arXiv subjects

Zonglin Jiang

Publications and source records attributed to Zonglin Jiang.

6 recordsLinked to original sources

arXiv2021

Reconstructing shock front of unstable detonations based on multi-layer perceptron

The dynamics of frontal and transverse shocks in gaseous detonation waves is a complex phenomenon bringing many difficulties to both numerical and experimental research. Advanced laser-optical visualization of detonation structure may provide certain information of its reactive front, but the corresponding lead shock needs to be reconstructed building the complete flow field. Using the Multi-Layer Perceptron (MLP) approach, we propose in this study a shock front reconstruction method which can predict evolution of the lead shock wavefront from the state of the reactive front. The method is verified through the numerical results of one- and two-dimensional unstable detonations based on the reactive Euler equations with a one-step irreversible chemical reaction model. Results show that the accuracy of the proposed method depends on the activation energy of the reactive mixture, which influences prominently the cellular detonation instability and hence, the distortion of the lead shock surface. To select the input variables for training and evaluate their influence on the effectiveness of the proposed method, five groups, one with six variables and the other with four variables, are tested and analyzed in the MLP model. The trained MLP is tested in the cases with different activation energies, demonstrates the inspiring generalization capability. This paper offers a universal framework for predicting detonation frontal evolution and provides a novel way to interpret numerical and experimental results of detonation waves.

physics.flu-dyn↗

arXiv2017

Block building programming for symbolic regression

Symbolic regression that aims to detect underlying data-driven models has become increasingly important for industrial data analysis. For most existing algorithms such as genetic programming (GP), the convergence speed might be too slow for large-scale problems with a large number of variables. This situation may become even worse with increasing problem size. The aforementioned difficulty makes symbolic regression limited in practical applications. Fortunately, in many engineering problems, the independent variables in target models are separable or partially separable. This feature inspires us to develop a new approach, block building programming (BBP). BBP divides the original target function into several blocks, and further into factors. The factors are then modeled by an optimization engine (e.g. GP). Under such circumstances, BBP can make large reductions to the search space. The partition of separability is based on a special method, block and factor detection. Two different optimization engines are applied to test the performance of BBP on a set of symbolic regression problems. Numerical results show that BBP has a good capability of structure and coefficient optimization with high computational efficiency.

cs.NE↗

arXiv2017

Fast Modeling Methods for Complex System with Separable Features

Data-driven modeling plays an increasingly important role in different areas of engineering. For most of existing methods, such as genetic programming (GP), the convergence speed might be too slow for large scale problems with a large number of variables. Fortunately, in many applications, the target models are separable in some sense. In this paper, we analyze different types of separability of some real-world engineering equations and establish a mathematical model of generalized separable system (GS system). In order to get the structure of the GS system, two concepts, namely block and factor are introduced, and a special method, block and factor detection is also proposed, in which the target model is decomposed into a number of blocks, further into minimal blocks and factors. Compare to the conventional GP, the new method can make large reductions to the search space. The minimal blocks and factors are optimized and assembled with a global optimization search engine, low dimensional simplex evolution (LDSE). An extensive study between the proposed method and a state-of-the-art data-driven fitting tool, Eureqa, has been presented with several man-made problems. Test results indicate that the proposed method is more effective and efficient under all the investigated cases.

cs.NE↗

arXiv2017

A multilevel block building algorithm for fast modeling generalized separable systems

Data-driven modeling plays an increasingly important role in different areas of engineering. For most of existing methods, such as genetic programming (GP), the convergence speed might be too slow for large scale problems with a large number of variables. It has become the bottleneck of GP for practical applications. Fortunately, in many applications, the target models are separable in some sense. In this paper, we analyze different types of separability of some real-world engineering equations and establish a mathematical model of generalized separable system (GS system). In order to get the structure of the GS system, a multilevel block building (MBB) algorithm is proposed, in which the target model is decomposed into a number of blocks, further into minimal blocks and factors. Compare to the conventional GP, MBB can make large reductions to the search space. This makes MBB capable of modeling a complex system. The minimal blocks and factors are optimized and assembled with a global optimization search engine, low dimensional simplex evolution (LDSE). An extensive study between the proposed MBB and a state-of-the-art data-driven fitting tool, Eureqa, has been presented with several man-made problems, as well as some real-world problems. Test results indicate that the proposed method is more effective and efficient under all the investigated cases.

math.OC↗

arXiv2017

A divide and conquer method for symbolic regression

Symbolic regression aims to find a function that best explains the relationship between independent variables and the objective value based on a given set of sample data. Genetic programming (GP) is usually considered as an appropriate method for the problem since it can optimize functional structure and coefficients simultaneously. However, the convergence speed of GP might be too slow for large scale problems that involve a large number of variables. Fortunately, in many applications, the target function is separable or partially separable. This feature motivated us to develop a new method, divide and conquer (D&C), for symbolic regression, in which the target function is divided into a number of sub-functions and the sub-functions are then determined by any of a GP algorithm. The separability is probed by a new proposed technique, Bi-Correlation test (BiCT). D&C powered GP has been tested on some real-world applications, and the study shows that D&C can help GP to get the target function much more rapidly.

cs.NE↗

arXiv2017

Elite Bases Regression: A Real-time Algorithm for Symbolic Regression

Symbolic regression is an important but challenging research topic in data mining. It can detect the underlying mathematical models. Genetic programming (GP) is one of the most popular methods for symbolic regression. However, its convergence speed might be too slow for large scale problems with a large number of variables. This drawback has become a bottleneck in practical applications. In this paper, a new non-evolutionary real-time algorithm for symbolic regression, Elite Bases Regression (EBR), is proposed. EBR generates a set of candidate basis functions coded with parse-matrix in specific mapping rules. Meanwhile, a certain number of elite bases are preserved and updated iteratively according to the correlation coefficients with respect to the target model. The regression model is then spanned by the elite bases. A comparative study between EBR and a recent proposed machine learning method for symbolic regression, Fast Function eXtraction (FFX), are conducted. Numerical results indicate that EBR can solve symbolic regression problems more effectively.

cs.DS↗