Statistical Simulation Method Research Articles

Stochastic modelling of material variability in structural dynamics: A threefold comparison of Monte Carlo, polynomial chaos, and random sampling techniques

This article investigates the influence of random elastic modulus on beam eigenfrequencies using multiple simulation techniques: Monte Carlo simulations (employing Cholesky decomposition (MCS-CD) and Kosambi-Karhunen-Loève expansion (MCS-KKL)), Polynomial Chaos expansion (PCE), and a proposed Random Sampling method (RSM). Anomalies in Monte Carlo simulations, where normally distributed elastic modulus led to negative values and imaginary eigenfrequencies, were effectively addressed by adopting a log-normal distribution. Comparative analyses focused on covariance variation of the first three eigenfrequencies with correlation length and standard deviation of the random field, highlighting nuanced differences between normal and log-normal distributions. PCE exhibited distinct responses, showcasing variations in covariance with different distributions. The study culminates in eigenfrequency estimation using the proposed RSM, wherein the beam is discretised into n elements with randomly assigned elastic moduli. The mean and variance of eigenfrequencies are compared with existing methods, which represent an alternative method for achieving similar outcomes.These comparative studies provide a comprehensive understanding of how different statistical treatments and simulation methods impact the reliability and accuracy of eigenfrequency predictions in beams with random elastic properties, thus contributing valuable insights for structural analysis and design under uncertainty.

Enhanced sampling strategies for molecular simulation of DNA

AbstractMolecular dynamics (MD) simulations can provide detailed insights into complex molecular systems, such as DNA, at high resolution in space and time. Using current computer architectures, time scales of tens of microseconds are feasible with contemporary all‐atom force fields. However, these timescales are insufficient to accurately characterize large conformational transitions in DNA and compare calculations to experimental data. This review discusses the advantages and drawbacks of two simulation approaches to overcome the timescale challenge. The first approach is based on adding biasing potentials to the system to drive transitions. Umbrella sampling, steered MD, and metadynamics are examples of these methods. A key challenge of such methods is the necessity of selecting one or a few efficient coordinates, commonly referred to as collective variables (CVs), along which to apply the biasing potential. The path‐metadynamics methodology addresses this issue by finding the optimal route(s) between states in a multi‐dimensional CV space. The second strategy is path sampling, which focuses MD simulations on the transitions. The assumption is that even though transitions between states are rare, they are generally fast. Stopping the simulations as soon as they reach a stable state can significantly increase simulation efficiency. We introduce these methods on the two‐dimensional Müller–Brown potential. DNA applications are featured for two different processes: the Watson–Crick–Franklin to Hoogsteen transition in adenine–thymine base pairs and the binding of a DNA‐binding protein domain to DNA.This article is categorized under: Molecular and Statistical Mechanics Molecular Dynamics and Monte‐Carlo Methods Molecular and Statistical Mechanics Free Energy Methods Software Simulation Methods

Statistical RTA simulations of atomic data for astrophysical opacity modeling in the context of kilonova emission

When considering some complex lanthanide ions characterized by a half-filled 4f subshell, the atomic structure Hamiltonian matrix sizes are so large that their diagonalization is challenging and therefore the atomic data of these ions are only used to compute the expansion opacity of a kilonova with difficulty. To avoid this problem, we propose a statistical simulation method to compute kilonova expansion opacities based on the resolved transition array (RTA) method of Bauche et al (1991 Phys. Rev. A 44 5707). The atomic structure relativistic Hartree–Fock (HFR) method has been employed to compute the radial integrals necessary for our statistical RTA simulations where the atomic data are randomly drawn using their corresponding statistical distributions and to determine the exact expansion opacities where the atomic data are obtained by the diagonalization of the Hamiltonian matrix. The statistical RTA simulations carried out for two specific ions, i.e. Sm VIII and Eu VI, for which it is still possible to diagonalize the Hamiltonian matrix, reproduce well the expansion opacities computed using HFR atomic data. Based on this good agreements, the statistical RTA method was used to compute the expansion opacity of Dy VIII, which is determined through diagonalization with difficulty. The proposed statistical RTA simulation method allows the computation of reliable astrophysical expansion opacities which are of paramount importance for kilonova light curve modeling and spectral analysis.

P001 MicroRNA-155-5p contributes to the development of Ulcerative Colitis by regulating T lymphocyte proliferation and functions

Abstract Background MicroRNA (miRNA) is a small non-coding RNA which regulate a variety of cell functions by suppressing target mRNAs in a post-transcriptional manner. Recent works have identified an increased expression of miR-155-5p in the colonic mucosa of UC patients. However, the role of miR-155-5p in the pathophysiology of UC remains understudied. This study aims to clarify the role of miR-155-5p in development of colitis in UC patients. Methods MiRNA and mRNA expression profiles in colon were compared between 15 UC and 5 healthy controls by running small RNA-sequencing (smRNA-Seq) and RNA-Seq on the matched colon tissue. Candidate target genes of miR-155-5p were identified by analyzing sequencing data sets using a statistical simulation method (miRhub). MiR-155-5p expressing cells were identified by in situ hybridization in combination with immunohistochemistry on inflamed colon tissue of UC patients. The impact of miR-155-5p on colonic inflammation was tested in the dextran sulfate sodium (DSS) -induced colitis model using miR-155 deficient mice. Results MiR-155-5p expression was significantly higher in the inflamed colonic tissue of UC patients than in healthy controls with more pronounced up-regulation in the treatment refractory UC patients compared to the treatment naïve UC patients (UC vs. healthy controls, log2FC = 0.83, adjusted p-value = 0.014). MiRhub analysis identified 10 candidate target genes of miR-155-5p including SHANK2, MYO1D, ADD3, AHCYL2, NR3C2, MIER3, TRIM2, GPD1L, SEMA5A, and SATB2 most of which were involved in cell proliferation and immune response (NR3C2, MIER3, TRIM2, GPD1L, SEMA5A, and SATB2). In situ hybridization identified a group of CD3 positive T lymphocytes with increased miR-155-5p expression in the inflamed colonic mucosa. MiR-155 deficient mice showed attenuated DSS-induced inflammation in colon compared to the control wild type mice (colon weight/length ratio, miR-155 deficient mice vs. controls, 27.2 vs. 44.6, p<0.01). Conclusion MiR-155-5p may contribute to the development of colitis in UC by regulating T lymphocyte proliferation and functions.

Assessment of Solar Energy with Respect to Bihar: A Case Study

A well-known statistical simulation method known as ARIMA was employed in this article to forecast the total daily solar energy output till the year 2040. The ARIMA model’s attractiveness resides in its simplicity, solar energy, which is created by sunshine, is a non-depleting renewable energy source that is unpolluting. The amount of solar energy that enters the earth every hour is sufficient to supply all of the energy needed for a year. In the modern period, we required electricity constantly. This solar energy is produced for use in commercial, industrial, and residential settings. It is simple to collect energy from direct sunshine. As a result, it is incredibly effective and does not pollute the environment. In this paper, we evaluated solar energy from sunlight and forecasted the sun radiation till 2040 through ARIMA Model.The model is created using sophisticated statistical approach. Error analysis is performed to demonstrate the effectiveness of the proposed method. The developed model’s accuracy can be improved in future research.

Integrating Statistical Simulation and Optimization for Redundancy Allocation in Smart Grid Infrastructure

It is a critical issue to allocate redundancy to critical smart grid infrastructure for disaster recovery planning. In this study, a framework to combine statistical prediction methods and optimization models for the optimal redundancy allocation problem is presented. First, statistical simulation methods to identify critical nodes of very large-scale smart grid infrastructure based on the topological features of embedding networks are developed, and then a linear integer programming model based on generalized assignment problem (GAP) for the redundancy allocation of critical nodes in smart grid infrastructure is presented. This paper aims to contribute to the field by employing a general redundancy allocation problem (GRAP) model from high-order nonlinear to linear model transformation. The model is specifically implemented in the context of smart grid infrastructure. The innovative linear integer programming model proposed in this paper capitalizes on the logarithmic multiplication property to reframe the inherently nonlinear resource allocation problem (RAP) into a linearly separable function. This reformulation markedly streamlines the problem, enhancing its suitability for efficient and effective solutions. The findings demonstrate that the combined approach of statistical simulation and optimization effectively addresses the size limitations inherent in a sole optimization approach. Notably, the optimal solutions for redundancy allocation in large grid systems highlight that the cost of redundancy is only a fraction of the economic losses incurred due to weather-related outages.

FLASH LiDAR SINGLE PHOTON IMAGING OVER 50 KM

Abstract. In order to demonstrate the feasibility of single-photon imaging of flash lidar in the permanent shadow area of the moon, a set of space-based single-photon imaging system is designed, including the lidar based on VCSEL array, the optical emitting system based on the uniform beam shaping meta-lens using propagation phase and geometric phase joint control method, the two-axis three-mirror optical receiving system, and the single-photon detector array based on photon counting mode. According to the heavy-tailed pulse laser function, Poisson statistical filtering theory and Monte Carlo simulation method, the echo photon number, the photon counting process, the ranging accuracy and the intensity image are simulated in the condition of 50 km detection distance by setting different of the object reflectivity, the repetition times and the gating interval time. The results show that according to the parameter settings in this paper, the number of echo photons is as low as about 10-4 orders. However, the photon counting waveform can better restore the transmission waveform. The setting of the repetition number and the gating interval time should not only consider the missing detection phenomenon, but also consider the noise accumulation. When the repetition number is 2000 and the gate number is 200, the ranging accuracy can reach 0.075m, and the imaging in the crater without light is realized.

Numerical Investigation of Radiation in a Shock-Heated CO2 and N2 Mixture by the Direct Statistical Simulation Method

Numerical Investigation of Radiation in a Shock-Heated CO2 and N2 Mixture by the Direct Statistical Simulation Method

Analysis of mathematical methods and principles of molecular dynamics and monte carlo method

In this era, molecular dynamics and Monte Carlo methods have become the primary simulation methods. With the emergence of computer simulation research methods, it has been possible to solve the sizeable computational volume and some other problems in the simulation process. At present, molecular dynamics simulations have taken an essential place in the substantial computational system and have a remarkable ability to solve multi-body problems. Therefore, researchers widely use it in many fields such as physics, chemistry, and materials science. Meanwhile, the Monte Carlo method is also a very effective statistical simulation method. This method can far surpass ordinary integration in efficiency with guaranteed computational accuracy. Furthermore, the derived kinetic Monte Carlo method can simulate and study dynamics problems. It can be seen that both simulation methods play an vital role in various disciplines. Therefore, it is very significant to understand the mathematical principles behind them and to know their advantages and disadvantages.

Application of Monte Carlo model in financial field

MC (Monte Carlo) model is also called statistical test method or statistical simulation method. According to the statistical sampling theory, it is a method of approximate solution through probability simulation and statistical test of random variable function. Compared with the traditional mathematical statistics method, MC method alleviates the difficulty of realization with the help of computer, and is easy to operate and understand. Other mathematical methods can find an appropriate way to deal with complex problems that are difficult or even impossible to deal with. This paper studies the application of MC model in the financial field: the application in the pricing of financial options and the application in the guaranteed price of multi-period income. Using MC simulation model, we can not only analyze the risk of investment projects, but also play a great role in management, financial analysis and marketing.

FORECASTING WORK OF INTENSIVE CARE UNIT ON THE BASIS OF STATISTICAL SIMULATION

The profound economic transformations taking place in Russia, the transition of health care to new management mechanisms, and the focus on insurance medicine give special actuality to improving the operational management of medical and prophylactic institutions and related services. Given the complexity of the system under study, a mathematic simulation was applied. Study purpose: To increase the efficiency of the resuscitation and intensive care unit through possible planning, based on studying the features of the functioning of this type units. Methods: A method of statistical simulation is proposed as a particular method of mathematical modeling for studying the functioning of the resuscitation and intensive care unit, which was not previously used in this direction. Results: During the work, the intensive care unit no. 2 of the Samara Regional Clinical Hospital named after V.D. Seredavin and the business process of the department’s functioning were studied, an averaged process was selected, a statistical study of the business process was carried out, and the distribution laws were identified and evaluated. Some simulation algorithms were developed based on a random number generator for individual random variables, and some statistical indicators were determined, which were calculated during implementation of all these algorithms. Using the specialized AnyLogic tool, we managed to develop a model of resuscitation and intensive care unit work, the number of runs was determined and considered in the program for the possibility of conducting experiments and comparing the data received. An experiment was performed on a model with changing various input data. The data obtained were analyzed, including using specialized software, and some consistent patterns were identified. Practical significance: Directions for optimizing the work of the department were proposed, and mathematical formulas were suggested for predicting and monitoring the operation of an intensive care unit.

Reliability analysis of optical IRS-enabled FSO system with multiple detectors and PCB under composite turbulence fading channels considering the impact of GML

Free space optical (FSO) communication with optical intelligent reflecting surface (IRS) assistance is one promising and evolving technology that can relax the line-of-sight requirement and enable more efficient and reliable link performance in obstacles areas. In this work, an optical IRS-enabled FSO system is proposed with partially coherent beam (PCB) and multiple detectors. Specifically, for an end-to-end (e2e) IRS-assisted FSO link, the statistical model of optical signal fluctuations due to atmospheric turbulence is assumed to follow Fisher–Snedecor F-distribution, and the random movements of IRS, transmitter (Tx), and receiver (Rx) due to building sway is modeled by geometric and misalignment losses. Considering the Gaussian–Schell model and intensity modulation/direct detection, the analytical average bit error rate (ABER) expressions of the studied system are obtained for a single detector and multiple detectors, respectively, with selected combining (SC), equal gain combining (EGC) and maximum ratio combining (MRC) aperture diversity schemes over independent identically distributed composite fading channels. And the correctness of the analytical results is verified through the Monte-Carlo based statistical simulation method. Results show that the ABER and outage probability performance of IRS-assisted FSO link degrades with the increase in the strength of atmospheric turbulence and building sway. And even the position fluctuations variances of Tx, IRS, and Rx are the same, their impacts on the e2e IRS-assisted FSO link are not the same. Interestingly, aperture diversity techniques can significantly mitigate these adverse effects, especially in the case of MRC scheme. Besides, the studied system with PCB can achieve better system performance compared to that using coherent beam, and the performance gap would become more obvious as the spatial coherence radius decreases. This work could serve as a guide for the design and research of IRS-enabled FSO communication systems.

Multiple Retest Systems for Screening High-Quality Chips

In this study, we develop a digital integrated circuit testing model (DITM) based on a statistical simulation method to evaluate the test quality and yield of integrated circuit products. This model can be used to quantify the characteristics of the device under test (DUT) and simulate the effect of the test guardband (TGB) on test results during testing. The complexity and functionality of integrated circuits have continued to increase over the past two decades. Moreover, the development in speed of automated test equipment (ATE), e.g., OTA or overall timing accuracy, according to the ITRS report, lags behind the progress of semiconductor manufacturing. Hence, using existing instruments and tools to select zero-defect products would be a considerable challenge for suppliers due to the slow development of the testing technology. We propose a new scheme of using multiple retest systems (MRSs) to improve the yield while maintaining the desired quality to address the product quality requirements of consumers. We also use a set of parameters from IRDS 2021 (International Roadmap for Devices and Systems 2021) to estimate the future test yield (Yt) and test quality through DITM calculations. MRS results showed that the test yield (Yt) can be improved while achieving the expected quality. MRSs not only improve the performance of the tester but also demonstrate effective performance in the yield improvement of high-quality products. This approach enables high-quality, high-yield chip delivery, and significantly increases the overall profit of the company.

Optimal reception of multiple phase shift keying and quadrature amplitude modulation signals with non-coherent processing of harmonic interference

Objectives . Analysis of the reception noise immunity of multiple phase shift keying (M-PSK) and quadrature amplitude modulation (M-QAM) signals has demonstrated a significant reduction in the quality of reception of discrete information due to the presence of various types of non-fluctuating interference in a radio communication channel including targeted harmonic interference. Therefore, the development of algorithms for compensating the influence of such forms of interference is an urgent task. While various methods for combatting this kind of interference, these vary in terms of their effectiveness. The aim of the present work is to synthesize and analyze the optimal algorithm for the reception of M-PSK and M-QAM signals with incoherent processing of harmonic interference. Methods . Various statistical radio engineering and computer simulation methods were used in accordance with optimal signal reception theory. Results . Synthesis and analysis of the optimal algorithm for receiving M-PSK and M-QAM signals with incoherent processing of harmonic interference were carried out. In addition to calculating the correlation integrals in the receiver, it is necessary to form weight coefficients, whose value depends on the correlation of the interference oscillation (extracted from the received mixture) with a sample of the interference stored in the receiver. The dependences of the bit error probability on the signal-to-noise ratio, interference detuning, and inaccuracy in setting the frequency and level of the interference sample in the receiver were obtained. It is shown that the higher the gain in the noise immunity of reception, the greater the intensity of the harmonic interference. Conclusions . The synthesized receiver circuit effectively compensates for harmonic interference. However, the efficiency of its operation depends on the detuning of the harmonic interference relative to the center frequency of the spectrum of the useful signal. The scheme for incoherent processing of harmonic interference remains operational even with small (within ±10%) inaccuracies in setting the frequency and the level of the interference copy in the receiver.

Radiotoxicity and health risk assessment of 222Rn in groundwater using statistical and Monte Carlo simulation approaches

Water is an important natural resource to humans, and itsquality has been a big concern from time immemorial. Water is polluted by the increasing activities of man. Pollutants of major concern include naturally occurring radioactive materials (NORM), heavy and potentially toxic metals, which are ubiquitous in the environment. Naturally occurring radionuclides such as 222Rn are the major precursors of lung and other types of cancer in humans. Exposure to radon in drinking water in excess of 300 pCi/L is treated as a radiological risk, while toxic metals in excess of the World Health Organization (WHO) maximum permissible levels in drinking water are considered both environmental and health risks to humans. A total of 34 groundwater samples were collected in the Akoko area of Ondo State, Nigeria for 222Rn activity concentration determination. The water samples were collected using standard techniques. RAD7 solid-state-detector was utilized for the 222Rn measurements. The results show the activity concentration of 222Rn ranging from 76 pCi/L to 3593 pCi/L with a mean value of 705 ± 76 pCi/L. Inhalation and ingestion doses from 222Rn dissolved in groundwater were evaluated for the infants, children, and adult populations in the study area. Radiological risks were evaluated through statistical and Monte Carlos simulation methods. It can be concluded from this study that there exists a likelihood of radiation-induced health risks due to inhalation of 222Rn from the sampled water.

ПРЕДПОСЫЛКИ ИМИТАЦИОННОГО МОДЕЛИРОВАНИЯ ПРОЦЕССОВ ОРГАНИЗАЦИИ РАБОТ ПО ТО И РЕМОНТУ АВТОМОБИЛЕЙ В АТП ОБЩЕГО ПОЛЬЗОВАНИЯ С ПОДКЛЮЧЕНИЕМ СПЕЦИАЛИЗИРОВАННЫХ ПРЕДПРИЯТИЙ АВТОСЕРВИСА

The modern tasks of organizing the maintenance and repair of ambulances, based on the cooperation of their implementation in motor transport organizations (ATP) and car service enterprises, are considered. Based on a preliminary analysis, research options for the rational or-ganization of such processes based on the application of statistical simulation methods tied to real operation are formulated.

Multiple-point statistics and non-colocational soft data integration

In geostatistics, available conditional information is typically categorized as either hard (with no uncertainty) or soft (associated with an uncertainty) data. 2-point based Gaussian (kriging) simulation methods have since their inception been able to account for hard and soft data. In contrast, multiple-point statistical (MPS) simulation methods, that allow quantifying more complex phenomena than Gaussian methods, have focused mostly on conditioning to hard data. The most widely used method for accounting for soft data is to consider only co-located soft data. Here we define conditional information data through a probability distribution and show how a general probabilistic solution, in the form of a posterior probability distribution, can be obtained, combining conditional categorical information with information from a categorical training image. We demonstrate how to compute the conditional distribution, as needed by most MPS-based sequential simulation algorithms, that allows accounting for both co- and non-co-located hard and soft data. Examples are provided comparing the direct computation of conditional statistics to using more computational demanding rejection sampling. In order to reduce the significant computational demands, a distance-based measure is proposed to increase the entropy of conditional data, based on the distance to the point being estimated and simulated.

Performance analysis of hybrid free space optical and visible light communications for underwater applications using spatial diversity

In this paper, we analyze a combination based on a hybrid triple hop terrestrial free-space optical (FSO), a fiber optic cable (FOC), and an underwater optical wireless communication (UOWC) link for providing high-speed optical connectivity between onshore and submerge systems. UOWC, scattering, absorption, and turbulence severely degrade the reliability and transmission rate of the UOWC link. In our manuscript, a bend-insensitive intermediate FOC link and a spatial diversity (SD) are exploited to improve the error performance of UOWC links, which involves the deployment of multiple input single outputs (MISO). For this purpose, different transmission signaling schemes, such as pulse position modulation (PPM) with spatial modulation (SM) and on–off keying (OOK) with repetition coding (RC), are employed to evaluate the system performance in terms of average bit error rate (ABER). The behavior of the entire system is obtained by applying a decode-and-forward (DF), where we consider log-normal channels for FSO and UOWC. The path loss and turbulence are obtained using intensity modulation and direct detection schemes. To obtain performance results, Monte Carlo-based statistical simulation method is applied to validate the analytical ABER performance of the system. The achieved results reveal that MISO-OOK-RC has superior ABER performance as compared to MISO-PPM-SM in higher signal-to-noise ratio (SNR) conditions with different underwater turbulence strengths.

Застосування числових методів газодинамічних розрахунків в задачах обтікання перешкод розрідженим струминним потоком

The development of competitive space hardware calls for continuing improvements in the accuracy of simulation of gas-dynamic processes in the space vehicle vicinity. This may contribute to extending the active life of spacecraft, thus improving the economic efficiency of space activities. In particular, quite a topical problem is the simulation of the interaction of rarefied jets from the propulsion system of a spacecraft with its individual components. To solve this problem in the case of a rather high surrounding vacuum, use is made of the molecular-kinetic concept of the gas structure based on the Boltzmann equation. The aim of this paper is to overview existing methods of simulation of gas-dynamic processes near spacecraft in a rarefied gas flow with account for propulsion system jets and to choose the most promising approaches to the solution of this problem. Among the methods considered, several main lines are set off: approximate, analytical, and numerical methods. Approximate methods use physical models of jet flow, approximation of numerical results, or a combination of both approaches. Analytical methods are based on essentially simplified assumptions and are intended for a very narrow class of problems. Numerical methods are the most universal tool of theoretical study. At the same time, each numerical method has a range of application of its own. At present, the most used and promising methods are statistical simulation methods: the direct simulation Monte Carlo method (DSMCM) and the test particle method (TPM). The former splits the continuous process of molecule motion and collisions in a rarefied gas into two successive independent stages (free-molecular transfer and relaxation) at each small time step. The simulation is done by time steps and in fact reproduces a nonstationary process. The latter, the TPM, consist in a statistical successive simulation of the wandering of test particles (molecules) on the background of field ones about the cells of the computational grid. Test particles, which move within the cells of the computational area, periodically collide with the obstacle in the flow and field particles, and in doing so they gradually change both their velocity and the field characteristics. For both statistical approaches, the simulation accuracy, as can be expected, is inversely proportional to the square root of the number of tests: the number of time steps and modeling particles for the DSMCM and the number of successively simulated test particle trajectories for the TPM. This may greatly affect the possibility of attaining a desired accuracy.

A probabilistic approach to the description of the crack kinetics and fatigue failure of structural components with allowance for the effect of crack retardation after overloads

A probabilistic approach to assessing fatigue strength and cyclic life based on Wheeler’s model is presented. The approach provides the possibility of estimating the probability of failure of the structural component under consideration, with allowance for the effect of crack retardation after the overload. The initial crack size, the parameters of the Paris equation, and the exponent of the crack retardation power function are assumed random parameters. The kinetics of a fatigue crack is described by cycle-by-cycle integration of the Paris equation written in finite differences. The probabilistic estimate is performed using the Monte Carlo statistical simulation method by repeatedly solving the Cauchy problem for various combinations of the values of random model parameters that are generated under the adopted laws of the probability distributions of those parameters. The probabilistic distributions of random parameters are selected proceeding from the level of the uncertainty of the problem using available statistical data without taking into accounting for data on the actual state of a particular structural component in real operation conditions. A computer code in Matlab environment has been developed for statistical description of the fatigue crack growth in structural components which allows accounting for the effect of crack retardation. An example of assessing the probability of the fatigue failure of a pipeline component with a longitudinal crack on the inner surface loaded by the internal pressure which varies according to a periodic law with a constant amplitude is presented for single tensile overload of the pipeline component. The dependencies of the fatigue failure probability on the number of loading cycles for various combinations of model parameters were obtained. The sensitivity of the fatigue failure probability under a given number of loading cycles to changes of the values of structural parameters was assessed.