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Abstract

This article studied the relationship between surface roughness and surface micro hardness of the hard-brittle materials and the process parameters in quick-point grinding, and then established the prediction model for the surface micro hardness and surface roughness by the back propagation network which was an improved genetic algorithm. Through the experiments of the quick-point grinding of ceramics, surface roughness and surface micro hardness were tested, and reliability of the model was validated thereby. Based on the least square fitting of the experiment value and prediction value, the one-dimensional analytic model for surface roughness and surface micro hardness had been, respectively, developed in terms of grinding speed, grinder work-table feed speed, grinding depth, incline angle, and deflection angle as process parameters. Both the correlation test and experiment verification indicated that the model exhibited a high level of accuracy. The multivariate model of surface roughness and surface micro hardness can be constructed by means of immune algorithms and orthogonal experiment data. With the optimum objective of the minimum surface roughness and maximum surface micro hardness, a set of optimized process parameters was obtained using immune algorithms, and experiment verification proved that the error value was less than 10%.

Keywords

Parameters optima point grinding hard-brittle materials surface roughness surface micro hardness back propagation neural network immune algorithms

Introduction

Hard-brittle materials are featured by high level of hardness, thermal stability, and corrosion resistance, thus enjoying a wide range of application in national defense, aerospace industry, precision instrument, and so on.^1–3 Quick-point grinding combines high surface quality of grinding and high efficiency of turning, and so far it has been widely utilized in the processing of axles.⁴ Among others, YD Gong et al.⁵ conducted research in the parameter relationship between temperature field and surface micro hardness in quick-point grinding. SC Xiu et al.⁶ studied the modeling of surrounding layer of the quick-point grinding. Intelligent algorithms, which were represented by genetic algorithm (GA), neural network, and immune algorithms, have been widely used in solving multi-dimensional non-derivable and optimization.^7–9 Liu et al.¹⁰ established a strain-predictive back propagation neural network improved by particle swarm optimization (PSO-BPNN) model for full-scale static experiment of a certain wind turbine blade. Back propagation (BP) neural network, after improved by GA, integrates the merits of the two and exhibits better adaptability, learning ability, and generalization ability, and meanwhile, solving the defect of falling into the trap of local optimal solution; therefore, it has made the data prediction more reliable.¹¹

The surface quality and process parameters of quick-point grinding are variable. This relationship is variable between the surface quality and process parameters in quick-point grinding. This article studied surface roughness and surface micro hardness of the finished product by quick-point grinding, designed three-layer BP neural network, and improved it with GA, which was abbreviated as GA-BP algorithm, and established one-dimensional and multivariate model of the process parameters, surface roughness, and surface micro hardness of quick-point grinding. Finally, it validated its accuracy with experiments and optimized bi-objective process parameters by means of immune algorithms.

Experiment

Fluorophlogopite, a machinable ceramics, was selected in quick-point grinding, with the density of 2.5–2.8 g/cm³, 850–900 Vickers hardness, 2.1-W/(m·K) heat conductivity, and 108-MPa bending strength. The grinding wheels for ceramic bond cubic boron nitride (CBN) are used, with the diameter of 180 mm, 3-mm width, 200 abrasive grain, and 5-mm abrasive thickness. As shown in Figure 1, the experiment was carried out on curve grinding machine MK9025A type, surface roughness was measured by Micromeasure II surface profiler, and the surface micro hardness was measured by FM-ARS9000 full automatic micro hardness (nanoindentation) measurement system. Single factor experiment condition is described in Table 1; orthogonal experiment is shown in Tables 2 and 3. In the process of point grinding, the positive and negative value of α and β indicate the rotation angle and deflection direction of the grinding wheel.

Figure 1.

Machine tools and testing equipment for experiment: (a and b) curve grinder of MK9025A type, (c) micromeasure type of 3D surface profiler, and (d) microhardness measurement system.

Table 1.

The process parameters of single factor experiment.

Group no.	v_s (m/s)	v_w (mm/min)	a_g (mm)	α (°)	β (°)
1–5	29.5–62.5	40	0.15	−0.5	1
6–10	62.5	10–75	0.15	−0.5	1
11–16	62.5	40	0.05–0.3	−0.5	1
17–21	62.5	40	0.15	−1 to 1	1
22–25	62.5	40	0.15	−0.5	−1 to 5

v_s: cutting velocity; v_w: feeding rate; a_g: cutting depth; α: the angle of inclination; β: deflection angle.

Table 2.

The factors and levels of orthogonal experiment.

Level	Factors
	v_s	v_w	a_g	α	β
1	29.5	15	0.05	−0.3	−1.0
2	40	40	0.14	0.3	−2.5
3	51	65	0.23	0.9	−4.0
4	62.5	90	0.32	1.2	−5.5

Table 3.

The results of five-factor and four-level orthogonal experiment.

Group no.	1	2	3	4
Hv (GPa)	2.8693	2.9206	3.0115	3.0153
Ra (μm)	0.448	0.274	0.325	0.355
Group no.	5	6	7	8
Hv (GPa)	3.1015	2.7636	2.5665	2.9016
Ra (μm)	0.516	0.301	0.403	0.721
Group no.	9	10	11	12
Hv (GPa)	2.8243	2.7819	2.4600	2.7290
Ra (μm)	0.422	0.354	0.282	0.476
Group no.	13	14	15	16
Hv (GPa)	2.4560	3.0690	2.7249	2.7611
Ra (μm)	0.246	0.327	0.218	0.491

GA-BP neural network

BP neural network

In three-layer BP neural network, the input training parameters included grinding speed, grinder work-table feed speed, grinding depth, incline angle, and deflection angle. And the output training parameters included surface roughness and surface micro hardness. The structure of BP neural network is shown in Figure 2.

Figure 2.

The structure of BP neural network.

In Figure 2, f¹ is the basis function of the implicit layer, via S tansig; f² is the basis function of the output layer, via purelin. The training function of the error correction adopts self adoptive self-adaption traingda. Suppose the node of the output layer is B = (b₁, b₂, …, b_n) and the desired vector of the output layer is Y = (y₁, y₂, …, y_n); after running on BP neural network, comes the overall error J (see equation (1))

$J = \sum_{k = 1}^{m} \sum_{i = 1}^{n} {(b_{i}^{k} - y_{i}^{k})}^{2}$ (1)

GA-BP neural network

Although BP neural network is characterized by greater adaptability, leaning ability, and generalization ability,¹² its convergence rate is slow and it is inclined to fall into the trap of local optimal solution. In order to remedy the drawback, it was developed with the help of GA (for short GA-BP neural network) in this article. The structure of BP neural network is shown in Figure 3. The basic steps are listed as the following:

Create initial population, whose individuals are encoded as the weights and thresholds of the BP neural network.

Based on the obtained population, run BP neural network, and find out the overall error J.

Calculate the adaptability of the population. Based on the findings, conduct operations, such as selecting, intersecting, and mutating the individuals in the populations, and finally get filial-population.

Repeat steps 2–3 until the conditions are satisfied.

Decode the obtained population, and get the optimum weights and thresholds of the BP neural network.

Figure 3.

The structure of GA-BP neural network.

The adaptability was calculated, based on the increasing sequences of the overall error J. And returned value for each individual adaptability will be obtained. The adaptability function is shown as equation (2)

$F (Pos) = 2 - sp + 2 \times (sp - 1) \times \frac{Pos - 1}{Nind - 1}$ (2)

where Nind is the number of the individuals in the population. Pos is the reordered position of each individual’s overall error J; sp is the intensity of selecting.

Construction of multivariate model based on GA-BP neural network

LJ Ma¹³ studied relationship between the ceramic surface roughness and process parameters of the quick-point grinding and came up with the model, as shown in equation (3), and it is so far the most perfect expression about the surface roughness of the quick-point grinding

$Ra = R_{1} {(\frac{v_{w} h_{m}}{v_{s}} \times b^{k \frac{α}{β}})}^{x}$ (3)

where h_m is maximum deformation cutting thickness. R₁, k, x, and b are undetermined constants.

One-dimensional model of surface roughness

In the quick-point grinding, the surface’s micro morphology is shown in Figure 4, the three-dimensional (3D) image of point grinding surface is shown in Figure 5. The flatness of the surface changed dramatically with the grinding speed. In the process of grinding, the materials were removed because of the grinding wheel contacted the machined surface. With increasing of the grinding speed, the contact probability of grinding grain with machining surface of work-piece increased. The residual micro defects on work-piece surface were more likely to be removed, and thus lower the surface roughness.¹⁴ As shown in Figure 6, the experimental result indicated that surface roughness dropped on the whole as the grinding speed increased.

Figure 4.

The micro topography of point grinding surface (1000×): (a) v_s = 29.5 m/s, v_w = 40 mm/min, a_g = 0.15 mm, α = –0.5°, β = 1°; (b) v_s = 38 m/s, v_w = 40 mm/min, a_g = 0.15 mm, α = –0.5°, β = 1°; (c) v_s = 47 m/s, v_w = 40 mm/min, a_g = 0.15 mm, α = –0.5°, β = 1°; and (d) v_s = 62.5 m/s, v_w = 40 mm/min, a_g = 0.15 mm, α = –0.5°, β = 3°.

Figure 5.

The 3D image of point grinding surface: (a) v_s = 38 m/s, v_w = 40 mm/min, a_g = 0.15 mm, α = –0.5°, β = 1° and (b) v_s = 62.5 m/s, v_w = 40 mm/min, a_g = 0.15 mm, α = –0.5°, β = 3°.

Figure 6.

The effect of grinding speed on the surface roughness.

According to the least square vector machine algorithm (LS-SVM)¹⁵ and experiment data, a group of prediction data could be obtained. Based on the GA-BP network algorithm, the single factor experiment data were used in training, the corresponding prediction data were obtained for the surface roughness in accordance with the grinding speed. After comparing the two groups of data of LS-SVM and GA-BP, it can be seen that GA-BP network data are more accurate (see Figure 6).

As shown in equation (3), according to this model, the hypothetical model was proposed about surface roughness’s change in accordance with the grinding speed (see equation (4)). After the least square fitting, the model in equation (5) can be attained, with the correlation coefficient r = 0.7614

$Ra = a {(\frac{b}{v_{s}})}^{x} - c$ (4)

$Ra = 2.751 \cdot {(\frac{6}{v_{s}})}^{0.15} - 1.539$ (5)

As shown in Figures 7 and 8, with the increasing of grinding work-table feed speed and grinding depth, the change tendency of the surface roughness was sinusoidal function. After introducing correction term $\sin (a \cdot a_{g} + b) \times e^{c \cdot a_{g}}$ and $\sin (a \cdot v_{w} + b) \times e^{c \cdot v_{w}}$ , the proposed models were established, respectively. And based on the experiment value and GA-BP network prediction value, as well as the least square fitting, the model in equations (6) and (7) could be achieved, with the correlation coefficient r = 0.9978 and 0.9478, respectively

$\begin{matrix} Ra = & 0.0659 \cdot v_{w}^{0.15} \cdot \\ \sin (0.1111 \cdot v_{w} + 0.9957) e^{- 0.01662 v_{w}} + 0.4559 \end{matrix}$ (6)

$\begin{matrix} Ra = & 1.335 \cdot {(0.6399 \cdot a_{g})}^{0.6} \\ \sin (45.58 \cdot a_{g} + 4.5314) \cdot e^{- 3.49 \cdot a_{g}} + 0.4327 \end{matrix}$ (7)

Figure 7.

The effect of grinder work-table feed speed on the surface roughness.

Figure 8.

The effect of grinding depth on the surface roughness.

As shown in Figures 9 and 10, the surface roughness increases with the increasing of incline angle, and the surface roughness decreases with the increasing of deflection angle. The new model was presented based on the experiment value (see equation (8))

$Ra = \frac{a}{b + e^{c \cdot α β}} + d$ (8)

Figure 9.

The effect of incline angle on the surface roughness.

Figure 10.

The effect of deflection angle on the surface roughness.

Based on the experiment value and GA-BP network prediction value, as well as the least square fitting, the model in equations (9) and (10) could be achieved, with the correlation coefficient r = 0.9724 and r = 0.9289, respectively

$Ra = \frac{0.5574}{1 + e^{- 0.8699 \cdot α}} + 1.499 \times 10^{- 5}$ (9)

$Ra = \frac{0.2}{0.4633 + e^{1 \cdot β}} + 0.3793$ (10)

Multivariate model of surface roughness based on GA-BP neural network

Based on the above five one-dimensional models (see equations (4), (6), (7), (9), and (10)), the multivariate model of the process parameters of surface roughness was proposed in grinding fluorophlogopite ceramic (see equation (11)). Through observing equations (4), (6), and (7), this model was composed of five parts. The first part was a power function and regarded as R₁(v_wa_g/v_s)^x. The second part was a sine function and regarded as sin(b₁a_gv_w + b₂). The third part was an exponential term and regarded as $e^{c_{1} a_{g} v_{w}}$ . By observing equations (9) and (10), the fourth part was proposed and regarded as $a_{1} / (a_{2} + e^{a_{3} α β})$ . The fifth part was the constant d₁

$\begin{matrix} Ra = & \overset{The first}{\overset{︷}{R_{1} {(\frac{v_{w}}{v_{s}} a_{g})}^{x}}} \overset{The second}{\overset{︷}{\sin (b_{1} a_{g} v_{w} + b_{2})}} \cdot \underset{The third}{\underset{︸}{e^{c_{1} a_{g} v_{w}}}} \\ \overset{The fourth}{\overset{︷}{\frac{a_{1}}{a_{2} + e^{a_{3} α β}}}} + \overset{The fifth}{\overset{︷}{d_{1}}} \end{matrix}$ (11)

where R₁, x, a₁, a₂, a₃, b₁, b₂, c₁, and d₁ were the constants.

One-dimensional model of surface micro hardness

Figures 11 –15 show the variation tendency of the surface micro hardness in accordance with the grinding speed, grinder work-table feed speed, grinding depth, incline angle, and the deflection angle. With fitting, the following equations can be proposed

$Hv = - 1.076 e^{- 0.001745 {(v_{s} - 42.37)}^{2}} + 3$ (12)

$\begin{matrix} Hv = & 29.99 (3.64 \times 10^{- 6} v_{w}^{2} - 6.533 \times 10^{- 4} v_{w} + 0.01745) \\ \sin (0.1226 v_{w} + 0.8476) + 2.159 \end{matrix}$ (13)

$\begin{matrix} Hv = & (- 1.03 a_{g} + 0.02685) \\ \sin (30.16 a_{g} + 5.878) e^{15.71 a_{g}} + 2.337 \end{matrix}$ (14)

$\begin{matrix} Hv = & 4.985 (- 0.7914 α^{2} - 0.0292 α + 0.0118) \cdot \\ \sin (- 2.376 α + 2.274) + 2.245 \end{matrix}$ (15)

$Hv = 0.3918 \sin (0.5924 β + 3.328) e^{0.07815 β} + 2.479$ (16)

Figure 11.

The effect of grinding speed on the surface micro hardness.

Figure 12.

The effect of grinder work-table feed speed on the surface micro hardness.

Figure 13.

The effect of grinding depth on the surface micro hardness.

Figure 14.

The effect of incline angle on the surface micro hardness.

Figure 15.

The effect of deflection angle on the surface micro hardness.

Equations (12)–(16) have the correlation coefficient r = 0.993, 0.9995, 0.9983, 0.9963, and 1, respectively.

Multivariate model of surface micro hardness based on GA-BP neural network

Based on the five one-dimensional models (see equations (12)–(16)), the multivariate model of the process parameters of surface micro hardness was proposed in grinding fluorophlogopite ceramic (see equation (17)). This model is composed of four parts.

The first part was a polynomial through observation equations (13)–(15), single factor experiment condition, and regarded as $a_{1} (a_{2} α^{2} + a_{3} α + a_{4}) (a_{5} v_{w}^{2} + a_{6} v_{w} a_{g} + a_{7})$ . The second part was a sine function and regarded as $\sin (b_{1} α β + b_{2}) \sin (b_{3} a_{g} v_{w} + b_{4})$ . The third part was an exponential term and regarded as $e^{c_{1} β + c_{2} a_{g} + c_{3} {(v_{s} - c_{4})}^{2}}$ . The fourth part was the constant d₁

$\begin{matrix} Hv = \overset{The first}{\overset{︷}{a_{1} (a_{2} α^{2} + a_{3} α + a_{4}) (a_{5} v_{w}^{2} + a_{6} v_{w} a_{p} + a_{7})}} \cdot \\ \overset{The \sec ond}{\overset{︷}{\sin (b_{1} α β + b_{2}) \sin (b_{3} a_{g} v_{w} + b_{4})}} \overset{The third}{\overset{︷}{e^{c_{1} β + c_{2} a_{g} + c_{3} {(v_{s} - c_{4})}^{2}}}} \\ + \overset{The fourth}{\overset{︷}{d_{1}}} \end{matrix}$ (17)

where a₁, a₂, a₃, a₄, a₅, a₆, a₇, b₁, b₂, b₃, b₄, c₁, c₂, c₃, c₄, and d₁ were the constants.

Establishment of multivariate model of the immune algorithms

Immune algorithms

Immune algorithms are smart algorithms, developed from the principles in the immune system. It owns the GA’s merit of being able to look for the overall optimization, and is also capable of refining the defects in the optimization process purposely.¹⁶ In immune algorithms, an investigating problem will be converted into the biological process of identifying antigen and destroying antigen in immune system. Then, by means of the intersection and variation of the lymphocyte cell genes and the adjustment of the antibody density, it may enable the lymphocyte cells to yield the optimum amount of antibodies.

In 1974, biologist Jerne,¹⁷ Denmark Nobel Prize winner, proposed the mathematics model of the immune system network, and laid the foundation of immune calculation. After that, Farmer and others proposed the related theory of immune system machine learning in 1986, and propelled further development of immune system.¹⁸ In 1996, artificial immune system, which is abbreviated as AIS, was proposed for the first time and was widely acknowledged all over the world.

The basic steps for calculation of the immune algorithms are first to produce initial antibody group, evaluate it, and produce the new generation of antibody group. Finally, judge whether the proposed conditions are met or not, and then output and save iteration results.

The adaptability function is shown as equation (18)

$F_{j} = \frac{10}{\sum_{i = 1}^{n} (f_{i} - {f'}_{i})}$ (18)

where f_i is the calculation value from the model, $f'_{i}$ is the experiment value.

Antibody concentration is represented by L, which is the sum of the Euclidean distance of each antibody (see equation (19))

$L = \sum_{i = 1}^{k} {[{(m_{1}^{i} - m_{1}^{j})}^{2} + {(m_{2}^{i} - m_{2}^{j})}^{2} + \dots + {(m_{n}^{i} - m_{n}^{j})}^{2}]}^{\frac{1}{2}}$ (19)

Evaluation function for the antibody group is decided by adaptability function and antibody density (see equation (20))

$P_{j} = α F_{j} + (1 - α) L_{j}$ (20)

where $α$ is the constant.

Choice mechanism is done by roulette, and the probability of being selected is shown as equation (21)

$P'_{j} = \frac{P_{j}}{\sum_{j = 1}^{k} P_{j}}$ (21)

Solution of the multivariate model of surface roughness

Based on the orthogonal experiment results (in Table 3), the model (equation (14)) can be solved via immune algorithms, with the following criterion (see equation (22))

$min [\sum_{i = 1}^{n} | R a_{i} - R a_{i}' |]$ (22)

where $R a_{i}$ is the calculation from the model, $R a'_{i}$ is the experiment value.

The error curve of the solution is shown Figure 16, and the multivariate model for change of surface roughness in accordance with the change of process parameters is shown in equation (23). According to Figure 16, the error of model tends to be stable after about 20 generations of evolution. The model accuracy was tested with validation, and its relative error is shown in Table 4

$\begin{matrix} Ra = 3.131 {(\frac{v_{w}}{v_{s}} a_{g})}^{0.8262} \frac{2.5757}{1.3158 + e^{1.1997 α β}} \cdot \\ \sin (0.734 a_{g} v_{w} + 6.5298) e^{- 0.2555 a_{g} v_{w}} + 0.3568 \end{matrix}$ (23)

Figure 16.

The curve of best individual fitness function value of surface roughness based on immune algorithm.

Table 4.

The relative error of the surface roughness between the multiple models’ predicted and experimental value.

Experiment no.	1	2	3
Error (%)	4.25	9.89	5.67

Solution of surface hardness of the multivariate model

Based on the orthogonal experiment results (in Table 3), the model (equation (20)) can be solved via immune algorithms, with the following criterion (see equation (24))

$min [\sum_{i = 1}^{n} | H v_{i} - H v_{i}' |]$ (24)

where $H v_{i}$ is the calculation from the model, $H v'_{i}$ is the experiment value.

The error curve of the solution is shown in Figure 17, and the multivariate model of the change of surface micro hardness in accordance with the change of process parameters is shown in equation (25). The model accuracy was tested with validation, and its relative error is shown in Table 5. According to Figure 17, the error of model tends to be stable after about 110 generations of evolution

$\begin{matrix} Hv = & 5.747 (- 0.0739 α^{2} - 0.0335 α + 0.0353) \cdot \\ (4.9 \times 10^{- 6} v_{w}^{2} - 0.0145 v_{w} a_{g} + 0.0337) \cdot \\ \sin (- 1.4572 α β + 3.2319) \cdot \\ \sin (0.4299 a_{g} v_{w} + 10.91) \cdot e^{0.2186 β + 11.43 a_{g} - 0.0013 {(v_{s} - 43.49)}^{2}} \\ + 2.7578 \end{matrix}$ (25)

Figure 17.

The curve of best individual fitness function value of surface micro hardness based on immune algorithm.

Table 5.

The relative error of the surface micro hardness between the multiple models’ predicted and the experimental value.

Experiment no.	1	2	3
Error (%)	6.06	4.95	1.23

Bi-objective optimization of process parameters based on the immune algorithms

In the real grinding, the influence of the process parameters on the surface roughness and surface micro hardness is variable. While trying to increase the surface micro hardness, it is desirable to decrease the surface roughness. Based on equations (23) and (25), the expression and restraint for the bi-objective optimization are given in equation (26)

${\begin{matrix} F_{1} = \max [H v (v_{s}, v_{w}, a_{g}, α, β)] \\ F_{2} = \min [R a (v_{s}, v_{w}, a_{g}, α, β)] \\ s . t . v_{s} = 29.5 - 62.5 m / s \\ v_{w} = 10 - 90 mm / \min \\ a_{g} = 0.05 - 0.32 mm \\ α = - 1 ° to 5 ° \\ β = - 5.5 ° to 5 ° \end{matrix}$ (26)

While solving from the perspective of immune algorithms, the optimum process parameters range was v_s = 34.0–36.0 m/s, v_w = 65–68 mm/min, a_g = 0.09–0.10 mm, α = –1.0° to −0.9°, and β = 3.15°–3.25°, the optimization results were Hv = 2.93–2.95 GPa and Ra = 0.045–0.126 μm. The evolutionary process of the solution is given in Figure 18.

Figure 18.

The evolution process based on immune algorithm.

Based on the above optimum process parameters, the following validation experiment is conducted as shown in Table 6; the Test 4 is in the optimal range, but the Tests 1–3 are not in the optimal range. The Ra of Test 4 is minimum; the Hv of Test 4 is maximum. Comparing the results, the reliability of optimum results is high.

Table 6.

The results and process parameters of verification experiment.

No.	v_s (m/s)	v_w (mm/min)	a_g (mm)	α (°)	β (°)	Hv (GPa)	Ra (μm)
1	40.0	40	0.14	−0.3	−2.5	2.921	0.274
2	29.5	40	0.05	0.3	−5.5	2.902	0.721
3	40.0	90	0.05	1.2	−4.0	2.725	0.218
4	35.5	66	0.1	1	3.2	2.9403	0.1012

Conclusion

BP neural network, after being improved by GA, can be used to predict the surface roughness and surface micro hardness in the quick-point grinding engineering ceramics.

Via least square fitting, one-dimensional model of the process parameters for the surface roughness and surface micro hardness can be established. Based on the orthogonal experiment, the solution to the multivariate model can be conducted by means of the immune algorithms, and after the validation, it is found that the result of the solution exhibits a higher level of accuracy.

Bi-objective optimization function is established as for the surface roughness and surface micro hardness. While looking for the solutions by resorting to immune algorithms, a set of ideal range for the process parameters can be identified, the optimized process parameters are v_s = 34.0–36.0 m/s, v_w = 65–68 mm/min, a_g = 0.09–0.10 mm, α = –1.0° to −0.9°, and β = 3.15°–3.25°.

Footnotes

Handling Editor: James Baldwin

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research,authorship,and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research,authorship,and/or publication of this article: This work was supported by the National Natural Science Foundation of China (51905183,51975113),the Natural Science Foundation of Hebei Province (E2019501094),the Science and Technology Research Project for Higher School of Hebei Province (QN2019321),the Fundamental Research Funds for the Central Universities (N172303008),and the Scientific Research Initiating Funds for Northeastern University at Qinhuangdao (XNY201806).

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Process parameters optima in quick-point grinding ceramics based on the intelligent algorithm

Abstract

Keywords

Introduction

Experiment

GA-BP neural network

BP neural network

GA-BP neural network

Construction of multivariate model based on GA-BP neural network

One-dimensional model of surface roughness

Multivariate model of surface roughness based on GA-BP neural network

One-dimensional model of surface micro hardness

Multivariate model of surface micro hardness based on GA-BP neural network

Establishment of multivariate model of the immune algorithms

Immune algorithms

Solution of the multivariate model of surface roughness

Solution of surface hardness of the multivariate model

Bi-objective optimization of process parameters based on the immune algorithms

Conclusion

Footnotes

Declaration of conflicting interests

Funding

References