considering the use of energy storage. This study can provide a reference for optimizing the design of integrated energy system (IES)-based architecture with different building loads.

A Novel Hybrid Feature Extraction Methods for EEG Based Emotions Classification Using Ensemble Approaches in HIED Dataset

Introduction: Emotions play a significant role in human relationships in everyday challenges. Human-machine interactions and the complexities of its research include humanoid robots which rely significantly on emotional queries. The present study recommends a novel methodology for human emotion identification using electroencephalogram (EEG) signals. Machine learning (ML) techniques based on electroencephalogram have demonstrated impressive results in distinguishing emotions. Method: The present study investigates five ensemble learning-based machine learning (EML) and five conventional machine learning (CML) algorithms for achieving the recognition of human emotions from EEG signals. The main objective of the current research study is to implement the optimal approach for classifying emotions and subsequently will achieve it by using physiological characteristics to categorise the seven main emotional states (stress, happy, sadness, anger, fear, disgust, and surprise). This research follows the study investigation of ensemble learning-based machine learning (EML) and conventional machine learning (CML) algorithms for achieving the recognition of human emotions from EEG signals. Initially, the EEG data in this study are categorized into theta, alpha, beta, and gamma bands using a DWT. Result: With this idea, the research elaborates on further decomposition based on bandseparated EEG signals known as intrinsic mode functions (IMFs) along with empirical mode decomposition is subsequently implemented. Then, 13 statistical characteristics are extracted from the IMFs using five multiclass EML algorithms: adaptive boosting, rotation random forest, bagging, random forest, and extreme gradient boost. The following procedure is carried out to construct an ML-based system. In the final phase, 10-fold cross-validation is used to assess the efficacy of these five EML algorithms. Accuracy, F1-score, and area-under-the-curve (AUC) are performance assessment metrics that are employed to compare the final results of these algorithms with the five CML techniques. Conclusion: The proposed method for EEG-based emotion analysis is significantly more effective and achieves greater outcomes than all of the techniques that were compared, based on the data from the experiments.

A topological analysis of Milan historical surface transport networks from 1856 to the present

This research examines the transport networks operating in Milan, Italy, in seven years, from 1856 to 2016. The networks are transformed into graphs and analysed with several techniques from graph theory, including a new centrality index called Icentr. With the help of this index, we identify the nodes, to be considered primary in the transportation network, that are better related both in terms of topology and more interconnected in terms of distance. The findings provide a detailed picture of how the primary nodes have shifted from the city’s inner core to outer areas over the course of the investigated decades, both for the topological case and when the graphs are weighted based on the distance between nodes. Particularly, the effect of distance is more evident in those historical phases when the city expands, creating longer connections between nodes, in contrast to phases when the city becomes denser. The proposed method of analysis appears suitable to be applied to other cities, both for simplicity and effectiveness.

Adaptation of the TIMBRE methodology for brownfields gully erosion analysis in urban areas

Soil erosion is a concern in many parts of the world, causing environmental and social impacts. Aiming at obtaining indicators of the recovery of brownfields created by gullies in urban areas, this study adapts the Tailored Improvement of Brownfield Regeneration in Europe (TIMBRE) for the analysis and classification of areas affected by gullies in the city of Bauru, Brazil. The TIMBRE methodology assists in the decision-making of priority areas for remediation and their reinsertion in urban spaces. The inventory of areas affected by gullies was compiled based on the analysis of two image sets (2004 and 2020) available on Google Earth. For the classification of brownfields, three classes were considered: Class 1 - local potential for business development, Class 2 - attractiveness and marketing, and Class 3 – environmental risks. These results demonstrate a correlation between gullies and urban expansion. The inventory identified 175 gullies in the municipality's urban perimeter in 2004, which affected an area of over 64 ha. In 2020, the number of gullies increased to 189, but the affected area decreased to 62 ha due to the recovery of some large gullies. The proposed methodology identified the area of Quinta da Bela Olinda as the one with the highest scores in all three classifications. Quinta da Bela Olinda is the location that has a local potential for business development, as it is the most attractive brownfield, as well as the area with the highest environmental risk. This area should, thus, be prioritized by public management for remediation. In conclusion, the proposed method of analysis can be transferred to other areas with adaptations in the criteria used and, therefore, may facilitate the management of urban areas affected by gullies in other places around the world.

From Sleep Patterns to Heart Rhythms: Predicting Atrial Fibrillation from Overnight Polysomnograms.

Atrial fibrillation (AF) is often asymptomatic and thus under-observed. Given the high risks of stroke and heart failure among patients with AF, early prediction and effective management are crucial. Importantly, obstructive sleep apnea is highly prevalent among AF patients (60-90%); therefore, electrocardiogram (ECG) analysis from polysomnography (PSG), a standard diagnostic tool for subjects with suspected sleep apnea, presents a unique opportunity for the early prediction of AF. Our goal is to identify individuals at a high risk of developing AF in the future from a single-lead ECG recorded during standard PSGs. We analyzed 18,782 single-lead ECG recordings from 13,609 subjects at Massachusetts General Hospital, identifying AF presence using ICD-9/10 codes in medical records. Our dataset comprises 15,913 recordings without a medical record for AF and 2,056 recordings from patients who were first diagnosed with AF between 1 day to 15 years after the PSG recording. The PSG data were partitioned into training, validation, and test cohorts. In the first phase, a signal quality index (SQI) was calculated in 30-second windows and those with SQI < 0.95 were removed. From each remaining window, 150 hand-crafted features were extracted from time, frequency, time-frequency domains, and phase-space reconstructions of the ECG. A compilation of 12 statistical features summarized these window-specific features per recording, resulting in 1,800 features. We then updated a pre-trained deep neural network and data from the PhysioNet Challenge 2021 using transfer-learning to discriminate between recordings with and without AF using the same Challenge data. The model was applied to the PSG ECGs in 16-second windows to generate the probability of AF for each window. From the resultant probability sequence, 13 statistical features were extracted. Subsequently, we trained a shallow neural network to predict future AF using the extracted ECG and probability features. On the test set, our model demonstrated a sensitivity of 0.67, specificity of 0.81, and precision of 0.3 for predicting AF. Further, survival analysis for AF outcomes, using the log-rank test, revealed a hazard ratio of 8.36 (p-value of 1.93 × 10 -52 ). Our proposed ECG analysis method, utilizing overnight PSG data, shows promise in AF prediction despite a modest precision indicating the presence of false positive cases. This approach could potentially enable low-cost screening and proactive treatment for high-risk patients. Ongoing refinement, such as integrating additional physiological parameters could significantly reduce false positives, enhancing its clinical utility and accuracy.

CИЛОВОЙ АНАЛИЗ ПЛОСКИХ РЫЧАЖНЫХ МЕХАНИЗМОВ ВЕКТОРНЫМ МЕТОДОМ

An analytical method is presented for force analysis of plain lever mechanisms with one degree of freedom, based on the vector method. Using the example of a two-drive structural group, a method is outlined for finding reaction vectors in all its kinematic pairs, while maintaining the clarity and consistency of the solution inherent in the graphic-analytical method of diagrams of component forces. An original analytical description is given for finding the vectors of tangential and normal components of reactions in kinematic pairs. Application of the proposed method of force analysis makes it possisble to find reaction vectors in kinematic pairs without compiling and solving complex systems of equilibrium equations or graphical construction. Adaptation of the proposed force analysis in modern mathematical packages allows for the study of plain lever mechanisms with one degree of freedom in a short time and with high accuracy.

Analysis of High-Rise Building Using Opensees

Numerical simulation has increasingly become an effective method and powerful tool for performance-based earthquake engineering research. Most existing numerical analyses use general-purpose commercial software, which can limit in-depth investigations on specific, complex topics. Consequently, this research focuses on the dynamic analysis of high-rise reinforced concrete (RC) frame-core tube structures using the open-source finite element (FE) code OpenSees to perform nonlinear seismic analyses. Various shear walls, a frame-core tube structure, and a tall building are simulated. The rationality and reliability of the proposed analysis method are validated through comparison with available experimental data and the analytical results of a well-validated commercial FE code. The research outcomes will provide a useful reference and an effective tool for further numerical analysis of the seismic behavior of tall buildings.

A statistical analysis method for significant wave height and spectral peak frequency considering the random and time-varying effects based on copula function and Bayesian inference

Random and time-varying effects are important factors for statistical analysis of wave characteristic variables, including the significant wave height and spectral peak frequency. This paper proposes a statistical analysis method for the accurate statistical analysis of the state of the ocean. Several common distributions are applied as candidates for describing a specific variable, denoted as the marginal distribution. The joint distribution for the wave characteristic variables is constructed using copula functions based on the marginal distributions. The probability and unknown parameters of the marginal distributions are then determined by fully Bayesian inference. The best-fitting marginal distribution is selected based on the posterior probabilities of the candidates. Then, unknown parameters of the candidate copula functions are estimated by maximum likelihood estimation. The best-fitting copula function is selected based on Akaike information criterion, root mean squared error and Nash Sutcliffe efficiency. The proposed method is verified using the National Data Buoy Center dataset for 2019. However, this dataset, collected from a network of almost 100 moored buoys and Coastal-Marine Automated Network (CMAN) stations, contains incomplete data. The results reveal that the best-fitting marginal distribution and copula function may vary with the month. The average and maximum values of the improved RMSE using the proposed method are only 0.0064 and 0.0187, respectively. This indicates the high accuracy of the proposed method for the statistical analysis of wave states even though missing some data.

Transfer from defective bridge information model to defect analysis model based on industry foundation classes

Bridges, as an important part in modern infrastructure networks, suffer from increasingly severe aging issues in recent years. Road agencies and authorities conduct regular inspections for their bridges and identify defects and deteriorations for condition assessment. Such defect information cannot be efficiently used for analysis in the structural domain. This study proposes an Industry Foundation Classes-based method to allow for the transfer from a defective bridge information model to a defect analysis model. The architectural model of bridge is first converted into analytical model and then the impacts of defects on structural properties are quantified with a stiffness reduction coefficient. Case studies are conducted to validate the applicability of the proposed method for defect analysis and a range of coefficients are tested on an illustrative case bridge. The results prove that the proposed method can generate instructive and informative knowledge on the safety and reliability of the entire structure. This study narrows the gap between the empirical condition assessment scheme and the numerical structural analysis scheme for bridge management and manages to make full use of inspection-related information within Building Information Modelling (BIM) environment.

Research and analysis of tower crane load behavior when the rope breaks

The object of research is the behavior of the load of the tower crane during the break of the sling. One of the most problematic areas is the safety of work and the prevention of emergency situations. Despite the presence of mandatory safety measures, during cargo transportation, one of the sling branches may be destroyed due to the presence of a dynamic component during the operation of the crane, or errors of the slinger when securing the cargo. Also, the presence of hidden internal or unnoticed defects in the sling construction itself cannot be ruled out. Also, one of the most problematic places is the chaotic fluctuations of the load, which negatively affect the stability of the crane and safety. The paper describes the case of the destruction of one of the branches of a two-rope sling during the transportation of a long product by a tower crane. The proposed method of cargo behavior analysis is based on the use of a dynamic description of cable system failure modes within the framework of setting and solving differential-algebraic equations. This makes it possible to more accurately describe the behavior of the cargo when the sling breaks. The obtained results show that the application of the proposed method makes it possible to bring the mathematical model of the two-link mathematical pendulum significantly closer to the actual mutual oscillations of the load during the sling break. This is due to the fact that the proposed method has a number of features, in particular, high sensitivity to changes in the behavior of the cargo and a quick reaction to a rope break. These results can be used in practice in the design and operation of tower cranes. Thanks to the application of the proposed method, it is possible to obtain accurate values of cargo behavior indicators and timely detection of a rope break. Compared to similar known methods, this method has such advantages as high efficiency, reliability and safety of operation.