Статті в журналах: "Stochastic inverse modeling"

1

Hestir, Kevin, Stephen J. Martel, Stacy Vail, Jane Long, Pete D'Onfro, and William D. Rizer. "Inverse hydrologic modeling using stochastic growth algorithms." Water Resources Research 34, no. 12 (December 1998): 3335–47. http://dx.doi.org/10.1029/98wr01549.

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2

Hohenegger, Christel, and M. Gregory Forest. "Direct and inverse modeling for stochastic passive microbead rheology." PAMM 7, no. 1 (December 2007): 1110505–6. http://dx.doi.org/10.1002/pamm.200700640.

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3

Ponski, Mariusz, and Andrzej Sluzalec. "Modeling and Simulation of Stochastic Inverse Problems in Viscoplasticity." Transactions of the Indian Institute of Metals 72, no. 10 (June 27, 2019): 2803–17. http://dx.doi.org/10.1007/s12666-019-01757-2.

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4

Boluh, Kateryna, and Natalija Shchestyuk. "Simulating Stochastic Diffusion Processes and Processes with “Market” Time." Mohyla Mathematical Journal 3 (January 29, 2021): 25–30. http://dx.doi.org/10.18523/2617-70803202025-30.

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The paper focuses on modelling, simulation techniques and numerical methods concerned stochastic processes in subject such as financial mathematics and financial engineering. The main result of this work is simulation of a stochastic process with new market active time using Monte Carlo techniques.The processes with market time is a new vision of how stock price behavior can be modeled so that the nature of the process is more real. The iterative scheme for computer modelling of this process was proposed.It includes the modeling of diffusion processes with a given marginal inverse gamma distribution. Graphs of simulation of the Ornstein-Uhlenbeck random walk for different parameters, a simulation of the diffusion process with a gamma-inverse distribution and simulation of the process with market active time are presented.To simulate stochastic processes, an iterative scheme was used: xk+1 = xk + a(xk, tk) ∆t + b(xk, tk) √ (∆t) εk,, where εk each time a new generation with a normal random number distribution.Next, the tools of programming languages for generating random numbers (evenly distributed, normally distributed) are investigated. Simulation (simulation) of stochastic diffusion processes is carried out; calculation errors and acceleration of convergence are calculated, Euler and Milstein schemes. At the next stage, diffusion processes with a given distribution function, namely with an inverse gamma distribution, were modelled. The final stage was the modelling of stock prices with a new "market" time, the growth of which is a diffusion process with inverse gamma distribution. In the proposed iterative scheme of stock prices, we use the modelling of market time gains as diffusion processes with a given marginal gamma-inverse distribution.The errors of calculations are evaluated using the Milstein scheme. The programmed model can be used to predict future values of time series and for option pricing.

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5

Preziosi, L., G. Teppati, and N. Bellomo. "Modeling and solution of stochastic inverse problems in mathematical physics." Mathematical and Computer Modelling 16, no. 5 (May 1992): 37–51. http://dx.doi.org/10.1016/0895-7177(92)90118-5.

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6

Abou-Elyazied Abdallh, Ahmed, and Luc Dupré. "Stochastic modeling error reduction using Bayesian approach coupled with an adaptive Kriging-based model." COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 33, no. 3 (April 29, 2014): 856–67. http://dx.doi.org/10.1108/compel-10-2012-0230.

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Purpose – Magnetic material properties of an electromagnetic device (EMD) can be recovered by solving a coupled experimental numerical inverse problem. In order to ensure the highest possible accuracy of the inverse problem solution, all physics of the EMD need to be perfectly modeled using a complex numerical model. However, these fine models demand a high computational time. Alternatively, less accurate coarse models can be used with a demerit of the high expected recovery errors. The purpose of this paper is to present an efficient methodology to reduce the effect of stochastic modeling errors in the inverse problem solution. Design/methodology/approach – The recovery error in the electromagnetic inverse problem solution is reduced using the Bayesian approximation error approach coupled with an adaptive Kriging-based model. The accuracy of the forward model is assessed and adapted a priori using the cross-validation technique. Findings – The adaptive Kriging-based model seems to be an efficient technique for modeling EMDs used in inverse problems. Moreover, using the proposed methodology, the recovery error in the electromagnetic inverse problem solution is largely reduced in a relatively small computational time and memory storage. Originality/value – The proposed methodology is capable of not only improving the accuracy of the inverse problem solution, but also reducing the computational time as well as the memory storage. Furthermore, to the best of the authors knowledge, it is the first time to combine the adaptive Kriging-based model with the Bayesian approximation error approach for the stochastic modeling error reduction.

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7

Llopis-Albert, Carlos, Francisco Rubio, and Francisco Valero. "Characterization and assessment of composite materials via inverse finite element modeling." Multidisciplinary Journal for Education, Social and Technological Sciences 6, no. 2 (October 3, 2019): 1. http://dx.doi.org/10.4995/muse.2019.12374.

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<p class="Textoindependiente21">Characterizing mechanical properties play a major role in several fields such as biomedical and manufacturing sectors. In this study, a stochastic inverse model is combined with a finite element (FE) approach to infer full-field mechanical properties from scarce experimental data. This is achieved by means of non-linear combinations of material property realizations, with a certain spatial structure, for constraining stochastic simulations to data within a non-multiGaussian framework. This approach can be applied to the design of highly heterogenous materials, the uncertainty assessment of unknown mechanical properties or to provide accurate medical diagnosis of hard and soft tissues. The developed methodology has been successfully applied to a complex case study.</p>

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8

Han, S. L., and Takeshi Kinoshita. "Stochastic inverse modeling of nonlinear roll damping moment of a ship." Applied Ocean Research 39 (January 2013): 11–19. http://dx.doi.org/10.1016/j.apor.2012.09.003.

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Llopis-Albert, Carlos, Francisco Rubio, Francisco Valero, Hunchang Liao, and Shouzhen Zeng. "Stochastic inverse finite element modeling for characterization of heterogeneous material properties." Materials Research Express 6, no. 11 (October 23, 2019): 115806. http://dx.doi.org/10.1088/2053-1591/ab4c72.

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10

Li, Liangping, Sanjay Srinivasan, Haiyan Zhou, and J. Jaime Gómez-Hernández. "A local–global pattern matching method for subsurface stochastic inverse modeling." Environmental Modelling & Software 70 (August 2015): 55–64. http://dx.doi.org/10.1016/j.envsoft.2015.04.008.

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11

Hu, Zhi Gang, Yong Lin Zhang, Jian Ping Ye, Shao Yun Song, and Li Ping Chen. "Numerical Modeling and Simulation of Random Road Surface Using IFFT Method." Advanced Materials Research 199-200 (February 2011): 999–1004. http://dx.doi.org/10.4028/www.scientific.net/amr.199-200.999.

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Based on the power spectral density (PSD) function of stochastic irregularities of the standard grade road and by means of inverse fast Fouerier transform (IFFT) based on discretized PSD sampling, an equivalent sample of stochastic road surface model in time domain was built. A one-dimensional model of stochastic road was developed into a 2D model of stochastic road surface. Through computer simulation practice based on the MATlab, a 2D sample of stochastic road surface in time domain was regenerated. Furthermore, given the sample data, the PSD was estimated and then compared with the theoretical 2D PSD Equation deduced from the one-dimensional PSD expreesion so as to prove the effectiveness and accuracy of the time-domain model regeneration of 2D stochastic road surface by means of IFFT method. The 2D stochastic road surface model directly provided basic road excitation input data for virtual prototyping (VP) and virtual proving ground (VPG) technology.

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12

Benth, F. E., and L. Vos. "Cross-Commodity Spot Price Modeling with Stochastic Volatility and Leverage For Energy Markets." Advances in Applied Probability 45, no. 2 (June 2013): 545–71. http://dx.doi.org/10.1239/aap/1370870129.

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Spot prices in energy markets exhibit special features, such as price spikes, mean reversion, stochastic volatility, inverse leverage effect, and dependencies between the commodities. In this paper a multivariate stochastic volatility model is introduced which captures these features. The second-order structure and stationarity of the model are analyzed in detail. A simulation method for Monte Carlo generation of price paths is introduced and a numerical example is presented.

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13

Benth, F. E., and L. Vos. "Cross-Commodity Spot Price Modeling with Stochastic Volatility and Leverage For Energy Markets." Advances in Applied Probability 45, no. 02 (June 2013): 545–71. http://dx.doi.org/10.1017/s0001867800006431.

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Spot prices in energy markets exhibit special features, such as price spikes, mean reversion, stochastic volatility, inverse leverage effect, and dependencies between the commodities. In this paper a multivariate stochastic volatility model is introduced which captures these features. The second-order structure and stationarity of the model are analyzed in detail. A simulation method for Monte Carlo generation of price paths is introduced and a numerical example is presented.

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14

Butko, A. A., O. I. Rodkin, and V. A. Pashinski. "Stochastic modeling of meteorological elements for solving environmental monitoring problems." Vesnik of Yanka Kupala State University of Grodno. Series 6. Engineering Science 12, no. 1 (September 9, 2022): 51–64. http://dx.doi.org/10.52275/2223-5396-2022-12-1-51-64.

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The purpose of the research presented in the publication is developing the stochastic model for simulating the series of meteorological elements used in predicting for transferring of biogenic elements into water bodies from the territory of agricultural land. The object of study is artificial series of meteorological elements with given statistical characteristics. As initial data, the meteorological data of the State Institution “Republican Hydrometeorological Center” for the Minsk object obtained for the period 2000–2020 were used. For development of the stochastic model, the following indicators were used: daily amount of total solar radiation, maximum and minimum air temperature, relative air humidity, amount of atmospheric precipitation, number of days with precipitation, maximum half-hour share of precipitation, wind speed at a height of 10 m above the earth’s surface. Artificial meteorological series are obtained on the basis of a sample set of randomly generated daily values with using the Monte Carlo method. The stochastic component of precipitation generation is a Markov chain gamma model; total precipitation – inverse method of two-parameter gamma distribution; relative air humidity – Simpson distribution; wind speed – inverse Weibull distribution method; the minimum and maximum air temperatures and solar radiation are determined using the Matalas first-order recurrent filter. For each of the elements, a differentiated correspondence of the statistical parameters determined from the measured and calculated series of meteorological elements were proved. The results of investigation can be used for modeling and forecasting of weather in areas with limited meteorological observation data for solving applied problems in biological and ecological systems.

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15

Azevedo, Leonardo, Dario Grana, and Leandro de Figueiredo. "Stochastic perturbation optimization for discrete-continuous inverse problems." GEOPHYSICS 85, no. 5 (July 28, 2020): M73—M83. http://dx.doi.org/10.1190/geo2019-0520.1.

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Accurate subsurface modeling and characterization require the prediction of facies and rock properties within the reservoir model. This is commonly achieved by inverting geophysical data, such as seismic reflection data, using a two-step approach either in the discrete or the continuous domain. We have adopted an iterative simultaneous method, namely, stochastic perturbation optimization, to invert seismic reflection data jointly for facies and rock properties. Facies first are simulated according to a Markov chain model, and then rock properties are generated with stochastic sequential simulation and cosimulation conditioned to each facies. Elastic and seismic data are computed by applying a rock-physics model to the realizations of petrophysical properties and a seismic convolutional model. The similarity between observed and synthetic seismic data is used to update the solution by perturbing facies and rock properties until convergence. Coupling the discrete and continuous domains ensures a consistent perturbation of the reservoir models throughout the iterations. We have evaluated the method in a 1D synthetic example for the estimation of facies and porosity from zero-offset seismic data assuming a linear rock-physics model to demonstrate the validity of the method. Then, we apply the method to a real 3D data set from the North Sea for the joint estimation of facies and petrophysical properties from prestack seismic data. The results show spatially consistent rock and fluid inverted models in which the predicted facies reproduce the vertical ordering as observed in the well data.

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16

Fu, Jianlin, and J. Jaime Gómez-Hernández. "A Blocking Markov Chain Monte Carlo Method for Inverse Stochastic Hydrogeological Modeling." Mathematical Geosciences 41, no. 2 (December 12, 2008): 105–28. http://dx.doi.org/10.1007/s11004-008-9206-0.

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17

Pace, Francesca, Alessandro Santilano, and Alberto Godio. "A Review of Geophysical Modeling Based on Particle Swarm Optimization." Surveys in Geophysics 42, no. 3 (April 13, 2021): 505–49. http://dx.doi.org/10.1007/s10712-021-09638-4.

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AbstractThis paper reviews the application of the algorithm particle swarm optimization (PSO) to perform stochastic inverse modeling of geophysical data. The main features of PSO are summarized, and the most important contributions in several geophysical fields are analyzed. The aim is to indicate the fundamental steps of the evolution of PSO methodologies that have been adopted to model the Earth’s subsurface and then to undertake a critical evaluation of their benefits and limitations. Original works have been selected from the existing geophysical literature to illustrate successful PSO applied to the interpretation of electromagnetic (magnetotelluric and time-domain) data, gravimetric and magnetic data, self-potential, direct current and seismic data. These case studies are critically described and compared. In addition, joint optimization of multiple geophysical data sets by means of multi-objective PSO is presented to highlight the advantage of using a single solver that deploys Pareto optimality to handle different data sets without conflicting solutions. Finally, we propose best practices for the implementation of a customized algorithm from scratch to perform stochastic inverse modeling of any kind of geophysical data sets for the benefit of PSO practitioners or inexperienced researchers.

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18

Klimczak, Konrad, Piotr Oprocha, Jan Kusiak, Danuta Szeliga, Paweł Morkisz, Paweł Przybyłowicz, Natalia Czyżewska, and Maciej Pietrzyk. "Inverse Problem in Stochastic Approach to Modelling of Microstructural Parameters in Metallic Materials during Processing." Mathematical Problems in Engineering 2022 (April 12, 2022): 1–15. http://dx.doi.org/10.1155/2022/9690742.

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The need for a reliable prediction of the distribution of microstructural parameters in metallic materials during processing was the motivation for this work. The model describing the evolution of dislocation populations, which considers the stochastic aspects of occurring phenomena, was formulated. The validation of the presented model requires the application of proper parameters corresponding to the considered materials. These parameters have to be identified through the inverse analysis, which, on the other hand, uses optimization methods and requires the formulation of the appropriate objective function. In our case, where the model involves the stochastic parameters, it is a crucial task. Therefore, a specific form of the objective function for the inverse analysis was developed using a measure based on histograms. The elaborated original stochastic approach to modeling the phenomena occurring during the thermomechanical treatment of metals was validated on commercially pure copper and selected multiphase steel.

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19

Chiodo, Elio, and Luigi Pio Di Noia. "Stochastic Extreme Wind Speed Modeling and Bayes Estimation under the Inverse Rayleigh Distribution." Applied Sciences 10, no. 16 (August 14, 2020): 5643. http://dx.doi.org/10.3390/app10165643.

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Inverse Rayleigh probability distribution is shown in this paper to constitute a valid model for characterization and estimation of extreme values of wind speed, thus constituting a useful tool of wind power production evaluation and mechanical safety of installations. The first part of this paper illustrates such a model and its validity to interpret real wind speed field data. The inverse Rayleigh model is then adopted as the parent distribution for assessment of a dynamical “risk index” defined in terms of a stochastic Poisson process, based upon crossing a given value with part of the maximum value of wind speed on a certain time horizon. Then, a novel Bayes approach for the estimation of such an index under the above model is proposed. The method is based upon assessment of prior information in a novel way which should be easily feasible for a system engineer, being based upon a model quantile (e.g., the median value) or, alternatively, on the probability that the wind speed is greater than a given value. The results of a large set of numerical simulation—based upon typical values of wind-speed parameters—are reported to illustrate the efficiency and the precision of the proposed method, also with hints to its robustness. The validity of the approach is also verified with respect to the two different methods of assessing the prior information.

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20

Dagan, Gedeon. "Stochastic Modeling of Groundwater Flow by Unconditional and Conditional Probabilities: The Inverse Problem." Water Resources Research 21, no. 1 (January 1985): 65–72. http://dx.doi.org/10.1029/wr021i001p00065.

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21

Cherpeau, Nicolas, Guillaume Caumon, Jef Caers, and Bruno Lévy. "Method for Stochastic Inverse Modeling of Fault Geometry and Connectivity Using Flow Data." Mathematical Geosciences 44, no. 2 (January 26, 2012): 147–68. http://dx.doi.org/10.1007/s11004-012-9389-2.

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22

Klein, Olaf, Daniele Davino, and Ciro Visone. "On forward and inverse uncertainty quantification for models involving hysteresis operators." Mathematical Modelling of Natural Phenomena 15 (2020): 53. http://dx.doi.org/10.1051/mmnp/2020009.

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Parameters within hysteresis operators modeling real world objects have to be identified from measurements and are therefore subject to corresponding errors. To investigate the influence of these errors, the methods of Uncertainty Quantification (UQ) are applied. Results of forward UQ for a play operator with a stochastic yield limit are presented. Moreover, inverse UQ is performed to identify the parameters in the weight function in a Prandtl-Ishlinskiĭ operator and the uncertainties of these parameters.

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23

Moura, Henrique Gomes, Edson Costa Junior, Arcanjo Lenzi, and Vinicius Carvalho Rispoli. "On a Stochastic Regularization Technique for Ill-Conditioned Linear Systems." Open Engineering 9, no. 1 (February 26, 2019): 52–60. http://dx.doi.org/10.1515/eng-2019-0008.

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AbstractKnowledge about the input–output relations of a system can be very important in many practical situations in engineering. Linear systems theory comes from applied mathematics as an efficient and simple modeling technique for input–output systems relations. Many identification problems arise from a set of linear equations, using known outputs only. It is a type of inverse problems, whenever systems inputs are sought by its output only. This work presents a regularization method, called random matrix method, which is able to reduce errors on the solution of ill-conditioned inverse problems by introducing modifications into the matrix operator that rules the problem. The main advantage of this approach is the possibility of reducing the condition number of the matrix using the probability density function that models the noise in the measurements, leading to better regularization performance. The method described was applied in the context of a force identification problem and the results were compared quantitatively and qualitatively with the classical Tikhonov regularization method. Results show the presented technique provides better results than Tikhonov method when dealing with high-level ill-conditioned inverse problems.

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24

Dell'Oca, A., A. Manzoni, M. Siena, N. G. Bona, L. Moghadasi, M. Miarelli, D. Renna, and A. Guadagnini. "Stochastic inverse modeling of transient laboratory-scale three-dimensional two-phase core flooding scenarios." International Journal of Heat and Mass Transfer 202 (March 2023): 123716. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2022.123716.

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25

Kravtsov, S., D. Kondrashov, and M. Ghil. "Multilevel Regression Modeling of Nonlinear Processes: Derivation and Applications to Climatic Variability." Journal of Climate 18, no. 21 (November 1, 2005): 4404–24. http://dx.doi.org/10.1175/jcli3544.1.

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Abstract Predictive models are constructed to best describe an observed field’s statistics within a given class of nonlinear dynamics driven by a spatially coherent noise that is white in time. For linear dynamics, such inverse stochastic models are obtained by multiple linear regression (MLR). Nonlinear dynamics, when more appropriate, is accommodated by applying multiple polynomial regression (MPR) instead; the resulting model uses polynomial predictors, but the dependence on the regression parameters is linear in both MPR and MLR. The basic concepts are illustrated using the Lorenz convection model, the classical double-well problem, and a three-well problem in two space dimensions. Given a data sample that is long enough, MPR successfully reconstructs the model coefficients in the former two cases, while the resulting inverse model captures the three-regime structure of the system’s probability density function (PDF) in the latter case. A novel multilevel generalization of the classic regression procedure is introduced next. In this generalization, the residual stochastic forcing at a given level is subsequently modeled as a function of variables at this level and all the preceding ones. The number of levels is determined so that the lag-0 covariance of the residual forcing converges to a constant matrix, while its lag-1 covariance vanishes. This method has been applied to the output of a three-layer, quasigeostrophic model and to the analysis of Northern Hemisphere wintertime geopotential height anomalies. In both cases, the inverse model simulations reproduce well the multiregime structure of the PDF constructed in the subspace spanned by the dataset’s leading empirical orthogonal functions, as well as the detailed spectrum of the dataset’s temporal evolution. These encouraging results are interpreted in terms of the modeled low-frequency flow’s feedback on the statistics of the subgrid-scale processes.

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Ni, C. F., Y. J. Huang, T. C. J. Yeh, J. J. Dong, J. S. Chen, and M. H. Li. "Stochastic inversion of sequential hydraulic tests for transient and highly permeable unconfined aquifer systems." Hydrology and Earth System Sciences Discussions 10, no. 12 (December 10, 2013): 14949–86. http://dx.doi.org/10.5194/hessd-10-14949-2013.

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Abstract. A hydraulic tomography survey (HTS) is a conceptually improved technique that has been recognized to be efficient for estimating high-resolution aquifer parameters. Based on the concept of HTS, this study presents a modified stochastic inverse model for estimating hydraulic conductivity (K) and specific yield (Sy) in shallow and highly permeable unconfined aquifers. A well field with 15 fully screened wells was developed for the purpose of model implementations. In this study a synthetic example was first employed to assess the accuracy of the inverse model. We then implemented the model to field-scale, cross-hole injection tests in a shallow and highly permeable unconfined aquifer near the middle reach of the Wu River in central Taiwan. To assess the effect of constant head boundary conditions on the estimation results, two additional modeling domains were evaluated based on the same field data from the injection tests. Results for the synthetic example show that the modified inverse model can reproduce well the predefined geologic features of the unconfined aquifer. The inverse model can estimate accurately the ln K patterns and magnitudes. However, slightly fewer details of the ln Sy field are obtained due to the insensitivity of transient hydraulic stresses for specified sampling times. Model implementations of field-scale injection tests show that the model can estimate ln K and ln Sy fields with high spatial resolution. The estimated K and Sy values for the test site vary by one order of magnitude, indicating a relatively homogeneous aquifer for the tested well field. Results based on three different modeling domains show similar patterns and magnitudes of ln K and ln Sy near the well locations. This result suggests that the case with domain 40 m × 20 m should be sufficient for the injection tests at the well field.

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Carletti, Margherita, and Malay Banerjee. "A Backward Technique for Demographic Noise in Biological Ordinary Differential Equation Models." Mathematics 7, no. 12 (December 9, 2019): 1204. http://dx.doi.org/10.3390/math7121204.

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Physical systems described by deterministic differential equations represent idealized situations since they ignore stochastic effects. In the context of biomathematical modeling, we distinguish between environmental or extrinsic noise and demographic or intrinsic noise, for which it is assumed that the variation over time is due to demographic variation of two or more interacting populations (birth, death, immigration, and emigration). The modeling and simulation of demographic noise as a stochastic process affecting units of populations involved in the model is well known in the literature, resulting in discrete stochastic systems or, when the population sizes are large, in continuous stochastic ordinary differential equations and, if noise is ignored, in continuous ordinary differential equation models. The inverse process, i.e., inferring the effects of demographic noise on a natural system described by a set of ordinary differential equations, is still an issue to be addressed. With this paper, we provide a technique to model and simulate demographic noise going backward from a deterministic continuous differential system to its underlying discrete stochastic process, based on the framework of chemical kinetics, since demographic noise is nothing but the biological or ecological counterpart of intrinsic noise in genetic regulation. Our method can, thus, be applied to ordinary differential systems describing any kind of phenomena when intrinsic noise is of interest.

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28

Nan, Jing, Zhonghua Jian, Chuanfeng Ning, and Wei Dai. "A Lightweight Learning Method for Stochastic Configuration Networks Using Non-Inverse Solution." Electronics 11, no. 2 (January 14, 2022): 262. http://dx.doi.org/10.3390/electronics11020262.

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Stochastic configuration networks (SCNs) face time-consuming issues when dealing with complex modeling tasks that usually require a mass of hidden nodes to build an enormous network. An important reason behind this issue is that SCNs always employ the Moore–Penrose generalized inverse method with high complexity to update the output weights in each increment. To tackle this problem, this paper proposes a lightweight SCNs, called L-SCNs. First, to avoid using the Moore–Penrose generalized inverse method, a positive definite equation is proposed to replace the over-determined equation, and the consistency of their solution is proved. Then, to reduce the complexity of calculating the output weight, a low complexity method based on Cholesky decomposition is proposed. The experimental results based on both the benchmark function approximation and real-world problems including regression and classification applications show that L-SCNs are sufficiently lightweight.

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Liu, Xiaoping, Zhenyu Wu, Dejun Cui, Bin Guo, and Lijie Zhang. "A Modeling Method of Stochastic Parameters’ Inverse Gauss Process Considering Measurement Error under Accelerated Degradation Test." Mathematical Problems in Engineering 2019 (May 21, 2019): 1–11. http://dx.doi.org/10.1155/2019/9752920.

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To solve the problem that the individual differences and the measurement errors affect the accuracy of life estimation in accelerated degradation test, the inverse Gauss process with stochastic parameters is applied in the accelerated degradation test with the consideration of the influence of individual differences, and the analysis of measurement uncertainty is carried out. An inverse Gauss accelerated degradation model considering both individual differences and measurement errors is established. In the maximum likelihood estimation of parameters, Genetic Algorithm and Monte Carlo integral are used to solve the problems caused by complex integral and the unobservable measurement errors in the calculation process. Finally, the proposed method is verified by the Monte Carlo simulation under the constant accelerated stress and step accelerated stress and the illustrative example of electrical connectors under the constant acceleration stress, respectively. The results show that the modeling tool is useful for improving the accuracy of the life prediction and the reliability evaluation.

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Glazunov, Andrey, Üllar Rannik, Victor Stepanenko, Vasily Lykosov, Mikko Auvinen, Timo Vesala, and Ivan Mammarella. "Large-eddy simulation and stochastic modeling of Lagrangian particles for footprint determination in the stable boundary layer." Geoscientific Model Development 9, no. 9 (August 31, 2016): 2925–49. http://dx.doi.org/10.5194/gmd-9-2925-2016.

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Abstract. Large-eddy simulation (LES) and Lagrangian stochastic modeling of passive particle dispersion were applied to the scalar flux footprint determination in the stable atmospheric boundary layer. The sensitivity of the LES results to the spatial resolution and to the parameterizations of small-scale turbulence was investigated. It was shown that the resolved and partially resolved (“subfilter-scale”) eddies are mainly responsible for particle dispersion in LES, implying that substantial improvement may be achieved by using recovering of small-scale velocity fluctuations. In LES with the explicit filtering, this recovering consists of the application of the known inverse filter operator. The footprint functions obtained in LES were compared with the functions calculated with the use of first-order single-particle Lagrangian stochastic models (LSMs) and zeroth-order Lagrangian stochastic models – the random displacement models (RDMs). According to the presented LES, the source area and footprints in the stable boundary layer can be substantially more extended than those predicted by the modern LSMs.

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31

Nádai, László. "Modeling Photon Counting Experiments using Fuzzy Logic Controller." Journal of Advanced Computational Intelligence and Intelligent Informatics 6, no. 2 (June 20, 2002): 72–78. http://dx.doi.org/10.20965/jaciii.2002.p0072.

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The concept of point fractal is applied to analyze the time-scale variability of point processes resulting from photon counting experiments. A new algorithm – using a fuzzy logic controller – for estimating the fractal dimension is proposed to eliminate systematic and stochastic errors. It is shown that scale invariance exists in time and clustering will decrease in accordance with the increase of the threshold that corresponds to the inverse sensitivity of the detector. Under the variation of the threshold, it is verified that the maximum values of the homogenous scale invariant interval are the same. In addition, taking the probability scale law on different levels of threshold value, a relation is established between the saturation scale (return period) and the threshold (design experiment variable).

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32

Hagemann, Paul, Johannes Hertrich, and Gabriele Steidl. "Stochastic Normalizing Flows for Inverse Problems: A Markov Chains Viewpoint." SIAM/ASA Journal on Uncertainty Quantification 10, no. 3 (September 28, 2022): 1162–90. http://dx.doi.org/10.1137/21m1450604.

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33

Kaulakys, B., M. Alaburda, and J. Ruseckas. "Modeling of long-range memory processes with inverse cubic distributions by the nonlinear stochastic differential equations." Journal of Statistical Mechanics: Theory and Experiment 2016, no. 5 (May 20, 2016): 054035. http://dx.doi.org/10.1088/1742-5468/2016/05/054035.

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34

Kaczka, David W., Christopher B. Massa, and Brett A. Simon. "Reliability of Estimating Stochastic Lung Tissue Heterogeneity from Pulmonary Impedance Spectra: A Forward-Inverse Modeling Study." Annals of Biomedical Engineering 35, no. 10 (June 9, 2007): 1722–38. http://dx.doi.org/10.1007/s10439-007-9339-1.

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35

Kaczka, David W., Christopher B. Massa, and Brett A. Simon. "Reliability of Estimating Stochastic Lung Tissue Heterogeneity from Pulmonary Impedance Spectra: A Forward-Inverse Modeling Study." Annals of Biomedical Engineering 35, no. 10 (June 26, 2007): 1838. http://dx.doi.org/10.1007/s10439-007-9342-6.

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36

G�mez-Hern�ndez, J. J., H. J. W. M. Hendricks Franssen, and A. Sahuquillo. "Stochastic conditional inverse modeling of subsurface mass transport: A brief review and the self-calibrating method." Stochastic Environmental Research and Risk Assessment (SERRA) 17, no. 5 (November 1, 2003): 319–28. http://dx.doi.org/10.1007/s00477-003-0153-5.

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37

Sun, Y., Z. Hou, M. Huang, F. Tian, and L. Ruby Leung. "Inverse modeling of hydrologic parameters using surface flux and runoff observations in the Community Land Model." Hydrology and Earth System Sciences 17, no. 12 (December 10, 2013): 4995–5011. http://dx.doi.org/10.5194/hess-17-4995-2013.

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Abstract. This study demonstrates the possibility of inverting hydrologic parameters using surface flux and runoff observations in version 4 of the Community Land Model (CLM4). Previous studies showed that surface flux and runoff calculations are sensitive to major hydrologic parameters in CLM4 over different watersheds, and illustrated the necessity and possibility of parameter calibration. Both deterministic least-square fitting and stochastic Markov-chain Monte Carlo (MCMC)-Bayesian inversion approaches are evaluated by applying them to CLM4 at selected sites with different climate and soil conditions. The unknowns to be estimated include surface and subsurface runoff generation parameters and vadose zone soil water parameters. We find that using model parameters calibrated by the sampling-based stochastic inversion approaches provides significant improvements in the model simulations compared to using default CLM4 parameter values, and that as more information comes in, the predictive intervals (ranges of posterior distributions) of the calibrated parameters become narrower. In general, parameters that are identified to be significant through sensitivity analyses and statistical tests are better calibrated than those with weak or nonlinear impacts on flux or runoff observations. Temporal resolution of observations has larger impacts on the results of inverse modeling using heat flux data than runoff data. Soil and vegetation cover have important impacts on parameter sensitivities, leading to different patterns of posterior distributions of parameters at different sites. Overall, the MCMC-Bayesian inversion approach effectively and reliably improves the simulation of CLM under different climates and environmental conditions. Bayesian model averaging of the posterior estimates with different reference acceptance probabilities can smooth the posterior distribution and provide more reliable parameter estimates, but at the expense of wider uncertainty bounds.

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38

Sun, Y., Z. Hou, M. Huang, F. Tian, and L. R. Leung. "Inverse modeling of hydrologic parameters using surface flux and runoff observations in the Community Land Model." Hydrology and Earth System Sciences Discussions 10, no. 4 (April 23, 2013): 5077–119. http://dx.doi.org/10.5194/hessd-10-5077-2013.

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Abstract. This study demonstrates the possibility of inverting hydrologic parameters using surface flux and runoff observations in version 4 of the Community Land Model (CLM4). Previous studies showed that surface flux and runoff calculations are sensitive to major hydrologic parameters in CLM4 over different watersheds, and illustrated the necessity and possibility of parameter calibration. Two inversion strategies, the deterministic least-square fitting and stochastic Markov-Chain Monte-Carlo (MCMC) Bayesian inversion approaches, are evaluated by applying them to CLM4 at selected sites. The unknowns to be estimated include surface and subsurface runoff generation parameters and vadose zone soil water parameters. We find that using model parameters calibrated by the least-square fitting provides little improvements in the model simulations but the sampling-based stochastic inversion approaches are consistent – as more information comes in, the predictive intervals of the calibrated parameters become narrower and the misfits between the calculated and observed responses decrease. In general, parameters that are identified to be significant through sensitivity analyses and statistical tests are better calibrated than those with weak or nonlinear impacts on flux or runoff observations. Temporal resolution of observations has larger impacts on the results of inverse modeling using heat flux data than runoff data. Soil and vegetation cover have important impacts on parameter sensitivities, leading to different patterns of posterior distributions of parameters at different sites. Overall, the MCMC-Bayesian inversion approach effectively and reliably improves the simulation of CLM under different climates and environmental conditions. Bayesian model averaging of the posterior estimates with different reference acceptance probabilities can smooth the posterior distribution and provide more reliable parameter estimates, but at the expense of wider uncertainty bounds.

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39

Al-Marzouki, Sanaa, Farrukh Jamal, Christophe Chesneau, and Mohammed Elgarhy. "Half Logistic Inverse Lomax Distribution with Applications." Symmetry 13, no. 2 (February 12, 2021): 309. http://dx.doi.org/10.3390/sym13020309.

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The last years have revealed the importance of the inverse Lomax distribution in the understanding of lifetime heavy-tailed phenomena. However, the inverse Lomax modeling capabilities have certain limits that researchers aim to overcome. These limits include a certain stiffness in the modulation of the peak and tail properties of the related probability density function. In this paper, a solution is given by using the functionalities of the half logistic family. We introduce a new three-parameter extended inverse Lomax distribution called the half logistic inverse Lomax distribution. We highlight its superiority over the inverse Lomax distribution through various theoretical and practical approaches. The derived properties include the stochastic orders, quantiles, moments, incomplete moments, entropy (Rényi and q) and order statistics. Then, an emphasis is put on the corresponding parametric model. The parameters estimation is performed by six well-established methods. Numerical results are presented to compare the performance of the obtained estimates. Also, a simulation study on the estimation of the Rényi entropy is proposed. Finally, we consider three practical data sets, one containing environmental data, another dealing with engineering data and the last containing insurance data, to show how the practitioner can take advantage of the new half logistic inverse Lomax model.

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40

Zhang, Chao, and Hong-Sen Yan. "Inverse control of multi-dimensional Taylor network for permanent magnet synchronous motor." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 36, no. 6 (November 6, 2017): 1676–89. http://dx.doi.org/10.1108/compel-12-2016-0565.

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Purpose The purpose of this paper is to propose a new control strategy based on adaptive inverse control aiming at high performance control of permanent magnet synchronous motor (PMSM). Design/methodology/approach This scheme adopts the vector control with double closed-loop structure and introduces a multi-dimensional Taylor network (MTN) inverse control method into velocity-loop. First, the invertibility of PMSM’s mathematical model is proved. Second, a novel dynamic network (MTN) is presented, which has simple structure and faster computing speed. Besides, to realize the high-precision speed control, three MTNs are applied to achieve system modeling, inverse modeling and noise disturbance elimination which correspond to the function of the adaptive identifier, adaptive feed-forward controller and nonlinear adaptive filter, respectively. Findings This scheme is designed with the full consideration of the PMSM’s particularity. For the PMSM’s unknown dynamics and time-varying characteristics, the variable forgetting factor recursive least squares algorithm is adopted to improve identification ability, and the weight-elimination algorithm is used to remove redundant regression items in the MTN identifier and inverse controller. In addition, to reduce the influence arose from measurement noise and other stochastic factors, adaptive MTN filter is introduced to eliminate noise disturbance. The computational results show that the proposed scheme possesses excellent control performance and better robustness against the load disturbance. Originality/value The paper presents a new inverse control scheme with MTN which is practical and flexible, and the MTN-based control system is very promising for real-time applications.

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41

Pukl, Radomír, Tereza Sajdlová, Drahomír Novák, and David Lehký. "Fracture-Mechanical Parameters for Modeling of Quasi-Brittle Materials and Structures." Advanced Materials Research 1106 (June 2015): 106–9. http://dx.doi.org/10.4028/www.scientific.net/amr.1106.106.

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The scatter of experimental results using specimens made of quasi-brittle materials, such as concrete, fibre-reinforced concrete, ultra high performance concrete etc., can be due to their heterogeneity rather high. An assessment of fracture-mechanical parameters is then difficult and problematic. To remain at deterministic level is therefore unrealistic and without virtual statistical approach, simulation and probabilistic result assessment the consequent practical design of quasi-brittle material-based structures can be risky. A key parameter of nonlinear fracture mechanics modeling is fracture energy of concrete. Numerical simulation of concrete failure and fracture phenomena in concrete as well as other cementitious materials became a field of an intensive research in the recent years. With respect to accuracy and efficiency of corresponding numerical models some few still open questions have to be focused. How the heterogeneity of cementitious materials can be taken into consideration in the most realistic way using commercially available finite element programs? A sophisticated option to get the parameters of the computational model indirectly is based on combination of fracture test with inverse analysis. This paper describes a methodology to get such parameters using experimental data from three-point bending tests used in inverse analysis based on combination of artificial neural networks and stochastic analysis.

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42

Thomas, Erin E., Daniel J. Vimont, Matthew Newman, Cécile Penland, and Cristian Martínez-Villalobos. "The Role of Stochastic Forcing in Generating ENSO Diversity." Journal of Climate 31, no. 22 (October 17, 2018): 9125–50. http://dx.doi.org/10.1175/jcli-d-17-0582.1.

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Abstract Numerous oceanic and atmospheric phenomena influence El Niño–Southern Oscillation (ENSO) variability, complicating both prediction and analysis of the mechanisms responsible for generating ENSO diversity. Predictability of ENSO events depends on the characteristics of both the forecast initial conditions and the stochastic forcing that occurs subsequent to forecast initialization. Within a linear inverse model framework, stochastic forcing reduces ENSO predictability when it excites unpredictable growth or interference after the forecast is initialized, but also enhances ENSO predictability when it excites optimal initial conditions that maximize deterministic ENSO growth. Linear inverse modeling (LIM) allows for straightforward separation between predictable signal and unpredictable noise and so can diagnose its own skill. While previous LIM studies of ENSO focused on deterministic dynamics, here we explore how noise forcing influences ENSO diversity and predictability. This study identifies stochastic forcing details potentially contributing to the development of central Pacific (CP) or eastern Pacific (EP) ENSO characteristics. The technique is then used to diagnose the relative roles of initial conditions and noise forcing throughout the evolution of several ENSO events. LIM results show varying roles of noise forcing for any given event, highlighting its utility in separating deterministic from noise-forced contributions to the evolution of individual ENSO events. For example, the strong 1982 event was considerably more influenced by noise forcing late in its evolution than the strong 1997 event, which was more predictable with long lead times due to its deterministic growth. Furthermore, the 2014 deterministic trajectory suggests that a strong event in 2014 was unlikely.

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43

Shcherbina, Yu V., S. D. Asabashvili, and A. M. Prokopenko. "SIMULATION OF ASYMMETRICALLY DISTRIBUTED PROCESSES." Key title: Zbìrnik naukovih pracʹ Odesʹkoï deržavnoï akademìï tehnìčnogo regulûvannâ ta âkostì -, no. 1(16) (2020): 42–47. http://dx.doi.org/10.32684/2412-5288-2020-1-16-42-47.

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The article deals with the problems of modeling asymmetrically distributed stochastic processes and assessing the quality of the modeling process based on the use of the Pearson chi-square criterion. The problems that arise in each individual case of modeling are identified. As a method of generating an output stream of random numbers distributed according to a given law of probability distribution, the method of inverse functions is proposed, and as a generator of the input stream, it is proposed to use a stream generated by the Mersenne generator. The analysis of research methods and evaluation of computer models of stochastic processes is given and the choice of a nonparametric research method based on histograms is substantiated. Suggestions on the choice of their main parameters are provided: the size of the interval for separating the statistical set of values of the output stream of the model and the number of such intervals, calculated on the basis of the size of the statistical sample. It is shown that the quality of statistical material significantly affects the success of modeling. In the case of an asymmetric nature of the distribution of the model's output stream, the accuracy of calculating the chi-square exponent is significantly affected by those values that fall into the extreme intervals of the histogram. It is shown that the reason for this is the incommensurability of their values with the values in the central part of the histogram and this is a separate modeling problem, as a solution to which there can be filtering of the statistical set, preceding the determination of the quality indicator. The sequence of procedures for forming a model of a stochastic process and processing the results of calculating the parameters of the histogram is determined.

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44

Russian, A., M. Riva, E. R. Russo, M. A. Chiaramonte, and A. Guadagnini. "Stochastic inverse modeling and global sensitivity analysis to assist interpretation of drilling mud losses in fractured formations." Stochastic Environmental Research and Risk Assessment 33, no. 10 (September 21, 2019): 1681–97. http://dx.doi.org/10.1007/s00477-019-01729-4.

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45

Bai, Jie, and Rishi Raj. "Inverse Problems in Stochastic Modeling of Mixed-Mode Power-Law and Diffusional Creep for Distributed Grain Size." Metallurgical and Materials Transactions A 41, no. 2 (December 18, 2009): 308–17. http://dx.doi.org/10.1007/s11661-009-0120-y.

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46

Rubin, Y., J. P. Lobo Ferreira, J. D. Rodrigues, and G. Dagan. "Estimation of the hydraulic parameters of the Rio-Maior aquifer in Portugal by using stochastic inverse modeling." Journal of Hydrology 118, no. 1-4 (October 1990): 257–79. http://dx.doi.org/10.1016/0022-1694(90)90262-v.

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47

Han, S. L., and Takeshi Kinoshita. "Stochastic Inverse Identification of Nonlinear Roll Damping Moment of a Ship Moving at Nonzero-Forward Speeds." Mathematical Problems in Engineering 2012 (2012): 1–22. http://dx.doi.org/10.1155/2012/769385.

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The nonlinear responses of ship rolling motion characterized by a roll damping moment are of great interest to naval architects and ocean engineers. Modeling and identification of the nonlinear damping moment are essential to incorporate the inherent nonlinearity in design, analysis, and control of a ship. A stochastic nonparametric approach for identification of nonlinear damping in the general mechanical system has been presented in the literature (Han and Kinoshits 2012). The method has been also applied to identification of the nonlinear damping moment of a ship at zero-forward speed (Han and Kinoshits 2013). In the presence of forward speed, however, the characteristic of roll damping moment of a ship is significantly changed due to the lift effect. In this paper, the stochastic inverse method is applied to identification of the nonlinear damping moment of a ship moving at nonzero-forward speed. The workability and validity of the method are verified with laboratory tests under controlled conditions. In experimental trials, two different types of ship rolling motion are considered: time-dependent transient motion and frequency-dependent periodic motion. It is shown that this method enables the inherent nonlinearity in damping moment to be estimated, including its reliability analysis.

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48

Jin, Bangti, Zehui Zhou, and Jun Zou. "On the Saturation Phenomenon of Stochastic Gradient Descent for Linear Inverse Problems." SIAM/ASA Journal on Uncertainty Quantification 9, no. 4 (January 2021): 1553–88. http://dx.doi.org/10.1137/20m1374456.

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49

Stanislavsky, Aleksander A., and Aleksander Weron. "Subdiffusive search with home returns via stochastic resetting: a subordination scheme approach." Journal of Physics A: Mathematical and Theoretical 55, no. 7 (January 28, 2022): 074004. http://dx.doi.org/10.1088/1751-8121/ac4a1c.

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Abstract Stochastic resetting with home returns is widely found in various manifestations in life and nature. Using the solution to the home return problem in terms of the solution to the corresponding problem without home returns (Pal et al 2020 Phys. Rev. Res. 2 043174), we develop a theoretical framework for search with home returns in the case of subdiffusion. This makes a realistic description of restart by accounting for random walks with random stops. The model considers stochastic processes, arising from Brownian motion subordinated by an inverse infinitely divisible process (subordinator).

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50

Kitanidis, Peter K. "Comment on “Stochastic Modeling of Groundwater Flow by Unconditional and Conditional Probabilities: The Inverse Problem” by Gedeon Dagan." Water Resources Research 22, no. 6 (June 1986): 984–86. http://dx.doi.org/10.1029/wr022i006p00984.

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