| 1. IntroductionIn skating motion, in order to improve the efficiency and quality of skate sharpening, it's necessary to develop automatic skate mullers whose key technique is how to auto-detect the edge wear. Paper [4] put forward a method that approximated the edge to an ellipse, and got the theoretical formula between the scattered light intensity and the radii of the edge. With the result, applying both CCD non-contact measurement and the theories of neural network and its improvement which is called wavelet neural network, a method for measuring the edge wear of skate is put forward in the paper. Through simulate test and the design of the hardware test equipment, We validate the feasibility of the method.2. Principle of wear measurementIn skating, the skate edge will be abraded in different degree because of different truck and different kinds of skates. With approximating the edge to an ellipse, there is a theoretical relationship between the wear and the scattered light intensity, by which the wear can be obtained if the scattered light intensity is given.2.1 Theoretical measurement formulasShown in Figure 1, the ellipse model of the skate edge is set up in rectangular axis, where a ,b respectively presents major semi-axis and minor semi-axis of the ellipse; x ? z plane is the cross-section of the edge; y is the direction along the edge; B is the tangent point of profile or working side with the edge;αis the internal angle of OB with z -axis, where O is the origin; h is the edge wear , and the internal angle of profile with working side is 90°. The cross-section shape of the edge is described by mathematic formulas as below: where, H is the edge length investigated; andIn Figure.2, the scattered light from the edge forms the diffraction pattern in reflex space. It is theoretically inferable that the scattered light intensity is related to a ,b as follows[1]:where, P ' ( x ' , y ' , z ')- an arbitrary point in the reflex space; U 0 - the amplitude per unit length of light source;λ- the wavelength of the incident light; r0 - the distance from the origin of coordinates to light source; s0 - the distance from the origin to P '; c - the velocity of light; - - the internal angle of the scattered light with x- z plane; - 0 - the internal angle of the incident light and x - z plane;Ψ- the internal angle of the scattered light and y - z plane, and ( )R (θ0 )exp{ik[bsinsinθ0a(cos-0cos)cosθ0]}cosθ0dθ0 (4) where,θ0 is the internal angle of the line OQ and y - z plane, in which Q ( x0 , y0 , z 0)is a point on the edge; R (θ0)is the reflectivity of point Q ( x0 , y0 , z0 ); k =2π/λ. Because the angle of working side with profile is 90°, the wear is obtained from formula 1 and 2 as follows:Then the relationship between the wear and the scattered light intensity is Fig1. The ellipse model of skate edge Fig2. The sketch of diffractionknown. If the scattered light intensity is given, the edge wear can be computed indirectly according to formula (3),(4) and 5.After normalization, the relative scattered light intensity is: Because the range of variableΨis confirmed, the vector I r is only determined by ( a , b ), and the value of ( a , b) can be obtained from I r. 2.2 The algorithm of the measurment: neural network theoryBased on the complexity of the formula (6), it is hard to obtain the parameter I r from the parameters a ,b . The neural network can resolve non-linear problem effectively and need no accurate mathematical expression. Therefore, the neural network is applied to compute a ,b, which has the capability of approximating an arbitrary continuous function if the transitive functions of its neurons are continuous.The number of training samples will increase exponentially along with the input dimension of the network. Due to lots of CCD photosensitive units, I r vector has so high dimension that it cannot be directly inputted to the network. Therefore, two meanses is used to extract the input vector: firstly, a 81-dimensional vector is obtained by area sampiling I r; secondly, DCT transformation is here used to extract the 81-dimensional vector to 9-dimensional vector p . The sketch of the algorithm is shown in Figure.3. Formula 6 can be approximated uniformly by a hidden-layer feedforword neural network whose input is the vector of eigenvalue coefficient p of I r and output two-dimensional vector ( a ,b).If ( a ,b) is obtained by above network, the wear h of the edge can be computed from formula 5.In order to prove its correctness, the algorithm is simulated using matlab tools.in the process of simulation, different training-function and different net-structure isused to train the weight of ANN. By compared with all of results, the appropriate training-function and net-structure is adopted. The simulantion prove the algorithm is correct, and draw a conclusion that: the net of double hidden layers and the number of hidden neurons is 75(56:19); the transfer function of the hidden neurons is hyperbolic tangent function and that of theoutput neurons is linear function; the training function adopts scaled conjugate gradient backpropagation.2.3 The improvement of the measuring algorithm: wavelet neural networkPutting forward the improved methed of wavelet neural network, based on the defectes of the BP neural network which are include slow training speed of the network and easy to get into partial minimum and so on. From the wavelet transform theory, we proposing the two combination ways of the wavelet and neural network, which are assistant combination and nesting combination. There use the later methed, which is change the transfer function of the middle layer into the wavelet function, at the same time substitute the bias which is from the input layer to the middle layer and the threshold of the middle layer by using the scaling factor and the translating factor of the wavelet function. For the continuous parameters of the wavelet neural networkg i = g( x-bj/aj), where g is the wavelet function, a j , bj are the scaling factor and the translating factor separately, and the output of the network f k isFor the discrete parameters of the wavelet neural network g_j=g( a0 mjxnjb0) where g is the wavelet function, a 0,b0 are the basic unit of scaling and the translating, and the output of the network f k isThe training and the lerning of the wavelet neural network can be the same as the traditional neural network. There is a defect of the traditional neural network which is the determination of the neurons of the middle layers, but the middle layers'neurons of the wavelet neural network can be self-adapted determined as follows:At first, set the middle layers'neurons of the wavelet neural network M equal 1, and there is only g 1 of the neurons of the middle layer. If the result meet the error condition after learning and caculateing many times, then the training will be stopped; and if it reachs the maximum learning times and still can not meet the error condition, then the neurons of the wavelet neural network shoud be added to 1, and now M equal 2. The neurons of the middle layer are g 1 and g 2, repeat the process until meeting the error condition. According to this method, the neurons of the wavelet neural network can be determined self-adaptive, and it can conquer the defect of the traditional neural network.Besides the improvement of the BP neural network by using wavelet neural network, we also use the RBF neural network to train and simulate the dates, the result proves that it is very good for the design.3. The hareware design validate of the measurement projectThe sketch of the measurement system is shown in Figure.4. It includes two parts: module of data acquiring and module of data processing. The first module is made up of CCD sensor, A/D device and FPGA, CCD sensor acquires the information of the scattered light intensity, and output the analog signals, A/D translates the information to digital data, and then saves the data to SRAM memory.Both the driver logic of CCD and A/D and the logic of controlling the process of acquiring data lie in FPGA, the SRAM memory which saves the data and can be accessed by DSP lies in FPGA also. The data processing module include the feature extract of discrete cosine transformation (DCT) and neural network computation. In the end we analyzed the two algorithms from the real-time ability and the accuracy separately, and compared the result of floating-point program with that of fixing-point program, the error is no more then 0.01. It demonstrated that the design was good.4. ConclusionThere is a scarcity of simple-handled devices in automatically measuring the wear of the skate edge. To solve the problem, applying the result of paper[4], a method for measuring the wear based on both CCD non-contact measurement technology and neural network theories and its improving method:wavelet neural network is proposed. The network simulation illustrates that the mean relative error of h is 0.1%, which is small enough to meet the requirement of measuring the edge wear, and this method is implemented based on DSP. The method is applicable for developing automatic apparatus for measuring the edge wear and on-line measurement devices for skate mullers. |
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