Method and device for preprocessing industrially generated data containing high-dimensional noise

Abstract

The invention discloses a method and a device for preprocessing industrial generated data containing high-dimensional noise, and relates to the field of data preprocessing, and the method comprises the following steps: outputting a sampling time point set and a multi-dimensional observation data set by collecting multi-dimensional function type observation data in a set time interval; and representing the real function of each dimension observation value as a primary function linear combination, extracting effective features, and outputting a primary function set and an expansion coefficient. And constructing a design matrix, and establishing association between the multi-dimensional observation data and the effective features. A combined objective function is constructed by combining multivariable synchronous processing requirements and signal importance differences, and a penalty matrix is constructed through an inner product of a second derivative of a primary function. And selecting a smoothing parameter by minimizing a generalized cross validation criterion, solving a target function to obtain an estimation expansion coefficient, and constructing and outputting a smoothing function as input data of a statistical process control or fault diagnosis model. The method solves the problems that in the prior art, effective features are prone to being lost, multi-dimensional collaboration is not considered, and smooth parameter selection lacks self-adaption.

Description

Technical Field

[0001] This invention relates to the field of data preprocessing technology, and specifically to a method and apparatus for preprocessing industrial generated data containing high-dimensional noise. Background Technology

[0002] Against the backdrop of the deep integration of intelligent manufacturing and the Industrial Internet, multidimensional functional data collected by multiple sensors in industrial production processes has become the core data support for achieving statistical process control, fault diagnosis, and quality optimization. Existing technologies for preprocessing noisy industrial data have been widely applied in various production scenarios, with three main technical paths: first, noise suppression methods based on traditional filtering, such as Kalman filtering and wavelet threshold filtering, which remove noise by filtering signal frequency or amplitude; second, feature extraction methods based on dimensionality reduction, such as Principal Component Analysis (PCA) and Locally Linear Embedding (LLE), which retain key information through dimensionality compression; and third, smoothing methods based on functional modeling, which represent the real function as a linear combination of basis functions such as B-splines and Fourier transforms to achieve data smoothing and feature characterization. Among these, basis function expansion is increasingly widely used in processing dynamic time-series industrial data because it can preserve the temporal continuity of the data.

[0003] Although existing preprocessing methods have been applied to some extent in the industrial field, many problems still need to be solved when dealing with functional data containing high-dimensional noise. On the one hand, existing methods mostly adopt a separate strategy of "denoising first and then feature extraction," which easily leads to the filtering out of effective features along with the noise. Especially in high-noise scenarios, the completeness and accuracy of feature extraction are difficult to guarantee. On the other hand, most methods lack consideration for the synergy of multi-dimensional signals, adopting a single-dimensional independent processing mode, which cannot adapt to the synchronous processing requirements of multi-variable industrial scenarios. Moreover, they do not take into account the differences in the importance of each dimension of the signal for targeted processing, resulting in preprocessing results that cannot fully reflect the production status. In addition, the selection of smoothing parameters mostly relies on empirical settings and lacks an adaptive optimization mechanism. It is difficult to balance the function fitting accuracy and smoothness, and problems such as over-smoothing that loses features or under-smoothing that leaves residual noise are prone to occur, which in turn affect the accuracy of subsequent statistical process control and fault diagnosis.

[0004] Therefore, there is an urgent need for a preprocessing method for industrial generated data containing high-dimensional noise to solve the problems of easy loss of effective features, lack of consideration for multi-dimensional synergy, and lack of adaptive selection of smoothing parameters in existing technologies. Summary of the Invention

[0005] To address this, the present invention provides a method and apparatus for preprocessing industrial generated data containing high-dimensional noise, which solves problems such as easy loss of effective features, lack of consideration of multi-dimensional synergy, and lack of adaptive selection of smoothing parameters in the preprocessing of industrial multidimensional functional data containing high-dimensional noise, thereby improving the accuracy of subsequent analysis.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for preprocessing industrial generated data containing high-dimensional noise, characterized in that it includes:

[0007] Within a single cycle of industrial production, by collecting multidimensional functional observation data defined within a set time interval, the set of sampling time points and the set of multidimensional observation data are output.

[0008] The true function of each dimension observation value in the multidimensional observation dataset is represented as a linear combination of several basis functions; by performing basis function screening and expansion coefficient quantization, effective features are extracted, and the basis function set and basis function expansion coefficients are output.

[0009] Based on the set of sampling time points and the set of basis functions, a design matrix is ​​constructed according to the mapping rules between discrete observations and basis functions; the design matrix is ​​used to establish the correlation between the multidimensional observation data set and the effective features.

[0010] Based on the design matrix, and considering the requirements for multivariate synchronous processing and the differences in the importance of signals in each dimension, a joint objective function is constructed.

[0011] A penalty matrix is ​​constructed based on the inner product of the second derivatives of the basis functions; the degree of curvature of the function is quantified and penalized using the penalty matrix.

[0012] Based on the joint objective function, a smoothing parameter is selected by minimizing the generalized cross-validation criterion; the smoothing parameter is used to balance the function fitting accuracy and smoothness.

[0013] Based on the smoothing parameters, the joint objective function is solved to obtain the estimated expansion coefficients of the basis functions; based on the estimated expansion coefficients and combined with the linear combination form of the basis functions, a smoothing function is constructed.

[0014] The smoothing function is output and used as input data for subsequent statistical process control or fault diagnosis models.

[0015] As a preferred scheme for industrial generated data preprocessing with high-dimensional noise, the observed value of each dimension in the multidimensional observation dataset is formed by superimposing the true function value at the corresponding time point with a random error term; the random error term satisfies the condition that the mean is zero and that they are independently and identically distributed.

[0016] The expression for the observed value is:

[0017]

[0018] In the formula, The observation value of the i-th dimension at the j-th sampling time point; This represents the actual function value at the corresponding time point; It is a random error term, and it satisfies the conditions that its mean is zero and that it is independently and identically distributed.

[0019] As a preferred embodiment of a preprocessing method for industrial generated data containing high-dimensional noise, the true function is represented as a linear combination of basis functions as follows:

[0020]

[0021] In the formula, For the actual function; Let m be the basis function; where are the expansion coefficients of the corresponding basis functions; K is the number of basis functions.

[0022] As a preferred method for preprocessing industrial generated data containing high-dimensional noise, in the process of constructing the design matrix according to the mapping rules between discrete observations and basis functions, the expression of the design matrix is:

[0023]

[0024] In the formula, n is the number of sampling time points; K is the number of basis functions;

[0025] The expression for the matrix elements of the design matrix is:

[0026]

[0027] In the formula, For the j-th sampling time point; Let be the function value of the i-th basis function at the j-th sampling time point.

[0028] As a preferred embodiment of a preprocessing method for industrial generated data containing high-dimensional noise, the expression for the joint objective function is:

[0029]

[0030] In the formula, This is the expansion coefficient vector of the basis functions in each dimension; This represents the number of basis functions for the corresponding dimension. , For observation data vectors in each dimension; , Design matrices for each dimension; It is a positive definite symmetric weight matrix; For smoothing parameters; For the penalty matrix; Let be the expansion coefficient vector of the basis functions in the k-th dimension.

[0031] As a preferred embodiment of a preprocessing method for industrial generated data containing high-dimensional noise, the expression for the penalty matrix is:

[0032]

[0033] In the formula, For the penalty matrix; , These are the second derivatives of the i-th and j-th basis functions, respectively.

[0034] The expression for the generalized cross-validation criterion is:

[0035]

[0036] In the formula, This is the original observation data vector of the k-th dimension; Let k be the fitted data vector of the k-th dimension; Let be the smoothing parameter for the k-th dimension; Let k be the amount of observation data in the k-th dimension; df represents the sum of squared residuals between the original observed data and the fitted data in the k-th dimension; df represents the effective degrees of freedom of the model.

[0037] As a preferred embodiment of a preprocessing method for industrial generated data containing high-dimensional noise, the expression for the smoothing function is:

[0038]

[0039] In the formula, Let be the smoothing function for the k-th dimension; k is the dimension index; t is the continuous time variable within the specified time interval. is the number of basis functions in the k-th dimension; m is the index of the basis function. These are the estimated expansion coefficients of the m-th basis function in the k-th dimension; Let m be the basis function of the k-th dimension.

[0040] This invention also provides a preprocessing apparatus for industrial generated data containing high-dimensional noise, employing the above-mentioned preprocessing method for industrial generated data containing high-dimensional noise, comprising:

[0041] The multidimensional functional observation data acquisition module is used to collect multidimensional functional observation data defined within a set time interval during a single cycle of industrial production, and output a set of sampling time points and a set of multidimensional observation data.

[0042] The effective feature extraction and basis function processing module is used to represent the true function of each dimension observation value in the multidimensional observation data set as a linear combination of several basis functions; by performing basis function screening and expansion coefficient quantization, effective features are extracted, and the basis function set and basis function expansion coefficients are output.

[0043] The design matrix construction and processing module is used to construct a design matrix based on the set of sampling time points and the set of basis functions, according to the mapping rules between discrete observations and basis functions; and to establish the correlation between the multidimensional observation data set and the effective features through the design matrix.

[0044] The joint objective function construction module is used to construct a joint objective function based on the design matrix, combined with the requirements for multivariate synchronous processing and the differences in the importance of signals in each dimension;

[0045] The penalty matrix construction module is used to construct a penalty matrix based on the inner product of the second derivatives of the basis functions; the penalty matrix is ​​used to quantify the degree of curvature of the function and impose penalties.

[0046] The smoothing parameter selection and processing module is used to select smoothing parameters based on the joint objective function by minimizing the generalized cross-validation criterion; and to balance the function fitting accuracy and smoothness through the smoothing parameters.

[0047] The smoothing function construction module is used to solve the joint objective function based on the smoothing parameters to obtain the estimated expansion coefficients of the basis functions; and to construct a smoothing function based on the estimated expansion coefficients and the linear combination form of the basis functions.

[0048] The smoothing function output module is used to output the smoothing function and use it as input data for subsequent statistical process control or fault diagnosis models.

[0049] As a preferred embodiment of an industrial data preprocessing device containing high-dimensional noise, in the multidimensional functional observation data acquisition module, the observed value of each dimension in the multidimensional observation data set is formed by superimposing the true function value at the corresponding time point with a random error term; the random error term satisfies the condition that the mean is zero and that they are independently and identically distributed.

[0050] The expression for the observed value is:

[0051]

[0052] In the formula, The observation value of the i-th dimension at the j-th sampling time point; This represents the actual function value at the corresponding time point; It is a random error term, and it satisfies the conditions that its mean is zero and that it is independently and identically distributed.

[0053] As a preferred embodiment of an industrial data preprocessing device containing high-dimensional noise, in the effective feature extraction and basis function processing module, the true function is represented as a linear combination of basis functions as follows:

[0054]

[0055] In the formula, For the actual function; Let m be the basis function; where are the expansion coefficients of the corresponding basis functions; K is the number of basis functions.

[0056] As a preferred embodiment of an industrial data preprocessing device containing high-dimensional noise, in the design matrix construction and processing module, during the process of constructing the design matrix according to the mapping rules between discrete observations and basis functions, the expression of the design matrix is:

[0057]

[0058] In the formula, n is the number of sampling time points; K is the number of basis functions;

[0059] The expression for the matrix elements of the design matrix is:

[0060]

[0061] In the formula, For the j-th sampling time point; Let be the function value of the i-th basis function at the j-th sampling time point.

[0062] As a preferred embodiment of an industrial data preprocessing device containing high-dimensional noise, the expression of the joint objective function in the joint objective function construction module is as follows:

[0063]

[0064] In the formula, This is the expansion coefficient vector of the basis functions in each dimension; This represents the number of basis functions for the corresponding dimension. , For observation data vectors in each dimension; , Design matrices for each dimension; It is a positive definite symmetric weight matrix; For smoothing parameters; For the penalty matrix; Let be the expansion coefficient vector of the basis functions in the k-th dimension.

[0065] As a preferred embodiment of an industrial data preprocessing device containing high-dimensional noise, the expression for the penalty matrix in the penalty matrix construction module is as follows:

[0066]

[0067] In the formula, For the penalty matrix; , These are the second derivatives of the i-th and j-th basis functions, respectively.

[0068] The expression for the generalized cross-validation criterion is:

[0069]

[0070] In the formula, This is the original observation data vector of the k-th dimension; Let k be the fitted data vector of the k-th dimension; Let be the smoothing parameter for the k-th dimension; Let k be the amount of observation data in the k-th dimension; df represents the sum of squared residuals between the original observed data and the fitted data in the k-th dimension; df represents the effective degrees of freedom of the model.

[0071] As a preferred embodiment of an industrial data preprocessing device containing high-dimensional noise, the expression of the smoothing function in the smoothing function construction module is:

[0072]

[0073] In the formula, Let be the smoothing function for the k-th dimension; k is the dimension index; t is the continuous time variable within the specified time interval. is the number of basis functions in the k-th dimension; m is the index of the basis function. These are the estimated expansion coefficients of the m-th basis function in the k-th dimension; Let m be the basis function of the k-th dimension.

[0074] The present invention has the following advantages:

[0075] First, it adopts an integrated design of "feature extraction and noise suppression". By simultaneously filtering the basis function and quantizing the expansion coefficient, it can effectively preserve features and suppress noise, avoid feature loss caused by separate processing, and improve the integrity and accuracy of feature extraction in high-noise scenarios.

[0076] Secondly, taking into account the synergy and importance differences of multi-dimensional signals, the priority of each dimension signal is incorporated through a weight matrix to adapt to the needs of multi-variable synchronous processing, so that the preprocessing results can fully reflect the overall state of industrial production.

[0077] Third, based on the generalized cross-validation criterion, the smoothing parameter is adaptively selected without relying on empirical settings. It can dynamically balance the function fitting accuracy and smoothness, avoiding the problems of over-smoothing or under-smoothing, and providing high-quality data support for subsequent analysis.

[0078] Fourth, by leveraging linear combinations of basis functions and matrix modeling, we can achieve dimensionality reduction and structured processing of high-dimensional data, balancing data temporal continuity with computational efficiency, and adapting to the dynamic time-series data processing needs of complex industrial scenarios. Attached Figure Description

[0079] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings in the following description are merely exemplary, and those skilled in the art can derive other embodiments based on the provided drawings without creative effort.

[0080] The structures, proportions, sizes, etc. illustrated in this specification are only for the purpose of assisting those skilled in the art in understanding and reading the content disclosed herein, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0081] Figure 1 This is a flowchart illustrating an industrial data preprocessing method containing high-dimensional noise, as provided in Embodiment 1 of the present invention.

[0082] Figure 2 This is a schematic diagram comparing data before and after processing in one possible embodiment of Embodiment 1 of the present invention;

[0083] Figure 3 This is a schematic diagram of the architecture of an industrial data preprocessing device containing high-dimensional noise, as provided in Embodiment 2 of the present invention. Detailed Implementation

[0084] The following specific embodiments illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0085] Example 1

[0086] See Figure 1 Embodiment 1 of the present invention provides a method for preprocessing industrial generated data containing high-dimensional noise, comprising the following steps:

[0087] S1. Within a single cycle of industrial production, by collecting multidimensional functional observation data defined within a set time interval, output the set of sampling time points and the set of multidimensional observation data.

[0088] S2. Represent the true function of each dimension observation value in the multidimensional observation data set as a linear combination of several basis functions; extract effective features by performing basis function screening and expansion coefficient quantization, and output the basis function set and basis function expansion coefficients;

[0089] S3. Based on the set of sampling time points and the set of basis functions, construct a design matrix according to the mapping rules between discrete observations and basis functions; establish the correlation between the multidimensional observation data set and the effective features through the design matrix;

[0090] S4. Based on the design matrix, and considering the requirements for multivariate synchronous processing and the differences in the importance of signals in each dimension, construct a joint objective function;

[0091] S5. Construct a penalty matrix based on the inner product of the second derivatives of the basis functions; use the penalty matrix to quantify and penalize the curvature of the function.

[0092] S6. Based on the joint objective function, a smoothing parameter is selected by minimizing the generalized cross-validation criterion; the smoothing parameter is used to balance the function fitting accuracy and smoothness.

[0093] S7. Based on the smoothing parameters, solve the joint objective function to obtain the estimated expansion coefficients of the basis functions; based on the estimated expansion coefficients and combined with the linear combination form of the basis functions, construct the smoothing function;

[0094] S8. Output the smoothing function and use it as input data for subsequent statistical process control or fault diagnosis models.

[0095] In this embodiment, in step S1, within a single cycle of industrial production, multidimensional functional observation data defined within a set time interval are collected, and a set of sampling time points and a set of multidimensional observation data are output.

[0096] Specifically, firstly, it is necessary to preset the time nodes of the industrial production cycle and define the data collection time interval within each cycle to ensure that the collection scope covers the key stages of the production process. Then, multi-dimensional time-series data is synchronously collected according to a preset sampling frequency using multiple types of sensors deployed at key locations on the production equipment. During the collection process, the sensor signals need to be calibrated in real time to eliminate abnormal data changes caused by sensor malfunctions, ensuring the reliability of the raw data. Finally, the collected data is structured, arranging the signals of each dimension in chronological order of sampling time to form a multi-dimensional observation data set. Simultaneously, the time information of each sampling moment is extracted and organized into a set of sampling time points, providing a time reference for subsequent mapping and matching with basis functions. This effectively solves the problem of subsequent processing deviations caused by non-standard data collection and asynchronous timing in existing technologies.

[0097] In this multidimensional observation dataset, the observed value of each dimension is formed by superimposing the true function value at the corresponding time point with a random error term; the random error term satisfies the condition that it has a mean of zero and is independently and identically distributed.

[0098] The expression for the observed value is:

[0099]

[0100] In the formula, The observation value of the i-th dimension at the j-th sampling time point; This represents the actual function value at the corresponding time point; It is a random error term, and it satisfies the conditions that its mean is zero and that it is independently and identically distributed.

[0101] In this embodiment, in step S2, the true function of each dimension observation value in the multidimensional observation data set is represented as a linear combination of several basis functions; by performing basis function screening and expansion coefficient quantization, effective features are extracted, and the basis function set and basis function expansion coefficients are output.

[0102] Specifically, firstly, based on the temporal continuity of industrial data, an appropriate basis function type is selected, and the true function corresponding to each dimension's observation is constructed as a linear combination model of basis functions, i.e., the true function. Next, basis function screening is conducted. Combining prior knowledge of industrial production, redundant basis functions irrelevant to effective features are eliminated, retaining core basis functions that accurately characterize changes in production status, thus optimizing the basis function set. Then, the expansion coefficients corresponding to the screened basis functions are quantitatively calculated. The magnitude of the coefficients reflects the strength of the features characterized by the corresponding basis function, completing the quantitative extraction of effective features. Finally, the set of basis functions and expansion coefficients carrying effective feature information are output, laying the foundation for establishing the correlation between data and features. This ensures the integrity of feature extraction and also initially achieves indirect noise suppression.

[0103] The true function is represented as a linear combination of basis functions as follows:

[0104]

[0105] In the formula, For the actual function; Let m be the basis function; where are the expansion coefficients of the corresponding basis functions; K is the number of basis functions.

[0106] In this embodiment, in step S3, based on the set of sampling time points and the set of basis functions, a design matrix is ​​constructed according to the mapping rules between discrete observations and basis functions; the design matrix is ​​used to establish the correlation between the multidimensional observation data set and the effective features.

[0107] Specifically, firstly, the mapping rule between discrete observations and basis functions is clarified: the observation value corresponding to each sampling time point can be represented by the combination of the function value of the basis function at that time point and the expansion coefficients. Based on this rule, a design matrix is ​​constructed with the number of sampling time points as the number of rows and the number of basis functions as the number of columns. The construction of the design matrix realizes the structured transformation of discrete observation data, mapping high-dimensional time series data to the basis function space. Subsequently, the design matrix establishes the correlation between the multidimensional observation data set and effective features; that is, the observation data can be fitted by the product of the design matrix and the expansion coefficients, and the effective features are jointly represented by the basis function set and the expansion coefficients, thereby achieving a precise correspondence between the observation data and the effective features, providing structured data support for subsequent multivariate collaborative processing.

[0108] In the process of constructing the design matrix based on the mapping rules between discrete observations and basis functions, the expression of the design matrix is ​​as follows:

[0109]

[0110] In the formula, n is the number of sampling time points; K is the number of basis functions;

[0111] The expression for the matrix elements of the design matrix is:

[0112]

[0113] In the formula, For the j-th sampling time point; Let be the function value of the i-th basis function at the j-th sampling time point.

[0114] In this embodiment, in step S4, a joint objective function is constructed based on the design matrix, taking into account the requirements for multivariate synchronous processing and the differences in the importance of signals in each dimension.

[0115] First, using the design matrix as the core input, and combining the observed data vectors and expansion coefficients of each dimension, a fitting error term is constructed to reflect the deviation between the observed data and the fitted values ​​of the basis functions. Then, fully considering the need for simultaneous processing of multiple variables, a positive definite symmetric weight matrix is ​​introduced. Based on the differences in the importance of each dimension's signals in production status assessment, different weights are assigned to the fitting errors of different dimensions, achieving differentiated processing of signals in each dimension. Finally, the fitting error weighted term and the subsequent smoothing penalty term are fused to construct a joint objective function. This function not only ensures the coordinated processing of multi-dimensional signals but also reflects the differences in signal importance through weight settings, making subsequent optimization directions more aligned with actual industrial needs.

[0116] The expression for the joint objective function is as follows:

[0117]

[0118] In the formula, This is the expansion coefficient vector of the basis functions in each dimension; This represents the number of basis functions for the corresponding dimension. , For observation data vectors in each dimension; , Design matrices for each dimension; It is a positive definite symmetric weight matrix; For smoothing parameters; For the penalty matrix; Let be the expansion coefficient vector of the basis functions in the k-th dimension.

[0119] In this embodiment, in step S5, a penalty matrix is ​​constructed based on the inner product of the second derivatives of the basis functions; the penalty matrix is ​​used to quantify and penalize the curvature of the function.

[0120] Specifically, firstly, based on the set of basis functions output in step S2, the second derivative of each basis function is calculated. Then, the inner product of the second derivatives of any two basis functions over a set time interval is calculated, and a penalty matrix is ​​constructed using this inner product as its elements. The core function of the penalty matrix is ​​to quantitatively evaluate the curvature of the function. When the curvature of the function is too great, the corresponding penalty term is increased, thus penalizing the excessively curved function shape in subsequent objective function optimization. Through this design, the smoothness of the function can be effectively constrained, preventing the true effective features from being obscured by drastic local fluctuations, and ensuring the stability of the features.

[0121] The expression for the penalty matrix is ​​as follows:

[0122]

[0123] In the formula, For the penalty matrix; , are the second derivatives of the i-th and j-th basis functions, respectively.

[0124] In this embodiment, in step S6, based on the joint objective function, a smoothing parameter is selected by minimizing the generalized cross-validation criterion; the smoothing parameter is used to balance the function fitting accuracy and smoothness.

[0125] Specifically, firstly, the core role of the smoothing parameter is clarified: a larger value imposes a stronger constraint on the smoothness of the function, making oversmoothing more likely; a smaller value results in higher fitting accuracy but may leave residual noise. Then, a generalized cross-validation criterion (GCV) is introduced to construct a criterion function. This criterion evaluates the preprocessing effect under different smoothing parameters by comprehensively considering fitting error and model complexity. Finally, the GCV criterion value is minimized using a numerical optimization algorithm, and the corresponding smoothing parameter is the optimal smoothing parameter. This process requires no manual intervention, achieving adaptive selection of the smoothing parameter, accurately balancing the fitting accuracy and smoothness of the function, and avoiding the problems of feature loss due to oversmoothing or residual noise due to insufficient smoothing.

[0126] The expression for the generalized cross-validation criterion is as follows:

[0127]

[0128] In the formula, This is the original observation data vector of the k-th dimension; Let k be the fitted data vector of the k-th dimension; Let be the smoothing parameter for the k-th dimension; Let k be the amount of observation data in the k-th dimension; df represents the sum of squared residuals between the original observed data and the fitted data in the k-th dimension; df represents the effective degrees of freedom of the model.

[0129] In this embodiment, in step S7, the joint objective function is solved based on the smoothing parameter to obtain the estimated expansion coefficients of the basis functions; based on the estimated expansion coefficients and combined with the linear combination form of the basis functions, a smoothing function is constructed.

[0130] Specifically, firstly, the optimal smoothing parameters obtained in step S6 are substituted into the joint objective function, and an adapted numerical optimization algorithm is used to solve for the minimum point of the objective function, obtaining the estimated expansion coefficients of the basis functions. These coefficients are the optimal solutions under multiple constraints of "fitting accuracy, smoothness, and multivariate synergy," and can accurately quantify the strength of effective features. Subsequently, based on the estimated expansion coefficients and the basis function set selected in step S2, a smoothing function is constructed in the form of a linear combination of basis functions. During the construction process, the core effective features are highlighted and the redundant information corresponding to noise is weakened through the weight allocation of the estimated expansion coefficients. The final smoothing function retains the key effective features of the industrial production state and has good smoothness, effectively solving the problem of low data quality after preprocessing in existing technologies.

[0131] The expression for the smoothing function is:

[0132]

[0133] In the formula, Let be the smoothing function for the k-th dimension; k is the dimension index; t is the continuous time variable within the specified time interval. is the number of basis functions in the k-th dimension; m is the index of the basis function. These are the estimated expansion coefficients of the m-th basis function in the k-th dimension; Let m be the basis function of the k-th dimension.

[0134] In this embodiment, in step S8, the smoothing function is output and used as input data for subsequent statistical process control or fault diagnosis models.

[0135] Specifically, firstly, the smoothing function constructed in step S7 is standardized to convert the continuous function form into a data format suitable for subsequent model input requirements. Then, the standardized smoothing function undergoes quality verification to check whether its effective feature retention and noise suppression effects meet preset thresholds. After successful verification, the smoothing function is output to subsequent statistical process control or fault diagnosis models via a standardized interface, providing high-quality input data for the models and effectively improving the analytical accuracy and reliability of subsequent models. This addresses the problem of poor compatibility and insufficient support between existing preprocessing results and subsequent applications.

[0136] In one possible embodiment, an injection molding example is provided as follows:

[0137] I. Data Sampling

[0138] A fully electric injection molding machine from an automotive parts manufacturing company was selected as the monitoring object. The following p=3-dimensional function signal was collected, with sampling occurring once per cycle, forming a function curve. Specific collection parameters are shown in Table 1.

[0139] Table 1. Data Acquisition Parameters

[0140] Approximately [number] samples were collected per cycle. One observation point.

[0141] Raw observations include measurement noise:

[0142]

[0143] In the formula, .

[0144] II. Constructing the Basis Function Model

[0145] For each variable Expanding using B-spline basis functions:

[0146]

[0147] Choose cubic B-splines (order=4), with 10 nodes, uniformly distributed in [0,8]. Set the number of basis functions: , .

[0148] III. Constructing the Design Matrix

[0149] Let the observation time be Construct the design matrix:

[0150]

[0151] For example, the pressure signal in the first cycle , It is an 800*15 matrix.

[0152] IV. Defining the Joint Optimization Objective Function

[0153] Minimize the following objective function with weights and penalties

[0154]

[0155]

[0156]

[0157] In the formula, For observation vectors; Let the weight matrix be a diagonal block matrix; weights This reflects the importance of different signals; The smoothing coefficient is initially set. ; Let be the penalty matrix, which is the roughness penalty based on the second derivative.

[0158] V. Automatic selection of smoothing parameters

[0159] Automatic optimization using the generalized cross-validation (GCV) criterion

[0160]

[0161]

[0162] In the formula, To smooth the matrix using a grid search The final value is determined by finding the value that minimizes the GCV within the specified range. .

[0163] VI. Solve for the coefficients and reconstruct the smoothing function

[0164] Solving the optimization problem yields estimated coefficients. Then, the smooth function is reconstructed:

[0165]

[0166] VII. Comparison of data before and after processing

[0167] Comparison of data before and after processing Figure 2 As shown:

[0168] Before processing: The original observed signals exhibit high-frequency jitter and irregular fluctuations; especially in the mold cavity pressure, melt temperature, or clamping force signals, random noise may be introduced due to sensor accuracy, electromagnetic interference, or mechanical vibration. The curves appear "rough" and not smooth.

[0169] After processing: The main trends and key features of the signal are preserved. Noise is effectively suppressed, and the curve becomes smoother, more continuous, and closer to the real physical process.

[0170] As can be seen, this invention integrates noise suppression and feature preservation, solving the pain point of "noise reduction and feature loss" in traditional methods; it also takes into account multi-dimensional synergy, improving data usability; and it provides high-quality support for subsequent analysis, highlighting the practicality and accuracy of the method.

[0171] The application scenarios of this invention are as follows:

[0172] In injection molding production scenarios, this invention can preprocess multi-dimensional time-series data such as cavity pressure, melt temperature, and clamping force, effectively suppressing noise caused by equipment vibration and electromagnetic interference, and fully preserving key process features such as holding pressure peak and pressure ramp rate, providing high-quality data support for injection molded part quality defect diagnosis and molding parameter optimization.

[0173] In continuous chemical reaction scenarios, this invention can process multi-dimensional monitoring data such as temperature, pressure, and material concentration inside the reactor, eliminate signal noise caused by sensor drift and fluid disturbance, accurately extract characteristic nodes of the reaction induction period, steady period, and termination period, and assist in the dynamic control and fault early warning of the chemical reaction process.

[0174] In CNC machine tool machining scenarios, this invention can smooth multi-dimensional data such as cutting force, spindle vibration, and tool temperature, remove noise generated by mechanical impact and environmental interference, and retain characteristic signals corresponding to tool wear and workpiece deformation, providing a reliable data foundation for machining accuracy control and tool life prediction.

[0175] In the lithium battery cell manufacturing process, this invention can preprocess multi-dimensional data such as thickness, pressure, and voltage in the cell coating, rolling, and formation processes, filter noise generated by the operation of production equipment, and extract core features such as coating uniformity and rolling density, supporting online detection of cell quality and optimization of process parameters.

[0176] In automotive parts welding scenarios, this invention can reduce noise and extract features from multi-dimensional time-series data such as welding current, voltage, and welding torch displacement, eliminate interference caused by power grid fluctuations and workpiece gaps, retain key features of weld nugget formation and weld cooling, and improve the accuracy of welding quality inspection and defect identification.

[0177] It should be noted that the method of this disclosure embodiment can be executed by a single device, such as a computer or server. The method of this embodiment can also be applied to a distributed scenario, where multiple devices cooperate to complete the task. In such a distributed scenario, one of these devices may execute only one or more steps of the method of this disclosure embodiment, and the multiple devices will interact with each other to complete the method described.

[0178] It should be noted that the above description describes some embodiments of this disclosure. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recorded in the claims can be performed in a different order than that shown in the above embodiments and still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0179] Example 2

[0180] See Figure 3 Embodiment 2 of the present invention also provides an industrial generated data preprocessing device containing high-dimensional noise, comprising:

[0181] The multidimensional functional observation data acquisition module 001 is used to acquire multidimensional functional observation data defined within a set time interval during a single cycle of industrial production, and output a set of sampling time points and a set of multidimensional observation data.

[0182] The effective feature extraction and basis function processing module 002 is used to represent the true function of each dimension observation value in the multidimensional observation data set as a linear combination of several basis functions; by performing basis function screening and expansion coefficient quantization, effective features are extracted, and the basis function set and basis function expansion coefficients are output.

[0183] The design matrix construction and processing module 003 is used to construct a design matrix based on the set of sampling time points and the set of basis functions, according to the mapping rules between discrete observations and basis functions; and to establish the correlation between the multidimensional observation data set and the effective features through the design matrix.

[0184] The joint objective function construction module 004 is used to construct a joint objective function based on the design matrix, combined with the requirements for multivariate synchronous processing and the differences in the importance of signals in each dimension;

[0185] The penalty matrix construction module 005 is used to construct a penalty matrix based on the inner product of the second derivatives of the basis functions; and to quantify the degree of curvature of the function by means of the penalty matrix.

[0186] The smoothing parameter selection and processing module 006 is used to select smoothing parameters based on the joint objective function by minimizing the generalized cross-validation criterion; and to balance the function fitting accuracy and smoothness through the smoothing parameters.

[0187] The smoothing function construction module 007 is used to solve the joint objective function based on the smoothing parameters to obtain the estimated expansion coefficients of the basis functions; and to construct a smoothing function based on the estimated expansion coefficients and the linear combination form of the basis functions.

[0188] The smoothing function output module 008 is used to output the smoothing function and use it as input data for subsequent statistical process control or fault diagnosis models.

[0189] In this embodiment, in the multidimensional functional observation data acquisition module 001, the observed value of each dimension in the multidimensional observation data set is formed by superimposing the true function value at the corresponding time point with a random error term; the random error term satisfies the condition that the mean is zero and that they are independently and identically distributed.

[0190] The expression for the observed value is:

[0191]

[0192] In the formula, The observation value of the i-th dimension at the j-th sampling time point; This represents the actual function value at the corresponding time point; It is a random error term, and it satisfies the conditions that its mean is zero and that it is independently and identically distributed.

[0193] In this embodiment, in the effective feature extraction and basis function processing module 002, the true function is represented as a linear combination of basis functions as follows:

[0194]

[0195] In the formula, For the actual function; Let m be the basis function; where are the expansion coefficients of the corresponding basis functions; K is the number of basis functions.

[0196] In this embodiment, in the design matrix construction and processing module 003, during the process of constructing the design matrix according to the mapping rules between discrete observations and basis functions, the expression of the design matrix is:

[0197]

[0198] In the formula, n is the number of sampling time points; K is the number of basis functions;

[0199] The expression for the matrix elements of the design matrix is:

[0200]

[0201] In the formula, For the j-th sampling time point; Let be the function value of the i-th basis function at the j-th sampling time point.

[0202] In this embodiment, in the joint objective function construction module 004, the expression of the joint objective function is:

[0203]

[0204] In the formula, This is the expansion coefficient vector of the basis functions in each dimension; This represents the number of basis functions for the corresponding dimension. , For observation data vectors in each dimension; , Design matrices for each dimension; It is a positive definite symmetric weight matrix; For smoothing parameters; For the penalty matrix; Let be the expansion coefficient vector of the basis functions in the k-th dimension.

[0205] In this embodiment, in the penalty matrix construction module 005, the expression of the penalty matrix is:

[0206]

[0207] In the formula, For the penalty matrix; , These are the second derivatives of the i-th and j-th basis functions, respectively.

[0208] The expression for the generalized cross-validation criterion is:

[0209]

[0210] In the formula, This is the original observation data vector of the k-th dimension; Let k be the fitted data vector of the k-th dimension; Let be the smoothing parameter for the k-th dimension; Let k be the amount of observation data in the k-th dimension; df represents the sum of squared residuals between the original observed data and the fitted data in the k-th dimension; df represents the effective degrees of freedom of the model.

[0211] In this embodiment, the expression of the smoothing function in the smoothing function construction module 007 is:

[0212]

[0213] In the formula, Let be the smoothing function for the k-th dimension; k is the dimension index; t is the continuous time variable within the specified time interval. is the number of basis functions in the k-th dimension; m is the index of the basis function. These are the estimated expansion coefficients of the m-th basis function in the k-th dimension; Let m be the basis function of the k-th dimension.

[0214] It should be noted that the information interaction and execution process between the modules of the above system are based on the same concept as the method embodiment in Embodiment 1 of this application, and the resulting technical effects are the same as those in the method embodiment of this application. For details, please refer to the description in the method embodiment shown above in this application, and it will not be repeated here.

[0215] Example 3

[0216] Embodiment 3 of the present invention provides a non-transitory computer-readable storage medium storing program code for a method of preprocessing industrial generated data containing high-dimensional noise. The program code includes instructions for executing the method of preprocessing industrial generated data containing high-dimensional noise according to Embodiment 1 or any possible implementation thereof.

[0217] Computer-readable storage media can be any available medium that a computer can access, or a data storage device such as a server or data center that integrates one or more available media. The available medium can be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., DVDs), or semiconductor media (e.g., solid-state drives (SSDs)).

[0218] Example 4

[0219] Embodiment 4 of the present invention provides an electronic device, including: a memory and a processor;

[0220] The processor and the memory communicate with each other via a bus; the memory stores program instructions that can be executed by the processor, and the processor can execute an industrial generated data preprocessing method containing high-dimensional noise according to Embodiment 1 or any possible implementation thereof by calling the program instructions.

[0221] Specifically, a processor can be implemented in hardware or software. When implemented in hardware, the processor can be a logic circuit, an integrated circuit, etc. When implemented in software, the processor can be a general-purpose processor that reads software code stored in memory. This memory can be integrated into the processor or located outside the processor and exist independently.

[0222] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of the present invention are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable system. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means.

[0223] It is obvious to those skilled in the art that the modules or steps of the present invention described above can be implemented using general-purpose computing systems. They can be centralized on a single computing system or distributed across a network of multiple computing systems. Optionally, they can be implemented using program code executable by a computing system, thereby storing them in a storage system for execution by the computing system. In some cases, the steps shown or described can be performed in a different order than those presented herein, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. Thus, the present invention is not limited to any particular combination of hardware and software.

[0224] Although the present invention has been described in detail above with general descriptions and specific embodiments, modifications or improvements can be made to it, which will be obvious to those skilled in the art. Therefore, all such modifications or improvements made without departing from the spirit of the present invention fall within the scope of protection claimed by the present invention.

Claims

1. A method for preprocessing industrial generated data containing high-dimensional noise, characterized in that, include: Within a single cycle of industrial production, by collecting multidimensional functional observation data defined within a set time interval, the set of sampling time points and the set of multidimensional observation data are output. The true function of each dimension observation value in the multidimensional observation dataset is represented as a linear combination of several basis functions; by performing basis function screening and expansion coefficient quantization, effective features are extracted, and the basis function set and basis function expansion coefficients are output. Based on the set of sampling time points and the set of basis functions, a design matrix is ​​constructed according to the mapping rules between discrete observations and basis functions; The design matrix is ​​used to establish the correlation between the multidimensional observation data set and the effective features; Based on the design matrix, and considering the requirements for multivariate synchronous processing and the differences in the importance of signals in each dimension, a joint objective function is constructed. A penalty matrix is ​​constructed based on the inner product of the second derivatives of the basis functions; The degree of curvature of the function is quantified and penalized using the penalty matrix. Based on the joint objective function, a smoothing parameter is selected by minimizing the generalized cross-validation criterion; the smoothing parameter is used to balance the function fitting accuracy and smoothness. Based on the smoothing parameters, the joint objective function is solved to obtain the estimated expansion coefficients of the basis functions; based on the estimated expansion coefficients and combined with the linear combination form of the basis functions, a smoothing function is constructed. The smoothing function is output and used as input data for subsequent statistical process control or fault diagnosis models.

2. The method for preprocessing industrial generated data containing high-dimensional noise according to claim 1, characterized in that, The observed value of each dimension in the multidimensional observation dataset is formed by superimposing the true function value at the corresponding time point with a random error term; the random error term satisfies the condition that the mean is zero and that they are independent and identically distributed. The expression for the observed value is: ； In the formula, The observation value of the i-th dimension at the j-th sampling time point; This represents the actual function value at the corresponding time point; It is a random error term, and it satisfies the conditions that its mean is zero and that it is independently and identically distributed.

3. The method for preprocessing industrial generated data containing high-dimensional noise according to claim 2, characterized in that, The true function is represented as a linear combination of basis functions in the following form: ； In the formula, For the actual function; Let m be the basis function; where are the expansion coefficients of the corresponding basis functions; K is the number of basis functions.

4. The method for preprocessing industrial generated data containing high-dimensional noise according to claim 3, characterized in that, In the process of constructing the design matrix based on the mapping rules between discrete observations and basis functions, the expression of the design matrix is: ； In the formula, n is the number of sampling time points; K is the number of basis functions; The expression for the matrix elements of the design matrix is: ； In the formula, For the j-th sampling time point; Let be the function value of the i-th basis function at the j-th sampling time point.

5. The method for preprocessing industrial generated data containing high-dimensional noise according to claim 4, characterized in that, The expression for the joint objective function is: ； In the formula, This is the expansion coefficient vector of the basis functions in each dimension; This represents the number of basis functions for the corresponding dimension. , For observation data vectors in each dimension; , Design matrices for each dimension; It is a positive definite symmetric weight matrix; For smoothing parameters; For the penalty matrix; Let be the expansion coefficient vector of the basis functions in the k-th dimension.

6. The method for preprocessing industrial generated data containing high-dimensional noise according to claim 5, characterized in that, The expression for the penalty matrix is: ； In the formula, For the penalty matrix; , These are the second derivatives of the i-th and j-th basis functions, respectively. The expression for the generalized cross-validation criterion is: ； In the formula, This is the original observation data vector of the k-th dimension; Let k be the fitted data vector of the k-th dimension; Let be the smoothing parameter for the k-th dimension; Let k be the amount of observation data in the k-th dimension; df represents the sum of squared residuals between the original observed data and the fitted data in the k-th dimension; df represents the effective degrees of freedom of the model.

7. The method for preprocessing industrial generated data containing high-dimensional noise according to claim 6, characterized in that, The expression for the smoothing function is: ； In the formula, Let be the smoothing function for the k-th dimension; k is the dimension index; t is the continuous time variable within the specified time interval. is the number of basis functions in the k-th dimension; m is the index of the basis function. These are the estimated expansion coefficients of the m-th basis function in the k-th dimension; Let m be the basis function of the k-th dimension.

8. An industrial generated data preprocessing apparatus containing high-dimensional noise, employing the industrial generated data preprocessing method containing high-dimensional noise as described in any one of claims 1-7, characterized in that, include: The multidimensional functional observation data acquisition module is used to collect multidimensional functional observation data defined within a set time interval during a single cycle of industrial production, and output a set of sampling time points and a set of multidimensional observation data. The effective feature extraction and basis function processing module is used to represent the true function of each dimension observation value in the multidimensional observation data set as a linear combination of several basis functions; by performing basis function screening and expansion coefficient quantization, effective features are extracted, and the basis function set and basis function expansion coefficients are output. The design matrix construction and processing module is used to construct a design matrix based on the set of sampling time points and the set of basis functions, according to the mapping rules between discrete observations and basis functions. The design matrix is ​​used to establish the correlation between the multidimensional observation data set and the effective features; The joint objective function construction module is used to construct a joint objective function based on the design matrix, combined with the requirements for multivariate synchronous processing and the differences in the importance of signals in each dimension; The penalty matrix construction module is used to construct the penalty matrix based on the inner product of the second derivatives of the basis functions; The degree of curvature of the function is quantified and penalized using the penalty matrix. The smoothing parameter selection and processing module is used to select smoothing parameters based on the joint objective function by minimizing the generalized cross-validation criterion; and to balance the function fitting accuracy and smoothness through the smoothing parameters. The smoothing function construction module is used to solve the joint objective function based on the smoothing parameters to obtain the estimated expansion coefficients of the basis functions; and to construct a smoothing function based on the estimated expansion coefficients and the linear combination form of the basis functions. The smoothing function output module is used to output the smoothing function and use it as input data for subsequent statistical process control or fault diagnosis models.

9. The industrial data preprocessing device containing high-dimensional noise according to claim 8, characterized in that, In the multidimensional functional observation data acquisition module, the observed value of each dimension in the multidimensional observation data set is formed by superimposing the true function value at the corresponding time point with a random error term; the random error term satisfies the condition that the mean is zero and that they are independently and identically distributed. The expression for the observed value is: ； In the formula, The observation value of the i-th dimension at the j-th sampling time point; This represents the actual function value at the corresponding time point; It is a random error term, and it satisfies the conditions that its mean is zero and that it is independently and identically distributed.

10. The industrial data preprocessing device containing high-dimensional noise according to claim 9, characterized in that, In the effective feature extraction and basis function processing module, the true function is represented as a linear combination of basis functions as follows: ； In the formula, For the actual function; Let m be the basis function; where are the expansion coefficients of the corresponding basis functions; K is the number of basis functions; In the design matrix construction and processing module, during the process of constructing the design matrix according to the mapping rules between discrete observations and basis functions, the expression of the design matrix is: ； In the formula, n is the number of sampling time points; K is the number of basis functions; The expression for the matrix elements of the design matrix is: ； In the formula, For the j-th sampling time point; The value of the i-th basis function at the j-th sampling time point; In the joint objective function construction module, the expression of the joint objective function is: ； In the formula, This is the expansion coefficient vector of the basis functions in each dimension; This represents the number of basis functions for the corresponding dimension. , For observation data vectors in each dimension; , Design matrices for each dimension; It is a positive definite symmetric weight matrix; For smoothing parameters; For the penalty matrix; Let be the expansion coefficient vector of the basis functions in the k-th dimension; In the penalty matrix construction module, the expression for the penalty matrix is: ； In the formula, For the penalty matrix; , These are the second derivatives of the i-th and j-th basis functions, respectively. The expression for the generalized cross-validation criterion is: ； In the formula, This is the original observation data vector of the k-th dimension; Let k be the fitted data vector of the k-th dimension; Let be the smoothing parameter for the k-th dimension; Let k be the amount of observation data in the k-th dimension; df represents the sum of squared residuals between the original observed data and the fitted data in the k-th dimension; df represents the effective degrees of freedom of the model. In the smoothing function construction module, the expression of the smoothing function is: ； In the formula, Let be the smoothing function for the k-th dimension; k is the dimension index; t is the continuous time variable within the specified time interval. is the number of basis functions in the k-th dimension; m is the index of the basis function. These are the estimated expansion coefficients of the m-th basis function in the k-th dimension; Let m be the basis function of the k-th dimension.

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