Spot color formula prediction method based on enhanced elephant search algorithm

Abstract

The application discloses a spot color formula prediction method based on an enhanced elephant trunk search algorithm, and comprises the following steps: acquiring the absorption spectrum of a base color and a spot color, calculating the molar concentration of the base color by using a least square method, and obtaining the base color composition quantity of the spot color; constructing an enhanced elephant trunk search algorithm; calculating the molar concentration of the base color by using the enhanced elephant trunk search algorithm, and predicting the spot color formula. The spot color formula prediction method based on the enhanced elephant trunk search algorithm narrows the base color search space by using the least square method, reduces the search workload, and improves the search speed; by constructing the enhanced elephant trunk search algorithm, the search range is increased suddenly, the possibility of the algorithm falling into a local optimum is reduced, the elephant search direction is corrected, the search direction behavior intervention is realized, the search ability and the search speed of the algorithm are improved, and finally the color matching efficiency and the accuracy are improved.

Description

Technical Field

[0001] This invention belongs to the field of computer color matching technology, specifically relating to a spot color formula prediction method based on an enhanced longhorn beetle whisker search algorithm. Background Technology

[0002] Spot colors are created by mixing base color inks, allowing for customized production. To formulate spot colors with higher saturation and a wider color gamut, cyan (C), magenta (M), yellow (Y), orange (O), blue (B), and red (R) are typically defined as base colors. While achieving higher quality spot colors, this also presents greater challenges in reproducing them. Accurate spot color prediction can improve color matching efficiency and save on prototyping costs.

[0003] Currently, the most widely used color matching theory both domestically and internationally is the Kulbelka-Munk theory, which posits that a linear increase in dye concentration leads to a linear increase in color. Other color matching theories include density-based methods, tristimulus value-based methods, the Stearns-Noechel color matching model, the Friele color matching model, and the Munsell color matching model. However, spot color mixing is a relatively complex process, with multiple variables influencing its color expression. The change in spot color is not entirely linearly related to changes in dye concentration. Furthermore, the aforementioned models and methods are primarily applied to opaque printing materials and are based on reflectance spectra.

[0004] PET polyester film, made from polyethylene terephthalate, is commonly used as a substrate for film printing due to its excellent mechanical properties, good heat resistance, cold resistance, oil resistance, and corrosion resistance. However, the high light transmittance of PET film means that color matching methods based on reflectance spectra are not very accurate in color prediction. Therefore, current PET film color matching relies heavily on manual experience, which increases costs and reduces production efficiency. Thus, to improve the efficiency and accuracy of PET film color matching, more effective solutions should be found. Summary of the Invention

[0005] The purpose of this invention is to provide a spot color formula prediction method based on an enhanced longhorn beetle whisker search algorithm, which solves the problems of low efficiency and accuracy in existing color matching methods.

[0006] The technical solution adopted in this invention is: a spot color formula prediction method based on an enhanced longhorn beetle whisker search algorithm, comprising the following steps:

[0007] Step 1: Obtain the absorption spectra of the primary color and the spot color, calculate the molar concentration of the primary color using the least squares method, and obtain the number of primary color components in the spot color;

[0008] Step 2: Construct an enhanced longhorn beetle whisker search algorithm;

[0009] Step 3: Based on the number of primary colors obtained in Step 1, use the enhanced beetle whisker search algorithm obtained in Step 2 to calculate the molar concentration of the primary colors and predict the spot color formula.

[0010] The invention is further characterized in that,

[0011] Step 1 specifically includes the following steps:

[0012] Step 1.1: Define the absorption spectrum of the six primary colors as {A} i If i = 1, 2, ..., 6, then the absorption spectrum of the spot color is expressed as:

[0013]

[0014] In equation (1), Q is the number of primary colors that make up the spot color, and c i The molar concentration of each component primary color;

[0015] Step 1.2: Calculate the set C of molar concentrations of each constituent primary color using the least squares method:

[0016] C = (A T A) -1 A T A mix (2)

[0017] In equation (2), C = {c i Let A be the set of absorption spectra, i = 1, 2, ..., N. T This is the transpose of set A;

[0018] Step 1.3: When the molar concentration c of a certain primary color in each of the constituent primary colors... i When <0, the absorption spectrum A corresponding to the primary color is... i Remove from matrix A and proceed to step 1.2 again;

[0019] When the molar concentration of each constituent primary color c i If the value is ≥0, then the number of base colors of the spot color at that time is obtained.

[0020] Step 2 specifically includes the following steps:

[0021] Step 2.1: Determine the location of the longhorn beetle in the D-dimensional search space, denoted as:

[0022]

[0023] Step 2.2: Define the positions of the two longhorn beetle antennae, add a mutation probability term p, and change the distance l between the beetle's center of mass and its antennae.

[0024]

[0025] In equation (4), X r and X l δ represents the position of the longhorn beetle's two tentacles; l represents the distance between the beetle's center of mass and its tentacles; t p represents the step size explored in the t-th iteration; p represents the mutation probability of the algorithm; rand is a random number used to control the mutation of the step size according to probability; k is the rate of change factor; The unit vector is represented as:

[0026]

[0027] Step 2.3: Based on the concentration difference sensed by the longhorn beetle's two antennae, determine the beetle's next location. The next position of the longhorn beetle is X. t+1 The update method is as follows:

[0028]

[0029] In equation (6), t is the current iteration number; δ t Let X be the search step size for the t-th iteration, which is reduced after each iteration; sign[.] is the sign function; f(.) is the fitness function; X t Given the current position of the longhorn beetle, when f(X) t ) <f(X best When X is... t Assigned to X best X best This is the optimal location where the longhorn beetle has ever appeared; The direction correction term is represented as:

[0030]

[0031] In step 2.3, δ t+1 =δ t *η, where η is the decay constant, η = 0.95.

[0032] Step 3 specifically includes the following steps:

[0033] Step 3.1: Determine the dimension D of formula (3) in step 2.1 based on the number of primary colors obtained in step 1, and set the objective function J and constraints as follows:

[0034]

[0035] Constraints:

[0036] 0≤c i ≤1, i=1,2,..., (9)

[0037] In equation (8), J1 is the mean square error; J2 is the regularization term; J3 is the constraint condition; p1 and p2 are penalty coefficients;

[0038] Step 3.2: Using formula (6), update the molar concentration c in the defined D-dimensional search space. i To minimize the objective function J, the corresponding molar concentration c is... i This refers to a spot color formula.

[0039] The beneficial effects of this invention are as follows: The spot color formula prediction method based on the enhanced beetle whisker search algorithm of this invention reduces the search space of primary colors by using the least squares method, thereby reducing the search workload and improving the search speed; by constructing the enhanced beetle whisker search algorithm, the growth of the search range is abruptly realized, reducing the possibility of the algorithm getting stuck in local optima, correcting the beetle search direction, realizing behavioral intervention in the search direction, improving the search ability and search speed of the algorithm, and ultimately improving the efficiency and accuracy of color matching. Attached Figure Description

[0040] Figure 1 This is a flowchart illustrating the spot color formula prediction method based on the enhanced longhorn beetle whisker search algorithm of the present invention.

[0041] Figure 2 This is a flowchart illustrating the enhanced longhorn beetle whisker search algorithm in the spot color formula prediction method based on the enhanced longhorn beetle whisker search algorithm of the present invention.

[0042] Figure 3 These are the actual absorption spectra of the six primary colors in the wavelength range of 200-900 nanometers in the embodiments of the present invention;

[0043] Figure 4 This is a comparison chart of the mean absolute percentage error between the algorithm of this invention and three other algorithms;

[0044] Figure 5 This is a convergence curve diagram of the algorithm of this invention and three other algorithms;

[0045] Figure 6 This is a comparison image of spot color restoration in an embodiment of the present invention. Detailed Implementation

[0046] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0047] This invention provides a method for predicting spot color formulas based on an enhanced longhorn beetle whisker search algorithm, such as... Figure 1 As shown, it includes the following steps:

[0048] Step 1: Analyze the primary color components of the spot color using the least squares method.

[0049] The absorption spectra of the six primary colors are defined as {A} i The absorption spectrum of a spot color satisfies the formula: (i = 1, 2, ..., 6)

[0050]

[0051] In the formula, Q represents the number of base colors that make up the spot color.

[0052] Then the set of molar concentrations of each constituent primary color is C = {c i The least squares method can be used to calculate the value of i = 1, 2, ..., N.

[0053] C = (A T A) -1 A T A mix

[0054] The molar concentration of each primary color should satisfy c i ≥0. When the calculation result c i When the value is less than 0, the primary color is irrelevant to the target spot color, and the corresponding A color can be used. i Remove the primary colors from matrix A, then perform a least squares method on the remaining primary colors until the molar concentrations of all remaining primary colors are greater than zero. The constraint that the molar concentrations calculated by the least squares method are all greater than zero is the termination condition for the least squares method. If the recalculated molar concentrations satisfy every c in C... i If the constraint is ≥0, then the target spot color is composed of the corresponding base color.

[0055] Step 2, as follows Figure 2 As shown, an enhanced beetle whisker search algorithm is constructed. The specific implementation process of the enhanced beetle whisker search algorithm is as follows:

[0056] Step 2.1: Determine the location of the longhorn beetle in the D-dimensional search space, denoted as [location missing].

[0057]

[0058] Step 2.2: Define the positions of the two longhorn beetle antennae, add a mutation probability term p, and change the distance l between the beetle's center of mass and the antennae. This achieves a mutation in the search range, reducing the possibility of the algorithm getting trapped in local optima.

[0059]

[0060] In the formula, X r and X l δ represents the position of the longhorn beetle's two tentacles; l represents the distance between the beetle's center of mass and its tentacles; tp represents the step size explored in the t-th iteration; p represents the mutation probability of the algorithm; rand is a random number used to control the mutation of the step size according to probability; k is the rate of change factor; unit vector

[0061]

[0062] Step 2.3: Determine the longhorn beetle's next location based on the concentration difference sensed by its two antennae. The enhanced beetle whisker search algorithm adds a direction correction term to the traditional beetle whisker algorithm.

[0063]

[0064] The search direction of the longhorn beetle is corrected, allowing for behavioral intervention in the search direction, thereby improving the algorithm's search capability and speed. So, where will the longhorn beetle next be located? t+1 The update method is as follows:

[0065]

[0066] In the formula, t is the current iteration number; f(.) is the fitness function; δ t X is the search step size for the t-th iteration; sign[.] is the sign function; X best This is the optimal position where the longhorn beetle has ever appeared; X t Given the current position of the longhorn beetle, when f(X) t ) <f(X best When X is... t Assigned to X best .

[0067] To improve the algorithm's local search capability, the search step size is reduced after each iteration. Therefore, δ t+1 =δ t *η, where η is the decay constant, typically η = 0.95.

[0068] Step 3: Combine the primary color space obtained by the least squares method in Step 1 with the enhanced beetle whisker algorithm designed in Step 2 to predict spot color formulas.

[0069] The search space is the number of primary colors selected in step 1. The objective function J and constraints are designed as follows:

[0070] J = J1 + J2 + J3

[0071]

[0072] J2=p1|∑c i -1|

[0073]

[0074] Constraint: 0 ≤ c i ≤1, i=1,2,...,

[0075] In the formula The mean square error (MSE) is J2 = p1|∑c i -1| is used to control the saturation concentration and is a regularization term; The number of primary colors used to reduce the color scheme is a constraint; p1 and p2 are penalty coefficients.

[0076] By applying the enhanced beetle whisker algorithm, the minimum value of the objective function J is iteratively calculated in the defined search space to obtain the molar concentration c of each component primary color of the spot color, thus obtaining the spot color formula.

[0077] Through the above methods, the spot color formula prediction method of the present invention can effectively reduce the selection space of primary colors, enhance the accuracy of spot color prediction, and improve color matching efficiency. First, this method uses the least squares method, which narrows the search space of primary colors, reduces the search workload, and improves the search speed. Second, by adding a mutation probability term p to the traditional longhorn beetle whisker algorithm, the distance l between the beetle's centroid and antennae is changed, achieving a rapid increase in the search range and reducing the possibility of the algorithm getting trapped in local optima; a direction correction term is also added. The search direction of the longhorn beetle was corrected, and behavioral intervention in the search direction was implemented to improve the algorithm's search ability and speed. Ultimately, this improved color matching efficiency.

[0078] Example

[0079] The experiment used a gravure printing press from RK (UK) on 0.15 mm thick transparent PET film for printing. A Mettler Toledo ME204 electronic balancer (Switzerland) was used to weigh the primary color inks according to the color formula. Transmission and absorption spectra were measured using a Shimadzu UV spectrophotometer (Japan). The actual absorption spectra of the six primary colors in the 200-900 nm wavelength range were measured. The actual absorption spectra are shown below. Figure 3 As shown.

[0080] Experiments were conducted on various spot color formulations. Spot colors were printed on transparent PET films, and their absorption spectra were obtained using a Shimadzu UV-Vis spectrophotometer. To verify the performance of the proposed algorithm, it was compared with traditional beetle whisker algorithms, particle swarm optimization, and ant colony optimization.

[0081] Four methods are implemented on computers equipped with AMD Ryzen 7 4800H chipsets.

[0082] Table 1 Preset Spot Color Formulas

[0083]

[0084] This experiment designed 20 spot color formulas, where S1 and S2 are spot color formulas mixing two primary colors, S3-S11 are spot color formulas mixing three primary colors, and S11-S20 are spot color formulas mixing four primary colors. The spot color formulas are shown in Table 1. Based on the measured absorption spectra, the MSE (Mean Sequence Equation) is less than 0.2. Therefore, the penalty factors p1 and p2 of the objective function should be set to less than 0.1; otherwise, the regularization term J2 and constraint condition J3 will severely affect the MSE term. To balance the MSE term and obtain accurate formulas, this invention sets the penalty factors p1 and p2 to 0.002 and 0.0005, respectively. In this experiment, the population size of the three comparison algorithms was set to the same value of 20. The number of iterations was set to 1000 to compare the convergence of each algorithm.

[0085] Table 2 Predicted Spot Color Formulas

[0086]

[0087] To obtain reasonable color prediction results, each of the four algorithms was repeated 20 times. The average values ​​X01-X20 of the predicted formulas by the four algorithms are listed in Table 2, and Table 3 lists the mean square error (MSE) and standard deviation (Std) of the prediction results.

[0088] Table 3 shows the mean squared error (MSE) and standard deviation (Std) of the prediction results (X01-X20).

[0089]

[0090]

[0091] According to Table 3 and Figure 4 As can be seen, compared with the other three methods, the method proposed in this invention has smaller mean square error (MSE), standard deviation (Std), and MAPE, indicating that the method has the best predictive ability and stability.

[0092] Figure 5 The convergence curves of four algorithms on spot colors S04, S06, S16, and S18 are shown. From Figure 5 As can be seen, compared with the other three methods, the method proposed in this invention requires fewer iterations to obtain the optimal solution and has a faster convergence speed.

[0093] To more intuitively compare the prediction results of the four algorithms, this invention uses color difference for further comparison. The calculated color difference values ​​are shown in Table 4.

[0094] Table 4 Color Difference

[0095]

[0096]

[0097] according to Figure 6 As shown in Table 4, the spot colors predicted by the algorithm of this invention are not significantly different from the preset formula spot colors. According to the calculation, the color difference between the preset spot colors and the predicted spot colors is less than 3, of which 90% of the color difference is less than 1 and 40% of the color difference is less than 0.1, all of which meet the requirement of faithful reproduction without color difference.

Claims

1. A method for predicting spot color formulas based on an enhanced longhorn beetle whisker search algorithm, characterized in that, Includes the following steps: Step 1: Obtain the absorption spectra of the primary color and the spot color, calculate the molar concentration of the primary color using the least squares method, and obtain the number of primary color components in the spot color; specifically including the following steps: Step 1.1: Define the absorption spectra of the six primary colors: cyan, magenta, yellow, orange, blue, and red. The absorption spectrum of a spot color is then expressed as: （1） In equation (1), The number of base colors that make up a spot color. The molar concentration of each component primary color; Step 1.2: Calculate the set of molar concentrations of each constituent primary color using the least squares method. : （2） In equation (2), , A A collection of absorption spectra. A T This is the transpose of set A; Step 1.3: When the molar concentration of a certain primary color in each of the constituent primary colors... When, the absorption spectrum corresponding to the primary color is... From the matrix Remove from the list and proceed to step 1.2 again; When the molar concentration of each constituent primary color When the time is right, obtain the number of primary color components of the spot color at that time; Step 2: Construct an enhanced longhorn beetle whisker search algorithm; specifically including the following steps: Step 2.1: Determine the location of the longhorn beetle in the D-dimensional search space, denoted as: （3） Step 2.2: Define the positions of the two longhorn beetle antennae and add a mutation probability term. Changing the distance between the longhorn beetle's center of mass and its antennae : （4） In equation (4), and Indicates the position of the longhorn beetle's two antennae; This indicates the distance between the longhorn beetle's center of mass and its antennae; For the first The step size explored in the next iteration; Indicates the probability of algorithm mutation; Random numbers are used to control the step size of mutations according to probability; The rate of change factor; The unit vector is represented as: （5） Step 2.3: Based on the concentration difference sensed by the longhorn beetle's two antennae, determine the beetle's next location. The next location of the longhorn beetle The update method is as follows: （6） In equation (6), , The decay constant, ; This represents the current iteration number; For the first The search step size is reduced after each iteration; It is a symbolic function; The fitness function; This is the current position of the longhorn beetle. At that time, Assign to , This is the optimal location where the longhorn beetle has ever appeared; The direction correction term is represented as: （7）； Step 3: Based on the primary color quantity obtained in Step 1, calculate the molar concentration of the primary colors using the enhanced beetle whisker search algorithm obtained in Step 2, and predict the spot color formula; specifically including the following steps: Step 3.1: Determine the dimension D of formula (3) in step 2.1 based on the number of primary colors obtained in step 1, and set the objective function. The constraints are as follows: （8） Constraints: （9） In equation (8), Mean square error; For regularization terms; These are constraints; and This is the penalty coefficient; Step 3.2: Using formula (6), update the molar concentration in the defined D-dimensional search space. , so that the objective function The minimum value is reached, at which point the molar concentration is... This refers to a spot color formula.

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