The Algorithm of Balanced Orthogonal Multiwavelets and Its Application in Denoising

In order to extract fault features of a weak signal from the strong noise and maintain signal smoothness, a new method of denoising based on the algorithm of balanced orthogonal multiwavelets is proposed. Multiwavelets have several scaling functions and wavelet functions, and possess excellent properties that a scalar wavelet cannot satisfy simultaneously, and match the different characteristics of signals. Moreover, the balanced orthogonal multiwavelets can avoid the Gibbs phenomena and their processes have the advantages in denoising. Therefore, the denoising based on the algorithm of balanced orthogonal multiwavelets is introduced into the signal process. The algorithm of bal- anced orthogonal multiwavelet and the implementation steps of this denoising are described. The experimental compar- ison of the denoising effect between this algorithm and the traditional multiwavelet algorithm was done. The experi- ments indieate that this method is effective and feasible to extract the fault feature submerged in heavy noise.

A CLASS OF COMPACTLY SUPPORTED ORTHOGONAL SYMMETRIC COMPLEX WAVELETS WITH DILATION FACTOR 3

When approximation order is an odd positive integer, a simple method is given to construct compactly supported orthogonal symmetric complex scaling function with dilation factor 3. Two corresponding orthogonal wavelets, one is symmetric and the other is antisymmetric about origin, are constructed explicitly. Additionally, when approximation order is an even integer 2, we also give a method to construct compactly supported orthogonal symmetric complex that illustrate the corresponding results. wavelets. In the end, there are several examples

Construction of Orthogonal Vector-valued Wavelets and Characteristics of Vector-valued Wavelet Packets

The notion of vector-valued multiresolution analysis is introduced and the concept of orthogonal vector-valued wavelets with 3-scale is proposed. A necessary and sufficient condition on the existence of orthogonal vector-valued wavelets is given by means of paraunitary vector filter bank theory. An algorithm for constructing a class of compactly supported orthogonal vector-valued wavelets is presented. Their characteristics is discussed by virtue of operator theory, time-frequency method. Moreover, it is shown how to design various orthonormal bases of space L^2（R, C^n） from these wavelet packets.

An Orthogonal Wavelet Transform Fractionally Spaced Blind Equalization Algorithm Based on the Optimization of Genetic Algorithm

An orthogonal wavelet transform fractionally spaced blind equalization algorithm based on the optimization of genetic algorithm(WTFSE-GA) is proposed in viewof the lowconvergence rate,large steady-state mean square error and local convergence of traditional constant modulus blind equalization algorithm(CMA).The proposed algorithm can reduce the signal autocorrelation through the orthogonal wavelet transform of input signal of fractionally spaced blind equalizer,and decrease the possibility of CMA local convergence by using the global random search characteristics of genetic algorithm to optimize the equalizer weight vector.The proposed algorithm has the faster convergence rate and smaller mean square error compared with FSE and WT-FSE.The efficiency of the proposed algorithm is proved by computer simulation of underwater acoustic channels.

On the Zeros of Daubechies Orthogonal and Biorthogonal Wavelets

In the last decade, Daubechies’ wavelets have been successfully used in many signal processing paradigms. The construction of these wavelets via two channel perfect reconstruction filter bank requires the identification of necessary conditions that the coefficients of the filters and the roots of binomial polynomials associated with them should exhibit. In this paper, orthogonal and Biorthogonal Daubechies families of wavelets are considered and their filters are derived. In particular, the Biorthogonal wavelets Bior3.5, Bior3.9 and Bior6.8 are examined and the zeros distribution of their polynomials associated filters are located. We also examine the locations of these zeros of the filters associated with the two orthogonal wavelets db6 and db8.

Real-time Extraction of Target Position Information Based on Bi-orthogonal Wavelets

Extraction of flying target position information is the prerequisite for passive infrared guided missiles to track the target. The existing missile detection system senses the target's infrared radiation, and then the generated signal is sent to signal processing circuits for extracting the target position information. In order to improve anti-interference capacity of the detection system, an algorithm of module maximum edge detection based on the bi-orthogonal wavelets is proposed to replace its hardware. The signal can be decomposed in one layer, only its high frequency detail is reconstructed. After some calculations, the average target position can be obtained. The algorithm's real-time implementation with DSP is also discussed. To reduce the execution time, the program structure can be optimized with double buffers in memory. This implementation is verified by simulations. The results show that the method has only a small amount of calculations, can meet the requirements for finding out the target position in real-time and needs not the traditional processing circuit.

Parameter estimation for chaotic systems using the cuckoo search algorithm with an orthogonal learning method

We study the parameter estimation of a nonlinear chaotic system,which can be essentially formulated as a multidimensional optimization problem.In this paper,an orthogonal learning cuckoo search algorithm is used to estimate the parameters of chaotic systems.This algorithm can combine the stochastic exploration of the cuckoo search and the exploitation capability of the orthogonal learning strategy.Experiments are conducted on the Lorenz system and the Chen system.The proposed algorithm is used to estimate the parameters for these two systems.Simulation results and comparisons demonstrate that the proposed algorithm is better or at least comparable to the particle swarm optimization and the genetic algorithm when considering the quality of the solutions obtained.

Solution for integer linear bilevel programming problems using orthogonal genetic algorithm

An integer linear bilevel programming problem is firstly transformed into a binary linear bilevel programming problem, and then converted into a single-level binary implicit programming. An orthogonal genetic algorithm is developed for solving the binary linear implicit programming problem based on the orthogonal design. The orthogonal design with the factor analysis, an experimental design method is applied to the genetic algorithm to make the algorithm more robust, statistical y sound and quickly convergent. A crossover operator formed by the orthogonal array and the factor analysis is presented. First, this crossover operator can generate a smal but representative sample of points as offspring. After al of the better genes of these offspring are selected, a best combination among these offspring is then generated. The simulation results show the effectiveness of the proposed algorithm.

Orthogonal genetic algorithm for solving quadratic bilevel programming problems

A quadratic bilevel programming problem is transformed into a single level complementarity slackness problem by applying Karush-Kuhn-Tucker（KKT） conditions.To cope with the complementarity constraints,a binary encoding scheme is adopted for KKT multipliers,and then the complementarity slackness problem is simplified to successive quadratic programming problems,which can be solved by many algorithms available.Based on 0-1 binary encoding,an orthogonal genetic algorithm,in which the orthogonal experimental design with both two-level orthogonal array and factor analysis is used as crossover operator,is proposed.Numerical experiments on 10 benchmark examples show that the orthogonal genetic algorithm can find global optimal solutions of quadratic bilevel programming problems with high accuracy in a small number of iterations.

AMicroseismic Signal Denoising Algorithm Combining VMD and Wavelet Threshold Denoising Optimized by BWOA

The denoising of microseismic signals is a prerequisite for subsequent analysis and research.In this research,a new microseismic signal denoising algorithm called the Black Widow Optimization Algorithm(BWOA)optimized VariationalMode Decomposition(VMD)jointWavelet Threshold Denoising(WTD)algorithm(BVW)is proposed.The BVW algorithm integrates VMD and WTD,both of which are optimized by BWOA.Specifically,this algorithm utilizes VMD to decompose the microseismic signal to be denoised into several Band-Limited IntrinsicMode Functions(BLIMFs).Subsequently,these BLIMFs whose correlation coefficients with the microseismic signal to be denoised are higher than a threshold are selected as the effective mode functions,and the effective mode functions are denoised using WTD to filter out the residual low-and intermediate-frequency noise.Finally,the denoised microseismic signal is obtained through reconstruction.The ideal values of VMD parameters and WTD parameters are acquired by searching with BWOA to achieve the best VMD decomposition performance and solve the problem of relying on experience and requiring a large workload in the application of the WTD algorithm.The outcomes of simulated experiments indicate that this algorithm is capable of achieving good denoising performance under noise of different intensities,and the denoising performance is significantly better than the commonly used VMD and Empirical Mode Decomposition(EMD)algorithms.The BVW algorithm is more efficient in filtering noise,the waveform after denoising is smoother,the amplitude of the waveform is the closest to the original signal,and the signal-to-noise ratio(SNR)and the root mean square error after denoising are more satisfying.The case based on Fankou Lead-Zinc Mine shows that for microseismic signals with different intensities of noise monitored on-site,compared with VMD and EMD,the BVW algorithm ismore efficient in filtering noise,and the SNR after denoising is higher.

Power Quality Disturbance Classification Method Based on Wavelet Transform and SVM Multi-class Algorithms

The accurate identification and classification of various power quality disturbances are keys to ensuring high-quality electrical energy. In this study, the statistical characteristics of the disturbance signal of wavelet transform coefficients and wavelet transform energy distribution constitute feature vectors. These vectors are then trained and tested using SVM multi-class algorithms. Experimental results demonstrate that the SVM multi-class algorithms, which use the Gaussian radial basis function, exponential radial basis function, and hyperbolic tangent function as basis functions, are suitable methods for power quality disturbance classification.

BLIND EQUALIZATION OF MIMO SYSTEMS BASED ON ORTHOGONAL CONSTANT MODULUS ALGORITHM

This paper investigates adaptive blind source separation and equalization for Multiple Input Multiple Output (MIMO) systems. To effectively recover input signals, remove Inter-Symbol Interference (ISI) and suppress Inter-User Interference (IUI), the array input is first transformed into the signal subspace, then with the derived orthogonality between weight vectors of different input signals, a new orthogonal Constant Modulus Algorithm (CMA) is proposed. Computer simulation results illustrate the promising performance of the proposed method. Without channel identification, the proposed method can recover all the system inputs simultaneously and can be adaptive to channel changes without prior knowledge about signals.

Manufacturing Supply Chain Optimization Problem with Time Windows Based on Improved Orthogonal Genetic Algorithm

Aim to the manufacturing supply chain optimization problem with time windows,presents an improved orthogonal genetic algorithm to solve it. At first,we decompose this problem into two sub-problems (distribution and routing) plus an interface mechanism to allow the two algorithms to collaborate in a master-slave fashion,with the distribution algorithm driving the routing algorithm. At second,we describe the proposed improved orthogonal genetic algorithm for solving giving problem detailedly. Finally,the examples suggest that this proposed approach is feasible,correct and valid.

Probability Simulation Optimization Approach Using Orthogonal Genetic Algorithm

In order to solve the complex optimization problem dealing with uncertain phenomenon effectively, this paper presents a probability simulation optimization approach using orthogonal genetic algorithm. This approach synthesizes the computer simulation technology, orthogonal genetic algorithm and statistical test method faultlessly, which can solve complex optimization problem effectively. In this paper, the author gives the correlative conception of probability simulation optimization and describes the probability simulation optimization approach using orthogonal genetic algorithm in detail. Theoretically speaking, it has a strong rationality and maneuverability that can apply probability method in solving the complex optimization problems with uncertain phenomenon. In demonstration, the optimization performance of this method is better than other traditional methods. Simulation resuh suggests that the approach referred to this paper is feasible, correct and valid.

AUTOMATIC ORTHOGONALIZATION DETECTION APPROACH FOR GS ALGORITHM

Gram-Schmidt orthogonalization algorithm is an interesting theme in the field of adaptive beam-forming and filtering as a fast algorithm. However, a key problem associated with this algorithm is that the number of orthogonalization, namely, the dimensions of interference subspace, is required to know prior. In this paper we derive a threshold and adopt it to detect the number of orthogonalization in the procedure of Gram-Schmidt(GS) orthogonalization decomposition, and this detection approach is simpler and faster than the approach based on eigenanalysis. Finally, computer simulation results were presented too.

NON-LINEAR DYNAMIC MODEL RETRIEVAL OF SUBTROPICAL HIGH BASED ON EMPIRICAL ORTHOGONAL FUNCTION AND GENETIC ALGORITHM

Aiming at the difficulty of accurately constructing the dynamic model of subtropical high, based on the potential height field time series over 500 hPa layer of T106 numerical forecast products, by using EOF（empirical orthogonal function） temporal-spatial separation technique, the disassembled EOF time coefficients series were regarded as dynamical model variables, and dynamic system retrieval idea as well as genetic algorithm were introduced to make dynamical model parameters optimization search, then, a reasonable non-linear dynamic model of EOF time-coefficients was established. By dynamic model integral and EOF temporal-spatial components assembly, a mid-/long-term forecast of subtropical high was carried out. The experimental results show that the forecast results of dynamic model are superior to that of general numerical model forecast results. A new modeling idea and forecast technique is presented for diagnosing and forecasting such complicated weathers as subtropical high.

A High Precision Biorthogonal 9/7 Wavelet Filter Implemented in the FPGA

An efficient high precision biorthogonal 9/7 wavelet filter structure for image processing applications was proposed. This structure aimed at high precision applications. A precision improved distributed algorithms (DA) had been proposed. Comparing with traditional DA implementations, the new DA had higher precision while preserves smaller area. The proposed structure was verified in Spartan-6 field programmable gate array (FPGA) and achieved 200 MHz operation frequency. The peak signal to noise ratio (PSNR) of reconstructed image (Lena) achieves 74 dB which is very high comparing with other implementations.

THE CONSTRUCTION OF ORTHOGONAL WAVELET BASIS ON[0,1] AND NUMERICAL SIMULATION

In this paper, we show the construction of orthogonal wavelet basis on the interval [0, 1],using compactly supportted Daubechies function. Forwardly, we suggest a kind of method to deal with the differential operator in view of numerical analysis and derive the appoximation algorithm of wavelet ba-sis and differential operator, which affects on the basis, to functions belonging to L2 [0, 1 ]. Numerical computation indicate the stability and effectiveness of the algorithm.

Schedule algorithm for mitigating inter-cell interference based on orthogonal complement space

In order to avoid severe performance degradation led by the inter-cell interference (ICI) in orthogonal frequency division multiple access (OFDMA) systems with a frequency reused factor (FRF) of 1,distributed schedule algorithm (DS-OCS) and distributed proportional fairness schedule algorithm (DPFS-OCS) based on orthogonal complement space (OCS) were proposed. The first right and left singular vectors of the channel that the user experienced were selected as the transmitting and receiving beamforming vectors. An interference space was spanned by the left singular vectors of the entire interference users in the same channel. The most suitable user lay in the OCS of the interference space was scheduled to avoid suffering interference from neighboring cells based on the criterion of system capacity maximizing and proportional fairness. The simulation results show that the average system capacity can be improved by 2%-4% compared with the DS-OCS algorithm with the Max C/I algorithm,by 6%-10% compared with the DPFS-OCS algorithm with the PF algorithm.

Explicit structure-preserving geometric particle-in-cell algorithm in curvilinear orthogonal coordinate systems and its applications to whole-device 6D kinetic simulations of tokamak physics

Explicit structure-preserving geometric particle-in-cell(PIC)algorithm in curvilinear orthogonal coordinate systems is developed.The work reported represents a further development of the structure-preserving geometric PIC algorithm achieving the goal of practical applications in magnetic fusion research.The algorithm is constructed by discretizing the field theory for the system of charged particles and electromagnetic field using Whitney forms,discrete exterior calculus,and explicit non-canonical symplectic integration.In addition to the truncated infinitely dimensional symplectic structure,the algorithm preserves exactly many important physical symmetries and conservation laws,such as local energy conservation,gauge symmetry and the corresponding local charge conservation.As a result,the algorithm possesses the long-term accuracy and fidelity required for first-principles-based simulations of the multiscale tokamak physics.The algorithm has been implemented in the Sym PIC code,which is designed for highefficiency massively-parallel PIC simulations in modern clusters.The code has been applied to carry out whole-device 6 D kinetic simulation studies of tokamak physics.A self-consistent kinetic steady state for fusion plasma in the tokamak geometry is numerically found with a predominately diagonal and anisotropic pressure tensor.The state also admits a steady-state subsonic ion flow in the range of 10 km s-1,agreeing with experimental observations and analytical calculations Kinetic ballooning instability in the self-consistent kinetic steady state is simulated.It is shown that high-n ballooning modes have larger growth rates than low-n global modes,and in the nonlinear phase the modes saturate approximately in 5 ion transit times at the 2%level by the E×B flow generated by the instability.These results are consistent with early and recent electromagnetic gyrokinetic simulations.