Die bonder thermal error modeling method based on GCRA-BP-AdaBoost algorithm

Abstract

The invention discloses a die bonder thermal error modeling method based on a GCRA-BP-AdaBoost algorithm, and relates to the technical field of numerical control machine tool semiconductors, and the method comprises the following steps: 1, taking a die bonder as an experiment object, and obtaining a plurality of groups of temperature data and corresponding thermal error data; 2, selecting temperature sensitive points for the multiple groups of temperature data by adopting density peak clustering; step 3, establishing a GCRA-BP-AdaBoost model of the thermal error of the die bonder; and 4, obtaining a thermal error of the GCRA-BP-AdaBoost model and the prediction performance of the GCRA-BP-AdaBoost model. According to the GCRA-BP-AdaBoost prediction model, the GCRA algorithm is used for optimizing the weight and bias of the BP neural network, the weight and bias are used as weak learners of the AdaBoost algorithm, multiple groups of weak learners are constructed, the strategy is used for integrating the weak learners into a model of a strong learner, and the model can meet the requirement of thermal error compensation and has the advantages of being high in adaptability and robustness and the like.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of numerical control machine tools, and particularly relates to a die bonder thermal error modeling method based on a GCRA-BP-AdaBoost algorithm. BACKGROUND

[0002] At present, along with the rapid development of the economic level of China, the demand for semiconductors is also rising. Under the condition that the scale of semiconductor equipment in China is expanding, the domestic equipment in the market still maintains a low market share. Among these devices, the die bonder is one of the key core devices on the semiconductor chip packaging test and light emitting diode chip packaging test production line. The main working scene of the die bonder is to accurately and effectively install a small chip or crystal on a specified substrate or packaging structure, so as to realize the device for electrical connection and packaging protection. The die bonder is widely used in many fields such as semiconductor manufacturing and electronic device manufacturing. Therefore, improving the precision of the die bonder is an indispensable step on the road of technological innovation. The precision of the die bonder is affected by many different factors.

[0003] The experimental modeling method is generally used for the current thermal error problem, and the research focus is generally focused on the field of numerical control machine tools. The research on the thermal error of the die bonder is relatively insufficient. The existing model system is relatively diverse, including a multivariate linear regression model based on basic mathematical principles, and covering optimized least square algorithms and advanced modeling techniques such as support vector machines. Although domestic and foreign scholars continue to work hard to improve the limitations existing in various modeling methods, when facing machine tools with complex structures and variable working conditions, a single error model is often difficult to meet the strict demand for compensation precision in actual application. SUMMARY

[0004] The purpose of the present application is to provide a die bonder thermal error modeling method based on a GCRA-BP-AdaBoost algorithm to solve the problems raised in the background.

[0005] To achieve the above purpose, the present application provides the following technical scheme: a die bonder thermal error modeling method based on a GCRA-BP-AdaBoost algorithm, comprising the following steps:

[0006] Step 1: obtaining a plurality of groups of temperature data and corresponding thermal error data by taking the die bonder as an experimental object;

[0007] Step 2: selecting temperature sensitive points for the plurality of groups of temperature data by using density peak clustering;

[0008] Step 3: establishing a die bonder thermal error GCRA-BP-AdaBoost model;

[0009] Step four: obtain GCRA-BP-AdaBoost model thermal error and model prediction performance.

[0010] Preferably, the step one sets a starting point and an end point on the X axis of the die bonder, and a fixed travel distance is formed between the two points. When a given speed is given to the welding head of the X axis, the time of the welding head passing through the start and end points is determined as the theoretical time. When the welding head runs again, the position reached by the starting point after the theoretical time is counted is the distance from the end point, which is the geometric error. At different sensitive temperatures, the distance between the two points obtained is the positioning error. Subtracting the positioning error from the geometric error can obtain multiple thermal errors.

[0011] Preferably, the step two adopts density peak clustering analysis for the selection of temperature sensitive points. The core idea of this algorithm is to determine the clustering center by identifying the density peak point in the data point, and to assign other data points to the nearest clustering center.

[0012] The local density ρ i is defined as the abscissa, and the relative distance δ i is defined as the ordinate to obtain the decision graph, and the clustering center is selected based on ρ i and δ i .

[0013] Preferably, the step two is for the given data set X i×j ={x1;x2;x3;…;x i}, wherein x i ={x i1 ;x i2 ;x i3 ;…;x ij}, there are i data points and j data point characteristics. The DPC algorithm usually has two measurement methods when calculating the local density: truncated kernel and Gaussian kernel. Gaussian kernel is commonly used when the data volume is small.

[0014] The truncated kernel local density formula is as follows:

[0015] ρ i =∑ i≠j χ(d ij -d c ) (1)

[0016] The Gaussian kernel local density formula is as follows:

[0017]

[0018] Wherein, if x<0, χ(x)=1, otherwise if x≥0, χ(x)=0, and d ijFor data point x i and x j The distance, d c The stage distance is specified by the user;

[0019] When data x i When the local density reaches its maximum value, the relative distance is given by the following equation:

[0020] δ i =max i≠j (d ij (3)

[0021] The relative distances of the remaining data points are shown in the formula:

[0022]

[0023] Density peak clustering is achieved through local density ρ i and relative distance δ j A decision graph was drawn and used to select cluster centers. The decision graph format can more intuitively assist in selecting the cluster centers for temperature data as T7, T9, and T. 10 .

[0024] Preferably, in step three, the GCRA-BP-AdaBoost model uses the GCRA algorithm to optimize the weights and biases of the BP neural network and uses it as a weak learner for the AdaBoost algorithm. Multiple such weak learners are constructed and the strategy set is used to form a strong learner.

[0025] The optimization process of GCRA begins with the population initialization using equation (5) to randomly generate a large sugarcane rat population X, which utilizes upper and lower bounds;

[0026]

[0027] Where X represents the entire sugarcane rat population, and the individual rat (xi) at the i-th position in the j-th dimension is randomly generated using equation (6). i，j Finally, n and d represent the population size and problem dimension, respectively;

[0028] x i,j =rand×(UB) j -LB j )+LB j (6)

[0029] The random number takes a value between 0 and 1;

[0030] Within the framework of the GCRA model design, the alpha male with route memory is considered to be the fittest, or the position vector produces the best value of the objective function, given this fittest rat leader group, the positions of other rats are adjusted according to the position of the dominant male, as shown in equation (7);

[0031]

[0032] wherein represents the new position of the large cane rat, x i,j represents the current position of the large cane rat, x k,j is the dominant male in the jth dimension.

[0033] Preferably, the steps of the AdaBoost algorithm applied to the regression prediction task in step three are as follows:

[0034] (1) Initialize the data set weight, assign the same weight to each sample set in the initial data set, that is, the weight of each sample set is D(x i ) = 1 / m, wherein m is the number of samples in the initial data set;

[0035] (2) Update the weight of the weak learner, a total of T groups of weak learners, the output of each group of weak learners is represented as g t (x). Using the tth weak learner with weight, the weight of the current weak learner is calculated as follows: t

[0036]

[0037] wherein D(x i ) is the weight of the ith sample in the tth group; y i is the output of the current sample; e t is the error of the tth sample; max is the maximum value function;

[0038] (3) Update the sample weight, after training the tth weak learner, the error calculated by equation (14) can be used to adjust the weight of the entire sample set, and the sample with larger error is given larger weight, so that the t+1th weak learner focuses on these sample data;

[0039]

[0040] wherein Z t is the sum of the weights of all samples, so that the sample weight is normalized;

[0041] (4) Construct the strong learner, repeat steps (2) and (3) until all weak learners are trained; then construct the strong learner G(x) according to the weight of each weak learner, the formula is: ​

[0042]

[0043] The GCRA-BP-AdaBoost prediction model is a model in which weights and biases of a BP neural network are optimized by using a GCRA algorithm, and the GCRA-BP-AdaBoost prediction model is used as a weak learner of an AdaBoost algorithm, a plurality of weak learners are constructed, and the plurality of weak learners are integrated into a strong learner by using the strategy.

[0044] Preferably, the fourth step is specifically implemented as follows.

[0045] ① Obtain the thermal error calculated by the model;

[0046] ② Calculate the RMSE and R 2 Two numerical values are used to evaluate the prediction performance of the model.

[0047] The RMSE formula is:

[0048]

[0049] The R 2 formula is:

[0050]

[0051] Wherein, the RMSE is a root mean square error, and the R 2 is a determination coefficient.

[0052] Compared with the prior art, the present application has the beneficial effects that:

[0053] The GCRA-BP-AdaBoost prediction model is a model in which weights and biases of a BP neural network are optimized by using a GCRA algorithm, and the GCRA-BP-AdaBoost prediction model is used as a weak learner of an AdaBoost algorithm, a plurality of weak learners are constructed, and the plurality of weak learners are integrated into a strong learner by using the strategy. The model can learn the input data and predict the error of a subsequent die bonder, so as to compensate for the thermal error of the die bonder. The algorithm has good prediction performance for the thermal error of the die bonder, good applicability, and strong robustness. BRIEF DESCRIPTION OF DRAWINGS

[0054] Fig. 1 The figure is a flowchart of the embodiment method of the present application.

[0055] Fig. 2 The figure is a GCRA-BP-AdaBoost prediction model provided by the embodiment of the present application.

[0056] Fig. 3 The figure is a fitting result diagram of the GCRA-BP-AdaBoost model provided by the embodiment of the present application. DETAILED DESCRIPTION

[0057] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all the other embodiments obtained by a person of ordinary skill in the art without creative effort belong to the scope of protection of the present application.

[0058] Please refer to Figs. 1-3 The present application provides a technical solution: a die bonder thermal error modeling method based on a GCRA-BP-AdaBoost algorithm, comprising the following steps:

[0059] Step one: obtaining multiple sets of temperature data and corresponding thermal error data by taking a die bonder as an experimental object;

[0060] Step two: selecting temperature sensitive points for the multiple sets of temperature data by using density peak clustering;

[0061] Step three: establishing a die bonder thermal error GCRA-BP-AdaBoost model;

[0062] Step four: obtaining the GCRA-BP-AdaBoost model thermal error and model prediction performance.

[0063] In the step one, a starting point and an ending point are set on the X-axis of the die bonder, forming a fixed travel distance between the two points. When a given speed is assigned to the X-axis welding head, the time for the welding head to pass through the starting and ending points is determined as the theoretical time. When the welding head runs again, the position reached by the starting point after the theoretical time is elapsed is determined. The distance between this position and the ending point is the geometric error. Under different sensitive temperatures, the distance between the two points obtained is the positioning error. The multiple thermal errors can be obtained by subtracting the multiple positioning errors from the geometric error.

[0064] In the step two, the temperature sensitive points are selected by using density peak clustering analysis. The core idea of this algorithm is to determine the clustering center by identifying the density peak points in the data points, and to assign other data points to the nearest clustering center.

[0065] The local density ρ i is defined as the horizontal coordinate, and the relative distance δ i is defined as the vertical coordinate to obtain a decision graph, and the clustering center is selected based on the decision graph. Finally, the data not classified is classified based on ρ i and δ i .

[0066] In the step two, the data set X i×j ={x1;x2;x3;…;xi}, wherein x i = { x i1 ; x i2 ; x i3 ;... ; x ij}, there are i data points and j data characteristics, and the DPC algorithm usually has two measurement methods when performing local density calculation: a truncated kernel and a Gaussian kernel, and the Gaussian kernel is usually used when the data volume is small;

[0067] The local density formula of the truncated kernel is as follows:

[0068] ρ i = ∑ i≠j χ (d ij - d c ) (1)

[0069] The local density formula of the Gaussian kernel is as follows:

[0070]

[0071] wherein, if x < 0, χ (x) = 1, otherwise if x ≥ 0, χ (x) = 0, in the formula, d ij is the distance between data points x i and x j , and d c is a stage distance artificially specified;

[0072] When the local density of data x i reaches a maximum value, the relative distance is as follows:

[0073] δ i = max i≠j (d ij ) (3)

[0074] The relative distance of the remaining data points is as follows:

[0075]

[0076] Density peak clustering draws a decision graph by using the local density p i and the relative distance d j , and selects a clustering center according to the decision graph, and the form of the decision graph can more directly assist in selecting the clustering centers of the temperature data as T7, T9 and T 10 .

[0077] In the third step, the GCRA-BP-AdaBoost model optimizes the weights and biases of the BP neural network by using the GCRA algorithm, and uses the GCRA-BP-AdaBoost model as a weak learner of the AdaBoost algorithm, constructs multiple groups of such weak learners, and integrates them into a strong learner by using the strategy;

[0078] The optimization process of GCRA begins with the population initialization using equation (5) to randomly generate a large sugarcane rat population X, which utilizes upper and lower bounds;

[0079]

[0080] Where X represents the entire sugarcane rat population, and the individual rat (xi) at the i-th position in the j-th dimension is randomly generated using equation (6). i，j Finally, n and d represent the population size and problem dimension, respectively;

[0081] x i,j =rand×(UB) j -LB j )+LB j (6)

[0082] The random number takes a value between 0 and 1;

[0083] Within the framework of the GCRA model design, the alpha male with route memory is considered the most suitable, or the position vector generates the best value of the objective function. Given that this most suitable rat guides the group, the positions of other rats are adjusted according to the position of the dominant male, as shown in Equation (7).

[0084]

[0085] in Indicates the location of the new giant cane rat, x i,j Indicates the current position of the large sugarcane rat, x k,j It is the dominant male in the j-th dimension;

[0086] The exploration phase consists of two parts: one part is the iterative update of the dominant rats, and the other part is the expansion of the exploration range by the large cane rats searching for females during the mating season. The premise of the iteration of the dominant rats is that the dominant males retain information about these traces, and the other rats adjust their positions based on this data. The new position of the remaining rat population in the search space is determined according to the position of the dominant males, as shown in Equation (8).

[0087]

[0088] in x represents the value in the j-th dimension; i,j Indicates the current position of the GCR; x k,j Indicates the position of the dominant male in the j-th dimension;

[0089] In the process of GCR movement simulation, if the objective function value of another rat exceeds that of the most suitable rat, indicating that the rat is more suitable to replace the dominant male position, then the position of the remaining rats is adjusted accordingly according to the new dominant rat, if not, then the GCR movement strategy needs to be further judged by equation (9), if the objective function value plays a certain optimization effect at this new position, then GCR needs to be repositioned to this newly calculated position, if the new position cannot achieve the purpose of improvement then GCR still maintains the previous position;

[0090]

[0091] where X i represents the ith arriving GCA; C is a random number defined within the boundary of the problem space, used to simulate dispersed food sources and shelters;

[0092] The GCRA algorithm is not only affected by the foraging and behavior of GCA, but also by the rich food source r, further promoting the further expansion of the GCR movement range, see equation (10)

[0093]

[0094] α = 2 x r x rand - r (11)

[0095] β = 2 x r x μ - r (12)

[0096] where is the objective function value of the dominant male; C iter is the current iteration; Max iter is the maximum iteration; α is the coefficient of simulated food source reduction, which will force GCR to find new food sources and shelters, its definition is as shown in equation (11), β is the coefficient that promotes GCR to move to other available rich food sources in the breeding area, its definition is as shown in equation (12);

[0097] In addition to the above exploration according to the dominant rat, food source and shelter, GCR will also make corresponding exploration according to the female in the breeding season, the simulation of this stage starts with the random selection of female m, so that m≠k (dominant male), since reproduction occurs around rich food sources, exploration occurs around the selected female, the modeling of this process is shown in equation (13), if the newly calculated GCR position enhances the value of the objective function, as shown in equation (9), it replaces the previous position;

[0098]

[0099] where x m,jXi,j represents the position of random female in the jth dimension; μ is a random number with a value of 1 to 4, representing the number of offspring born by the female GCR; the parameters C, r, μ, ρ, α, β play a role in enabling the model to better iterate;

[0100] The position of the GCR is evaluated using a fitness function, and the most suitable GCR is the one whose position returns the minimum or maximum value of the fitness function. The optimization process is repeated multiple times and determined by the maximum number of iterations, except for the initial creation of the population;

[0101] In the GCRA-based BP neural network, the GCRA algorithm is used to optimize the weights and biases of the BP neural network, and then the AdaBoost algorithm is used for ensemble learning of the BP neural network to further improve the prediction performance and stability of the model.

[0102] The steps of the AdaBoost algorithm applied to the regression prediction task in step three are as follows:

[0103] (1) Initialize the data set weight, assign the same weight to each sample in the initial data set, i.e. the weight of each sample is D(x i ) = 1 / m, where m is the number of samples in the initial data set;

[0104] (2) Update the weight of the weak learner, a total of T groups of weak learners, the output of each group of weak learners is represented as g t (x). Using the tth weak learner with weight, the weight of the current weak learner α t is calculated as follows:

[0105]

[0106] where D(x i ) is the weight of the ith sample in the tth group; y i is the output of the current sample; e t is the error of the tth group of samples; max is the maximum value function;

[0107] (3) Update the sample weight, after training the tth weak learner, the error calculated by formula (14) can be used to adjust the weight of the entire sample set, and the samples with larger error are given larger weight, so that the t+1th weak learner focuses on these sample data;

[0108]

[0109] where Z t is the sum of the weights of all samples, so that the sample weight is normalized;

[0110] (4) constructing a strong learner, repeating steps (2) and (3) until all weak learners are trained, and then constructing a strong learner G(x) according to the weight of each weak learner, the formula being:

[0111]

[0112] The GCRA-BP-AdaBoost prediction model is a model in which the weights and bias of the BP neural network are optimized by using the GCRA algorithm, and the optimized weights and bias are used as weak learners of the AdaBoost algorithm, multiple groups of such weak learners are constructed, and the strategy is used to integrate the strong learners.

[0113] The specific implementation of step four is as follows:

[0114] ① Obtain the thermal error calculated by the model;

[0115] ② Calculate the RMSE and R 2 Two numerical values are used to evaluate the prediction performance of the model;

[0116] The RMSE formula is:

[0117]

[0118] The R 2 formula is:

[0119]

[0120] Wherein, RMSE is the root mean square error, R 2 is the determination coefficient.

[0121] It should be noted that in this paper, relationship terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between the entities or operations. Moreover, the term "includes", "contains" or any other variant thereof is intended to cover non-exclusive inclusion, so that the process, method, article or equipment including a series of elements not only includes those elements, but also includes other elements not explicitly listed or inherent to such process, method, article or equipment.

[0122] Although the embodiments of the present application have been shown and described, it will be understood by those of ordinary skill in the art that various changes, modifications, substitutions and variations can be made to the embodiments without departing from the principles and spirit of the present application, and the scope of the present application is defined by the appended claims and their equivalents.

Claims

1. A method for modeling thermal errors of a die bonder based on the GCRA-BP-AdaBoost algorithm, characterized in that... Includes the following steps: Step 1: Using the die bonder as the experimental object, obtain multiple sets of temperature data and corresponding thermal error data; Step 2: Use density peak clustering to select temperature-sensitive points from multiple sets of temperature data; Step 3: Establish the GCRA-BP-AdaBoost model for the thermal error of the die bonder; Step 4: Obtain the thermal error and prediction performance of the GCRA-BP-AdaBoost model.

2. The die bonder thermal error modeling method based on the GCRA-BP-AdaBoost algorithm according to claim 1, characterized in that: In step one, a starting point and an ending point are set on the X-axis of the die bonder, forming a fixed travel distance between the two points. When the X-axis welding head is given a predetermined speed, the time it takes for the welding head to pass through the starting and ending points is a fixed theoretical time. When the welding head runs again, the position reached after the theoretical time is counted from the starting point. The distance between this position and the ending point is the geometric error. Under different sensitive temperatures, the distance between these two points is the positioning error. Subtracting multiple positioning errors from geometric errors yields multiple thermal errors.

3. The die bonder thermal error modeling method based on the GCRA-BP-AdaBoost algorithm according to claim 2, characterized in that: In step two, the selection of temperature-sensitive points adopts density peak clustering analysis. The core idea of ​​this algorithm is to determine the cluster center by identifying the density peak points in the data points and assign other data points to the nearest cluster center. By defining the local density ρ i The x-axis represents the relative distance δ. i The decision graph is obtained by using ρ as the ordinate, and cluster centers are selected based on this graph. Finally, based on ρ... i and δ i Classify the data that has not been categorized.

4. The die bonder thermal error modeling method based on the GCRA-BP-AdaBoost algorithm according to claim 3, characterized in that: In step two, for the given data set X i×j ={x1;x2;x3;…;x i }, where x i ={x i1 ;x i2 ;x i3 ;…;x ij There are i data points and j data point characteristics. When performing local density calculation, the DPC algorithm usually has two metric methods: truncated kernel and Gaussian kernel. Gaussian kernel is often used when the amount of data is small. The formula for the local density of the truncated nucleus is shown in the equation: r i =∑ i≠j x(d ij -d c ) (1) The formula for the local density of the Gaussian kernel is shown in the following equation: Where, if x < 0, then χ(x) = 1; conversely, if x ≥ 0, then χ(x) = 0, where d ij For data point x i and x j The distance, d c The stage distance is specified by the user; When data x i When the local density reaches its maximum value, the relative distance is given by the following equation: d i =max i≠j (d ij ) (3) The relative distances of the remaining data points are shown in the formula: Density peak clustering is achieved through local density ρ i and relative distance δ j A decision graph was drawn and used to select cluster centers. The decision graph format can more intuitively assist in selecting the cluster centers for temperature data as T7, T9, and T. 10 .

5. The die bonder thermal error modeling method based on the GCRA-BP-AdaBoost algorithm according to claim 4, characterized in that: In step three, the GCRA-BP-AdaBoost model uses the GCRA algorithm to optimize the weights and biases of the BP neural network and uses it as a weak learner for the AdaBoost algorithm. Multiple such weak learners are constructed and the strategy set is used to form a strong learner. The optimization process of GCRA begins with the population initialization using equation (5) to randomly generate a large sugarcane rat population X, which utilizes upper and lower bounds; Where X represents the entire sugarcane rat population, and the individual rat (xi) at the i-th position in the j-th dimension is randomly generated using equation (6). i，j Finally, n and d represent the population size and problem dimension, respectively; x i,j =rand×(UB j -LB j )+LB j (6) The random number takes a value between 0 and 1; Within the framework of the GCRA model design, the alpha male with route memory is considered the most suitable, or the position vector generates the best value of the objective function. Given that this most suitable rat guides the group, the positions of other rats are adjusted according to the position of the dominant male, as shown in Equation (7). in Indicates the location of the new giant cane rat, x i,j Indicates the current position of the large sugarcane rat, x k,j It is the dominant male in the j-th dimension.

6. The die bonder thermal error modeling method based on the GCRA-BP-AdaBoost algorithm according to claim 5, characterized in that: The steps in step three when applying the AdaBoost algorithm to a regression prediction task are as follows: (1) Initialize the dataset weights by assigning the same weight to each group of samples in the initial dataset, i.e., the weight D(x) of each group of samples. i ) = 1 / m, where m is the number of samples in the initial dataset; (2) Update the weights of the weak learners. There are a total of T groups of weak learners. Represent the output of each group of weak learners as g. t (x). Using the t-th weak learner with weights, the weights α of the current weak learner are... t The calculation formula is: Where D(x) i ) represents the weight of the i-th sample in group t; y i The output for the current sample; e t Let be the error of t groups of samples; max is the function to find the maximum value. (3) Update the sample weights. After training the t-th weak learner, the error calculated by equation (14) can be used to adjust the weights of the entire sample set. For samples with larger errors, larger weights are assigned so that the (t+1)-th weak learner can focus on these sample data. Among them, Z t The sum of the weights of all samples is used to normalize the sample weights. (4) Construct a strong learner, repeating steps (2) and (3) until all weak learners are trained; then construct a strong learner G(x) based on the weights of each weak learner, using the formula: The GCRA-BP-AdaBoost prediction model utilizes the GCRA algorithm to optimize the weights and biases of a BP neural network, and uses it as a weak learner for the AdaBoost algorithm. Multiple such weak learners are constructed and combined using this strategy to form a strong learner model.

7. The die bonder thermal error modeling method based on the GCRA-BP-AdaBoost algorithm according to claim 6, characterized in that: The specific implementation details of step four are as follows; ① Obtain the thermal error calculated by the model; ②Through RMSE and R 2 Two numerical values ​​are used to evaluate the overall predictive performance of the model; The RMSE formula is: R 2 The formula is: Where RMSE is the root mean square error, R 2 The coefficient of determination.

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