Manufacturing quality adaptive control method considering data uncertainty and fuzziness
By combining fuzzy weak dataset pre-detection and tracking algorithms with feature element acquisition algorithms, and using PSNN networks and TEWMA control charts, the problem of traditional methods being insensitive to small quality characteristic drifts during the manufacturing process is solved. This enables early warning and autonomous feedback, improving the sensitivity and stability of the manufacturing process.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- UNIV OF ELECTRONICS SCI & TECH OF CHINA
- Filing Date
- 2022-11-28
- Publication Date
- 2026-07-21
AI Technical Summary
Existing technologies struggle to effectively detect small-scale quality characteristic drifts in weak data during the manufacturing process. Traditional control charts have delayed and insensitive alarm times, and existing models perform poorly when dealing with data ambiguity, requiring long training times.
By combining fuzzy weak dataset pre-detection and tracking algorithms with feature element acquisition algorithms, a manufacturing quality adaptive control method is constructed using a PSNN network. By combining the FWDS-PSNN prediction model with the TEWMA control chart, early detection and autonomous feedback adjustment of small quality characteristic drifts are achieved.
It enables early warning of minor quality characteristic drifts during the manufacturing process, shortens model training time, improves the ability to process fuzzy and weak data, and enhances the sensitivity and stability of the manufacturing process.
Smart Images

Figure CN115860533B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of manufacturing process quality control, and specifically relates to an adaptive control method for manufacturing quality that takes into account data uncertainty and fuzziness. Background Technology
[0002] Due to both systemic and accidental factors, most quality indicators in the manufacturing process are always fluctuating. To assess whether quality indicators are up to standard, statistical data can be used to evaluate whether data fluctuations exhibit patterns or anomalies, thereby enabling quality control and process improvement in the manufacturing process. With societal development, the manufacturing industry faces increasingly stringent and complex manufacturing requirements and standards, with a lower tolerance for inconsistent product quality, urgently requiring more sensitive data prediction and control methods. Since manufacturing quality deterioration is often an uncertain evolutionary process, process data exhibits various uncertainties and ambiguities, posing challenges to data statistical prediction. This is particularly true for the weakened data characteristics exhibited by a few key quality features, making it extremely difficult to discover their fluctuation patterns. Therefore, establishing weak data prediction models can help to anticipate potential trends in quality indicators, allowing for early prevention of quality defects and ensuring quality stability.
[0003] With societal development, the manufacturing industry faces increasingly stringent and complex manufacturing requirements and standards. Standardized manufacturing processes have a lower tolerance for inconsistent product quality, necessitating the examination of weak data related to key quality characteristics in the manufacturing process. Common weak data include the dimensions of precision parts in machining, the assembly tolerances of precision equipment, and minor deformations of parts during welding and heat treatment.
[0004] Control charts used in manufacturing process control to analyze data fluctuation patterns, such as traditional Shewhart control charts, CUSUM control charts, and EWMA control charts, are all univariate control charts. Most of them can only detect large and medium-sized quality fluctuations, and are not sensitive to small-scale quality characteristic drifts with weak data. Furthermore, due to the statistical nature of control charts, they often only provide warnings after process quality has runaway, or even after a considerable period of time. For predicting quality characteristic data, most regression algorithms are applicable, such as Bayesian networks, random forests, LGBM (Light Gradient Boost Machine), multilayer perceptrons, RNNs (Recurrent Neural Networks), and deep neural networks. These are widely used models, but they are not very effective at handling data ambiguity, and achieving good results requires a long training time. Summary of the Invention
[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a manufacturing quality adaptive control method that can effectively analyze the trend of quality characteristic changes, detect whether there is weak data and small quality characteristic drift, issue early warnings, and autonomously adjust the manufacturing process considering data uncertainty and fuzziness.
[0006] The objective of this invention is achieved through the following technical solution: an adaptive control method for manufacturing quality considering data uncertainty and fuzziness, comprising the following steps:
[0007] S1. Construct a fuzzy weak data prediction model for manufacturing quality characteristics, which includes the following steps:
[0008] S11. Establish a fuzzy weak data pre-detection and tracking algorithm to obtain the discovery domain, number of intervals, interval length, and proportional trend change value of the fuzzy weak data set of quality characteristics.
[0009] S12. Obtain feature elements of the fuzzy weak dataset of quality characteristics;
[0010] S13. Use principal component analysis to reduce the dimensionality of elements in the fuzzy weak dataset of quality characteristics.
[0011] S14. Combine the elements of the fuzzy weak dataset of quality characteristics after dimensionality reduction with the proportional trend change values of the standardized weak dataset of quality characteristics into a vector, and input it into the PSNN network.
[0012] S2. Establish an adaptive early warning method for small drifts in manufacturing quality data.
[0013] The beneficial effects of this invention are as follows: Addressing the problems of delayed alarm times and insensitivity to minor quality characteristic drifts in traditional control charts, this invention proposes a manufacturing process quality control method combining the FWDS-PSNN prediction model with TEWMA control charts. This method can effectively analyze quality characteristic change trends, detect weak data and minor quality characteristic drifts, issue early warnings, and autonomously adjust the manufacturing process based on feedback. Furthermore, thanks to the combination of fuzzy weak data set pre-detection and tracking algorithms, feature element acquisition algorithms, and PSNN, this method can effectively handle fuzzy weak data and shorten model training time. Attached Figure Description
[0014] Figure 1 This is a flowchart of the manufacturing quality adaptive control method of the present invention;
[0015] Figure 2 Construct a graph for the PSNN input vectors;
[0016] Figure 3 Design diagram of PSNN network structure;
[0017] Figure 4This is a graph showing the overall mean change of the data in this embodiment;
[0018] Figure 5 This is the sample data for this embodiment;
[0019] Figure 6 A comparison chart of predicted and actual data;
[0020] Figure 7 This is a graph showing the forecast of the mean.
[0021] Figure 8 This is the original TEWMA control chart;
[0022] Figure 9 A TEWMA control chart using predicted values. Detailed Implementation
[0023] This invention discusses the cutting process of a certain intelligent CNC machine tool. With the rapid development and widespread application of precision and ultra-precision manufacturing technologies, the accuracy requirements of CNC technology are constantly increasing. Among these requirements, thermal error has the greatest impact on the positioning error of CNC machine tools. Related research shows that the adverse effects caused by thermal error account for 50% to 75% of the total error, significantly affecting machining accuracy and stability. The mutual friction between various moving pairs in the CNC machine tool transmission system causes the surface temperature of machine tool components to rise. Currently, thermal error compensation is a popular method to improve the positioning accuracy of machine tools. This method uses control software to generate human error to offset thermal error, effectively improving the operating accuracy of CNC machine tools. In a certain thermal compensation control algorithm, the lead screw is divided into several segments, and the thermal deformation of each segment is monitored in real time. The degree of thermal deformation of each segment is measured, and then compensation parameters are calculated. In this process, the degree of thermal deformation of each segment of the lead screw is quite weak, belonging to the weak dataset of key quality characteristics in the manufacturing process discussed in this invention. In this invention, the input data is y = [y1, y2, ..., y...]. n ] T This represents a vector of thermal deformation data obtained by measuring the change of a certain section of the lead screw over time, t=[t1,t2,...,t n ] T This is the measurement time vector.
[0024] This invention proposes a manufacturing quality control method that combines a fuzzy weak dataset (FWDS) prediction model with a TEWMA control chart. The fuzzy weak dataset is calculated using membership probabilities and fuzzy weak data feature elements, thus effectively describing both statistical and non-statistical uncertainties in the data. The data is processed using a fuzzy weak dataset pre-detection and tracking algorithm and a feature element acquisition algorithm. A high-learning-rate PSNN (Pi-Sigma neural network) is used to construct fuzzy logical relationships for high-order time series prediction of the weak data. The predicted data is then used at regular intervals to construct a TEWMA (Triple Exponentially Weighted Moving Average) control chart, which accelerates the verification of potential small-scale quality characteristic drifts in the data and provides early quality warnings. The technical solution of this invention is further illustrated below with reference to the accompanying drawings.
[0025] like Figure 1 As shown, the adaptive manufacturing quality control method of the present invention, which considers data uncertainty and fuzziness, includes the following steps:
[0026] S1. Construct a fuzzy weak data prediction model for manufacturing quality characteristics, which includes the following steps:
[0027] S11. Establish a fuzzy weak data pre-detection and tracking algorithm to obtain the discovery domain (UOD), number of intervals (NOI), length of intervals (LOI), and ratio trend variation (RTV) of the fuzzy weak dataset with quality characteristics.
[0028] The Pre-inspection and Tracking Algorithm (PTA) takes a time-series data vector and an observation time vector as input, and outputs the trend set T of the dataset, the set of proportional trend changes V, the discovery domain UOD of the fuzzy weak data set, the number of intervals NOI, and the interval length LOI. Specifically, it includes the following sub-steps:
[0029] S111. Calculate the trend set cardinality b0 and the change factor b1 of the weak dataset:
[0030]
[0031] In the formula, y = [y1, y2, ..., y n ] TThis is a time series data vector of key quality characteristics in the manufacturing process, t = [t1, t2, ..., t]. n ] T The observation time vector for key quality characteristics in the manufacturing process;
[0032] S112. Calculate the trend set T of the weak dataset:
[0033] T = b0 + b1t = [T1, T2, ..., T n ] T (2);
[0034] S113. Calculate the set V of proportional trend changes in the weak dataset:
[0035]
[0036] Sort the elements of set V in ascending order and remove duplicate values to get a new set, denoted as V:
[0037] V = [V1, V2, ..., V m ] T V1<V2,V2<V3,...,V m-1 <V m (4)
[0038] Obtain the median Md(V) of the permuted set;
[0039] S114. Establish two subsets A and B of V, where A is the set of smaller values and B is the set of larger values, and the number of elements in both sets is k:
[0040]
[0041] S115. Calculate the set of absolute values of the first-order differences of two subsets A and B. diff B diff :
[0042]
[0043] S116, Calculate A diff B diff The mid-range numbers AD and BD:
[0044]
[0045] S117. Determine the decision factor D for interval partitioning. f :
[0046]
[0047] S118. Calculate the discovery domain UOD of the weak dataset, where UL and UR are the left and right bounds of the universe of discourse, respectively:
[0048]
[0049] S119. Calculate the number of intervals (NOI) and the interval length (LOI) of the weak dataset:
[0050]
[0051] In the formula, α is the interval scaling factor, and n is the data length.
[0052] S12. After obtaining the discovery domain and interval number of the fuzzy weak dataset of quality characteristics, the feature elements of the fuzzy weak dataset of quality characteristics are obtained. The input of the feature element acquisition algorithm (FEAA) is the time series data vector y, the set of proportional trend change values V, the discovery domain UOD of the time series fuzzy weak dataset, the interval number NOI, and the interval length LOI. The output is the fuzzy weak data feature set elements FWDS. ij Specifically, it includes the following sub-steps:
[0053] S121. Divide UOD into sub-intervals u based on NOI and LOI. j =[ul j ,ur j ],j=1,2,...,NOI, whereul j Let ur be the left endpoint of the j-th interval. j Let j be the right endpoint of the j-th interval; denote the fuzzy weak data set of each interval as .
[0054] S122. Calculate the trapezoidal membership function f for each interval. Aij :
[0055]
[0056] Where i = 1, 2, ..., n, j = 1, 2, ..., NOI; X is the original data, i.e., the time series data vector y = [y1, y2, ..., y1]. n ] T Any element in;
[0057] S123. Calculate the membership value of the i-th element in set V belonging to the j-th interval using the trapezoidal membership function of formula (11), denoted as [formula missing].
[0058] S124. Calculate the probability of each membership value.
[0059]
[0060] In the formula, L, m i σ is located in the fuzzy set The membership values, interval widths, mean, and standard deviations of all fuzzy numbers within the trapezoidal fuzzy function;
[0061] S125. Calculate the affirmativeness (Ime) of the intuitionistic fuzzy elements of set V. ij And hesitation level Inme ij :
[0062]
[0063] Let be the minimum membership value of all elements belonging to interval j. The maximum membership value for all elements belonging to interval j;
[0064] S126. Calculate the determination APIme based on weak data probabilities. ij And uncertainty based on weak data probability APInme ij :
[0065]
[0066] S127. Calculate the elements of the fuzzy weak dataset FWDS. ij :
[0067]
[0068] S13. After obtaining the elements of the fuzzy weak data set of quality characteristics, the dimensionality of the elements may be large due to the large number of fuzzy weak data intervals. Principal component analysis is used here to reduce the dimensionality of the elements in the fuzzy weak data set of quality characteristics. The specific implementation method of step S13 is as follows: Assume that there are m quality characteristic samples in the dataset X, and the elements of the fuzzy weak data set of each sample are n-dimensional vectors:
[0069]
[0070] Let X represent the set of all real numbers. ij It is a real number;
[0071] The covariance matrix of X is:
[0072]
[0073] E() represents the expectation;
[0074] To obtain principal components, we calculate eigenvectors λ and eigenvalues u, which must satisfy Cu = λu and ||u|| = 1. We then use Xu as the new principal component, where λ / ∑λi ×100% variance information (variance information refers to the information of the covariance matrix, λ / ∑λ) i ×100% variance information corresponds to λ / ∑λ i The eigenvectors (100% of the original vectors) were preserved.
[0075] S14. The trend change value of the ratio between the elements of the fuzzy weak data set of quality characteristics after dimensionality reduction and the standardized weak data set of quality characteristics [V′1,V′2,...,V′] n ] T (Standardization refers to subtracting the mean of a set of numbers from the set of numbers and then dividing by the standard deviation of the set of numbers, which can be expressed by the formula:) (This is a commonly used data processing method) The data is combined into vectors and input into the PSNN network; for example... Figure 2 As shown, the dashed box on the right contains the elements of the FWDS matrix after principal component analysis (step S13). The elements of the FWDS matrix are accumulated, and the resulting vector is calculated by the softmax function and then combined with the RTV value to form a vector.
[0076] The Softmax function is shown below:
[0077]
[0078] This is a commonly used function, where X is a vector, x i These are elements in a vector; the variables themselves have no specific meaning. The prediction order refers to the order of prediction when predicting the next value based on the previous n values; the prediction order is n.
[0079] The PSNN network will be designed with a variant structure that separately inputs the raw quality characteristic weak data and the standardized quality feature vector into the network. Its structure is as follows: Figure 3 As shown. The sliding window segmentation method is used to segment the standardized quality characteristic weak data in the input vector into proportional trend values [V′1,V′2,...,V′]. n ] T Separate the FWDS values and input them into two independent fully connected layers. Figure 3 The calculation is performed in Sigma Layer 1 and Sigma Layer 2 of the fully connected layer. The activation function of the fully connected layer is tanh, and its formula is as follows:
[0080]
[0081] The outputs of the two fully connected layers are then combined into a multiplication node for multiplication calculation. The activation function of the node is also tanh. The result after passing through the activation function is the network output.
[0082] The predicted value is obtained after deblurring.
[0083]
[0084] Where output is the output of the PSNN network, and Trend is the proportional trend change value of the corresponding index;
[0085] The PSNN network parameters are optimized using the particle swarm optimization algorithm, and the optimization process is as follows:
[0086] S141. Determine the algorithm's hyperparameters, including the number of iterations (epoch), the number of particles (n), and the absolute velocity of the particles (v). m Variable boundary X a and X b Self-learning factor c1 and social learning factor c2, where the self-learning factor points to the degree of tendency towards the self-optimal solution, and the social learning factor points to the degree of tendency towards the global optimal solution; inertia coefficient w;
[0087] S142. Initialize the particle position x and velocity v, where X a <x<X b -v m <x<v m ;
[0088] S143. Convert particle positions into network parameters, predict results and compare them with the target, using RMSE as the evaluation function, as shown in the following formula:
[0089]
[0090] prediction i and target i These refer to the predicted and actual values of the i-th parameter, respectively.
[0091] S144, Update the velocity and position of each particle:
[0092]
[0093] Where Pbest and Gbest are the historical best solutions for each particle and all particles, respectively; r follows a uniform distribution from 0 to 1, i.e., r ~ U(0,1); if the values of velocity and position exceed the constraint values, the corresponding constraint values are taken (if they are greater than the upper limit, the upper limit is taken; if they are less than the lower limit, the lower limit is taken).
[0094] S145. Determine if the number of iterations (epoch) has been reached. If yes, end the operation; otherwise, return to S143.
[0095] S2. Establish an adaptive early warning method for small drifts in manufacturing quality weak data; the specific implementation method is: to construct a TEWMA control chart by taking the predicted data at certain intervals;
[0096] Definition of a triple exponentially weighted moving average based on current and past observations of weak-quality data:
[0097]
[0098] Among them, Y t Z t W t μ0 and μ0 are the values of the single-fold exponentially weighted moving average, double-fold exponentially weighted moving average, triple-fold exponentially weighted moving average, and the control chart midline, respectively; λ is the smoothing parameter; W t The expected value and variance are:
[0099]
[0100] For the constructed TEWMA, its control limit UCL t / LCL t for:
[0101]
[0102] UCL t LCL t These are the upper and lower control lines at time t, respectively; CL refers to the value of the middle line of the control chart; UCL t LCL t Specifically, it means a line that data will almost never cross under the same probability distribution; CL refers to the expected data value, which is the UCL. t LCL t The line of symmetry; L is the width of the control limits. When t is large, the variance is stable, and the control limits tend to the asymptote:
[0103]
[0104] If the point W is drawn t If the control limit is not exceeded, the process quality is considered to be in-control (IC); otherwise, the process quality is considered to be out-of-control (OOC), and μ0 drifts.
[0105] The effectiveness of the present invention will be further verified through experiments below.
[0106] A case study using simulation data was conducted. A quality characteristic data sample size of 200 was used, with each sample drawn from a population with a uniformly shifted mean. Sample 1 followed a distribution N(0,1), and sample 200 followed a distribution N(0.1,1). Process control was implemented. Under normal circumstances, the quality characteristic data followed N(0,1). When the mean deviated from the target value by 0.05, the process quality was considered out of control. That is, the data for samples 1 to 100 were collected under controlled process quality conditions, while the data for samples 101 to 200 were collected when the process quality was out of control. The data situation is as follows... Figure 4 As shown, the original data is as follows Figure 5 As shown.
[0107] By using the fuzzy weak dataset + PSNN prediction method of this invention, the mean characteristics of the dataset are grasped. The first 100 samples are used as the training set, and the last 100 samples are used as the test set. The PSNN model has an order of 2, meaning that the actual values of the first two steps are used to predict the possible values of the next step. The prediction results are as follows: Figure 6 As shown in the figure, Target represents the target data and Prediction represents the predicted data.
[0108] Table 1 shows a comparison of the prediction performance of the fuzzy weak dataset + PSNN prediction of the present invention and the traditional fuzzy weak dataset + SVR.
[0109] Table 1
[0110] RMSE 1.3414 2.0928
[0111] In the table, RMSE stands for Root Mean Square Error, calculated using the following formula:
[0112]
[0113] Simultaneously, the predictive model's grasp of the mean was examined. The mean was calculated and compared with the actual value, grouped into sets of 10 values. The results are as follows: Figure 7 As shown, the FWDS-PSNN method has a good effect on controlling the mean.
[0114] The TEWMA chart drawn from the raw data is as follows: Figure 8 As shown (taking L = 1.886, λ = 0.05), it can be seen that the process quality was out of control when the 183rd sample point was collected.
[0115] To expedite the assessment of the likelihood of quality runaway, and since only mean information is monitored here, batch predictions can be performed each time a new sample is obtained. Five steps constitute one prediction batch, and W is calculated using the last predicted value from each batch and the actual value. t Values, and plot control charts, such as Figure 9As shown in the diagram, the control chart drawn in this way indicates that the process quality is out of control at the 180th sample point, while in reality, this prediction was made when the 175th sample was collected. Therefore, a warning could be issued when the 175th sample was collected.
[0116] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.
Claims
1. A manufacturing quality adaptive control method considering data uncertainty and fuzziness, characterized in that, Includes the following steps: S1. Construct a fuzzy weak data prediction model for manufacturing quality characteristics, which includes the following steps: S11. Establish a fuzzy weak data pre-detection and tracking algorithm to obtain the discovery domain, number of intervals, interval length, and proportional trend change value of the fuzzy weak data set of quality characteristics; fuzzy weak data set of quality characteristics This represents a vector of thermal deformation data obtained by measuring the change over time of a certain section of the lead screw; S12. Obtain feature elements of the fuzzy weak dataset of quality characteristics; S13. Use principal component analysis to reduce the dimensionality of elements in the fuzzy weak dataset of quality characteristics. S14. Combine the elements of the fuzzy weak dataset of quality characteristics after dimensionality reduction with the proportional trend change values of the standardized weak dataset of quality characteristics into a vector, and input it into the PSNN network. S2. Establish an adaptive early warning method for small drifts in manufacturing quality weak data; the specific implementation method is: to construct a TEWMA control chart by taking the predicted data at certain intervals; Definition of a triple exponentially weighted moving average based on current and past observations of weak-quality data: (20); in, , , , These are the values of the single-level exponentially weighted moving average, the double-level exponentially weighted moving average, the triple-level exponentially weighted moving average, and the control chart's middle line. For smoothing parameters; The expected value and variance are: (21); For the constructed TEWMA, its control limits for: (22); These are the upper control line and the lower control line at time t, respectively. This refers to the value of the middle line of the control chart; L is the width of the control limits. When t is large, the variance is stable, and the control limits tend to the asymptote. (23); If the points are drawn If the control limits are not exceeded, the process quality is considered to be under control; otherwise, the process quality is considered to be out of control. Drifting occurred.
2. The manufacturing quality adaptive control method considering data uncertainty and fuzziness according to claim 1, characterized in that, Step S11 specifically includes the following sub-steps: S111, Calculate the trend set cardinality of the weak dataset. and change ratio : (1); In the formula, , The observation time vector for key quality characteristics in the manufacturing process; S112. Calculate the trend set T of the weak dataset: (2); S113. Calculate the set V of proportional trend changes in the weak dataset: (3); Sort the elements of set V in ascending order and remove duplicate values to obtain a new set denoted as V. : (4); Get the median of the permuted set ; S114, Establish Given two subsets A and B, where A is the set of smaller values and B is the set of larger values, and the number of elements in both sets is k: (5); S115. Calculate the set of absolute values of the first-order differences between two subsets A and B. , : (6); S116, Calculation , The mid-range numbers AD and BD: (7); S117. Determine the decision factor D for interval partitioning. f : (8); S118. Calculate the discovery domain UOD of the weak dataset, where UL and UR are the left and right bounds of the universe of discourse, respectively: (9); S119. Calculate the number of intervals (NOI) and the interval length (LOI) of the weak dataset: (10); In the formula It is the interval scaling factor, and n is the data length.
3. The adaptive manufacturing quality control method considering data uncertainty and fuzziness according to claim 2, characterized in that, Step S12 includes the following sub-steps: S121. Divide UOD into smaller intervals based on NOI and LOI. ,in Let j be the left endpoint of the j-th interval. Let j be the right endpoint of the j-th interval; denote the fuzzy weak data set of each interval as . ; S122. Calculate the trapezoidal membership function for each interval. : (11); in, ; The original data, i.e., the thermal deformation data vector. Any element in; S123. Calculate the membership value of the i-th element in set V belonging to the j-th interval using the trapezoidal membership function of formula (11), denoted as [formula missing]. ; S124. Calculate the probability of each membership value. : (12); In the formula, For located in fuzzy set The membership values, interval widths, mean, and standard deviations of all fuzzy numbers within the trapezoidal fuzzy function; S125. Calculate the affirmativeness of the intuitive fuzzy elements of set V. and hesitation : (13); Let be the minimum membership value of all elements belonging to interval j. The maximum membership value for all elements belonging to interval j; S126. Calculate the degree of certainty based on weak data probabilities. and uncertainty based on weak data probability : (14); S127, Calculate elements of fuzzy weak dataset : (15)。 4. The manufacturing quality adaptive control method considering data uncertainty and fuzziness according to claim 1, characterized in that, The specific implementation method of step S13 is as follows: Assume that there are m quality characteristic samples in the dataset X, and the data length n of the fuzzy weak dataset for each sample is: (16); Denotes the set of all real numbers, i.e. It is a real number; The covariance matrix of X is: (17); This indicates a demand for expectation; Calculate eigenvectors To obtain principal components using eigenvalues u, they need to satisfy... , Xu is taken as the new principal component, where The variance information was retained.
5. The adaptive manufacturing quality control method considering data uncertainty and fuzziness according to claim 1, characterized in that, The PSNN network separates the standardized proportional trend change value and FWDS value of weak quality characteristics in the input vector and inputs them into two independent fully connected layers respectively. The outputs of the two fully connected layers are then combined into a multiplication node for multiplication calculation. The activation function of the node is tanh. The result after passing through the activation function is the network output. Then, after deblurring, the predicted value is obtained. : ; Where output is the output of the PSNN network, and Trend is the proportional trend change value of the corresponding index; The PSNN network parameters are optimized using the particle swarm optimization algorithm. The optimization process is as follows: S141. Determine the algorithm's hyperparameters, including the number of iterations (epoch), the number of particles (d), and the absolute velocity of the particles. Variable boundaries and Self-learning factor Social learning factors Among them, the self-learning factor points to the degree of tendency towards the self-optimal solution, the social learning factor points to the degree of tendency towards the global optimal solution; the inertia coefficient w; S142. Initialize the particle position x and velocity v, where , ; S143. Convert particle positions into network parameters, predict results and compare them with the target, using RMSE as the evaluation function, as shown in the following formula: (18); and These refer to the predicted and actual values of the i-th parameter, respectively. S144, Update the velocity and position of each particle: (19); in, and These are the historical optimal solutions for each particle and all particles, respectively; r follows a uniform distribution from 0 to 1, i.e. If the values of velocity and position exceed the constraint values, then the corresponding constraint values will be used. S145. Determine if the number of iterations (epoch) has been reached. If yes, end the operation; otherwise, return to S143.