Parametric Neural Network Modeling in Engineering

Lazovskaya, Tatiana; Tarkhov, Dmitriy; Vasilyev, Alexander

doi:10.2174/1872212111666161207155157

Cited by 31 publications

(18 citation statements)

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“…A simpler case leads to refinement of model parameters, which is mathematically expressed in coefficients of inverse problems. To solve such problems, there are a number of approaches, one of which is the use of neural networks [4,7]. A variant (to which the problem considered in this article belongs) is also possible, when no choice of parameters allows us to reflect experimental data with reasonable accuracy.…”

Section: Resultsmentioning

confidence: 99%

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A Two-layer Semi Empirical Model of Nonlinear Bending of the Cantilevered Beam

Zulkarnay

Kaverzneva

Tarkhov

et al. 2018

J. Phys.: Conf. Ser.

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Section: Resultsmentioning

confidence: 99%

“…Previously, we solved such problems using our methodology for constructing the neural network model of the object by differential equations and additional data [1][2][3][4][5][6][7][8]. However, the training of neural networks requires a fairly large computational cost.…”

Section: Introductionmentioning

confidence: 99%

A Two-layer Semi Empirical Model of Nonlinear Bending of the Cantilevered Beam

Zulkarnay

Kaverzneva

Tarkhov

et al. 2018

J. Phys.: Conf. Ser.

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“…The first method will compare to a neural network approach [10,11]. We will find a solution in the form of a neural network approximation: where neural network weights are linear input parameters c i and non-linear input parameters a i as well as material constants α, m, and a.…”

Section: Neural Network Approachmentioning

confidence: 99%

Multilayer method for solving a problem of metals rupture under creep conditions

et al. 2019

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The paper deals with a parameter identification problem for creep and fracture model. The system of ordinary differential equations of kinetic creep theory is applied for describing this model. As for solving the parameter identification problem, we proposed to use the technique of neural network modeling, as well as the multilayer approach. The procedures of neural network modeling and multilayer approximation constructing application is demonstrated by the example of finding parameters for uniaxial tension model for isotropic steel 45 specimens at creep conditions. The solution corresponding to the obtained parameters agrees well with theoretical strain-damage characteristics, experimental data, and results of other authors.

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“…These solutions should allow for the possibility of refinement according to monitoring data of the object. The complex of our methods for constructing approximate neural network solutions is described and tested on a variety of problems for ODE and PDE, [1][2][3][4][5][6][7]. In particular, methods of adjusting models to new data are presented.…”

Section: Introductionmentioning

confidence: 99%

Comparison of two neural network approaches to modeling processes in a chemical reactor

et al. 2019

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In this paper, we conduct the comparative analysis of two neural network approaches to the problem of constructing approximate neural network solutions of non-linear differential equations. The first approach is connected with building a neural network with one hidden layer by minimization of an error functional with regeneration of test points. The second approach is based on a new continuous analog of the shooting method. In the first step of the second method, we apply our modification of the corrected Euler method, and in the second and subsequent steps, we apply our modification of the Störmer method. We have tested our methods on a boundary value problem for an ODE which describes the processes in the chemical reactor. These methods allowed us to obtain simple formulas for the approximate solution of the problem, but the problem is special because it is highly non-linear and also has ambiguous solutions and vanishing solutions if we change the parameter value.

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Parametric Neural Network Modeling in Engineering

Cited by 31 publications

References 0 publications

A Two-layer Semi Empirical Model of Nonlinear Bending of the Cantilevered Beam

A Two-layer Semi Empirical Model of Nonlinear Bending of the Cantilevered Beam

Multilayer method for solving a problem of metals rupture under creep conditions

Comparison of two neural network approaches to modeling processes in a chemical reactor

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