Application of Adaptive Filter in Neural Network

The snag of common linear filtered Inverse Control (AIC) method is modify to hold with the characteristic of non-linear object with time delay and corresponding filtered ∈ -adaptive Algorithm based on Real-Time Recurrent Learning (RTRL) is presented to identify the parameters and d controller. The simulation result on a non model of “The R.O.V. Zeefakkel” and Adaptive PID control keeps the same dynamic response performance, and also mathematical model for ship Course keeping be discussed. A neural network adaptive filter is introduced for the removal of impulse noise in digital images.


INTRODUCTION
Adaptive Inverse Control (AIC) is novel approaches which can make a plant track the input command signal with a controller whose transfer function approximates the inverse of plant transfer function. Compared with traditional methods, AIC can achieve specified dynamic responses more easily and has better ability of disturbance rejection. Simulation comparison with previous scheme and adaptive PID control are performed on the non maneuvering to test the effect of improved algorithm. The impulse noise detection and removal of impulse noise while preserving the integrity of an image expressed mathematically be discussed.
The Improved Filtered-∈ Adaptive Inverse Control The Single Input Single Output (SISO) discrete nonlinear system to be considered is described by n dimension state equations as below @ IJTSRD | Available Online @ www.ijtsrd.com | Volume -2 | Issue -5 | Jul-Aug 2018 Mathematics, Vivekanandha College of Arts and Sciences for Elayampalayam, Thiruchengode, Namakkal, Tamil Nadu The snag of common linear filtered-∈ Adaptive Inverse Control (AIC) method is modify to hold with linear object with time delay adaptive Algorithm Time Recurrent Learning (RTRL) is presented to identify the parameters and design the controller. The simulation result on a non-linear ship Zeefakkel" and Adaptive PID control keeps the same dynamic response performance, and also mathematical model for ship Course keeping be discussed. A neural network ive filter is introduced for the removal of Adaptive Inverse Control, Ship course keeping, impulse noise detection and removal.
Adaptive Inverse Control (AIC) is novel approaches which can make a plant track the input command signal with a controller whose transfer function approximates the inverse of plant transfer function. Compared with traditional methods, AIC can achieve fied dynamic responses more easily and has better ability of disturbance rejection. Simulation comparison with previous scheme and adaptive PID control are performed on the non-linear ship maneuvering to test the effect of improved algorithm.
oise detection and removal of impulse noise while preserving the integrity of an image

Adaptive Inverse
The Single Input Single Output (SISO) discrete-time idered is described by n is a non-linear function, respect output and input variables, respectively. The principles of inverse control can be extended to deal with non-linear system, through non no strict inverse model. Whereas a linear system possesses a unique inverse, non only local inverses, valid in a bounded region of the signal space. The non-linear system is supposed to has Bounded-Input Bounded Output(BIBO) stability, i.e., there are existing constants input ( ) ∈ , = { : | ( system output ( ) satisfies: linearized system is observable at balance point = 0, the non-linear system described by (1) linear function, ( ) and ( ) respect output and input variables, respectively. The principles of inverse control can be extended to deal linear system, through non-linear system has no strict inverse model. Whereas a linear system possesses a unique inverse, non-linear systems have only local inverses, valid in a bounded region of the linear system is supposed to has Input Bounded Output(BIBO) stability, i.e., and , and for the ) |≤ , ∀ ≥ }, the satisfies: |y(k)|≤ . If its linearized system is observable at balance point linear system described by (1) has linear Auto-Regressive Average) are the orders of input time series and output time series respectively: < , is system delay which can ensure the existence of ( . ) is certain non-linear is monotonic change with ( ) , system (1)is invertible in the input spectrum . If the ) at time( + 1), the controller can be expressed as ( ) … … . . , − + are both unique. Under the the plant output will track the input signal of the inverse controller.
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Identification of Delay Time Complexity
The output of a non-linear system with time characteristic can be described as below form Where ( ) and ( ) represent the input and output of system at time , and are the input and output order , is system delay time, and ( . ) function of this non-linear system.
If we use neural network to model such a non plant, the training effectiveness will be greatly influenced by the samples of input vector collected in different range. Therefore, such network can as delay-time identifier. Here a non regressive with exogenous inputs ( NARX) network is used, which can be described as Where a and b denotes the length of tapped delay lines of input and output feedback, respectively. The plant input/output data pairs collected in certain time period are used to train the NARX network, and many research result have demonstrated that the sa range of ( ) changing from not including the first delayed input signal = − 1 to including it, i.e., = − 1 → = , will cause the training effectiveness having a great improvement, and hence the delay time d of controlled plant can be confirmed.

Improved Filtered-Algorithm
The NARX filter is also used to the controller modeling. For including self-feedback, it must be adapted using a method such as Real-Time Recurrent Learning (RTRL) or Back-propogation Through Time (BPTT). Considering the real-time requirement of practical application, we propose the filtered algorithm based on RTRL. To model , RTRL usually needs to obtain the error * between controller outputs, and then parameters can be adjusted via the principle of gradient descent to minimize the objective function = ( is unknown in practical AIC implementation. In improved filtered-algorithm, * is replaced by system error ΄ which is filtered by Δ parameters. The update algorithm can be expressed as follows represent the input and output are the input and output ) is the transfer If we use neural network to model such a non-linear plant, the training effectiveness will be greatly influenced by the samples of input vector collected in different range. Therefore, such network can be used time identifier. Here a non-linear auto-( NARX) network Where a and b denotes the length of tapped delay lines of input and output feedback, respectively. The plant input/output data pairs collected in certain time period are used to train the NARX network, and many research result have demonstrated that the sample changing from not including the first to including it, , will cause the training effectiveness having a great improvement, and hence the delay time d of controlled plant can be confirmed.
The NARX filter is also used to the controller feedback, it must be Time Recurrent propogation Through Time time requirement of practical application, we propose the filtered-, RTRL usually and the ideal parameters can be adjusted via the principle of gradient descent to * ) /2 , but * is unknown in practical AIC implementation. In is replaced by Δ to adapt parameters. The update algorithm can be expressed as Where and denote the step size and momentum co-efficient respectively, and gradient of with respect to controller weights Where ( ∆) is the ∆ −delayed partial derivative of output ( ) with respect to its weights It is updated by the chain rule: ( ) ) and effect of a change in the weights, previous inputs and outputs on the current output respectively, and these partial derivatives may be computed directly using the back-propagation algorithm.
previously-calculated and stored value of = 0, −1, −2, … . , ( ) are set to zero. We also note that ( ) , the partial derivative of the input of with respect to its weights, is zero for

SIMULATION RESEARCH
We apply the improved Filtered proposed in this paper to the control of non maneuvering. As a typical non time-lag characteristic, ship can be described by the non-linear model.

̈+̇+̇ = +
Where is the yaw angle, angle, , and are the model parameter, and the external disturbance. Page: 1992 denote the step size and momentum efficient respectively, and ∇ ( ) represents the with respect to controller weights : delayed partial derivative of with respect to its weights at time . It is updated by the chain rule: ) are the direct effect of a change in the weights, previous inputs and outputs on the current output respectively, and these partial derivatives may be computed directly using the propagation algorithm.
( ) is simply a ted and stored value of ( ) . For i are set to zero. We also note , the partial derivative of the input of with respect to its weights, is zero for all .

SIMULATION RESEARCH
improved Filtered-AIC method proposed in this paper to the control of non-linear ship . As a typical non-linear system with lag characteristic, ship can be described by the In order to evaluate the performance of the improved filtered--AIC scheme, conventional filtered-AIC and adaptive PID control are also performed. In the simulation, the sampling period ΄ = 0.1 .
(a)Firstly the ship ±10° course-changing test is performed without external disturbance, namely = 0. At = 300 , the ship time constant constant changes from 31 s to 45 s. Clearly the conditional filtered-AIC has much better dynamic performances than that of the adaptive PID control, but there existing static error in it for the influence of the change of plant delay time. In contrast, the improved scheme avoids static error and at the mean time, it has kept the same dynamic performances as conventional filtered-AIC method.
(a) The second simulation to be examined is the disturbance rejection ability. The external disturbance is chosen as = 4.5° + 3.44° Where and are normally distributed random numbers with mean 0, varience = 1. The comparison of the response curves between improved method and conventional ones. It can be clearly seen that the improved scheme has better disturbance rejection ability.

Ship Course-Keeping Mathematical Model
Equation (1) gives linear first-Order Nomoto model which is used for ship course-keeping Among these, is the ship heading angle, is the rudder angle, is the steering gain index, is the ship following index. It presents a Nomoto model based responding type of non-linear mathematical model, that is using a non-linear item ( / ) (̇) to replace ̇/ , and Where , represent the scale co-efficient of the first and the third power of the rate of turning ̇ . Specific parameter value depends on the factors like ship type, stowage, ship speed, etc. Taking as ship heading angle, then ̇= ; meanwhile, taking the frequently influence from uncertain interference such as wind, wave and current into consideration, the non-linear dynamic equation of ship course-keeping system could be written as: Where ∆ is the uncertain interference. According to engineering practice, ∆ is usually bounded disturbance, assuming there is an unknown constant could meet the equation (1) on the basis of hypothesis.

Impulse Noise Detection and Removal
When an image is coded and transmitted over a noisy channel or degraded by electrical sensor noise, as in a vidiction TV camera, degradation appear as "salt and-paper" noise (i.e., positive and negative impulses). Two models have been proposed to describe impulsive noise (Justusson, 1981 each input pattern. Each set of features is considered as a vector in the M-dimensional feature space. Pattern classification is accomplished by a selforganising neural network which is capable of cluster analysis for image data. The neural network proposed in this paper is a simplified version of ART I (Carpenter & Gross berg, 1987). However, it is capable of grey -level classification. It has two layers: the input layer and the output layer. These layers are connected by feed forward paths. The nodes of output layer are lateral inhibitive to one another. They are designed as a competitive network capable of choosing the winning node. The set of weights for any specific node constitute the prototype pattern for cluster . The clustering algorithm starts from isolated patterns and coalesces the nearest patterns or groups according to a threshold from the bottom up to form hierarchies. The essential point of this algorithm is to build up the clusters using the Euclidean distance measure between the input and the weights . Assume a sequence of pattern samples = ( , ,…. ) and a set of weight vectors = ( , , … , ) ∈ It is well known that similarities exist between ART and Kohonen's self-organising map.

CONCLUSION
In this paper, an improved nonlinear filtered-method is introduced and adaptive PID control are performed on the control of non-linear ship maneuvering and also mathematical model for ship Course-Keeping and impulsive noise be expressed.