Analysis of the Teaching Quality of Physical Education Class by Using the Method of Gradient Difference

The quality of physical education classes must be evaluated in three major ways: class attitude, class level, and class effect.

The specific contents are as follows:

Teaching attitude. Including the quality of writing lesson plans; preparation before class (site, equipment, safety measures).

Figure 1 is a diagram showing a network structure of a model, which is composed of an input layer, a concealment layer, and an output layer, the 3-layer structure can solve most nonlinear problems as long as the appropriate number of neurons is taken, and the data curve can be simulated. The input layer uses 5 neurons, corresponding to the 5 dimensions of teaching quality evaluation; The output layer uses 1 neuron, corresponding to the evaluation results; Empirically, the number of neurons in the hidden layer is half the number of neurons in the losing layer and the output layer, that is, three [10]. Once the training sample is determined, the number of neurons in the input and output layers is determined, but the number of secret layers and neurons is an important and difficult problem: There are too few points to have the learning and information processing capabilities required for the network; If the score is too high, the complexity of the network structure increases, and it is easy to fall into a local local minimum value during learning, and the learning speed becomes slow. In order to meet the accuracy, it is a principle to adopt the structure as compact as possible. You can also try the following methods for primary selection:

Method 1: The relationship between the number of hidden neurons s and the number of patterns N: s = log 2 N;

Figure 1

A large number of symbols are involved in the model, and the following provisions are made: training sample set X_p; training sample X_i = [X₁, X₂, X₃, X₄, X₅] (1×5 matrix); Hidden layer weight W⁽²⁾_ji (5×3 matrix), The weight of the connection from neuron X_i in the input layer to neuron H_j in the hidden layer; Hidden layer input H_inj = X * W⁽²⁾_ji; hidden layer output H_outj = sigmoid (H_inj); Hidden layer weight W⁽³⁾_ji (3×1 matrix), that is, the connection weight of hidden layer neuron H_j to output layer neuron Y; Output layer input Y_in = H_outj * W⁽³⁾_ji output layer output Y_out sigmoid(Y_m); expected value T_p.

In the level difference value method, the input value of each neuron is the accumulation of the output value of all neurons in the previous layer multiplied by the weight, and the activation function processes the input value to generate the output of the neuron [11]. The step function is an ideal activation function, but it is discontinuous, non-derivative, and not smooth, therefore, the sigmoid function shown in Figure 2 is often used as the activation function in the level difference method. Whether the input value tends to + ∞ or − ∞, the output has a certain convergence limit to keep the model stable; At the same time, the derivative of the sigmoid function is simple and easy to calculate, as shown in equations 1 and 2. (1) f(x)=11+exp−x f\left( x \right) = {1 \over {1 + {{\exp }^{ - x}}}} (2) df(x)dx=exp−x(1+exp−x)2=11+exp−x(1−11+exp−x)=f(x)(1−f(x)) \matrix{ {{{df\left( x \right)} \over {dx}}} \hfill & = \hfill & {{{{{\exp }^{ - x}}} \over {{{\left( {1 + {{\exp }^{ - x}}} \right)}^2}}} = {1 \over {1 + {{\exp }^{ - x}}}}\left( {1 - {1 \over {1 + {{\exp }^{ - x}}}}} \right)} \hfill \cr {} \hfill & = \hfill & {f\left( x \right)\left( {1 - f\left( x \right)} \right)} \hfill \cr }

Figure 2

It can be seen from the sigmoid function diagram that the input is outside the [−5,5] interval, and the change in the function value is small, brings the gradient closer to zero This causes the gradient disappearance phenomenon in the step value calculation method. The five dimensions of evaluation are percentile, so the input X data is mapped to the range of [0,1] by formula (3). Use the “read delimited spreadsheet control” in labview to read the training sample set from the Excel table [12]. (3) X=Xi−XminXmax−Xmin X = {{{X_i} - {X_{\min }}} \over {{X_{\max }} - {X_{\min }}}}

Extract a sample matrix [X₁, X₂, X₃, X₄, X₅, X₆] from the normalized sample set and multiply it with the weight matrix W⁽²⁾_ji, the H_inj input matrix of the three neurons in the hidden layer is obtained, and the H_outj output matrix of the three neurons in the hidden layer is calculated through the activation function sigmoid. In the same way, the output value Y_out of the output layer neuron Y can be obtained. Select 30 samples for training, the program adopts the While loop structure, the loop body calculates the output value of 1 sample every time it is executed, uses the shift register to execute 30 times and ends the loop, and obtains the output value array of 30 samples [13].

The recognition model is shown in Figure 3.

Figure 3

Theoretically proven: A network with bias and at least one S-type implicit layer and one linear output layer can be approximated to any rational number. Increasing the number of layers can further reduce the error and improve the accuracy, but at the same time complicate the network and increase the training time of the weight value of the network. Since the improvement in error accuracy can actually be obtained by increasing the number of neurons, it is easier to observe and adjust than increasing the number of layers. Therefore, increasing the number of neurons in the implicit layer is a priority. In this experiment, the number of implicit layers is set to 1, and one input layer and one output layer are added to form a three-layer hierarchical network[14].

The accuracy of network training can be improved by adopting one implicit layer to increase the number of neurons. So how many implicit layer nodes should we choose? This is not clearly defined in theory. When designing concretely, it is realistic to compare and train the number of each neuron and add a little margin. In this experiment, we compared several cases and set the number of neurons in the implicit layer to 6.

Since the system is non-linear, the initial values are largely related to whether learning is locally minimized, whether it can converge, and how long the training time is. Empirically, it generally takes a random number with an initial weight between (−1,1).

The learning step determines the amount of change in weight that occurs in each cycle training. Large learning steps make the system unstable; Small learning steps result in long training times and may be slow to converge, but ensure that the error values in the network do not extend beyond the valleys of the error surface and eventually approach the minimum error values. Therefore, in general, smaller learning rates tend to be chosen to ensure the stability of the system. The learning rate is selected in the range of 0.01–0.8. According to the above, the author chooses a 3-layer differential network. The number of neurons in the input layer is determined by the number of variables in the training sample, the number of neurons in the implicit layer is 6, and the number of neurons in the output layer is 1. The transformation function of the node selects the sigmoid function. The initial weight is between (−1, 1), which is randomly generated [15]. The learning step size is determined to be 0.1, Figure 4 is the learning result, and Figure 5 is the error curve.

Figure 4

Figure 5

The author divides the teaching quality evaluation results into five grades, namely: Excellent, good, moderate, pass, and fail. The corresponding relationship between the network output value and the evaluation level is shown in Table 1.