A stochastic gradient-based two-step sparse identification algorithm for multivariate ARX systems

We consider the sparse identification of multivariate ARX systems, i.e., to recover the zero elements of the unknown parameter matrix. We propose a two-step algorithm, where in the first step the stochastic gradient (SG) algorithm is applied to obtain initial estimates of the unknown parameter matrix and in the second step an optimization criterion is introduced for the sparse identification of multivariate ARX systems. Under mild conditions, we prove that by minimizing the criterion function, the zero elements of the unknown parameter matrix can be recovered with a finite number of observations. The performance of the algorithm is testified through a simulation example.

A Local Sparse Screening Identification Algorithm with Applications

Extracting nonlinear governing equations from noisy data is a central challenge in the analysis of complicated nonlinear behaviors.Despite researchers follow the sparse identification nonlinear dynamics algorithm(SINDy)rule to restore nonlinear equations,there also exist obstacles.One is the excessive dependence on empirical parameters,which increases the difficulty of data pre-processing.Another one is the coexistence of multiple coefficient vectors,which causes the optimal solution to be drowned in multiple solutions.The third one is the composition of basic function,which is exclusively applicable to specific equations.In this article,a local sparse screening identification algorithm(LSSI)is proposed to identify nonlinear systems.First,we present the k-neighbor parameter to replace all empirical parameters in data filtering.Second,we combine the mean error screening method with the SINDy algorithm to select the optimal one from multiple solutions.Third,the time variable t is introduced to expand the scope of the SINDy algorithm.Finally,the LSSI algorithm is applied to recover a classic ODE and a bi-stable energy harvester system.The results show that the new algorithm improves the ability of noise immunity and optimal parameters identification provides a desired foundation for nonlinear analyses.

Multi-Objective Adaptive Optimization Model Predictive Control:Decreasing Carbon Emissions from a Zinc Oxide Rotary Kiln

The zinc oxide rotary kiln,as an essential piece of equipment in the zinc smelting industrial process,is presenting new challenges in process control.China’s strategy of achieving a carbon peak and carbon neutrality is putting new demands on the industry,including green production and the use of fewer resources;thus,traditional stability control is no longer suitable for multi-objective control tasks.Although researchers have revealed the principle of the rotary kiln and set up computational fluid dynamics(CFD)simulation models to study its dynamics,these models cannot be directly applied to process control due to their high computational complexity.To address these issues,this paper proposes a multi-objective adaptive optimization model predictive control(MAO-MPC)method based on sparse identification.More specifically,with a large amount of data collected from a CFD model,a sparse regression problem is first formulated and solved to obtain a reduction model.Then,a two-layered control framework including real-time optimization(RTO)and model predictive control(MPC)is designed.In the RTO layer,an optimization problem with the goal of achieving optimal operation performance and the lowest possible resource consumption is set up.By solving the optimization problem in real time,a suitable setting value is sent to the MPC layer to ensure that the zinc oxide rotary kiln always functions in an optimal state.Our experiments show the strength and reliability of the proposed method,which reduces the usage of coal while maintaining high profits.

Extracting governing system for the plastic deformation of metallic glasses using machine learning

This paper shows hidden information from the plastic deformation of metallic glasses using machine learning.Ni_(62)Nb_(38)(at.%)metallic glass(MG)film and Zr_(64.13)Cu_(15.75)Al_(10)Ni_(10.12)(at.%)BMG,as two model materials,are considered for nano-scratching and compression experiment,respectively.The interconnectedness among variables is probed using correlation analysis.The evolvement mechanism and governing system of plastic deformation are explored by combining dynamical neural networks and sparse identification.The governing system has the same basis function for different experiments,and the coefficient error is≤0.14%under repeated experiments,revealing the intrinsic quality in metallic glasses.Furthermore,the governing system is conducted based on the preceding result to predict the deformation behavior.This shows that the prediction agrees well with the real value for the deformation process.