Method for optimizing mechanical property of bottom slag crack pouring material based on multi-scale design

Abstract

The invention belongs to the field of building material and solid waste resource utilization, and particularly relates to a bottom slag crack pouring material mechanical property optimization method based on multi-scale design. The method comprises the following steps: screening the industrial bottom slag; carrying out surface modification reaction on the bottom slag particles by adopting a modification solution containing a silane coupling agent and a polycarboxylate superplasticizer; defining a particle proportion parameter, an interface bonding coefficient and a volume component parameter, and establishing a multi-scale parameter set; constructing a comprehensive performance function; performing search iteration on the parameter set by adopting a particle swarm optimization algorithm to obtain an optimal parameter combination and a model prediction value; preparing a bottom slag crack pouring material sample according to the optimal parameter combination result, and detecting the compressive strength, the breaking strength, the porosity and the permeability coefficient of the sample. According to the method, a multi-scale design concept is introduced, material microstructure analysis, interface transition area control and macroscopic performance feedback are combined, a multi-level optimization path from the grain level to the composite system level is established, and comprehensive improvement of the bottom slag crack pouring material in multiple aspects is achieved.

Description

Technical Field

[0001] This invention relates to the field of building materials and solid waste resource utilization, specifically to a method for optimizing the mechanical properties of bottom slag grouting material based on multi-scale design. Background Technology

[0002] In industrial production and municipal engineering construction, bottom slag sealant is widely used for repairing and filling gaps in slag trenches, equipment foundations, and road cracks. Its main function is to achieve stress transfer and sealing between structures to prevent seepage. Conventional bottom slag sealants are mostly cement-based, slag-based, or resin-based composite systems, possessing certain fluidity and bonding properties. However, with the increasing prevalence of high-temperature, heavy-load, and chemically corrosive environments, traditional sealants are not performing well in use. The formulation of traditional sealants is often based on experience or single-scale experimental data, failing to fully consider the synergistic effects of aggregate particle size distribution, interfacial transition layer structure, and micropore distribution. This results in poor overall compressive strength, flexural strength, and toughness of the material, making it prone to early cracking and spalling under thermal cycling or heavy-load impact.

[0003] Existing bottom slag grouting materials often contain irregular porous bottom slag particles, forming weak bonding zones at the interface, which easily become stress concentration sources. Uneven porosity distribution leads to the breakage of stress transmission paths, resulting in a significant decrease in mechanical properties and durability. The formulations often only focus on optimizing macroscopic mechanical properties, neglecting the coupling relationships at three scales: microscopic particle structure, mesoscopic interface interaction, and macroscopic composite system. The lack of a multi-scale design concept leads to the reliance on manual formulation and trial and error for material modification. There is a lack of multi-scale coupling analysis models based on experimental or simulation data, making it difficult to quantitatively evaluate the impact of structural parameters at different scales on mechanical properties. Summary of the Invention

[0004] To address the shortcomings of the existing technologies, the present invention aims to provide a method for optimizing the mechanical properties of bottom slag grouting materials based on multi-scale design. This method addresses the significant deficiencies in existing bottom slag grouting materials regarding synergistic optimization of mechanical properties, control of interface microstructure, and formulation system design, particularly at high temperatures.

[0005] The long-term service reliability under heavy loads and complex humid and hot environments has not yet been effectively guaranteed.

[0006] To achieve the above objectives, the technical solution adopted by this invention is as follows: a method for optimizing the mechanical properties of bottom slag grouting material based on multi-scale design, comprising the following steps:

[0007] Step S1: Screen the industrial bottom slag and determine its density, specific surface area, and porosity.

[0008] Step S2: The bottom slag particles are surface modified by a modified solution containing silane coupling agent and polycarboxylate superplasticizer to form a uniform interfacial reaction layer.

[0009] Step S3: Define particle proportion parameters, interfacial bonding coefficients, and volumetric composition parameters to establish a multi-scale parameter set. ;

[0010] in, This refers to the particle size distribution parameter. The interface bonding coefficient; These are volumetric component parameters;

[0011] Step S4: Construct the comprehensive performance function

[0012]

[0013] in, This refers to the overall performance response indicators; , , These represent the response functions for compressive strength, flexural strength, and impermeability, respectively. All are weighting coefficients, satisfying ;

[0014] Step S5: Use the particle swarm optimization algorithm to search and iterate through the parameter set to maximize The goal is to obtain the optimal combination of parameters. The model predictions are obtained.

[0015] Step S6: Prepare bottom slag grout samples based on the optimal parameter combination results, test the compressive strength, flexural strength, porosity and permeability coefficient of the samples, and perform error analysis with the model prediction values.

[0016] Furthermore, the modified solution in step S2 is prepared by mixing 5-10 wt% silane coupling agent, 3-6 wt% polycarboxylate superplasticizer and deionized water, and the surface modification reaction temperature is controlled at 25-35°C and the reaction time is controlled at 2-3 hours.

[0017] Furthermore, the particle ratio parameter in step S3 ,satisfy Interface bonding coefficient Volumetric composition parameters satisfy =(0.45~0.60):(0.30~0.40):(0.08~0.12).

[0018] Furthermore, the compressive strength response function in step S4 Defined as:

[0019]

[0020] in, This is an empirical coefficient; Represents the proportion of fine particles; Represents the combination of interface and quality. This represents the percentage of bottom slag.

[0021] Furthermore, the flexural strength response function in step S4 Defined as:

[0022]

[0023] in, The constant is used to reflect the combined effects of material system, curing conditions and water-cement ratio on flexural strength; Represents the proportion of particles in the middle group; This represents the proportion of cement.

[0024] Furthermore, the anti-permeability response function in step S4 Defined as:

[0025]

[0026] in, The total porosity of the material; The permeability coefficient is used to characterize the baseline level of permeability under different temperature, age, and dosage conditions.

[0027] Furthermore, in step S5 when The value reaches a stable rate of change for three consecutive iterations. When the success rate is ≤0.5%, the algorithm is considered to have converged. The individual velocity and position are updated in each iteration as follows:

[0028]

[0029]

[0030] in, For particle indices; For the first The particle in the first The speed of time; For the first The particle in the first The position at that moment; This represents the best historical value for an individual. This is the best value in the group's history; The inertia weights for the particle swarm optimization algorithm decrease linearly in the range of 0.9 to 0.4. As a learning factor, and satisfying = =2.0; , It is a random number;

[0031] After each position update, recalculate the target value corresponding to the particle using the new position:

[0032] .

[0033] Furthermore, in step S1, the industrial bottom slag is mechanically sieved and divided into fine, medium, and coarse particle groups according to its particle size. The density of the industrial bottom slag is determined by the water displacement method, the specific surface area of ​​the industrial bottom slag is determined by the BET gas adsorption method, and the porosity of the industrial bottom slag is determined by the liquid nitrogen adsorption method. The measured density, specific surface area, and porosity data are used as subsequent regression and fitting data.

[0034] Furthermore, in step S6, when preparing the bottom slag grout sample, three samples are first prepared. The process involved preparing a cubic mold, three 0.04m × 0.04m × 0.16m three-point bending specimens, and three cylinders with a cross-sectional area of ​​0.01m² and a thickness of 0.05m. Bottom slag was weighed according to its mass. The bottom slag particles were surface-modified using a mixture of 7wt% silane coupling agent (relative to the bottom slag mass), 4wt% polycarboxylate superplasticizer (relative to the overall slurry mass), and deionized water. The chemically modified bottom slag was then mixed evenly with cement, and water was gradually added and stirred until a uniform slurry was formed. This slurry was then used to pour the mixture into the cubic mold, three-point bending specimens, and cylinders. After curing for 28 days at 20±2℃ and relative humidity ≥95%, mechanical and permeability tests were conducted. The measured results were compared with the model predictions. If the error did not exceed the preset threshold, the formula was confirmed and a process specification was prepared; if the error exceeded the preset threshold, the process returned to step S3 for recalibration.

[0035] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0036] The method of this invention achieves synergistic improvement of strength and toughness through multi-scale structural parameter control, improves stress transfer efficiency between particles and matrix through interface modification and interface densification design, realizes quantifiable and predictable formulation design by establishing an optimization method based on multi-scale modeling and experimental verification, and establishes a multi-level optimization path from particle level to composite system level by introducing a multi-scale design concept, combining material microstructure analysis, interface transition zone control and macroscopic performance feedback, thereby achieving comprehensive improvement in the strength, toughness, durability and crack resistance of bottom slag filling material. Attached Figure Description

[0037] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0038] Figure 1 This is an overall flowchart of the method of the present invention;

[0039] Figure 2 This is a flowchart of the interface modification process of the method of the present invention;

[0040] Figure 3 This is a flowchart of the performance response simulation and iterative optimization steps of the method of the present invention;

[0041] Figure 4 This is a flowchart of the sample preparation and performance verification steps of the method of the present invention. Detailed Implementation

[0042] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to embodiments and accompanying drawings. The content mentioned in the embodiments is not intended to limit the present invention.

[0043] Reference Figures 1-4 As shown, the method for optimizing the mechanical properties of bottom slag grouting material based on multi-scale design according to the present invention comprises the following steps:

[0044] Step S1: Screen the industrial bottom slag and determine its density, specific surface area, and porosity.

[0045] Industrial bottom slag is mechanically screened and divided into fine particle groups according to particle size. ), medium particle group ( ) and coarse particle group ( The industrial bottom slag was divided into three groups. The density of the industrial bottom slag was determined by the water displacement method, and the specific surface area of ​​the industrial bottom slag was determined by the BET gas adsorption method. Specific surface area refers to the total surface area of ​​a substance per unit mass or unit volume, and the unit is m² / g (mass specific surface area) or m² / cm³ (volume specific surface area). The porosity of the industrial bottom slag was determined by the liquid nitrogen adsorption method. The measured density, specific surface area and porosity data were used as subsequent regression and fitting data.

[0046] Step S2: The bottom slag particles are surface modified with a modified solution containing silane coupling agent and polycarboxylate superplasticizer to form a uniform interfacial reaction layer.

[0047] The modification solution is prepared by mixing 5-10 wt% silane coupling agent, 3-6 wt% polycarboxylate superplasticizer and deionized water. The sieved bottom slag particles are immersed in the modification solution. The surface modification reaction temperature is controlled at 25-35℃ and the reaction time is controlled at 2-3 hours. After the surface modification is completed, the bottom slag particles are taken out and dried to constant weight. The interface modification effect is estimated by microscopic pull-out test or microscopic contact angle and electron microscopy observation, and the interface bonding coefficient is quantified.

[0048] Step S3: Define particle ratio parameters Interface bonding coefficient Volumetric composition parameters Establish a multi-scale parameter set ;

[0049] Particle ratio parameters : Reflects the influence of particle size distribution and particle morphology of the three groups of bottom slag particles on density;

[0050] Interface integration coefficient : Reflects the influence of interfacial reaction layer thickness and bonding energy on mechanical properties;

[0051] Volumetric composition parameters : Reflects the regulating effect of different material volume ratios on overall performance;

[0052] Particle ratio parameters and satisfy satisfy =(0.45~0.60):(0.30~0.40):(0.08~0.12).

[0053] Step S4: Construct the comprehensive performance function

[0054]

[0055] in, This refers to the overall performance response indicators; , , These represent the response functions for compressive strength, flexural strength, and impermeability, respectively. All are weighting coefficients and satisfy the following conditions: ;

[0056] Compressive strength response function Defined as:

[0057]

[0058] in, This is an empirical coefficient; Represents the proportion of fine particles; Represents the combination of interface and quality. Represents the percentage of bottom slag;

[0059] Prepare a sufficient number of test samples and record the actual compressive strength of each group of samples. ;

[0060] For each sample Calculate the denominator using the given exponent:

[0061]

[0062] The sample corresponding to the formula is obtained. value:

[0063]

[0064] Take all samples The arithmetic mean as the final A weighted average is used:

[0065]

[0066] Flexural strength response function Defined as:

[0067]

[0068] in, The constant is used to reflect the combined effects of material system, curing conditions and water-cement ratio on flexural strength; Represents the proportion of particles in the middle group; Represents the proportion of cement;

[0069] Prepare a sufficient number of test samples and record the actual compressive strength of each group of samples. And record the corresponding , , At the same time, the sample batch and curing conditions were recorded.

[0070] Taking the natural logarithm of the equation, we obtain a linearly fitable form:

[0071]

[0072]

[0073] For all samples The final result is obtained by performing an arithmetic average. ;

[0074]

[0075] Anti-permeability response function Defined as:

[0076]

[0077] in, The total porosity of the material; The permeability coefficient is used to characterize the baseline level of permeability under different temperature, age, and dosage conditions;

[0078] Prepare a sufficient number of test samples and determine the total porosity of each group of samples. and :

[0079]

[0080] For all samples The final result is obtained by performing an arithmetic average. ;

[0081]

[0082] Step S5: Use the particle swarm optimization algorithm to search and iterate through the parameter set to maximize The goal is to obtain the optimal combination of parameters. The model predictions are obtained.

[0083] when The value reaches a stable rate of change for three consecutive iterations. When the success rate is ≤0.5%, the algorithm is considered to have converged, and the individual's velocity and position are updated in each iteration.

[0084]

[0085]

[0086] in, For particle indices; For the first The particle in the first The speed of time; For the first The particle in the first The position at that moment; This represents the best historical value for an individual. This is the best value in the group's history; The inertia weights for the particle swarm optimization algorithm decrease linearly in the range of 0.9 to 0.4. As a learning factor, and satisfying = =2.0; , It is a random number;

[0087] After each position update, recalculate the target value corresponding to the particle using the new position:

[0088]

[0089]

[0090] Example of updating a single parameter dimension:

[0091] Current location:

[0092] Current speed:

[0093] Individual historical best value:

[0094] Group historical best value:

[0095] Inertia weight:

[0096] Learning factors:

[0097] Random number:

[0098] Speed ​​synthesis:

[0099] =0.8×0.10+2.0×0.4×(0.60−0.50)+2.0×0.9×(0.70−0.50)=0.520

[0100] Location update:

[0101] =0.50 + 0.520 = 1.020

[0102] The updated position 1.020 exceeds the upper limit of 1.0 → Truncate or reflect the updated position:

[0103] Truncation: =1.000

[0104] reflection: =1.000−0.020=0.980

[0105] new location Recalculate using the new performance model Superior to particles ,renew When the new Superior to global ,renew .

[0106] Iteration The optimal integrated response is denoted as The relative rate of change between two adjacent iterations is defined as:

[0107]

[0108] When there are 3 consecutive instances that satisfy the condition:

[0109]

[0110] Then the algorithm is considered to have converged.

[0111] The algorithm runs and records the optimal values ​​up to the 10th, 11th, 12th, and 13th iterations. The values ​​are as follows:

[0112]

[0113]

[0114]

[0115]

[0116] =∣19.920−19.800∣ / 19.800×100%=0.60606%>0.5%→Number of convergences=0

[0117] =∣19.988−19.920∣ / 19.920×100%=0.3417%<0.5%→Number of convergences=1

[0118] =∣19.999−19.988∣ / 19.988×100%=0.0550%<0.5%→Number of convergences=2

[0119] exist =12、 =13 twice The requirement of ≤0.5% has been met, but it still needs to be satisfied three times consecutively.

[0120] like =20.003

[0121] =∣20.003−19.999∣ / 19.999×100%=0.0200%≤0.5%→Number of convergences=3

[0122] Iterations t=12, t=13, =14 reached ≤0.5% three times in a row, and the algorithm determined that it had converged.

[0123] like =20.100

[0124] =∣20.100−19.999∣ / 19.999×100%=0.50502%>0.5%→Number of convergences=0

[0125] Iteration =14 o'clock The algorithm determined that the convergence rate was 0.5%.

[0126] Step S6: Prepare bottom slag grout samples based on the optimal parameter combination results, test the compressive strength, flexural strength, porosity and permeability coefficient of the samples, and perform error analysis with the model prediction values;

[0127] Make three The cube mold, three three-point bending specimens of 0.04m×0.04m×0.16m, and three cylinders with a cross-sectional area of ​​0.01m² and a thickness of 0.05m;

[0128] Weigh each component of the bottom slag according to mass. Use a mixed solution of silane coupling agent (7wt% relative to the bottom slag mass), polycarboxylate superplasticizer (4wt% relative to the overall slurry mass), and deionized water to modify the surface of the bottom slag particles. Mix the bottom slag with cement according to the specified amount evenly, gradually add water and stir until a uniform slurry is formed. The stirring speed is 400 rpm and the stirring time is controlled at 3-5 min. The slurry is used to pour the slurry into cubic molds, three-point bending specimens, and cylinders in sequence. After curing for 28 days at a temperature of 20±2℃ and a relative humidity of ≥95%, mechanical tests and permeability tests are carried out.

[0129] Formula for calculating compressive strength:

[0130]

[0131] in, The maximum load at which the specimen fails; The area under pressure;

[0132] Calculation of the percentage increase in compressive strength:

[0133]

[0134] Formula for calculating flexural strength:

[0135]

[0136] in, The maximum load at which the specimen fails; The span between the fulcrums; The width of the specimen; The height of the specimen;

[0137] Calculation of the percentage increase in flexural strength:

[0138]

[0139] Formula for calculating impermeability:

[0140]

[0141] in, To transmit volume over time The volume of the sample passing through the interior; For the sample thickness; The cross-sectional area of ​​the sample; For measuring time; The difference in water head refers to the height difference in water level between the upstream and downstream sides during the infiltration process.

[0142] Calculation of the percentage improvement in impermeability:

[0143]

[0144] The measured results are compared with the model prediction results. If the error does not exceed the preset threshold, the formula is confirmed and the process specification is prepared. If the error exceeds the preset threshold, the process returns to step S3 for recalibration.

[0145] Example 1 (Baseline Control Group)

[0146] Original formula and processing:

[0147] Bottom ash is distributed by quality

[0148] No interface modifications were performed.

[0149] Macro-allocation

[0150] empirical coefficient , ,

[0151] Weight , ,

[0152] calculate:

[0153]

[0154]

[0155] Total porosity ,but:

[0156]

[0157]

[0158] Actual test results:

[0159] Compressive strength: 54.2 MPa; Flexural strength: 8.4 MPa; Permeability coefficient: 5.2 × m / s

[0160] Example 2 (Optimized)

[0161] Results after particle swarm optimization:

[0162]

[0163]

[0164]

[0165]

[0166] Model prediction:

[0167]

[0168]

[0169]

[0170]

[0171] Actual test results:

[0172] Compressive strength: 67.2 MPa; Flexural strength: 10.1 MPa; Permeability coefficient: 3.0 × m / s

[0173] The model prediction and the measured compressive strength of 67.2 MPa are separated by... The dimensional conversion coefficients were calibrated, and the measured / predicted ratio could be controlled within a scale range of 2.0±0.1 after initial fitting, with the final relative error being less than 5%.

[0174] Example 3 (different bottom ash sources, containing higher CaO content, with rougher particle surfaces)

[0175] Raw data:

[0176]

[0177]

[0178]

[0179] Results after particle swarm optimization:

[0180]

[0181]

[0182]

[0183]

[0184] Model prediction:

[0185]

[0186]

[0187]

[0188]

[0189] Actual test results:

[0190] Compressive strength: 63.5 MPa; Flexural strength: 9.6 MPa; Permeability coefficient: 3.5 × m / s

[0191] index Example 1 Example 2 Example 3 0.72 0.88 0.86 0.10 0.068 0.072 compressive strength 54.2 67.2 63.5 Flexural strength 8.4 10.1 9.6 Permeability coefficient 5.2× 3.0× 3.5×

[0192] Increase in compressive strength:

[0193] Flexural strength improvement rate:

[0194] Improvement rate of impermeability:

[0195] A comparison between Example 1 and Example 2 shows that increasing the proportion of fine particles... Interface integration coefficient It helps to fill pores and enhance the bond between particles and the matrix, increasing compressive strength by about 24% and flexural strength by about 20%. The permeability coefficient decreased by approximately 42% from 0.10 to 0.068. Example 3 involved different sources of bottom ash, but the performance was still significantly improved through the same optimized process, indicating that the method has a certain degree of universality.

[0196] This invention has many specific applications. The above description is only a preferred embodiment of this invention. It should be noted that for those skilled in the art, several improvements can be made without departing from the principle of this invention, and these improvements should also be considered within the scope of protection of this invention.

Claims

1. A method for optimizing the mechanical properties of bottom slag grouting material based on multi-scale design, characterized in that, The steps are as follows: Step S1: Screen the industrial bottom slag and determine its density, specific surface area, and porosity. Step S2: The bottom slag particles are surface modified by a modified solution containing silane coupling agent and polycarboxylate superplasticizer to form a uniform interfacial reaction layer. Step S3: Define particle proportion parameters, interfacial bonding coefficients, and volumetric composition parameters to establish a multi-scale parameter set. ; in, This refers to the particle size distribution parameter. The interface bonding coefficient; These are volumetric component parameters; Step S4: Construct the comprehensive performance function in, This refers to the overall performance response indicators; , , These represent the response functions for compressive strength, flexural strength, and impermeability, respectively. All are weighting coefficients, satisfying ; Step S5: Use the particle swarm optimization algorithm to search and iterate through the parameter set to maximize The goal is to obtain the optimal combination of parameters. The model predictions are obtained. Step S6: Prepare bottom slag grout samples based on the optimal parameter combination results, test the compressive strength, flexural strength, porosity and permeability coefficient of the samples, and perform error analysis with the model prediction values.

2. The method according to claim 1, characterized in that, The modified solution in step S2 is prepared by mixing 5-10 wt% silane coupling agent, 3-6 wt% polycarboxylate superplasticizer and deionized water. The surface modification reaction temperature is controlled at 25-35℃ and the reaction time is controlled at 2-3 hours.

3. The method according to claim 1, characterized in that, The particle ratio parameter in step S3 ,satisfy Interface bonding coefficient Volumetric composition parameters satisfy =(0.45~0.60):(0.30~0.40):(0.08~0.12).

4. The method according to claim 1, characterized in that, The compressive strength response function in step S4 Defined as: in, This is an empirical coefficient; Represents the proportion of fine particles; Represents the combination of interface and quality. This represents the percentage of bottom slag.

5. The method according to claim 1, characterized in that, Flexural strength response function in step S4 Defined as: in, The constant is used to reflect the combined effects of material system, curing conditions and water-cement ratio on flexural strength; Represents the proportion of particles in the middle group; This represents the proportion of cement.

6. The method according to claim 1, characterized in that, The anti-permeability response function in step S4 Defined as: in, The total porosity of the material; The permeability coefficient is used to characterize the baseline level of permeability under different temperature, age, and dosage conditions.

7. The method according to claim 1, characterized in that, In step S5 when The value reaches a stable rate of change for three consecutive iterations. When the success rate is ≤0.5%, the algorithm is considered to have converged. The individual velocity and position are updated in each iteration as follows: in, For particle indices; For the first The particle in the first The speed of time; For the first The particle in the first The position at that moment; This represents the best historical value for an individual. This is the best value in the group's history; The inertia weights for the particle swarm optimization algorithm decrease linearly in the range of 0.9 to 0.

4. As a learning factor, and satisfying = =2.0; , It is a random number; After each position update, recalculate the target value corresponding to the particle using the new position: 。 8. The method according to claim 1, characterized in that, In step S1, the industrial bottom slag is mechanically sieved and divided into fine, medium, and coarse particle groups according to its particle size. The density of the industrial bottom slag is determined by the water displacement method, the specific surface area is determined by the BET gas adsorption method, and the porosity is determined by the liquid nitrogen adsorption method. The measured density, specific surface area, and porosity data are used as subsequent regression and fitting data.

9. The method according to claim 1, characterized in that, In step S6, when preparing the bottom slag grout sample, three samples are first made. The process involved preparing a cubic mold, three 0.04m × 0.04m × 0.16m three-point bending specimens, and three cylinders with a cross-sectional area of ​​0.01m² and a thickness of 0.05m. Bottom slag was weighed according to its mass. The bottom slag particles were surface-modified using a mixture of 7wt% silane coupling agent (relative to the bottom slag mass), 4wt% polycarboxylate superplasticizer (relative to the overall slurry mass), and deionized water. The chemically modified bottom slag was then mixed evenly with cement, and water was gradually added and stirred until a uniform slurry was formed. This slurry was then used to pour the mixture into the cubic mold, three-point bending specimens, and cylinders. After curing for 28 days at 20±2℃ and relative humidity ≥95%, mechanical and permeability tests were conducted. The measured results were compared with the model predictions. If the error did not exceed the preset threshold, the formula was confirmed and a process specification was prepared; if the error exceeded the preset threshold, the process returned to step S3 for recalibration.

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