Neural network has been well applied in many fields, but there are still many aspects to be studied. Among them, the combination of neural network and other technologies has the advantages of distributed storage, parallel processing, self-learning, self-organization and nonlinear mapping, and the resulting hybrid method and hybrid system have become a research hotspot. Because other methods also have their own advantages, combining neural network with other methods to learn from each other's strengths can achieve better application results. At present, the work in this field includes the fusion of neural network with fuzzy logic, expert system, genetic algorithm, wavelet analysis, chaos, rough set theory, fractal theory, evidence theory and grey system.
The following mainly analyzes the fusion of neural network with wavelet analysis, chaos, rough set theory and fractal theory.
Combined with wavelet analysis
198 1 year, French geologist Morlet creatively studied the similarities and differences, characteristics and function construction of Fourier transform and windowed Fourier transform in seeking geological data, put forward the concept of wavelet analysis for the first time, and established Morlet wavelet named after him. Since 1986, wavelet analysis has rapidly developed into a new subject due to the basic work of YMeyer, S.Mallat and IDaubechies. Meyer's Wavelet and Operator and Daubechies's Ten Lectures on Wavelet are the most authoritative works in the field of wavelet research.
Wavelet transform is a breakthrough of Fourier analysis method. It not only has good positioning characteristics in time domain and frequency domain, but also has good resolution for low-frequency signals and high-frequency signals in time domain, so it can converge to any detail of the object. Wavelet analysis is equivalent to a mathematical microscope, which has the functions of amplification, reduction and translation. The dynamic characteristics of signals are studied by examining the changes under different magnification. Therefore, wavelet analysis has become a powerful tool in geophysics, signal processing, image processing, theoretical physics and many other fields.
Wavelet neural network combines the good time-frequency localization characteristics of wavelet transform with the self-learning function of neural network, so it has strong approximation ability and fault tolerance. In the combination method, wavelet function can be used as the basis function to construct a neural network to form a wavelet network, and wavelet transform can also be used as the input preprocessing tool of feedforward neural network, that is, the multi-resolution characteristics of wavelet transform are used to process the process state signal, realize the separation of signal and noise, and extract the state feature that has the greatest influence on machining error as the input of neural network.
Wavelet neural network has many applications in motor fault diagnosis, high voltage power grid fault signal processing and protection research, bearing mechanical fault diagnosis and many other aspects. The application of wavelet neural network in intelligent control of induction servo motor makes the system have good tracking control performance and robustness. The wavelet packet neural network is used for intelligent diagnosis of cardiovascular diseases, and the wavelet layer is used for adaptive feature extraction in time and frequency domain, and the correct classification rate is 94%.
Although wavelet neural network has been applied in many aspects, there are still some shortcomings. From the requirements of extraction accuracy and real-time wavelet transform, it is necessary to construct some special wavelet bases that meet the application requirements according to the actual situation in order to achieve better results in application. In addition, the real-time requirement in application also requires the development of DSP to develop special processing chips to meet this requirement.
Chaotic neural network
The first definition of chaos was put forward by Li-Yorke in 1970s. Because of its wide application value, it has attracted wide attention from all sides since its advent. Chaos is an irregular movement in a certain system, and chaos is a common phenomenon in nonlinear systems. Chaotic motion has the characteristics of ergodicity and randomness, and it can traverse all the States in a certain range without repetition according to its own laws. Chaos theory determines the chaos of nonlinear dynamics, aiming at revealing the simple laws that may be hidden behind seemingly random phenomena, so as to find the * * * identity laws that a large class of complex problems generally follow.
1990, Kaihara, T.Takabe and M.Toyoda put forward the chaotic neural network model for the first time according to the chaotic characteristics of biological neurons, and introduced chaos into neural networks to make artificial neural networks have chaotic behavior, which is closer to the actual human brain neural networks. Therefore, chaotic neural network is considered as one of the intelligent information processing systems that can realize its real-world computing, and it has become one of the main research directions of neural networks.
Compared with the conventional discrete Hopfield neural network, chaotic neural network has richer nonlinear dynamic characteristics, which are as follows: (1) introducing chaotic dynamic behavior into neural network; Synchronization characteristics of chaotic neural networks: attractors of chaotic neural networks.
When the input of neural network changes greatly in practical application, the inherent fault-tolerant ability of application network is often insufficient, and amnesia often occurs. The dynamic memory of chaotic neural network belongs to deterministic dynamic motion, and the memory occurs on the trajectory of chaotic attractor. Memory patterns are interrelated through continuous movement (memory process), especially for those memory patterns whose state space is closely distributed or partially overlapped, chaotic neural network can always reproduce and identify them through dynamic associative memory without confusion, which is the unique performance of chaotic neural network and will greatly improve the memory ability of Hopfield neural network. The existence of attraction domain of chaotic attractor forms the inherent fault-tolerant function of chaotic neural network. This will play an important role in complex pattern recognition, image processing and other engineering applications.
Another reason why chaotic neural networks are concerned is that chaos exists in the neural networks of real neurons and organisms and plays a certain role, which has been confirmed by electrophysiological experiments in zoology.
Because of its complex dynamic characteristics, chaotic neural network has attracted great attention in the fields of dynamic associative memory, system optimization, information processing, artificial intelligence and so on. Chaotic neural network has associative memory function, but its search process is unstable. A control method is proposed to control chaotic phenomena in chaotic neural networks. The application of chaotic neural network in combinatorial optimization problems is studied.
In order to better apply the dynamic characteristics of chaotic neural network and effectively control its chaotic phenomenon, it is still necessary to further improve and adjust the structure of chaotic neural network and further study the chaotic neural network algorithm.
Based on rough set theory
Rough set theory was first proposed by Z.Pawlak, a professor at Warsaw University of Technology in Poland, in 1982. It is a mathematical theory to analyze data and a method to study the expression, learning and induction of incomplete data and inaccurate knowledge. Rough set theory is a new mathematical tool to deal with fuzzy and uncertain knowledge. Its main idea is to derive the decision-making or classification rules of the problem through knowledge reduction on the premise of keeping the classification ability unchanged. At present, rough set theory has been successfully applied to machine learning, decision analysis, process control, pattern recognition and data mining.
Rough set and neural network are similar in that they can both work well in natural environment. Rough set theory and method simulate abstract logical thinking of human beings, while neural network method simulates intuitive thinking of images, so they have different characteristics. Rough set theory takes qualitative, quantitative or mixed information closer to people's description of things as input. The mapping relationship between input space and output space is simplified by a simple decision table. It considers the importance of different attributes in knowledge expression to determine which knowledge is redundant and which knowledge is useful. Neural network uses the idea of nonlinear mapping and parallel processing method, and uses the structure of neural network itself to express the implicit function coding of input and output related knowledge.
There are two major differences between rough set theory method and neural network method in processing information: first, neural network can not simplify the dimension of input information space, and when the dimension of input information space is large, the network is not only complex in structure, but also takes a long time to train; Rough set method can not only remove redundant input information, but also simplify the expression space dimension of input information by discovering the relationship between data. Secondly, rough set method is sensitive to noise when dealing with practical problems, so the result of learning reasoning with noise-free training samples is not effective in noisy environment. Neural network method has a good ability to suppress noise interference.
Therefore, the two methods are combined, and the information is preprocessed by rough set method, that is, rough set network is used as the pre-system, and then a neural network information processing system is formed according to the information structure preprocessed by rough set method. The combination of the two can not only reduce the number of attributes of information expression and the complexity of neural network system, but also have strong fault tolerance and anti-interference ability, which provides a powerful way to deal with uncertain and incomplete information.
At present, the combination of rough set and neural network has been applied to speech recognition, expert system, data mining, fault diagnosis and other fields. Neural network and rough set are used for automatic identification of sound source position, and neural network and rough set are used for knowledge acquisition of expert system, which has achieved better results than traditional expert system, in which rough set deals with uncertain and inaccurate data and neural network classifies.
Although the combination of rough set and neural network has been applied in many fields, in order to make this method play a greater role, the following problems need to be considered: (1) the combination of rough set theory method to simulate abstract logical thinking of human beings and neural network method to simulate intuitive thinking of images is more effective; The development of software and hardware integration platform improves its practicability.
Combined with fractal theory
Since Benoit B. Mandelbrot, a professor of mathematics at Harvard University, put forward the concept of fractal in the mid-1970s, fractal geometry has developed into a scientific methodology-fractal theory, which is regarded as an important stage of mathematics in the 20th century. It has been widely used in almost all fields of natural science and social science, and has become one of the frontier research topics of many disciplines in the world.
Due to the rapid development in many disciplines, fractal has become a discipline that describes the regularity of many irregular things in nature. It is widely used in biology, geography, astronomy, computer graphics and other fields.
Using fractal theory to explain irregular, unstable and highly complex phenomena in nature can achieve remarkable results, while combining neural network with fractal theory and making full use of the advantages of nonlinear mapping, computing power and self-adaptation of neural network can achieve better results.
The application fields of fractal neural network include image recognition, image coding, image compression and fault diagnosis of mechanical equipment system. Fractal image compression/decompression method has the advantages of high compression rate and low loss rate, but its computing power is not strong. Due to the parallel operation of neural network, the application of neural network in fractal image compression/decompression improves the computing power of the original method. Combining neural network with fractal to identify fruit shape. Firstly, the irregularity of several fruit contour data is obtained by fractal, and then these data are identified by three-layer neural network, and then their irregularity is evaluated.
Fractal neural network has made many applications, but there are still some problems worthy of further study: the physical significance of fractal dimension; Research on computer simulation and practical application of fractal. With the deepening of research, fractal neural network will be continuously improved and achieve better application results. ?
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