The application research on improvement of genetic algorithm in linear CCD detection

2.1. The object of study

In this paper, the research object is an online optimization problem of “spot on CCD imaging curve”, the problem comes from photoelectric measuring system of “light reflection method of micro friction test project”, the photoelectric testing system structure as shown in Fig. 1.

Its composition is: two sets of laser generator, collimating focusing lens, two sets of silicon sensor, two sets of linear CCD detector. Working principle is: the laser light laser, the collimating lens focus after the incident to the silicon sensor, then through the reflection into the linear CCD detector photosensitive surface, light spot online CCD imaging curve is shown in Fig. 2.

Analysis: the location of the curve peak in imaging should be linear CCD photosensitive light reflection on the surface of the position.

Laser and CCD imaging curve’s maximum position is unchanged. The amplitude of the silicon wafer action directly reflects the actual test of friction and the size of the positive pressure, maximum position is reflected in the CCD imaging curve changes, the real value of the friction force and the positive pressure can be obtained through calculation of the calibration.

To sum up, the CCD imaging curve optimization problem is an important part of the photoelectric testing system, how can fast and accurate positioning the maximum points and calculating the variation has become the key to realization the high precision, high sensitivity testing system.

Fig. 1Photoelectric detection system structure

Fig. 2Spot on the CCD imaging curve

2.2. Mathematical model

By the Fig. 2 can get the following data: intensity value corresponding to the maximum value of imaging curve is about 275, the Yu Guangjiang values less than 100 are believed to be points not spot, speckle imaging pixel points about 200 pixels wide. The optimization solution model can be established:

(1) The objective function.

According to the above data, determine the maximum light intensity with the curve 275 and search the difference between the light intensity value as objective function, the function expression is:

(2) Constraint conditions.

Because of the light intensity value maximum 275 only, so establishing the constraint expression for the following:

(3) Termination conditions.

According to the actual situation, to establish differential value is 0, or the time difference is equal to the first I – five times to the average of the time difference I to termination conditions, its function is as follows:

On Eqs. (1)-(3) parameters are defined as follows: ${\mathrm{\Delta }}_{max}$ for maximum light intensity 275, ${\mathrm{\Delta }}_{\mathrm{I}}$ get effective light intensity for arbitrary point, ${\mathrm{\Delta }}_j$ for arbitrary point of the actual light intensity, to take the number of $N$.

3.1. Improve the principle

The improvement of GA can be embodied in every steps of the algorithm implementation, such as the establishment of the coding, initial population, the establishment of a fitness function, and so on.

Improvement scheme in this paper is proposed to the SGA termination conditions, the author in the SGA termination conditions combined with adaptive technology and dynamic threshold constraint technology, makes the improved algorithm on such optimization problem has obvious superiority. Specific implementation plan is as follows (based on the actual research object).

Known to the system, the optimal values of the linear array CCD detection of maximum light intensity is about 275, speckle imaging point of pixels wide approximately 200 pixels, the CCD signal of the position of the light intensity is about the biggest 200 pixels, in the middle of the position, due to the above two known data, so the constraint can be set like this:

(1) Compare the random-access target value of the relative light intensity value and the threshold of 100 (light intensity value is less than 100 are believed to be spot not point), because the ultimate goal intensity value is about 275, so they can think the light intensity more than 100 in the target location is in speckle imaging points of 200 pixels wide. If all individual target values are less than the threshold of 100, then redistribute system to get light intensity values and continue to compare, until there is individual target value is greater than the threshold of 100. If setting up reasonable population size, can get individuals greater than the threshold of 100 within three time.

(2) After individual target value is greater than the threshold of 100, then narrow the randomly assigned space, according to the individual target position corresponding pixel value as the center, the backward and forward 60 pixel length open space (spot the corresponding pixel wide for 200, half of 100, so the selection of 60, the two can cover the whole optimal solution area), to form a 120 pixels in the allocation of space, and to increase the number of total group of individuals and to change previous constraints, constraints into each individual size comparison between the target, so much. Due to allocate space on this for individual target has been more and more close to the optimal solution, so the increase in the total group of individual number can improve the optimization efficiency and optimization precision. According to the above scheme performed several times to get the maximum of the curve.

3.2. Implementation steps

IGA, as a kind of adaptive global efficient optimization algorithm, for any need to be optimized calculation model, according to the following steps, the solution generally can be construct: 1) determine the decision variables and constraints, including individual phenotype and problem solution space; 2) to determine the initial population and scale; 3) determine the method of feasible solution of chromosome coding; 4) determine the individual fitness function; 5) to determine the genetic operators, including selection, crossover and mutation operator; 6) the related operation parameters of improved genetic algorithm, including population size $M$, the largest evolution algebra $T$, crossover probability $Pc$ and mutation probability $Pm$, initial constraint threshold TV1 and extension field TV2.7) set up the dynamic adaptive termination conditions.