Printing ink formula correction method based on fuzzy logic

Abstract

The invention provides an ink formula optimization method based on fuzzy logic for solving the problem of formula correction caused by material characteristics and color theory complexity in ink color matching. The method comprises the following steps: firstly, obtaining a preliminary formula through a Kubelka-Munk spectral color matching method, performing proofing, measuring spectral characteristics of a color matching sample page, comparing the spectral characteristics with a target color, and calculating and analyzing chromatic aberration; then, on the basis of a fuzzy logic method, pre-prepared printing ink prepared according to the initial formula serves as the basis, and the type and the adding amount of primary color printing ink needing to be added are determined through a fuzzy rule; and finally, performing weighted normalization processing on the corrected ink formula to obtain an optimized final formula. And the established fuzzy rule can realize high-precision automatic formula adjustment according to chromatic aberration. According to the method, the color difference of ink color matching is effectively reduced, the experiment adjustment frequency is reduced, the color matching efficiency and precision are remarkably improved, and the color consistency and stability of ink products are ensured.

Description

Technical Field

[0001] The invention relates to the field of printing technology, and in particular to an ink formula correction method based on fuzzy logic. Background Art

[0002] Ink color matching is a key technical process to obtain the target color by mixing different base color inks, which is widely used in the printing and coating industries. In the traditional ink color matching process, it usually relies on the experience of color matching engineers to mix the base color inks by presetting the ratio. However, due to the nonlinear relationship between the spectral characteristics of inks and color performance, the traditional empirical color matching method is difficult to ensure accuracy and consistency when facing complex color matching requirements.

[0003] In recent years, computer color matching technology has developed rapidly. By establishing a mathematical model to calculate the mixing ratio of the base color ink, the color matching efficiency and accuracy have been significantly improved. In the color matching process, formula correction is an indispensable step, which aims to optimize the ink ratio to reduce color difference by measuring the deviation between the initial color matching and the target color. The existing formula correction methods mainly include the following: (1) Linear regression correction: Linear regression fits the relationship between color parameters and ink concentration through linear equations, which has the advantages of simple calculation and convenient implementation. However, this method is often unable to cope with complex colors or significant nonlinear relationships and is difficult to meet actual needs. (2) Neural network model: Neural networks can fit complex nonlinear relationships through training on a large amount of experimental data, providing a flexible solution for color matching correction. However, neural network models have high data requirements, time-consuming training process, and low interpretability of the model, which is not conducive to promotion and application in actual production. (3) Spectral analysis method: The spectral analysis method based on Kubelka-Munk (KM) theory accurately calculates the spectral difference between the target color and the initial formula by measuring the spectral reflectance of the ink at different wavelengths. Although this method has high theoretical accuracy, its computational complexity is high and the requirements on measurement equipment and algorithm performance are also relatively high.

[0004] Although these methods have improved the accuracy and efficiency of color correction to a certain extent, the following problems still exist: it is difficult to strike a balance between versatility and accuracy when dealing with the spectral characteristics of different base color inks; in the face of complex color systems, the effectiveness of traditional correction methods still depends on the experience of technicians; color difference adjustment requires multiple experimental verifications, which increases production costs and time costs. Summary of the invention

[0005] In view of the defects in the prior art, the present invention provides an ink formula correction method based on fuzzy logic.

[0006] The present invention is achieved through the following technical solutions:

[0007] A method for ink formula correction based on fuzzy logic:

[0008] S1: Establish a base color ink database: select three colors of base color ink and diluent, mix each base color ink with diluent at different concentrations to obtain n groups of mixed inks, evenly spread the n groups of mixed inks of each base color ink on coated paper to prepare n samples, and obtain 3n samples in total, and use a spectrophotometer to measure the spectral reflectance coefficient R of the coated paper itself p (λ), and the spectral reflectance coefficients of the prepared 3n samples (i=1, 2, ..., n), where λ is the wavelength, and the measured spectral reflectance data and the corresponding ink concentration are stored as a spectral database;

[0009] S2: Spectral characteristic measurement of target color sample; use a spectrophotometer to measure the spectral reflectance R of the target color sample under the same light source conditions. T (λ), and record the spectral reflectance R of the paper TP (λ);

[0010] Calculate the ratio of the absorption coefficient to the scattering coefficient of the target color sample and the target paper. The formulas are:

[0011] Use a spectrophotometer to measure the Lab value L of the target color sample t , a t , b t , as the color parameter of the target color;

[0012] S3: Calculate the ratio of the absorption coefficient to the scattering coefficient of the primary color ink: According to the spectrum database established in S1, calculate the ratio of the absorption coefficient to the scattering coefficient K / S of n samples for each primary color ink: Then calculate the ratio of the absorption coefficient and scattering coefficient of coated paper K / S:

[0013] Interpolation calculation of K / S value of any concentration: According to the formula The sequence [0, f(λ, c1), f(λ, c2), …, f(λ, c n )], where f(λ, c i ) indicates that the concentration at wavelength λ is c i The K / S value of the base color ink can be obtained by interpolation algorithm, and the K / S value f(λ, c) function of the base color ink corresponding to the wavelength λ and any concentration c can be obtained: in represents the interpolation function;

[0014] Establish a spectral color matching model: Based on the K / S value function f of the three primary color inks c(λ, c), f m (λ, c), f y (λ, c), get the color matching model where c c 、c m 、c y They are the concentrations of the three primary color inks respectively; is the predicted K / S value;

[0015] Optimization solution preliminary formula: The objective function is defined by intelligent optimization algorithm as Where β(c y , c m , c c ) is the spectral deviation, Ω is the wavelength range, and the color matching model is used as an equality constraint during intelligent optimization calculation, while considering the inequality constraint condition 0 <c c , c m , c y ≤1, and c c +c m +c y ≤1, the final optimization calculation obtains the concentration c of each base color ink in the preliminary formula c 、c m 、c y ;

[0016] Calculate the diluent ratio: According to the total concentration of the base color ink, calculate the concentration ratio of the diluent: c d =1-(c c +c m +c y ), the resulting mixing ratio c c :c m :c y :c d This is the initial formula;

[0017] S4: Pre-proofing: According to the preliminary formula in S3, the base color ink and diluent are mixed in the calculated proportion to prepare a pre-color sample, and the coated paper with the same conditions is used for color development;

[0018] Spectral reflectance measurement: Use a spectrophotometer to measure the spectral reflectance of the pre-matched color sample and calculate the K / S value of the pre-matched color sample:

[0019] Color deviation calculation: measure the Lab value L of the pre-matched color sample p 、a p , b p , and calculate the color difference between the target color and the pre-matched color: And Δa=a p -a t , Δb=bp -b t ;

[0020] Calculate the spectral deviation:

[0021] Determine the deviation range: Based on the color difference ΔE and spectral deviation E λ The size of the pre-matched color is used to evaluate whether the pre-matched color meets the requirements of the target color. If ΔE≤ε1 and E λ ≤ε2, the preliminary formula can be directly used as the final formula; if it does not meet the requirements, enter S5 to modify the formula; ε1 and ε2 are thresholds;

[0022] S5: Determine the range of each variable: define deviation Δa and Δb as input variables, ranging from -d to d, define u c 、u m 、u y is an output variable, indicating the concentration of the three primary color inks that need to be adjusted, specifically the percentage of the amount of added ink to the total mass of the pre-prepared ink, ranging from 0 to p; the pre-prepared ink refers to the ink prepared according to the preliminary formula in S4. If S6 returns to execute this step, the pre-prepared ink refers to the mixed ink prepared in step S6;

[0023] Fuzzification of input and output quantities: Input variables Δa and Δb are divided into five fuzzy sets: negative large NB, negative small NS, zero ZE, positive small PS, positive large PB, and the membership functions correspond to m1(x), m2(x), m3(x), m4(x), and m5(x) respectively:

[0024]

[0025] The output variables are also divided into five fuzzy sets: zero ZE, positive small PS, medium PM, positive large PB, and very large VB. The membership functions correspond to m o，1 (x), m o，2 (x), m o，3 (x), m o，4 (x), m o，5 (x):

[0026]

[0027]

[0028] Establish fuzzy control rules, and the weight of each fuzzy rule is 1;

[0029] Perform fuzzy reasoning: first, activate the rules and determine which rules are activated based on the input membership degree; then calculate the fuzzy output, specifically, calculate the output fuzzy set of each activated rule; then perform aggregate output, aggregate the output fuzzy sets of all rules to obtain the final output fuzzy set;

[0030] Defuzzification: Obtain the output variable u by calculating the centroid of the fuzzy set c 、u m 、u y ;

[0031] Calculate the corrected concentration: Calculate the normalized new base color ink ratio based on the defuzzified output variable:

[0032]

[0033] The sum of all base color ink ratios and diluent ratios is 1, which gives the diluent ratio c' d is: c′ d =1-(c′ c +c′ m +c′ y ), the corrected formula is the result of normalization: c′ c :c′ m :c′ y :c′ d ;

[0034] S6: Verify the revised recipe:

[0035] The mass of the pre-mixed ink obtained in S5 is m 预 Finally, the masses of the three base color inks added to the pre-mixed ink are determined to be m c =m 预 *u c 、m m =m 预 *u m 、m y =m 预 *u y ;

[0036] The pre-mixed ink obtained in step S5 is added to the mixed ink of the base color ink and mixed evenly, and the color is spread on the coated paper to obtain a test sample, and the Lab value is measured, and ΔE, Δa, and Δb are calculated according to the formula of S4;

[0037] If ΔE≤3, and Δa≤1 and Δb≤1 are satisfied at the same time, then it is determined that the corrected formula meets the color difference requirements, and the final corrected formula is: c′ c :c′ m :c′ y :c′ d ;

[0038] If ΔE≤3, Δa≤1, and Δb≤1 cannot be satisfied at the same time, it is determined that the corrected formula does not meet the color difference requirements. c =c′ c , c m =c′ m , c y =c′ y , c d =c′ d , and then return to step S5 to re-execute the formula correction until the color difference requirements are finally met, and the final corrected formula is obtained.

[0039] Preferably, the mixing ratio of each base color ink and the diluent in S1 is c:(1-c), where c represents the concentration of the base color ink, and 0<c≤1.

[0040] Preferably, in S1, n=20, and the concentration gradient is 5%.

[0041] Preferably, the wavelength λ is set to range from 400 nm to 700 nm with a step length of 10 nm.

[0042] Preferably, the ratio of the absorption coefficient to the scattering coefficient of the 3n samples satisfies: Since the K / S value and concentration usually do not conform to a linear relationship, a nonlinear function f(λ, c i ) instead of get: where f(λ, c i ) indicates that the concentration at wavelength λ is c i The K / S value of the base color ink is further obtained:

[0043] Preferably, the K / S value sequences [0, f c (λ,c1),fc(λ,c2),…,f c (λ,c n )], [0, f m (λ, c1), f m (λ, c2), …, f m (λ,c n )], [0, f y (λ, c1), f y (λ, c2), …, f y (λ,c n )], through the interpolation algorithm, the K / S value f of the three primary color inks corresponding to the calculated wavelength λ and arbitrary concentration c is further obtained. c (λ, c), fm (λ, c), f y Functional relationship of (λ, c).

[0044] Preferably, the ranges of Δa and Δb are from -2 to 2; u c , u m , u y ranges from 0% to 5%.

[0045] Preferably, the following 25 fuzzy rules are established:

[0046] if (Δa is NB) and (Δb is NB) then (u c is ZE) (u m is PM) (u y is PM);

[0047] if (Δa is NB) and (Δb is NS) then (u c is ZE) (u m is PM) (u y is PS);

[0048] if (Δa is NB) and (Δb is ZE) then (u c is ZE) (u m is PM) (u y is ZE);

[0049] if (Δa is NB) and (Δb is PS) then (u c is PS) (u m is PB) (u y is ZE);

[0050] if (Δa is NB) and (Δb is PB) then (u c is PM) (u m is VB) (u y is ZE);

[0051] if (Δa is NS) and (Δb is NB) then (u c is ZE) (u m is PS) (u y is PM);

[0052] if (Δa is NS) and (Δb is NS) then (u c is ZE) (um is PS)(u y is PS);

[0053] if(Δa is NS)and(Δb is ZE)then(u c is ZE)(u m is PS)(u y is ZE);

[0054] if(Δa is NS)and(Δb is PS)then(u c is PS)(u m is PM)(u y is ZE):

[0055] if(Δa is NS)and(Δb is PB)then(u c is PM)(u m is PB)(u y is ZE);

[0056] if(Δa is ZE)and(Δb is NB)then(u c is ZE)(u m is ZE)(u y is PM);

[0057] if(Δa is ZE)and(Δb is NS)then(u c is ZE)(u m is ZE)(u y is PS);

[0058] if(Δa is ZE)and(Δb is ZE)then(u c is ZE)(u m is ZE)(u y is ZE):

[0059] if(Δa is ZE)and(Δb is PS)then(u c is PS)(u m is PS)(u y is ZE);

[0060] if(Δa is ZE)and(Δb is PB)then(u c is PM)(u m is PM)(uy is ZE);

[0061] if(Δa is PS)and(Δb is NB)then(u c is PS)(u m is ZE)(u y is PM);

[0062] if(Δa is PS)and(Δb is NS)then(u c is PS)(u m is ZE)(u y is PS):

[0063] if(Δa is PS)and(Δb is ZE)then(u c is PS)(u m is ZE)(u y is ZE);

[0064] if(Δa is PS)and(Δb is PS)then(u c is PM)(u m is PS)(u y is ZE);

[0065] if(Δa is PS)and(Δb is PB)then(u c is ZE)(u m is PM)(u y is ZE);

[0066] if(Δa is PB)and(Δb is NB)then(u c is PM)(u m is ZE)(u y is PM);

[0067] if(Δa is PB)and(Δb is NS)then(u c is PM)(u m is ZE)(u y is PS):

[0068] if(Δa is PB)and(Δb is ZE)then(u c is PM)(u m is ZE)(u y is ZE);

[0069] if(Δa is PB)and(Δb is PS)then(u c is PB)(u m is PS)(u y is ZE);

[0070] if(Δa is PB)and(Δb is PB)then(u c is VB)(u m is PM)(u y is ZE).

[0071] Preferably, the Fuzzy Logic Designer tool in Matlab software is used to design a fuzzy reasoning system to realize fuzzy reasoning and defuzzification; first, a Mamdani Type 1 fuzzy reasoning system is established using the Fuzzy Logic Designer tool, and the And method is set to use min, the Or method is set to use max; the fuzzy implication method is set to use min, the fuzzy aggregation method is set to use max, and the defuzzification method is set to use centroid; then the input variables and output variables of the fuzzy reasoning system are configured, the two input variables are Δa and Δb, and the three output variables are u c 、u m 、u y ; Set the variable range according to S5, and fuzzify the input and output according to S5, and set the parameters of the membership function of the input and output variables; then configure the fuzzy rules of the fuzzy inference system; after configuring the fuzzy inference system, you can implement fuzzy inference and defuzzification through the rule inference module in the FuzzyLogic Designer tool, enter the values ​​of Δa and Δb in the rule inference module interface, and the fuzzy inference system will perform fuzzy inference and defuzzification to obtain u c 、u m 、u y .

[0072] The beneficial effects of the present invention are embodied in:

[0073] The present invention uses fuzzy logic algorithms and detailed spectral data for color matching correction, which significantly improves the accuracy of ink color matching. By accurately matching the spectral characteristics of the target color, the consistency and accuracy of the color matching results can be ensured, thereby effectively avoiding product quality problems caused by color difference problems.

[0074] The method of the present invention applies fuzzy logic to ink color matching, providing a flexible way to represent color matching knowledge. Through fuzzy rules, expert knowledge and experience can be directly applied to ink formula correction, without the need for an accurate formula correction mathematical model, with small calculation amount, low complexity, and easy implementation.

[0075] This formula correction method is highly efficient and can quickly perform color analysis and color matching correction, reduce the number of ink trial matching, and significantly reduce the time required for manual trial and error adjustments, while reducing raw material waste and improving production efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following is a brief introduction to the drawings required for the specific embodiments or the description of the prior art. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn according to the actual scale.

[0077] Figure 1 The figure is a flow chart of the ink formula correction method based on fuzzy logic in the present invention.

[0078] Figure 2 Schematic diagram of the membership function curve of the input variable and the output variable in the embodiment of the present invention. In the figure, det_a is Δa, det_b is Δb; the horizontal axis of the coordinate axis is the input variable or the output variable, and the vertical axis is the membership.

[0079] Figure 3 is a structural diagram of the fuzzy inference system in an embodiment of the present invention. In the figure, det_a is Δa, det_b is Δb; uc, um, uy are u respectively c 、u m 、u y ; "5MF" represents 5 membership functions. The two modules on the left represent inputs (corresponding to input variables Δa and Δb), the middle module represents the fuzzy inference device (using the Mandani Type 1 structure), and the three modules on the right represent outputs (corresponding to output variables u c 、u m 、u y ).

[0080] Figure 4 This is an example result diagram of fuzzy reasoning in an embodiment of the present invention. In the figure, "input values" are input variables; det_a is Δa, det_b is Δb; uc, um, uy are u c 、u m 、u yIn the figure, the fuzzy set operations are illustrated according to the established fuzzy rules; the fuzzy set operations within the rules take the intersection, i.e., the minimum operation, and the fuzzy set operations between the rules take the union, i.e., the maximum operation. Detailed implementation manners

[0081] In the following description, many specific details are set forth in order to provide a thorough understanding of the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without departing from the connotation of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed below.

[0082] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the technical field to which this invention belongs. The terms used herein in the description of the present invention are for the purpose of describing specific embodiments only and are not intended to limit the present invention. The term "and / or" used herein includes any and all combinations of one or more of the associated listed items.

[0083] The implementation process of the method of the present invention is divided into six main steps, from S1 to S6. Step S1 is the preparation stage, and a spectral database of the base color inks is established for use in subsequent color matching. In steps S2 to S6, first, a preliminary color matching is performed according to the given target color, and then the formula is corrected using the fuzzy logic method; after correction, a proof is made. If the color difference does not meet the requirements, continue to repeat the cycle from step S5 until the color matching requirements are finally met. Figure 1 This is a flowchart of the formula correction method based on fuzzy logic in the present invention, corresponding to steps S1 to S6.

[0084] The present invention is realized through the following technical solutions:

[0085] S1: Establish a spectral database of the base color inks.

[0086] S11. Mixing of the base color inks and the diluent. Select three base color inks of cyan, magenta, and yellow and the diluent, and prepare copperplate paper with high gloss and smoothness. Each base color ink is mixed with the diluent in a certain ratio to obtain n groups of mixed inks. The mixing ratio formula is: c:(1 - c), where c represents the concentration of the base color ink, and 0 < c ≤ 1. Preferably, n = 20 is set, and the concentration gradient is 5%. For the three base color inks of cyan, magenta, and yellow, a total of 3n groups of mixed inks are obtained.

[0087] S12. Prepare proof sheets. The mixed inks are evenly spread on the copperplate paper. For each base color ink, n proof sheets are prepared, and it is ensured that the surface of the proof sheets is smooth and free of bubbles for accurate measurement.

[0088] S13. Spectral reflectance measurement. For each base color ink, use a spectrophotometer to measure the spectral reflectance coefficient R of the coated paper itself under standard light source conditions (D65 light source). p (λ), and the spectral reflectance coefficients of the prepared n samples (i=1, 2, ..., n). The wavelength λ range is set to 400nm to 700nm with a step size of 10nm.

[0089] S14, data storage and organization. The measured spectral reflectance data and the corresponding ink concentration are stored as a spectral database, which contains the spectral reflectance characteristics of each base color ink and diluent at different mixing ratios, providing a basis for subsequent calculations.

[0090] S2: Measurement of spectral characteristics of target color sample.

[0091] S21. Spectral reflectance measurement of target color sample. Use the same spectrophotometer as S1 to measure the spectral reflectance R of the target color sample under the same light source conditions. T (λ), and record the spectral reflectance R of the target paper TP (λ).

[0092] S22. Calculate the ratio of the absorption coefficient to the scattering coefficient of the target color. According to the Kubelka-Munk theory, calculate the ratio of the absorption coefficient to the scattering coefficient of the target color sample and the target paper, and the formulas are:

[0093] S23. Lab value measurement. Use a spectrophotometer to measure the Lab value L of the target color sample. t 、a t , b t , as the color parameter of the target color, providing data support for subsequent color difference calculation.

[0094] S3: Spectral color matching based on Kubelka-Munk theory.

[0095] S31, calculate the absorption and scattering coefficient ratio of the primary color ink. According to the spectral database established in S1, for each primary color ink, the absorption coefficient and scattering coefficient ratio K / S of n samples are calculated using the Kubelka-Munk theory: Then calculate the ratio of the absorption coefficient and scattering coefficient of coated paper K / S: The wavelength λ ranges from 400nm to 700nm with a step size of 10nm.

[0096] S32, interpolation calculation of K / S value of any concentration. Based on Kubelka-Munk theory, the ratio of absorption coefficient to scattering coefficient of a single primary color ink has a linear relationship with concentration; is the K / S value of the primary ink per unit concentration at wavelength λ, then the ratio of the absorption coefficient to the scattering coefficient of n samples satisfies: Considering that the K / S value and concentration usually do not conform to a linear relationship, a nonlinear function f(λ, c i ) instead of get: where f(λ, c i ) indicates that the concentration at wavelength λ is c i The K / S value of the base color ink; further obtain: Thus, for the wavelength λ, we can obtain the sequence [0, f(λ, c1), f(λ, c2), ..., f(λ, c n )]; Through the interpolation algorithm, the K / S value f(λ, c) function of the primary color ink corresponding to the wavelength λ and any concentration c can be obtained: in represents an interpolation function; preferably, the interpolation function adopts cubic spline interpolation.

[0097] The cubic spline interpolation is a commonly used numerical interpolation method for constructing a smooth interpolation function between known data points. Specifically, cubic spline interpolation approximates the data by multiple cubic polynomials, each of which is defined between data points. Given a sequence of data points (x0, y0), (x1, y1), ..., (x n ,y n ), the goal of the cubic spline interpolation function is to find the value of each pair of adjacent data points (x i ,y i ) and (x i+1 ,y i+1 )Construct a cubic polynomial so that the function has continuous values, continuous first-order derivatives, and continuous second-order derivatives at these points.

[0098] The specific expression of the cubic spline interpolation is as follows: i , x i+1 ], interpolation function S i (x) is represented by the following cubic polynomial: S i (x) = a i (xx i ) 3 +b i (xx i ) 2 +c i (xx i )+d i , where a i , b i , ci , d i are the coefficients to be found, and these coefficients are solved by the following conditions:

[0099] (1) Interpolation condition (function value matching): S i (x i )=y i and S i (x i+1 )=y i+1

[0100] (2) First-order derivative continuity: S′ i (x i+1 ) = S′ i+1 (x i+1 )

[0101] (3) Second-order derivative continuity: S″ i (x i+1 )=S″ i+1 (x i+1 )

[0102] (3) Boundary conditions: natural boundary conditions are generally used, namely: S″0(x0)=0 and S″ n (x n )=0 Based on the above conditions, a linear equation system can be established to solve all coefficients a i , b i , c i , d i , thus obtaining the final cubic spline interpolation function. The cubic spline interpolation solves the coefficients in the above way to ensure that the function and its first-order and second-order derivatives are continuous at each data point, thus obtaining a smooth interpolation curve.

[0103] Specifically, the interpolation function The method to determine is: first let (x0, y0), (x1, y1), ..., (x n ,y n ) corresponds to (0, 0), (c1, f(λ, c1)), …, (c n , f(λ, c n )); then solve all coefficients a in cubic spline interpolation i , b i , c i , d i , thus obtaining the final cubic spline interpolation function; then, determine In which interval is the parameter c, such as c∈[x i , x i+1 ], then the interpolation function expression is S i (x), that is:

[0104]

[0105] Thus, for the cyan, magenta, and yellow primary inks, the K / S value sequence [0, f c (λ, c1), f c (λ, c2), …, f c (λ,c n )], [0, f m (λ, c1), f m (λ, c2), …, f m (λ,c n )], [0, f y (λ, c1), f y (λ, c2), …, f y (λ,c n )], wavelength λ=400,410,…,700; through the interpolation algorithm, the K / S value f of the cyan, magenta and yellow primary ink corresponding to the calculated wavelength λ and arbitrary concentration c is further obtained. c (λ, c), f m (λ, c), f y The functional relationship of (λ, c).

[0106] S33, establish a spectral color matching model. According to the single constant additivity principle of Kubelka-Munk theory, the K / S value function f of the cyan, magenta and yellow primary inks is further c (λ, c), f m (λ, c), f y (λ, c), we get the color matching model,

[0107]

[0108] where c c 、c m 、c y are the concentrations of cyan, magenta and yellow primary inks respectively; is the predicted K / S value; The K / S value of the target color paper can be calculated in step S2.

[0109] S34, optimizing and solving the preliminary formula. To obtain the best preliminary formula, an optimization problem needs to be constructed, and the optimization goal is to minimize the spectral deviation. The spectral deviation β(c y , c m , c c ) is defined as follows:

[0110]

[0111] in is the K / S value of the target color sample, is the K / S value predicted by the color matching model, and Ω = {400, 410, …, 700} is the wavelength range.

[0112] In order to ensure the rationality and physical feasibility of the ink formula, the following constraints must be met: <c c , c m , c y ≤1, c c +c m +c y ≤1; at the same time, the color matching model expression in step S33 is also used as an equality constraint of the optimization problem.

[0113] For the constructed optimization problem, the present invention uses an intelligent optimization algorithm to solve and obtain the best preliminary formula parameter c c 、c m 、c y The intelligent optimization algorithm adopts the particle swarm optimization algorithm, denoted as PSO. PSO is an intelligent optimization algorithm that simulates the foraging behavior of bird flocks. Through the cooperation and competition of individuals and groups, the optimal solution is gradually found. The steps of the PSO algorithm are as follows:

[0114] (1) Initialize the particle swarm. Initialize N particles, each particle represents an ink formula (c c , c m , c y ), and randomly generate initial values ​​within the preset concentration range. Initialize the fitness, the fitness of each particle is determined by the objective function β(c y , c m , c c ), the smaller the fitness value, the smaller the spectral deviation. Initialize the position and velocity, each particle has a position v i and speed x i The position represents the current solution, and the speed represents the adjustment direction of the solution. Position initialization is randomly generated within the concentration range of the ink formula, such as [0, 1]. Speed ​​initialization is usually randomly generated within a certain range, such as 1% of the ink concentration range. Initialize the local optimal solution and the global optimal solution, and each particle stores its historical optimal position (i.e., the local optimal solution, denoted as pbest). i ) and initialize the global optimal solution (i.e. the optimal solution of the entire particle swarm, denoted as gbest). Initially, the local optimal solution of the particle is usually set to the initial position of the particle; the global optimal solution is usually not directly set to zero, but the best one is selected from the local optimal solutions of all particles.

[0115] (2) Fitness evaluation and update. Calculate the fitness of each particle, that is, calculate the objective function β(c y , c m, c c ), and update its optimal position pbest i And the global optimal position gbest. If the fitness of the current particle is better than its historical optimal solution (lower fitness), update the local optimal solution of the particle: pbest i =x i ; If the local optimal solution of the particle is better than the global optimal solution, update the global optimal solution: gbest = pbest i .

[0116] (3) Particle velocity and position update. The position of the particle in the search space represents the ink formula, while the velocity represents the adjustment direction of the formula. The update formula is as follows:

[0117]

[0118] Among them, v i is the velocity of the particle, x i is the position of the particle; is the velocity and position of the particle in generation t; pbest i is the local optimal solution of the particle, gbest is the global optimal solution; l1, l2 are learning factors that control the attraction of particles to the local optimal solution and the global optimal solution, usually set to 1.5; r1, r2 are random numbers between [0, 1], used to increase the randomness of the search space; ω is the inertia weight, usually set to between 0.4 and 0.9.

[0119] (4) Iterate and update and determine the termination condition. Through the iterative evolution of the particle swarm, the global optimal solution of the particle swarm will gradually approach the optimal formula that minimizes the spectral deviation. After a certain number of iterations or when the spectral deviation threshold Δβ is met max After that, the algorithm stops, and the output gbest is the global optimal solution, that is, the optimal formula (c c , c m , c y ).

[0120] Finally, the concentration c of each base color ink in the preliminary formula is obtained by optimization calculation. c 、c m 、c y .

[0121] S35, calculate the diluent ratio. According to the total concentration of the base color ink, calculate the diluent concentration ratio:

[0122] c d =1-(c c +c m +c y ),

[0123] The resulting mixing ratio cc :c m :c y :c d This is the initial recipe.

[0124] S4: Pre-color matching and deviation analysis. Pre-color matching and proofing are carried out according to the preliminary formula, and the spectral reflectance of the proof is measured to determine the color deviation between the pre-color matching and the target color.

[0125] S41, formula pre-proofing. According to the preliminary formula in S3, the base color ink and the diluent are mixed in the calculated proportion to prepare a pre-color matching sample, and the coated paper with the same conditions is used for color development.

[0126] S42. Spectral reflectance measurement. Use a spectrophotometer to measure the spectral reflectance of the pre-proofing sample and calculate the K / S value of the pre-color matching sample: The wavelength λ ranges from 400nm to 700nm with a step size of 10nm.

[0127] S43, color deviation calculation. Measure the Lab value L of the pre-matched color sample p 、a p , b p , and calculate the color difference between the target color and the pre-matched color:

[0128]

[0129] And Δa=a p -a t , Δb=b p -b t . At the same time, the spectral deviation is calculated:

[0130] S44, determine the deviation range. λ The size of the pre-matched color is used to evaluate whether the pre-matched color meets the requirements of the target color: if ΔE≤ε1 and E λ ≤ε2, the preliminary formula can be directly used as the final formula; if it does not meet the requirements, proceed to the next step (S5) to modify the formula. The thresholds ε1 and ε2 are determined by production requirements.

[0131] S5: Correcting the formula using fuzzy rules. This step uses fuzzy logic rules to correct the proportion of the base color ink according to the deviation of the preliminary formula to reduce the difference between the target color and the pre-matched color, and obtain a corrected formula.

[0132] S51: Determine the range of each variable. Define the deviation Δa and Δb as input variables, ranging from -d to d, preferably ranging from -2 to 2; determine u c 、u m 、u yis an output variable, indicating the concentration of cyan, magenta and yellow inks that need to be adjusted, specifically the percentage of the added ink amount to the total mass of the pre-mixed ink, ranging from 0 to p, preferably, ranging from 0% to 5%.

[0133] The pre-prepared ink refers to the ink prepared according to the preliminary formula in step S4; however, if step S6 returns to the present step S51 for execution, the pre-prepared ink will refer to the mixed ink prepared in step S6.

[0134] S52: Fuzzification of input and output. Input variables Δa and Δb are divided into five fuzzy sets: negative large (NB), negative small (NS), zero (ZE), positive small (PS), positive large (PB), and the membership functions correspond to m1(x), m2(x), m3(x), m4(x), and m5(x) respectively:

[0135]

[0136] The output variables are also divided into five fuzzy sets: zero (ZE), positive small (PS), positive medium (PM), positive large (PB), and very large (VB), and the membership functions correspond to m o，1 (x), m o，2 (x), m o，3 (x), m o，4 (x), m o，5 (x):

[0137]

[0138] S53: Establish fuzzy control rules. Based on expert experience and experimental data, the following 25 fuzzy rules are designed and described in the form of "IF A THEN B":

[0139] if(Δa is NB)and(Δb is NB)then(u c is ZE)(u m is PM)(u y is PM);

[0140] if(Δa is NB)and(Δb is NS)then(u c is ZE)(u m is PM)(u y is PS);

[0141] if(Δa is NB)and(Δb is ZE)then(u c is ZE)(u m is PM)(u yis ZE);

[0142] if(Δa is NB)and(Δb is PS)then(u c is PS)(u m is PB)(u y is ZE);

[0143] if(Δa is NB)and(Δb is PB)then(u c is PM)(u m is VB)(u y is ZE);

[0144] if(Δa is NS)and(Δb is NB)then(u c is ZE)(u m is PS)(u y is PM);

[0145] if(Δa is NS)and(Δb is NS)then(u c is ZE)(u m is PS)(u y is PS);

[0146] if(Δa is NS)and(Δb is ZE)then(u c is ZE)(u m is PS)(u y is ZE);

[0147] if(Δa is NS)and(Δb is PS)then(u c is PS)(u m is PM)(u y isZE);

[0148] if(Δa is NS)and(Δb is PB)then(u c is PM)(u m is PB)(u y isZE);

[0149] if(Δa is ZE)and(Δb is NB)then(u c is ZE)(u m is ZE)(u y isPM);

[0150] if(Δa is ZE)and(Δb is NS)then(u c is ZE)(u m is ZE)(u y isPS);

[0151] if(Δa is ZE)and(Δb is ZE)then(u c is ZE)(u m is ZE)(u y isZE);

[0152] if(Δa is ZE)and(Δb is PS)then(u c is PS)(u m is PS)(u y isZE);

[0153] if(Δa is ZE)and(Δb is PB)then(u c is PM)(u m is PM)(u y isZE);

[0154] if(Δa is PS)and(Δb is NB)then(u c is PS)(u m is ZE)(u y isPM);

[0155] if(Δa is PS)and(Δb is NS)then(u c is PS)(u m is ZE)(u y isPS);

[0156] if(Δa is PS)and(Δb is ZE)then(u c is PS)(u m is ZE)(u y isZE);

[0157] if(Δa is PS)and(Δb is PS)then(u c is PM)(u m is PS)(u y isZE);

[0158] if(Δa is PS)and(Δb is PB)then(u c is ZE)(u m is PM)(u y isZE);

[0159] if(Δa is PB)and(Δb is NB)then(u c is PM)(u m is ZE)(u y isPM);

[0160] if(Δa is PB)and(Δb is NS)then(u c is PM)(u m is ZE)(u y is PS);

[0161] if(Δa is PB)and(Δb is ZE)then(u c is PM)(u m is ZE)(u y is ZE);

[0162] if(Δa is PB)and(Δb is PS)then(u c is PB)(u m is PS)(u y is ZE);

[0163] if(Δa is PB)and(Δb is PB)then(u c is VB)(u m is PM)(u y is ZE);

[0164] The weight of each fuzzy rule is 1.

[0165] Take the first rule as an example: "if (Δa is NB) and (Δb is NB) then (u c is ZE)(u m is PM)(u y is PM)”, which simulates the situation when Δa=a p -a t NB (negative large), Δb = b p -b t NB (negative large), that is, when the pre-matched color is green or blue, no cyan ink will be added, and magenta and yellow ink will be added appropriately (uc ZE, u m For PM, u y PM). The weight of each fuzzy rule in fuzzy reasoning is 1. According to the established fuzzy rules, the fuzzy relationship set can be obtained through fuzzy set operations. The fuzzy set operation within the rule takes the intersection, that is, the minimum operation, and the fuzzy set operation between the rules takes the union, that is, the maximum operation.

[0166] S54: Perform fuzzy reasoning and defuzzification.

[0167] Fuzzy reasoning is to calculate the output fuzzy set based on the input fuzzy set and fuzzy rules. Common fuzzy reasoning methods include Mamdani reasoning and Sugeno reasoning. The present invention adopts Mamdani reasoning. The steps are as follows: first, the rules are activated, and which rules are activated are determined according to the input membership degree; then the fuzzy output is calculated, that is, the output fuzzy set of each activated rule is calculated; then the aggregate output is performed, and the output fuzzy sets of all rules are aggregated to obtain the final output fuzzy set. The aggregation operation adopts the maximum-minimum method. After obtaining the output fuzzy set, defuzzification is performed next, and the fuzzy set obtained by fuzzy reasoning needs to be converted into an exact value. The present invention adopts the centroid method as the defuzzification method, and obtains the output variable by calculating the centroid of the fuzzy set.

[0168] The present invention uses the Fuzzy Logic Designer tool in Matlab software to design a fuzzy reasoning system to achieve fuzzy reasoning and defuzzification. First, use the Fuzzy Logic Designer tool to establish a Mamdani Type 1 fuzzy reasoning system, and set the And method to use min, the Or method to use max; the fuzzy implication method to use min, the fuzzy aggregation to use max, the defuzzification method to use centroid, the number of input variables to be 2, the number of output variables to be 3, and the number of fuzzy rules to be 25. Then configure the input variables and output variables of the fuzzy reasoning system. The two input variables are Δa and Δb, and the three output variables are u c 、u m 、u y. Set the variable range according to S51, and fuzzify the input and output according to S52, and set the parameters of the membership function of the input variables and output variables. The parameters are set in the membership function editor. Then configure the fuzzy rules of the fuzzy inference system. Enter the fuzzy rules one by one in the rule editor, and set the weight of each rule to 1. After configuring the fuzzy inference system, you can implement fuzzy reasoning and defuzzification through the rule reasoning module in the Fuzzy Logic Designer tool. Finally, enter the values ​​of Δa and Δb in the rule reasoning module interface, and the fuzzy reasoning system will perform fuzzy reasoning and defuzzification to obtain u c 、u m 、u y .

[0169] S55, calculate the corrected concentration. According to the defuzzified output variable, calculate the normalized new base color ink ratio:

[0170]

[0171] The sum of all base color ink ratios and diluent ratios is 1, which gives the diluent ratio c' d for:

[0172] c′ d =1-(c c ′+c′ m +c′ y )

[0173] The corrected formula is the result of normalization: c ′:c′ m :c′ y :c′ d .

[0174] S6: Verify the revised formula. If the color difference requirement is not met, repeat step S5. If the color difference requirement is met, the revised formula is used as the final revised formula.

[0175] The mass of the pre-mixed ink obtained in step S5 is m 预 Finally, it is determined that the mass of cyan, magenta and yellow ink added to the pre-mixed ink is m c =m 预 *u c 、m m =m 预 *u m 、m y =m 预 *u y .

[0176] The pre-mixed ink obtained in step S5 is added to the mixed ink of the base color ink and mixed evenly, and the color is spread on coated paper to obtain a test sample, and the Lab value is measured. The color deviation ΔE, Δa, and Δb from the target color are calculated according to the formula of S4.

[0177] If ΔE≤3, and Δa≤1 and Δb≤1 are satisfied at the same time, then it is determined that the corrected formula meets the color difference requirements, and the final corrected formula is: c c ′:c′ m :c′ y :c′ d .

[0178] If ΔE≤3, Δa≤1, and Δb≤1 cannot be satisfied at the same time, the corrected formula is judged to not meet the color difference requirement. c =c c ′,c m =c′ m , c y =c′ y ,c d =c′ d , and then return to step S5 to re-execute the formula correction until the color difference requirements are finally met, and the final corrected formula is obtained.

[0179] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein by equivalents. These modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be included in the scope of the claims and specification of the present invention.

Claims

1. A method for correcting ink formula based on fuzzy logic, characterized in that: S1: Establish a base color ink database: select three colors of base color ink and diluent, mix each base color ink with diluent at different concentrations to obtain n groups of mixed inks, evenly spread the n groups of mixed inks of each base color ink on coated paper to prepare n samples, and obtain 3n samples in total, and use a spectrophotometer to measure the spectral reflectance coefficient R of the coated paper itself p (λ), and the spectral reflectance coefficients of the prepared 3n samples Where λ is the wavelength, and the measured spectral reflectance data and the corresponding ink concentration are stored as a spectral database; S2: Spectral characteristic measurement of target color sample; use a spectrophotometer to measure the spectral reflectance R of the target color sample under the same light source conditions. T (λ), and record the spectral reflectance R of the paper TP (λ); Calculate the ratio of the absorption coefficient to the scattering coefficient of the target color sample and the target paper. The formulas are: Use a spectrophotometer to measure the Lab value L of the target color sample t ,a t ,b t , as the color parameter of the target color; S3: Calculate the ratio of the absorption coefficient to the scattering coefficient of the primary color ink: According to the spectrum database established in S1, calculate the ratio of the absorption coefficient to the scattering coefficient K / S of n samples for each primary color ink: Then calculate the ratio of the absorption coefficient and scattering coefficient of coated paper K / S: Interpolation calculation of K / S value of any concentration: According to the formula Available sequences [0,f(λ,c1),f(λ,c2),…,f(λ,c n )], where f(λ,c i ) indicates that the concentration at wavelength λ is c i The K / S value of the base color ink can be obtained by interpolation algorithm, and the K / S value f(λ,c) function of the base color ink corresponding to the wavelength λ and any concentration c can be obtained: in represents the interpolation function; Establish a spectral color matching model: Based on the K / S value function f of the three primary color inks c (λ,c),f m (λ,c),f y (λ,c), and get the color matching model where c c 、c m 、c y They are the concentrations of the three primary inks; is the predicted K / S value; Optimization solution preliminary formula: The objective function is defined by intelligent optimization algorithm as Where β(c y ,c m ,c c ) is the spectral deviation, Ω is the wavelength range, and the color matching model is used as an equality constraint during intelligent optimization calculation, while considering the inequality constraint condition 0 <c c ,c m ,c y ≤1, and c c +c m +c y ≤1, the final optimization calculation obtains the concentration c of each base color ink in the preliminary formula c 、c m 、c y ; Calculate the diluent ratio: According to the total concentration of the base color ink, calculate the concentration ratio of the diluent: c d =1-(c c +c m +c y ), the resulting mixing ratio c c :c m :c y :c d This is the initial formula; S4: Pre-proofing: According to the preliminary formula in S3, the base color ink and diluent are mixed in the calculated proportion to prepare a pre-color sample, and the coated paper with the same conditions is used for color development; Spectral reflectance measurement: Use a spectrophotometer to measure the spectral reflectance of the pre-matched color sample and calculate the K / S value of the pre-matched color sample: Color deviation calculation: measure the Lab value L of the pre-matched color sample p 、a p , b p , and calculate the color difference between the target color and the pre-matched color: And Δa=a p -a t , Δb=b p -b t ; Calculate the spectral deviation: Determine the deviation range: Based on the color difference ΔE and spectral deviation E λ The size of the pre-matched color is used to evaluate whether the pre-matched color meets the target color requirements. If ΔE≤μ1 and E λ ≤μ2, the preliminary formula can be directly used as the final formula; if it does not meet the requirements, enter S5 to modify the formula; μ1 and ε2 are thresholds; S5: Determine the range of each variable: define deviation Δa and Δb as input variables, ranging from -d to d, define u c 、u m 、u y is an output variable, indicating the concentration of the three primary color inks that need to be adjusted, specifically the percentage of the amount of added ink to the total mass of the pre-prepared ink, ranging from 0 to p; the pre-prepared ink refers to the ink prepared according to the preliminary formula in S4. If S6 returns to execute this step, the pre-prepared ink refers to the mixed ink prepared in step S6; Fuzzification of input and output quantities: Input variables Δa and Δb are divided into five fuzzy sets: negative large NB, negative small NS, zero ZE, positive small PS, positive large PB, and the membership functions correspond to m1(x), m2(x), m3(x), m4(x), and m5(x) respectively: The output variables are also divided into five fuzzy sets: zero ZE, positive small PS, medium PM, positive large PB, and very large VB. The membership functions correspond to m o,1 (x), m o,2 (x), m o,3 (x), m o,4 (x), m o,5 (x): Establish fuzzy control rules, and the weight of each fuzzy rule is 1; Perform fuzzy reasoning: first, activate the rules and determine which rules are activated based on the input membership degree; then calculate the fuzzy output, specifically, calculate the output fuzzy set of each activated rule; then perform aggregate output, aggregate the output fuzzy sets of all rules to obtain the final output fuzzy set; Defuzzification: Obtain the output variable u by calculating the centroid of the fuzzy set c 、u m 、u y ; Calculate the corrected concentration: According to the defuzzified output variable, calculate the normalized new base color ink ratio: The sum of all base color ink ratios and diluent ratios is 1, which gives the diluent ratio c' d is: c′ d =1-(c′ c +c′ m +c′ y ), the corrected formula is the result of normalization: c′ c :c′ m :c′ y :c′ d ; S6: Verify the revised recipe: The mass of the pre-mixed ink obtained in S5 is m 预 Finally, the masses of the three base color inks added to the pre-mixed ink are determined to be m c =m 预 *u c 、m m =m 预 *u m 、m y =m 预 *u y ; The pre-mixed ink obtained in step S5 is added to the mixed ink of the base color ink and mixed evenly, and the color is spread on the coated paper to obtain a test sample, and the Lab value is measured, and ΔE, Δa, and Δb are calculated according to the formula of S4; If ΔE≤3, and Δa≤1 and Δb≤1 are satisfied at the same time, then it is determined that the corrected formula meets the color difference requirements, and the final corrected formula is: c′ c :c′ m :c′ y :c′ d ; If ΔE≤3, Δa≤1, and Δb≤1 cannot be satisfied at the same time, it is determined that the corrected formula does not meet the color difference requirements. c =c′ c , c m =c′ m , c y =c′ y ,c d =c′ d , and then return to step S5 to re-execute the formula correction until the color difference requirements are finally met, and the final corrected formula is obtained.

2. The ink formula correction method based on fuzzy logic according to claim 1, characterized in that: The mixing ratio of each base color ink and diluent in S1 is c:(1-c), where c represents the concentration of the base color ink, 0 <c≤1。 3. The ink formula correction method based on fuzzy logic according to claim 1, characterized in that: In the S1, n=20, and the concentration gradient is 5%.

4. The ink formula correction method based on fuzzy logic according to claim 1, characterized in that: The wavelength λ is set to range from 400 nm to 700 nm with a step length of 10 nm.

5. The ink formula correction method based on fuzzy logic according to claim 1, characterized in that: The ratio of the absorption coefficient to the scattering coefficient of the 3n samples satisfies: Since the K / S value and concentration usually do not conform to a linear relationship, a nonlinear function f(λ,c i ) replaces get: where f(λ,c i ) indicates that the concentration at wavelength λ is c i The K / S value of the base color ink is further obtained:

6. The ink formula correction method based on fuzzy logic according to claim 1, characterized in that: According to the formula of S3, the K / S value sequence of the three primary color inks at wavelength λ is calculated respectively [0,f c (λ,c1),f c (λ,c2),…,f c (λ,c n )]、[0,f m (λ,c1),f m (λ,c2),…,f m (λ,c n )]、[0,f y (λ,c1),f y (λ,c2),…,f y (λ,c n )], through the interpolation algorithm, the K / S value f of the three primary color inks corresponding to the calculated wavelength λ and arbitrary concentration c is further obtained. c (λ,c),f m (λ,c),f y The functional relationship of (λ,c).

7. The ink formula correction method based on fuzzy logic according to claim 1, characterized in that: The range of Δa and Δb is -2 to 2; u c 、u m 、u y The range is 0% to 5%.

8. The ink formula correction method based on fuzzy logic according to claim 1, characterized in that: The following 25 fuzzy rules are established: if(Δa is NB)and(Δb is NB)then(u c is ZE)(u m is PM)(u y is PM); if(Δa is NB)and(Δb is NS)then(u c is ZE)(u m is PM)(u y is PS); if(Δa is NB)and(Δb is ZE)then(u c is THEY)(u m is PM)(u y is THEY); if(Δa is NB)and(Δb is PS)then(u c is PS)(u m is PB)(u y is ZE); if(Δa is NB)and(Δb is PB)then(u c is PM)(u m is VB)(u y is ZE); if(Δa is NS)and(Δb is NB)then(u c is ZE)(u m is PS)(u y is PM); if(Δa is NS)and(Δb is NS)then(u c is ZE)(u m is PS)(u y is PS); if(Δa is NS)and(Δb is ZE)then(u c is THEY)(u m is PS)(u y is THEY); if(Δa is NS)and(Δb is PS)then(u c is PS)(u m is PM)(u y is ZE); if(Δa is NS)and(Δb is PB)then(u c is PM)(u m is PB)(u y is ZE); if(Δa is ZE)and(Δb is NB)then(u c is THEY)(u m is THEY)(u y is PM); if(Δa is ZE)and(Δb is NS)then(u c is THEY)(u m is THEY)(u y is PS); if(Δa is ZE)and(Δb is ZE)then(u c is THEY)(u m is THEY)(u y is THEY); if(Δa is ZE)and(Δb is PS)then(u c is PS)(u m is PS)(u y is ZE); if(Δa is ZE)and(Δb is PB)then(u c is PM)(u m is PM)(u y is ZE); if(Δa is PS)and(Δb is NB)then(u c is PS)(u m is ZE)(u y is PM); if(Δa is PS)and(Δb is NS)then(u c is PS)(u m is ZE)(u y is PS); if(Δa is PS)and(Δb is ZE)then(u c is PS)(u m is THEY)(u y is THEY); if(Δa is PS)and(Δb is PS)then(u c is PM)(u m is PS)(u y is ZE); if(Δa is PS)and(Δb is PB)then(u c is ZE)(u m is PM)(u y is ZE); if(Δa is PB)and(Δb is NB)then(u c is PM)(u m is ZE)(u y is PM); if(Δa is PB)and(Δb is NS)then(u c is PM)(u m is ZE)(u y is PS); if(Δa is PB)and(Δb is ZE)then(u c is PM)(u m is THEY)(u y is THEY); if(Δa is PB)and(Δb is PS)then(u c is PB)(u m is PS)(u y is ZE); if(Δa is PB)and(Δb is PB)then(u c is VB)(u m is PM)(u y is ZE)。 9. The ink formula correction method based on fuzzy logic according to claim 1, characterized in that: The Fuzzy Logic Designer tool in Matlab software is used to design a fuzzy reasoning system to achieve fuzzy reasoning and defuzzification. First, a Mamdani Type 1 fuzzy reasoning system is established using the Fuzzy Logic Designer tool, and the And method is set to use min, the Or method is set to use max; the fuzzy implication method is set to use min, the fuzzy aggregation method is set to use max, and the defuzzification method is set to use centroid. Reconfigure the input variables and output variables of the fuzzy inference system. The two input variables are Δa and Δb, and the three output variables are u. c 、u m 、u y ; Set the variable range according to S5, and fuzzify the input and output according to S5, and set the parameters of the membership function of the input and output variables; then configure the fuzzy rules of the fuzzy inference system; after configuring the fuzzy inference system, you can implement fuzzy inference and defuzzification through the rule inference module in the Fuzzy LogicDesigner tool, enter the values ​​of Δa and Δb in the rule inference module interface, and the fuzzy inference system will perform fuzzy inference and defuzzification to obtain u c 、u m 、u y .

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