Mathematics and Mechanics. Vestnik MGTU

Analysis of Least Squares Method Efficiency with L-BFGS-B Optimization for Bilinear Autoregression Parameter Estimation Under Various Noise Distributions

Wed, 29 Jul 2026 00:00:00 +0400

Abstract

The article investigates the influence of various distributions of the updating process on the accuracy of parameter estimates for a bilinear autoregressive model, obtained using the least squares method with the L-BFGS-B optimization algorithm. The research examines the effectiveness of parameter estimation using the least squares method for normal, contaminated normal (Tukey distribution), Student’s t-distribution with various degrees of freedom, Laplace distribution, and uniform distribution. Special attention is given to analyzing the dependence of estimation accuracy on the degrees of freedom in the Student t-distribution and contamination parameters in the Tukey distribution. Calculations of errors and biases of the model parameters are conducted based on extensive computer modeling with the generation of stationary time series. The results show that the accuracy of estimates significantly depends on the type of distribution of the updating process, with the highest sensitivity observed for the parameter associated with the nonlinear term of the model. For the Student’s t-distribution, a nonlinear relationship between estimation errors and the number of degrees of freedom is established, while for the contaminated normal distribution, a critical influence of contamination parameters on the accuracy of estimates is revealed. The obtained results can be used in constructing bilinear time series models under conditions of non-standard residual distributions

Please cite this article in English as:

Goryainov V.B., Masyagin M.M., Semernya V.M. Analysis of least squares method efficiency with L-BFGS-B optimization for bilinear autoregression parameter estimation under various noise distributions. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2026, no. 3 (126), pp. 4--23 (in Russ.). EDN: VVLPJN

Numerical Simulation of Laser Lap Welding--Brazing of Titanium and Aluminum Plates

Wed, 29 Jul 2026 00:00:00 +0400

Abstract

The developed mathematical model for the numerical study of laser welding thermophysical processes is applied to simulate the overlap welding of titanium and aluminum plates. The article investigates the influence of laser power and welding speed on the temperature distribution in the calculation area, and searches for optimal welding modes. To obtain quantitative process characteristics, a repeatedly tested numerical method of collocation and least squares for solving differential and integral equations is used, which is implemented in the Laser Welding3D software package. The problem is solved in a three-dimensional formulation, taking into account both heat exchange with the environment and the formation of a vapor-gas channel in the weld zone. The simulation is performed for various plate arrangements over a wide range of laser power values and plate speeds relative to the laser beam. It is shown that the choice of plate arrangement affects the characteristics of the resulting joint. A range of conditions has been determined that achieves the optimal welding-brazing mode for titanium and aluminum, when the temperature in the contact zone exceeds the melting point of aluminum, but is lower than the melting point of titanium. This mode produces a permanent joint that is free of brittle intermetallic phases that degrade joint quality. A comparison with the experimental results has been conducted. The results can be used to develop an effective technology for producing lap joints between titanium and aluminum plates using laser welding

The work was carried out as part of the State Assignment of the ITAM SB RAS (no. 124021400039-8)

Please cite this article in English as:

Shmagunov O.A., Shapeev V.P. Numerical simulation of laser lap welding-brazing of titanium and aluminum plates. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2026, no. 3 (126), pp. 24--39 (in Russ.). EDN: VHPNNG